Applied Science, Faculty of
Mechanical Engineering, Department of
DSpace
UBCV
Lim, Jihoon
Doctor of Philosophy - PhD
University of British Columbia
Diesel engines have an excellent reputation due to higher torque and better fuel efficiency compared to gasoline engines. However, as a drawback, diesel combustion generates harmful nitrogen oxides (NOx) emissions. To reduce NOx emissions, the studies for selective catalytic reduction (SCR) control systems have been conducted. The SCR control system computes an optimal amount of liquid-reductant agent such as ammonia (NH₃) or urea and injects it upstream of the SCR catalyst. Thus, NOx emissions chemically react with NH₃ in the SCR catalyst resulting in ideally harmless gas coming out of the tailpipe. However, in practice, control challenges such as nonlinearity and unmeasurable catalyst conditions cause undesirable NOx and NH₃ downstream of the SCR catalyst. This thesis makes three contributions in designing the SCR controllers overcoming the control challenges. Firstly, this thesis proposes a new approach to designing a gain-scheduling (GS) SCR controller consisting of multiple linear time-invariant H infinity controllers, each of which provides satisfactory control performance for different operating points. Secondly, this thesis presents a GS linear parameter-varying SCR controller with a theoretical guarantee of stability and performance. Finally, this thesis introduces a preview-feedback SCR controller based on state augmentation techniques using previewed NOx information with a low computational requirement. The effectiveness of the proposed controllers is validated by the simulation tests using experimentally obtained data over the non-road transient driving cycle. It is shown that the proposed controllers significantly maximize NOx conversion efficiency with low ammonia out of the tailpipe even with model parameter variation and sensor noise.
Gain-scheduling and Preview Control ofSelective Catalytic Reduction Systems inDiesel EnginesbyJihoon LimA THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Mechanical Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)November 2020© Jihoon Lim 2020The following individuals certify that they have read, and recommend to the Faculty of Graduate and Post-doctoral Studies for acceptance, the dissertation entitled:Gain-scheduling and Preview Control of Selective Catalytic Reduction Systems in Diesel Enginessubmitted by Jihoon Lim in partial fulfillment of the requirements forthe degree of Doctor of Philosophyin Mechanical EngineeringExamining Committee:Dr. Ryozo Nagamune, Mechanical EngineeringSupervisorDr. Patrick Kirchen, Mechanical EngineeringCo-SupervisorDr. Bhushan Gopaluni, Chemical and Biological EngineeringUniversity ExaminerDr. Shahriar Mirabbasi, Electrical and Computer EngineeringUniversity ExaminerAdditional Supervisory Committee Members:Dr. Clarence De Silva, Mechanical EngineeringSupervisory Committee MemberDr. Steven Rogak, Mechanical EngineeringSupervisory Committee MemberDr. Rudolf Seethaler, Mechanical EngineeringSupervisory Committee MemberiiAbstractDiesel engines have an excellent reputation due to higher torque and better fuel efficiency compared togasoline engines. However, as a drawback, diesel combustion generates harmful nitrogen oxides (NOx)emissions. To reduce NOx emissions, the studies for selective catalytic reduction (SCR) control systemshave been conducted. The SCR control system computes an optimal amount of liquid-reductant agent suchas ammonia (NH3) or urea and injects it upstream of the SCR catalyst. Thus, NOx emissions chemicallyreact with NH3 in the SCR catalyst resulting in ideally harmless gas coming out of the tailpipe. However,in practice, control challenges such as nonlinearity and unmeasurable catalyst conditions cause undesirableNOx and NH3 downstream of the SCR catalyst.This thesis makes three contributions in designing the SCR controllers overcoming the control chal-lenges. Firstly, this thesis proposes a new approach to designing a gain-scheduling (GS) SCR controllerconsisting of multiple linear time-invariant H∞ controllers, each of which provides satisfactory control per-formance for different operating points. Secondly, this thesis presents a GS linear parameter-varying SCRcontroller with a theoretical guarantee of stability and performance. Finally, this thesis introduces a preview-feedback SCR controller based on state augmentation techniques using previewed NOx information with alow computational requirement.The effectiveness of the proposed controllers is validated by the simulation tests using experimentallyobtained data over the non-road transient driving cycle. It is shown that the proposed controllers significantlymaximize NOx conversion efficiency with low ammonia out of the tailpipe even with model parametervariation and sensor noise.iiiLay SummaryHarmful emissions from transportation systems, such as cars, ships, and airplanes, have been increasingenvironmental and health concerns around the world. One of the most effective systems reducing harmfulemissions is a Selective Catalytic Reduction (SCR) System due to remarkable nitrogen oxides (NOx) reduc-tion rate. Although an SCR system shows outstanding performance, in practice, there are still possibilitiesfor improving the performance of the SCR systems.This research aims to improve the SCR system’s performance by means of advanced control technolo-gies called gain-scheduling control and preview control. The proposed controller’s effectiveness is provedbased on the simulation test using practical data obtained over the transient driving cycle. After functionalvalidation, the proposed controller will be able to be adopted in heavy-duty trucks and construction equip-ment. The research outcomes of this thesis will contribute to making us go one more step towards a cleaner,greener world.ivPrefaceThe results presented in this thesis are based on my ideas and disscussion with my supervisor Dr. RyozoNagamune and co-supervisor Dr. Patrick Kirchen. I formulated research objectives and approaches, designedthe proposed controllers and performed the simulation tests under the supervision of Dr. Nagamune andDr. Kirchen. The input data for the simulation test was experimentally acquired with my co-workers atDoosan Infracore Co. Ltd.• One of the results relevant with Chapter 3, a single LTI controller, was presented in the first BCUniversities Systems and Control Meeting (2018). The main result in Chapter 3 was submitted as ajournal paper.– J. Lim, P. Kirchen, and R. Nagamune, “Diesel Engine SCR Control Gain-scheduled by AmmoniaSlip Measurement,” Journal of the Franklin Institute, submitted, 2020.• The result relevant with Chapter 4 was accepted in Engine Technologies Conference and presentedin the third BC Universities Systems and Control Meeting (2020). The main result in Chapter 4 wassubmitted as a journal paper.– J. Lim, P. Kirchen, and R. Nagamune, “Linear Parameter-Varying Controller Gain-scheduled byExhaust Gas Temperature for Selective Catalytic Reduction Systems,” ICET 2020: InternationalConference on Engine Technologies, 2020. (Best Presentation Award).– J. Lim, P. Kirchen, and R. Nagamune, “LPV Controller Design for Diesel Engine SCR Af-tertreatment Systems based on Quasi-LPV Models,” IEEE Control Systems Letters, submitted,2020.• The results in Chapter 5 was accepted as a journal paper.– J. Lim, P. Kirchen, and R. Nagamune, “Discrete-Time Preview-Feedback H∞ Control for Selec-tive Catalytic Reduction Systems,” International Journal of Automotive Technology, 2020.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Diesel Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Existing Reduction Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 SCR Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Challenges in SCR Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4.1 Nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4.2 Unmeasurable catalyst condition . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.4.3 Slow dynamics of the SCR system . . . . . . . . . . . . . . . . . . . . . . . . . . 61.4.4 Time delay of the sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.4.5 Other challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.5 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7viTable of Contents1.5.1 SCR models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.5.2 Open-loop control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.5.3 Feedforward-feedback control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.5.4 Gain-scheduling control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.5.5 Model predictive control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.5.6 Preview control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.5.7 Challenges covered by the previous research . . . . . . . . . . . . . . . . . . . . . 121.6 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.7 Research Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.8 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.1 SCR Operating Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.1.1 NOx reduction in SCR reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.1.2 NH3 oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.1.3 NH3 adsorption and desorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2 Nonlinear State-space Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3.1 Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3.2 Parameter values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.3.3 Non-road transient driving cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 SCR Control Gain-scheduled by Ammonia Slip Measurement . . . . . . . . . . . . . . . . . 253.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.3 GS H∞ SCR Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.3.1 Operating range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.3.2 Motivation of GS controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.3.3 Feedforward-feedback control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3.4 Gain-scheduling control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.4 Design of SCR Control Gain-scheduled by Ammonia Slip Measurement . . . . . . . . . . . 31viiTable of Contents3.4.1 Design of LTI H∞ controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.4.2 Design of sub-regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.5.1 Controllers for simulation test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.5.2 An SCR model for simulation test . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.5.3 Control performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.5.4 Robustness analysis: model uncertainty . . . . . . . . . . . . . . . . . . . . . . . . 393.5.5 Robustness analysis: sensor noise . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 Linear Parameter-Varying SCR Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.2 Control-oriented SCR model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.3 Quasi-LPV (qLPV) SCR model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.3.1 Regarding (x1, x2) as varying parameters . . . . . . . . . . . . . . . . . . . . . . . 464.3.2 Regarding x3 as a varying parameter . . . . . . . . . . . . . . . . . . . . . . . . . 464.4 Quasi-LPV SCR Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.4.1 Proposed control structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.4.2 LPV controller design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.5.1 Simulation settings: model parameters . . . . . . . . . . . . . . . . . . . . . . . . 494.5.2 Simulation settings: controller design parameters . . . . . . . . . . . . . . . . . . . 504.5.3 Simulation settings: exogenous signals . . . . . . . . . . . . . . . . . . . . . . . . 514.5.4 Performance analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.5.5 Robustness analyses: model parameter variation and sensor noise . . . . . . . . . . 534.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 Preview-Feedback SCR Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.2 Proposed Preview-Feedback Control Approach . . . . . . . . . . . . . . . . . . . . . . . . 575.3 Design of Discrete-time Preview-Feedback H∞ Controller . . . . . . . . . . . . . . . . . . 58viiiTable of Contents5.3.1 Structure of preview-feedback H∞ controller . . . . . . . . . . . . . . . . . . . . . 595.3.2 Control-oriented SCR model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.3.3 Derivation of the discrete-time generalized plant . . . . . . . . . . . . . . . . . . . 615.3.4 Design of an H∞ controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.4.1 Simulation setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.4.2 Control performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.4.3 Comparison with MPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665.4.4 Robsutness analysis based on uncertainties . . . . . . . . . . . . . . . . . . . . . . 675.4.5 Computational requirement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 706 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74AppendicesA Open-loop simulation tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81B Operating point values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85C Parameter values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86ixList of Tables1.1 Challenges covered by the previous SCR research:(1.4.1: Nonlinearity, 1.4.2: UnmeasurableCatalyst Condition, 1.4.3: Slow dynamics of the SCR system, 1.4.4: Time delay of Sensor) . 132.1 Specification of the diesel engine test facility . . . . . . . . . . . . . . . . . . . . . . . . . 222.2 Reaction constants in (2.7) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.1 Comparison of control performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.2 Performance with parameter perturbations . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.1 Notations and their meanings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.2 Parameter values for chemical reaction constants . . . . . . . . . . . . . . . . . . . . . . . 504.3 Comparison of control performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.4 Robustness against model parameter variation . . . . . . . . . . . . . . . . . . . . . . . . . 544.5 Robustness against sensor noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545.1 Comparison of control performance based on preview length . . . . . . . . . . . . . . . . . 655.2 Quantitative comparison between MPC and preview-feedback H∞ controllers . . . . . . . . 675.3 Robustness analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69B.1 Operating points for controller design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85C.1 Parameter values of KPID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86xList of Figures1.1 Schematics of NOx adsorber catalysts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Schematic of an HC-SCR catalyst . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Schematic of an after-treatment system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Schematic of an open-loop controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.5 Schematic of a feedforward-feedback controller . . . . . . . . . . . . . . . . . . . . . . . . 91.6 Schematic of a gain-scheduling controller . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.7 Schematic of a model predictive controller . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.8 Schematic of a preview controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.1 Schematic of the SCR system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2 SCR control system equipped on a heavy-duty diesel engine: Variable Turbine Geome-try (VTG), Diesel Oxidation Catalyst (DOC), Diesel Particulate Filter (DPF) . . . . . . . . . 212.3 Speed and torque profile of the NRTC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.4 Input signals to the SCR model for the simulation test . . . . . . . . . . . . . . . . . . . . . 233.1 FF-FB GS SCR controller structure (The controller, K(r), consists of the feedforward andfeedback controllers. Dotted arrows indicate gain-scheduling parameters.) . . . . . . . . . . 293.2 The gain-scheduling parameters and the multiple LTI controllers . . . . . . . . . . . . . . . 303.3 Block diagram of the weighted control system . . . . . . . . . . . . . . . . . . . . . . . . . 323.4 The gain-scheduling parameters and multiple GS controllers designed based on differentlyselected operating point values (θ, NH3,out, and NOx,out) . . . . . . . . . . . . . . . . . . 353.5 Violation-Time-based Decision method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.6 Input signals to the SCR model for the simulation test . . . . . . . . . . . . . . . . . . . . . 38xiList of Figures3.7 Comparison of control performance among KFF , KPID, KSMC , and proposed KH∞ : Theinitial values are NOx,out = 58 ppm, NH3,out = 38 ppm, and θ = 0.2 . . . . . . . . . . . . . 393.8 NOx,out change due to SCR model parameter perturbation (On each box, the red-horizontalline indicates the median, and the bottom and top edges of the box indicate the 25th and 75thpercentiles, respectively. The blue-horizontal line out of the box represents the most extremedata points not considered outliers. The outliers are plotted individually using the ’+’ symbol) 403.9 Performance with parameter perturbation (E1) . . . . . . . . . . . . . . . . . . . . . . . . . 403.10 Performance with sensor noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.1 Block Diagram of the Proposed LPV Control System . . . . . . . . . . . . . . . . . . . . . 474.2 LFT Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.3 Signals in an Experimental NRTC Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.4 Controller Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.5 Performance by KLPV1 with parameter perturbation . . . . . . . . . . . . . . . . . . . . . . 534.6 Performance by KLPV1 with sensor noise . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.1 Schematic of an SCR control system (EGR and VTG stand for exhaust gas recirculation andvariable turbine geometry, respectively) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575.2 SCR preview-feedback H∞ controller structure . . . . . . . . . . . . . . . . . . . . . . . . 595.3 Block diagram for SCR preview-feedback controller design . . . . . . . . . . . . . . . . . . 615.4 SCR control system in LFT form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635.5 Experimental data measured under NRTC mode . . . . . . . . . . . . . . . . . . . . . . . . 655.6 The performance of the preview-feedback H∞ controllers with various preview lengths . . . 665.7 Control performance of MPC and preview-feedback H∞ controllers . . . . . . . . . . . . . 665.8 The structure of the simulation test with uncertain previewed signal x∆[k] . . . . . . . . . . 675.9 NOx disturbance signal with uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.10 The robustness of the preview-feedback H∞ controllers . . . . . . . . . . . . . . . . . . . . 69A.1 Input signals for open-loop simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81A.2 Parameter perturbation of Ered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82A.3 Parameter perturbation of Eox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82xiiList of FiguresA.4 Parameter perturbation of Eads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83A.5 Parameter perturbation of Edes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84xiiiAcknowledgmentsFirst of all, I would like to express my sincere gratitude to my Ph.D. supervisor, Professor Ryozo Nagamune.During my Ph.D. program, he has always been very supportive and encouraging me to go forward. Heintroduced me to the field of modern control, robust control, and gain-scheduling control. Without hisenthusiasm, encouragement, and support, this work would hardly have been completed. It was a great honorand pleasure to work with him in my life.I am highly thankful to my co-supervisor, Professor Patrick Kirchen. His expertise and knowledge in en-gine and aftertreatment systems were invaluable to our research work. His advice was always very supportiveof solving my questions on combustion and chemical reactions. I would also like to thank my supervisorycommittee members, Professor Clarence De Sliva, Professor Steven Rogak, and Professor Rudolf Seethaler,for their help and instructional feedback for my research work.I would like to thank all my current and previous labmates of the Control Engineering Lab at UBC.Special thanks go to Dr. Pan Zhao for his help in LPV control and to Marcin Mirski, Ali Cherom Kheirabadi,and Jacob Morrison for their help in proofreading and to Dr. Shuo Kang and Riky Dong for their help inSMC control and to Mohammadreza Rostam for his help in MPC control and to Dr. Ting Yue for his help inDynamics and to Chenlu Han and Cristopher Cortes for their help in lab life. I am also thankful to EduardoEscobar, Sara Hosseinirad, Nafise Faridi Rad, Kai Wang, Ran Fan, Yue Niu, Dr. Tiancheng Zhong, AndersonSoares, Bixuan Huang for their friendship and for creating a cordial working environment.I would like to express my gratitude to the Natural Sciences and Engineering Research Council of Canada(NSERC) and Doosan Infracore Co. Ltd. in South Korea for financial contributions.My parents-in-law deserve the deepest gratitude for their unfailing emotional support. I also thank mybrothers-in-law and their families for heart-warming kindness. I am forever indebted to my parents for givingme unconditional love and support. I deeply thank my sister and brother-in-law since they took care of myparents while I was not around them. Last but not least, I would like to express the greatest appreciation to mywife and sons, Eunah, David Donghyun, and Daniel Dongjoon, for their love, patience, and encouragement.xivDedicationThis thesis is dedicated to my family.xvChapter 1Introduction1.1 Diesel EnginesThe diesel engine is widely adopted in heavy-duty applications such as off-road vehicles and constructionequipment, due to their advantages of higher torque and better fuel economy over gasoline engines [1]. Theseadvantages of diesel engines are due to the nature of diesel fuel and engine structure.Diesel fuel is a mixture of hydrocarbons (HC). One of improtant properties of HC is self-ignitionwhich can be indexed by cetane number1 (or cetane index). To make successful self-ignition, diesel enginesare designed with a turbocharger and a longer piston stroke than gasoline engines. The turbocharger is aforced induction device that increases engine’s volumetric efficiency by forcing extra compressed air intothe combustion chamber. The longer piston stroke in diesel engines contributes higher compression ratio(up to 25:1) than that by gasoline engines (around 12:1). This higher compression ratio ends up generatinghigher torque in diesel engines than that in gasoline engines [2].Diesel fuel has lower calorific value and is denser than gasoline fuel [2]. Diesel also burns steadily andfaster than gasoline. Since density compensates for the lower mass heating value of diesel, the volumetricheating value of diesel is higher. Thus, diesel fuel yields more energy for a liter of fuel than gasoline does.Besides, the operation principle of the diesel engine leads to relatively lean combustion compared to gasolineengines. Theoretically, the air needed to combust diesel fuel 1 [kgf] is approximately 15 [kgf]. The air-fuelequivalence ratio (λ) can be defined asλ :=AFRAFRstoich, (1.1)where AFR and AFRstoich represent the air-fuel ratio and stoichiometric air-fuel ratio, respectively. Thevalue of λ greater than 1 means the lean burn. In general, λ is around 1.2–1.4 at full load and over 2.5 at lowor medium load. The higher compression ratio and the lean operation lead to the higher efficiency of diesel1Cetane number is an indicator of the combustion speed of diesel fuel and compression needed for ignition.11.2. Existing Reduction Technologiesengines than gasoline engines.Despite the advantages of diesel engines over gasoline ones, there is a crucial disadvantage, which is thetoxic nitrogen oxides (NOx) emissions. The NOx is formed in cylinders of diesel engines because of hightemperature caused by high compression ratio and abundant oxygen (O2) generated by turbocharger. TheNOx emissions are one of the main pollutants causing severe health problems such as asthma, cancer, andpremature death. Because of the NOx emissions from diesel cars, around 10,000 people prematurely dieevery year across Europe [3].1.2 Existing Reduction Techonologies in Diesel EnginesTo reduce NOx emissions, mainly three types of aftertreatment systems have been developed [4]: a NOxadsorber [5, 6], a lean NOx catalyst [7], and a selective catalytic reduction (SCR) system [8].First, a NOx adsorber, also known as lean NOx traps (LNT), was developed based on acid-base wash-coat chemistry. The NOx emissions are stored on the catalyst washcoat during lean exhaust conditions asdepicted in the first plot in Fig. 1.1. The adsorbed NOx emissions are converted into nitrogen (N2) duringrich exhaust condition as depicted in the second plot. By changing exhaust conditions between lean and rich,NOx adsorber catalystOxidation catalystNOX CO2N2NOXCO CO2CONOXN2CO2NOXNOXCO2N2 NOXNOX NOXN2NOX(a) Lean exhaust conditionNOx adsorber catalyst𝑁2Oxidation catalystNOX CO2H2OHCNOXHCHCCO CO2H2OCOHCNOXH2O𝑁2CO2(b) Rich exhaust conditionFigure 1.1: Schematics of NOx adsorber catalysts21.2. Existing Reduction Technologiesthe NOx adsorber reduces NOx emissions without an additional reductant and its infrastructure. Due to itssimplicity, theNOx adsorber catalyst was firstly considered as an aftertreatment system forNOx emissions.However, the usage of the NOx adsorber is limited to light-duty engines because of its declining NOx re-duction performance at high exhaust temperatures which happen in heavy-duty engines [9]. Besides, theNOx adsorber also has efficiency penalty during rich operation. The performance and the durability havenot yet been demonstrated in heavy-duty applications.Secondly, a lean NOx catalyst, also referred to as HC-SCR, utilizes a selective reaction with hydrocar-bons (HC) to reduce NOx emissions as depicted in Fig. 1.2. Since HC is simply utilized as the reductantEnginecontrollerHC-SCR catalyst𝐻𝐶CO2𝑁2𝐻2𝑂Dosing valve𝑁𝑂𝑥 sensor𝑁𝐻3 sensor𝑁𝑂𝑥 sensorTemperature sensorNOXFigure 1.2: Schematic of an HC-SCR catalystfrom the fuel tank, the lean NOx catalyst does not need any additional tank for the reductant. It is advanta-geous for the lean NOx catalyst to be adopted on a compact space of the small or mid-size trucks. However,due to low HC concentration relative to NOx concentration, low NOx reduction of only about 50-60% canbe achieved even with the extraHC injection. Besides, since the leanNOx catalyst has a narrow operationaltemperature range, it is only applicable to limited applications.The last but not the least, the most commonly adopted aftertreatment system for NOx reduction is aselectve catalytic reduction (SCR) system, where the chemical reaction between NOx emissions and am-monia (NH3), injected in the form of urea, converts them into non-toxic gases. In practice, many SCRapplications utilize water-based urea which converts into NH3 on the catalyst surface because urea is saferto store rather than toxic NH3 [10]. The SCR system has been studied for many decades to improve theNOx conversion efficiency. Using the reducing agent, the SCR system was patented in the US by the Engel-31.3. SCR Systemshard Corporation in 19572. The commercial SCR systems were typically found on industrial boilers, thermalpower plants, and large ships. Nowadays, the SCR system has also been installed in automotive industriesdue to its high NOx conversion rate [8]. The objective of the SCR system in automotive and heavy-dutyapplications is to reduce NOx emissions over various driving conditions [11]. Accomplishing this objectiveis quite challenging, since the environmental conditions surrounding the SCR catalyst, such as exhaust gastemperature, NOx amount coming from the diesel engine, and exhaust gas flow rate, can vary drasticallybased on the driving conditions.In the next section, we will overview the structure of the SCR system to prepare for the discussion aboutwhat the control challenges exist in the SCR system.1.3 SCR Systems in Diesel EnginesAs we disscused before, the diesel engine provides the aforementioned advantages such as high torque andbetter fuel economy with a cost, i.e., toxic gas emissions such as carbon monoxide (CO), hydrocarbons(HC), particulate matter (PM ) and nitrogen oxides (NOx). The aftertreatment system consisting of adiesel oxidation catalyst (DOC), a diesel particulate filter (DPF), and a selective catalytic reduction (SCR)system has been developed to meet the stringent emission regulations, as depicted in Fig. 1.3.SCRcontrollerSCR catalyst𝑁𝐻3,𝑖𝑛CO2𝑁2𝐻2𝑂𝑁𝑂𝑥,𝑜𝑢𝑡𝑁𝐻3,𝑜𝑢𝑡Dosing valve𝑁𝑂𝑥 sensor𝑁𝐻3 sensor𝑁𝑂𝑥 sensorTemperature sensorNOX,inDOC DPFCO CO2HC H2OFiltering PMCOHCPMNOX,inPMNOX,inFigure 1.3: Schematic of an after-treatment systemWhen toxic gas emissions enter the exhaust gas manifold from the diesel engine, the DOC firstly con-verts CO and HC into CO2 and H2O, by oxidation reaction. The DPF then filters PM , and thus only2US2975025A, US2927141A, US2909578A41.4. Challenges in SCR ControlNOx comes out of DPF in the ideal situation. Harmful toxic gas emissions, nitric oxide (NO) and nitrogendioxide (NO2), collectively denoted by NOx,in [mole/m3], pass into the SCR catalyst.In order to reduce the amount of NOx exiting from the tailpipe, denoted by NOx,out [mole/m3], theSCR controller computes the optimal amount of NH3,in [mole/m3] based on its control algorithm andsensor signals. These signals can include the exhaust gas temperature (T [K]) upstream of a catalyst,NOx up/downstream of a catalyst (NOx,in, NOx,out), and NH3 downstream of a catalyst, denoted byNH3,out [mole/m3]. The SCR controller then injects the computed amount NH3,in by using the dosingvalve. Within the SCR catalyst, NOx andNH3,in chemically react and ideally result only in harmless gases,nitrogen (N2) and water vapor (H2O), coming out of the tailpipe without any NOx,out and NH3,out.The efficiency of the SCR system heavily depends on the SCR controller which decides the amount andthe timing of NH3 injection upstream of the SCR catalyst. Too little NH3,in results in high NOx,out due toinsufficient chemical reaction in the catalyst, while too much injection leads to the so-called ammonia slip,a phenomenon where a part of the injected NH3,in passes through the catalyst without reacting. Due to tox-icity of ammonia, the ammonia slip is typically required to be below 10 ppm average in commercial dieselengines. This level of ammonia slip does not result in plume formation or human health hazards [12]. Asfar as the injection timing is concerned, NH3 injection much earlier than the NOx arrival at the catalyst canmake the catalyst “ready” to handle the incoming NOx, but at the same time, creates the risk of increasingthe ammonia slip. Thus, the mitigation of outgoing NOx without excessive ammonia slip must be achievedby injecting the “right” amount of NH3 at the “right” timing.1.4 Challenges in SCR ControlThere are control challenges of SCR control systems which hamper the perfect elimination of NOx,out andNH3,out, that is, nonlinearity, unmeasurable catalyst condition, the slow dynamics of the SCR system, thetime delay of the sensors, and the degradation of the SCR catalyst.1.4.1 NonlinearityThe SCR system contains the nonlinear dynamics due to chemical reactions. When the NOx disturbancecoming from diesel engines meets with the NH3 injected through the dosing valve, they chemically reactwith each other and result in harmless gas emissions, N2 and H2O (see Fig. 1.3). These chemical reactions51.4. Challenges in SCR Controloccur based on the reaction rates which will be discussed in Chapter 2. Since the reaction rates can varysignificantly at different combinations of NOx, NH3, and NH3 level in the SCR catalyst, they cause non-linearity of the SCR dynamics. This nonlinearity then brings out serious difficulties to the SCR controller.Since the linear controller cannot cover the entire operating area of the nonlinear system, the SCR controllerdesigned based on linear control techniques does not yield satisfactory performance.1.4.2 Unmeasurable catalyst conditionTo improve the NOx reduction efficiency, the studies for SCR catalysts and ammonia storage capacity havebeen conducted in [13, 14] since the amount of NH3 adsorbed in the SCR catalyst is a significant variable.Insufficient NH3 stored on the catalyst relative to the NOx,in results in NOx coming out of the tailpipe. Onthe other hand, the NH3 in the SCR catalyst may slip out when more NH3 is in the catalyst than desired.If the controller were able to access the information of NH3 storage level, then the controller would be ableto compute and maintain its desirable control input based on the NH3 storage level. However, such storagelevel cannot be explicitly measured, and thus this storage level information needs to be estimated based onstate estimators such as extended Kalman filter [15], sliding mode observer [16], and Luenberger-slidingmode observer [17]. Although the results based on these estimation techniques are preferable, the resultsmay contain possible estimation errors.1.4.3 Slow dynamics of the SCR systemThe dynamics of the SCR system is slow because of the delays coming from atomization of the injected ureain the exhaust pipe and chemical reactions in the catalyst [18]. On the contrary, the dynamics of the engine isfaster than the dynamics of the SCR system. Due to this difference between the SCR system and the engine,the amount of NH3,in computed by the SCR controller based on the NOx,in generated by the engine doesnot always effectively reduce NOx,out.1.4.4 Time delay of the sensorThe NOx and NH3 sensors in the SCR systems as depicted in Fig. 1.3 are utilized for the SCR controller tocompute NH3,in to effectively reduce NOx,out. However, the information from each sensor is delivered to61.5. Literature Reviewthe SCR controller appoximately 700 ms late due to the sensor delay. This sensor delay may cause unstableSCR controller operation and degraded performance, even with conservative controllers. Designing the con-troller to take the sensor delay into account makes the SCR control system more conservative, exacerbatingthe performance problems caused by slow system dynamics.1.4.5 Other challengesOther than primary challenges mentioned above, there are still many other challenges caused by the SCRhardware, such as NOx sensor cross-sensitivity, sensor noise, measurement uncertainty, defective dosingvalve, and degradation of SCR catalysts. Among them, NOx sensor cross-sensitivity and degradation ofSCR catalysts are noticable challenges since both challenges may affect serious performance degradation.NOx sensor cross-sensitivity means that NOx sensor is cross-sensitive to ammonia. Because of NOxsensor cross-sensitivity, the SCR controller continues to increase ammonia injection with wrong informationwhile ammonia slip increases. This NOx sensor cross-sensitivity has been challenging to be overcome andmany studies have been conducted in [19–22].Since the SCR system is located near the exhaust manifold of diesel engines, the SCR system is largelyexposed to a thermal environment ranging approximately from 200 ◦C to 750 ◦C and pollutants. Due tothe hazardous environment, the SCR system is easily prone to become degraded or defective. It is observedthat the degradation in activity of the catalyst is strongly affected by hydrothermal aging because of catalystagglomeration and change in washcoat morphology [23, 24]. To overcome this degradation, studies havebeen conducted based on adaptive control [25] and nonlinear control technique [26].Some researchers proposed that using nonlinear model-based controllers may be necessary for SCRsystems [27–29]. However, such nonlinear controller may cause computational resources issue of EngineControl Unit (ECU).1.5 Literature ReviewIn this section, the literature review is carried out to understand various aspects of SCR control develop-ment. This section consists of six parts. First of all, Section 1.5.1 presents an overview of the SCR models.Then, Section 1.5.3, Section 1.5.4, Section 1.5.5, and Section 1.5.6 respectively discuss existing works on71.5. Literature Reviewfeedforward–feedback control design, gain-scheduling control design, model predictive control design, andpreview control design. Section 1.5.7 reviews the control challenges covered by the previous research.1.5.1 SCR modelsThe SCR model was typically built based on heat transfer, mass transfer, and chemical reactions in an SCRcatalyst [30]. The SCR model was also developed as a 3D model based on energy and mass balance [31]. Toaccurately predict the concentrations of NO, NO2, and NH3, the high-order models including 105-stateswas developed based on mass transfer and chemical kinetics of six reactions on the SCR catalyst [32]. TheSCR model containing 42-states was also studied based on energy and mass balance using seven chemicalreactions [33]. These studies led to a remarkable contribution to understanding of the SCR systems. Themain purpose of the SCR models in [32, 33] was to compare the performance of the high-order models withthe reduced models.To designing the model-based SCR controllers, the studies for the reduced-order SCR model containingtwo, three, or four-states have been performed in recent years [34–37]. The reduced model based on tem-perature and ammonia surface coverage was proposed in [35]. As another representative reduced model, theSCR model developed based on the concentrations of NOx, NH3, and ammonia coverage ratio on the SCRcatalyst was developed in [36, 37]. Based on these reduced models, many studies for controller design havebeen performed as discussed in the following subsections.1.5.2 Open-loop controlAn open-loop control is a control strategy to track the desired setpoint without considering “plant output (y)”as depicted in Fig. 1.4. Since the open-loop controller does not use any feedback information, there is noOpen-loop ControllerPlantsetpoint yuFigure 1.4: Schematic of an open-loop controllerguarantee of the control peroformance. The open-loop controller yields control input (u) based on the applied81.5. Literature Reviewsetpoint value.Based on open-loop control strategy, the SCR controller design has been conducted in [38]. The proposedcontroller consists of the look-up tables dependent on engine speed, engine temperature, fuel quantity, andexhaust gas temperature to generate the setpoint value. The generated setpoint value is also corrected by andynamic model and then the control input (u) is finally determined. The result showed approximately 60%ofNOx conversion efficiency with an average ammonia slip of 2 ppm over European Transient Cycle (ETC).This implies that there is doubt to adopt the open-loop control staretgy in the SCR applications due to lowNOx conversion efficiency. The study was conducted that the closed-loop control is necessary to improvethe performance over the transient driving cycle in [20]1.5.3 Feedforward-feedback controlA feedforward-feedback control consists of a feedforward controller and a feedback controller, as depictedin Fig. 1.5. Here, d, e, u, n, and y represent disturbance, error signals between setpoint values and measuredFeedback ControllerPlant++Sensor measurementdnesetpoint u+-yFeedforward Controller++Figure 1.5: Schematic of a feedforward-feedback controllersignals, a control input, a sensor noise, and measured outputs, respectively. The feedforward control is acontrol method to eliminate disturbance (d) when the disturbance is measurable by sensors, or it can be esti-mated by other signals. The benefit of feedforward control includes fast disturbance attenuation. In additionto feedforward control, the feedback control strategy uses a sensor measurement (y) to inform about how theplant is responding. Based on this measurement, the feedback controller can compute a control input (u) forreducing the error (e).Based on the feedforward-feedback SCR control strategy, several works have been studied in [39–42]. Toachieve a highNOx,out reduction rate with lowNH3,out, a map-based feedforward-feedback control strategywas presented in [42]. A model-based feedforward control strategy was also studied with a Proportional-91.5. Literature ReviewIntegral (PI) feedback controller to determine the urea amount under the European Driving Cycle in [40, 41].The feedback controller based on the self-tuning control strategy with the on-line adaptation of controllergains was studied in [39] and demonstrated to reduce the Federal Test Procedure (FTP) cycleNOx emissionsby 84% with 7 ppm of NH3 slip.1.5.4 Gain-scheduling controlThe gain-scheduling controller which consists of multiple local feedforward-feedback controllers, denotedby Ki, (i = 1, . . . , N ), and a switch, is commonly used for controlling nonlinear systems with dynamicschanging from one operating condition to another as depicted in Fig. 1.6.Plant(Nonlinear System)++Sensor measurementdnesetpointu+-yKNK1Figure 1.6: Schematic of a gain-scheduling controllerThe gain-scheduling controller is operated based on the pre-defined gain-scheduling parameters byswitching a controller (see a red arrow on the switch). A nonlinear controller is typically time-consumingto design and difficult to implement as well as to troubleshoot. This is because the mathematics behindnonlinear control is often highly complicated. In other words, nonlinear equations are pretty much diffi-cult to solve than linear equations. That is why the gain-scheduling controller consisting of multiple LinearTime-Invariant (LTI) controllers is practically adopted when a single LTI controller does not yield desiredperformance throughout the entire range of operating conditions for the plant.A gain-scheduling controller based on feedback-feedforward control strategy has been studied in [43,44]. The feedback control approach using gain-scheduling control strategy was proposed based on pro-portional and integral gains which depend on exhaust gas temperature and exhaust gas flow rate in [43].A gain-scheduling controller using exhaust gas temperature and exhaust gas mass flow was also presented101.5. Literature ReviewPlantu yPlantoptimizationmodelPredictionsetpointSensor measurementobjective,constraintsFigure 1.7: Schematic of a model predictive controllerbased on Linear Parameter Varying (LPV) control strategy using the Principal Component Analysis (PCA)method to reduce the number of the gain-scheduling parameters [44].1.5.5 Model predictive controlA model predictive controller (MPC) utilizes a plant model and an optimizer to compute the control input (u)as depicted in Fig. 1.7. The MPC uses a model to make predictions about the future plant output. TheMPC also relies on an optimizer to ensure that the predicted future output follows the setpoint value whilesatisfying given constraints [45].Model predictive control has been used for decades in many industries such as the automotive and thechemical process industries [46]. Especially, for the SCR systems, further performance improvements tothe SCR control system in comparison to the aforementioned control methods can be expected by utilizinga prediction of the amount of NOx reaching the catalyst in the future. This is because, by knowing theincoming NOx amount in advance, the SCR system can be prepared by injecting the sufficient amountof NH3 beforehand to deal with the incoming NOx variations. Such NOx prediction can be realizedin various ways, for example, by installing NOx sensors between the engine outlet and the SCR system,and by estimating the upcoming NOx amount from the engine operating condition, the operator’s throttlemanipulation, and even information about the terrain which a vehicle encounters [47].To make use of the predicted NOx information in an SCR control system, model predictive control(MPC) has been applied, e.g., linear MPC [48], nonlinear MPC [49], and adaptive MPC [50]. These MPCtechniques were able to successfully bring down the levels of NOx and NH3 emitted. The study for predic-tive ammonia coverage ratio generator has been recently conducted based on adaptive neuro-fuzzy inferencemethod in [51]. Model predictive control stragey has been also studied for the transient load share manage-111.5. Literature Reviewment of a diesel-electric marine propulsion plant containing the SCR system in [52]. However, the maindrawback of MPC is that it involves real-time optimization and thus increases the computational burden ofon-board micro-controllers.1.5.6 Preview controlTo cover the computational drawback of MPC, another control method that has the capability of handling thepredicted NOx information, called preview control, has been studied as depicted in Fig. 1.8. The previewedsignal can be computed by using estimation algorithms and sensor measurement signals.Plant𝑑Previewed signal𝑦𝑢++PreviewcontrollerFigure 1.8: Schematic of a preview controllerThe performance of the preview controllers was investigated in many applications [53, 54]. The primarydifference of preview control from MPC is that the preview controller is designed offline and that its im-plementation demands only simple algebraic calculations (products of matrices and vectors), in contrast toreal-time optimization required in MPC.The performance of the preview controller under transient conditions was demonstrated using the pre-viewed disturbance in [55]. This study showed that the solution via state augmentation technique on ser-vomechanism design delivered better performance than non-preview controllers. A preview linear quadraticcontroller and a nonlinear preview controller were also designed in vehicle rollover prevention and robotdesign, respectively [56, 57]. There has been no previous work on preview SCR control.1.5.7 Challenges covered by the previous researchThe aforementioned studies were performed to cover the control challenges raised in Section 1.4. Table 1.1lists the control challenges covered by the primary SCR control studies previously performed. To overcomethe nonlinearity, many studies utilized various design methods such as gain-scheduling control, adaptive121.5. Literature ReviewReference Challenges Technique1.4.1 1.4.2 1.4.3 1.4.4[40] O Model based FFC and FBC based on estimated θ[39] O O FF-FB adaptive control based on SCR reduction capability[37] O O FF-FB sliding mode control based on estimated θ[43] O GS control based on T and exhaust gas flow rate[44] O O GS LPV control based on T and estimated θ[47] O O O Nonlinear MPC[48] O O Linear MPC[49] O O O Nonlinear MPC[50] O O O Adaptive MPCTable 1.1: Challenges covered by the previous SCR research:(1.4.1: Nonlinearity, 1.4.2: UnmeasurableCatalyst Condition, 1.4.3: Slow dynamics of the SCR system, 1.4.4: Time delay of Sensor)control, and nonlinear model predictive controlin [37, 39, 44, 47, 49, 50]. To tackle the unmeasurablecatalyst condition, model-based control, feedforward-feedback control, nonlinear control have been studiedin [37, 39, 40, 43, 44]. To overcome the challenge for the slow dynamics and sensor delay, the controllerdesigned based on model predictive control method demonstrated significant results [47–50].Among control methods, the most remarkable work was conducted by gain-scheduling controllers. Thefeedback control approach using a gain-scheduling control strategy was proposed based on proportional andintegral gains, which depend on exhaust gas temperature and exhaust gas flow rate in [43]. Although theresult was demonstrated through simple simulations and transient tests, it is limited to only NOx reductionwithout any discussion of ammonia slip. A gain-scheduling SCR controller using exhaust gas temperatureand ammonia coverage ratio was also presented [44]. Simulation results were reasonable, but the methodin [44] has some drawbacks. Firstly, there is a possibility that conservatism may exist with large variation ofgain-scheduling parameters [58]. Secondly, the ammonia slip sensor located downstream of the SCR catalystwas not used for feedback control. Thirdly, only one quasi-LPV model was employed for controller design,while there was another quasi-LPV model which has a potential benefit. Lastly, the feedforward controllerand the feedback controller were designed separately.The MPC controllers delivered successful results by using predictive information such as NOx distur-bance and system outputs based on on-line optimization. However, even with successful results by MPCcontrollers, there are still concerns about high computational requirement and some lack of studies for de-signing controllers with low computational requirement in their implementations in engine control units.As a nonlinear controller, a sliding mode controller (SMC) was studied based on NH3 sensor measure-131.6. Research Objectivesment in [59]. The main purpose of this study was that NH3 sensor can be a potential alternative to NOxsensor for the SCR control applications. There is little doubt about the control performance of the proposedcontroller under transient driving conditions.In summary, by the literature review of SCR control, we identified conservatism caused by large variationof gain-scheduling parameters and high computational requirement arose by on-line optimization as researchgaps.1.6 Research ObjectivesWith the identified research gaps in SCR control, the research objectives (O1), (O2), and (O3) of this thesisare stated as follows.(O1) To fill the research gap for the conservatism caused by large variation of gain-scheduling parameters,the first objective is to design a gain-scheduling controller capable to maximize NOx conversion effi-ciency while keeping affordably low ammonia slip without conservatism in large dynamics variationof gain-scheduling parameters.(O2) To address the research gap for some drawbacks of the existing LPV controller, the second objec-tive is to design the LPV controller based on a quasi-LPV model using measurable gain-schedulingparameters with co-design strategy of the feedforward and feedback controllers.(O3) To close the research gap for high computational requirement due to on-line optimization, the thirdobjective is to design the SCR controller using predictive information with low computational require-ment while maintaining the first objective.1.7 Research ApproachesTo reach the objectives discussed in Section 1.6, the research approaches of this thesis are stated as follows.To achieve the objective (O1), a gain-scheduling (GS) controller utilizing ammonia slip measurement asone of the gain-scheduling parameters is proposed. This GS controller consists of linear time-invariant (LTI)H∞controllers, each of which provides satisfactory control performance for different operating points. The sub-regions of T andNOx disturbance are determined by typical engine operating conditions, but the sub-region141.7. Research Approachesof ammonia slip should be decided by the control performance. Thus, to determine the sub-region of am-monia slip, the efficient decision method by using ammonia slip measurement is also proposed. The (O1) isachievable by the proposed controller since the gain-scheduling controller switching multiple LTI controllersdoes not make any conservatism. Instead, there is a limitation of the theoretical stability guarantee in the pro-posed controller. Therefore, the simulation test for the robustness analysis is conducted using sensor noiseand parameter perturbation to practically guarantee the stability of the proposed controller over the non-roadtransient cycle.To reach the objective (O2), the gain-scheduling LPV controller is proposed as an alternative method,since LPV technique provides a systematic way for gain-scheduling with a theoretical guarantee of stabilityand performance. This proposed LPV controller is also an extended controller to cover the drawbacks of theexisting LPV controller. The LPV controller is obtained by solving an optimization problem containing lin-ear matrix inequalities (LMIs) that guarantee the stability and performance of the closed-loop system underall admissible trajectories of the scheduling parameters. This controller is designed based on a quasi-LPVmodel using NOx and NH3 downstream of the catalyst which has more potential compared to ammoniacoverage ratio. It is also designed based on the co-design strategy of the feedback and feedforward con-trollers. For the case studies, two LPV controllers are designed using different gain-scheduling parameters:(1) θ and (2) NOx and NH3 slip. The simulations for the control performance and the robustness analysisare conducted over a non-road transient cycle (NRTC) test mode.To accomplish the objective (O3), a preview-feedback controller is proposed based on discrete-time H∞control design approach using previewed NOx information. To make use of the previewed NOx informa-tion, the proposed controller is designed based on the state augmentation technique. The simulation tests forthe effectiveness of the preview-feedback controller, performance comparison, and robustness analysis areconducted over a non-road transient cycle (NRTC) test mode.The SCR model used in this thesis is acquired with model parameters in the previous research [37, Table4.2]. The input data for realistic simulations was experimentally measured over the non-road transient cycleat Doosan Infracore Co. Ltd.151.8. Outline of the Thesis1.8 Outline of the ThesisThe outline of this thesis is given as follows.Chapter 2 represents the control-oriented SCR model based on chemical reactions. This SCR model isused to design the proposed SCR controllers in Chapters 3–5. In the simulation setup, the obtained datasuch as NOx disturbance, exhaust gas temperature T , and exhaust gas flow rate Q are introduced. Theexperimental test facility and test mode called Non-Road Transient Cycle (NRTC) are briefly overviewed.Chapter 3 is devoted to the development of a gain-scheduling SCR controller based on gain-schedulingparameters, NOx disturbance, T , and NH3 downstream of the SCR catalyst. The Violation Time-basedDecision (VTD) method is also proposed to design the subregion of the gain-scheduling parameter, NH3measurement. The performance of the proposed controller is demonstrated compared to a feedforward con-troller, a gain-scheduling PID controller, and a sliding mode controller.Chapter 4 describes the design of the LPV SCR controller gain-scheduled by NH3 level stored in theSCR catalyst, NOx,out, and NH3,out. This controller is an alternative controller which ensures internalstability even with conservative performance. The control performance is evaluated with the simulation test.The robustness analysis using sensor noises and parameter perturbation is also demonstrated.Chapter 5 introduces the design of a discrete-time preview-feedback SCR controller using previeweddisturbance information. To design the preview-feedback SCR controller, the discrete-time generalized plantis derived based on previewed disturbance signals and weighting functions. The simulation tests for thecontrol performance, the robustness analysis, the comparison with an MPC controller, and the computationalrequirement are conducted under the simulated environment with NRTC mode.Chapter 6 concludes this thesis by stating the key contributions, and provides the future work.16Chapter 2PreliminariesThis chapter provides the preliminaries for presenting our main results in Chapters 3–5. In Section 2.1, theSCR operating principle will be introduced based on the chemical reactions. The nonlinear state-space modelwill be reviewed in Section 2.2, which is to be used in both controller design and controller validations basedon simulations. For the usage in the simulations, the simulation setup will also be reviewed in 2.3.2.1 SCR Operating PrincipleThe schematic of the SCR system is depiced in Fig. 2.1. To reduce nitrogen oxide (NOx,in) coming fromSCR catalyst𝑁𝐻3,𝑖𝑛𝑁2𝐻2𝑂𝑁𝑂𝑥,𝑜𝑢𝑡𝑁𝐻3,𝑜𝑢𝑡Dosing valve 𝑁𝐻3 sensor𝑁𝑂𝑥 sensorTemperature sensor𝑁𝑂𝑥,𝑖𝑛ChemicalReactions𝑁𝑂𝑥 sensor𝑢𝑟𝑒𝑎Figure 2.1: Schematic of the SCR systema diesel engine, urea is injected through a urea dosing value. The injected urea is chemically convertedinto ammonia (NH3) under the suitable range of exhaust gas temperature. The ammonia is then adsorbedon the surface of an SCR catalyst and chemically reacted with nitrogen oxide (NOx) resulting in nitro-gen (N2) and water vapor (H2O). If ammonia is less injected than the desired value, NOx is going out oftailpipe (NOx,out). On the other hand, if ammonia is excessivly injected or exhaust gas temperature goesup to higher than proper range, the ammonia is then desorbed and goes out of tailpipe (NH3,out). The mainreactions in the SCR catalyst are SCR reactions, ammonia oxidation, ammonia adsorption, and desorption172.1. SCR Operating Principleas follows.2.1.1 NOx reduction in SCR reactionsInjected NH3 and NOx disturbance chemically react in the SCR catalyst and result in harmless gas suchas N2 and H2O coming out of tailpipe. The three main chemical reactions for NOx reductions in the SCRcatalyst are given as2NH3 +NO +NO2 −→ 2N2 + 3H2O, (2.1)rfred := kfred · CNO · CNO2 · θ · Ω, (2.2)4NH3 + 4NO +O2 −→ 4N2 + 6H2O, (2.3)rred := kred · CNO · CO2 · θ · Ω, (2.4)4NH3 + 3NO2 −→ 3.5N2 + 6H2O, (2.5)rsred := ksred · CNO2 · θ · Ω, (2.6)where equations (2.1), (2.3), and (2.5) represent fast SCR reaction, standard SCR reaction, and slow SCRreaction, respectively. Here, rfred, rred, and rsred [mole/m3·sec] represent respectively fast reaction rate,standard reaction rate, and slow reaction rate of NOx reduction in SCR catalyst. The Ci [mole/m3], θ [-],and Ω [mole/m3] represent the concentration of i-th species, ammonia coverage ratio, and ammonia storagecapacity, respectively.In the chemical equations, the chemical reaction constants, ki, are defined aski = αi · e−EiRT , i = fred, red, sred, ox, ads, des, (2.7)where αi, Ei, R, and T represent respectively the pre-exponential factors, activation energy of each reaction,universal gas constant, and exhaust gas temperature where the reaction takes place.182.2. Nonlinear State-space Model2.1.2 NH3 oxidationThe chemical reaction equation for ammonia oxidation and its reaction rate rox are given by4NH3 + 3O2 −→ 2N2 + 3H2O, (2.8)rox := kox · θ · Ω. (2.9)The NH3 oxidation is considered as an undesirable reaction since NH3 is consumed without NOx reduc-tion.2.1.3 NH3 adsorption and desorptionThe NH3 is adsorbed on the surface of the SCR catalyst while some NH3 is desorbed. These reactionprocesses for adsorption and desorption and their reaction rates are represented asNH3 + S −→ NH3∗, (2.10)rads :=kads · (1− θ) · CNH3 · Ω, (2.11)NH3∗ −→ NH3 + S, (2.12)rdes :=kdes · θ · Ω, (2.13)where S, NH∗3 , rads, and rdes represent respectively a free site of the SCR catalyst, adsorbed NH3 on thesurface of the SCR catalyst, the reaction rates of NH3 adsorption and desorption.2.2 Nonlinear State-space ModelIn this section, the nonlinear state-space model developed in [37] is reviewed to design the proposed con-trollers. This SCR model includes the standard SCR reaction (2.3), NH3 oxidation (2.8), NH3 adsorp-tion (2.10) and desorption (2.12) for simplicity. The nonlinear state-space model is represented byx˙ = Ax+ f(x) +Bdd+Buu,y = Cx. (2.14)192.2. Nonlinear State-space ModelHere, the state vector x, the output vector y, the input u, and the disturbance d are defined respectively asx :=CNOx,outCNH3,outθ , y := CNOx,outCNH3,out , u := NH3,in, , d := NOx,in. (2.15)The matrices A, B, C, and the nonlinear function f(x) in (2.14) are defined byA :=−Q¯ 0 00 −(kadsΩ + Q¯) kdesΩ0 kads −(kred + kox) , (2.16)Bd :=Q¯00 , Bu :=0Q¯0 , C := 1 0 00 1 0 , (2.17)f(x) :=−kredΩx1kadsΩx3−(kredx1 + kadsx3)x2, (2.18)where Ω [mole/m3] represents the ammonia storage capacity of the SCR catalyst. The matrices Bd and Bucontain the normalized exhaust gas flow rate given byQ¯ :=QV, (2.19)where Q [m3/sec] is the exhaust gas flow rate and V [m3] is the volume of exhaust gas in the substratechannel.The model (2.14) is a nonlinear parameter-varying model. It is nonlinear due to the term f in (2.18),and it is parameter-varying because of the exponential dependence of ki in (2.7) on T . Besides, the reactionrates (2.3), (2.8), (2.10), and (2.12) depend on state variables (2.15). The matrix A, Bd, and Bu also dependon the exhaust gas flow rate (Q). The model (2.14), with the parameter values to be given in Section 2.3,will be used in Chapters 3 - 5 for both controller design and controller validation.202.3. Simulation SetupVTG SensorsAfter-treatment system Heavy-duty diesel engineExhaust gas flowT: Temperature sensorNOX: NOX sensor NH3: NH3sensorDP: Differential Pressure sensorNOX T DPDPUrea InjectorNOXTNH3TDOC DPF SCRUreapumpUrea tankUreainjectorFigure 2.2: SCR control system equipped on a heavy-duty diesel engine: Variable Turbine Geometry (VTG),Diesel Oxidation Catalyst (DOC), Diesel Particulate Filter (DPF)2.3 Simulation SetupIn this thesis, the simulations will be performed to evaluate the proposed controllers. To make the simu-lation environment be realistic, the sensor data measured with the open-loop experimental setup at DoosanInfracore Co. Ltd. will be used.2.3.1 Data acquisitionThe diesel engine system for the data acquisition is shown in Fig. 2.2. The specifications of the engine systeminclude: a heavy-duty diesel engine equipped with Variable Turbine Geometry (VTG) and aftertreatmentsystems. A Bosch ETK-ECU3 was used to control the diesel engine systems. The Integrated Calibration andAcquisition software (INCA4) was used to operate the system and to measure data. The specification of thediesel engine test facility is listed on Table 2.1.3ETK-ECU is a development ECU, which is capable of interfacing with INCA software for calibration and measurement.4INCA is a calibration and measurement software designed by ETAS.212.3. Simulation SetupTable 2.1: Specification of the diesel engine test facilityParameter ValueCylinder 6Displacement 7.6 litresFuel injection Common-rail direct injectionMax. Power 286 Hp (1800 rpm)Max. Torque 1275 Nm (1300 rpm)Aspiration TurbochargedAftertreatment DOC, DPF, SCRSCR volume 19.87 dm32.3.2 Parameter valuesTable 2.2 lists the numerical values of chemical reactions taken from the previous research [37, Table 4.2].The values in Table 2.2 were selected based on the system identification and validated with the high-fidelitySCR model and the actual engine [37]. Since the 3-state control-oriented SCR model was derived basedon four chemical reactions as discussed in Section 2.2, the model parameters for four reaction constantswere listed on Table. These model parameters related to the chemical reaction constants can be utilized forrobustness analysis. The results obtained by perturbing each model parameter under open-loop simulationsdemonstrate how sensitive the parameters are, as provided in Appendix A. The most sensitive parameter isthen selected and the closed-loop simulation test is conducted by perturbing the most sensitive parameter forrobustness analysis.Table 2.2: Reaction constants in (2.7)Reactions Pre-exponential factor Activation energy [KJ/mol]SCR reaction 3.32E+09 [m3/mole-sec] 85NH3 oxidation 4.33E+06 [1/sec] 112NH3 adsorption 2.13E+07 [m3/mole-sec] 42NH3 desorption 3.28E+11 [1/sec] 1132.3.3 Non-road transient driving cycleThe NRTC test mode is a transient driving cycle developed by the United States Environmental ProtectionAgency (EPA) [60]. The engine speed and torque during NRTC test are shown in Fig. 2.3. In general, the222.3. Simulation SetupNRTC is run twice, with a cold and a hot start, with a 20 minute soak period between the tests. The cold startweighting factors are 10% in the EU and 5% in the United States. In this thesis, we used data experimentallymeasured over the NRTC test mode with a hot start. This transient test mode is used internationally0 200 400 600 800 1000 1200010002000Speed [rpm]0 200 400 600 800 1000 1200Time [sec]050010001500Torque [Nm]Figure 2.3: Speed and torque profile of the NRTC0 200 400 600 800 1000 120001000NOx,in [ppm]0 200 400 600 800 1000 1200400500600Temperature [K]0 200 400 600 800 1000 1200Time [sec]00.10.2Flow rate [m3 /s]Figure 2.4: Input signals to the SCR model for the simulation testfor a non-road diesel engine emission certification over engine dynamometers. Since the NRTC test mode232.3. Simulation Setuprepresents almost all practical driving conditions, controllers demonstrating satisfactory performances withthe data from this mode are considered to be practically usable.As shown in Fig. 2.4, the data containing NOx disturbance (CNOx,in), exhaust gas temperature (T ), andexhaust gas flow rate (Q) were measured under the non-road transient cycle (NRTC) mode. Since the NOxdisturbance measurement system took 200 [sec] to be activated, the NOx disturbance signal from 0 to 200[sec] is different from an actual signal and the actual signal starts from 200 [sec]. These measured signalsover the NRTC test mode are used as input data in the SCR model (2.15), (2.16), (2.17), and (2.18).24Chapter 3SCR Control Gain-scheduled by AmmoniaSlip Measurement3.1 IntroductionAs discussed in Chapter 1, diesel engines are normally used in heavy-duty applications since higher torqueand better fuel efficiency can be obtained compared to gasoline engines. However, diesel combustion gener-ates harmful nitrogen oxide (NOx) emissions. Since NOx emissions cause health concerns such as respira-tory illnesses, heart disease, and cancer, emission regulations for diesel engines are continuously becomingmore stringent. To meet the emission regulations, diesel engine manufacturers have adopted selective cat-alytic reduction (SCR) systems in their products since mid-2000s because of their high reduction of NOxemissions[61].An SCR control system injects a water-based urea to achieve a high NOx reduction rate with acceptablylow ammonia (NH3) downstream of the SCR catalyst. The injected urea forms NH3 on the surface of theSCR catalyst, which reacts with NOx emissions, resulting in the production of nitrogen (N2) and watervapor (H2O). However, in practice, NOx and NH3 come out of tailpipe since system nonlinearity, slowdynamics, and sensor uncertainty cause the challenge of computing the optimal amount of urea [62].To overcome the control challenges, many studies have been conducted as discussed in Section 1.5.Among them, some remarkable studies on gain-scheduling control strategy for SCR systems have been donein [43, 44], and demonstrated simulation results based on the selected gain-scheduling parameters: exhaustgas temperature, exhaust mass flow rate, and NH3 coverage ratio. However, there may be two concerns.Firstly, it is well-known that the NH3 coverage ratio is an estimated value, not a measurable one. Thismeans that there may be control performance degradation when there is a difference between calculated val-ues and actual ones. Secondly, there is a possibility that the conservatism may be existed with large variation253.2. Preliminariesof gain-scheduling parameters [58]. To the best of the authors’ knowledge, there has been little discussionabout two aformentioned concerns to date.In this chapter, we propose a gain-scheduling (GS) controller utilizing ammonia slip measurement asone of the gain-scheduling parameters. This GS controller consists of linear time-invariant (LTI) H∞ con-trollers, each of which provides satisfactory control performance for different operating points. The proposedcontroller is capable to maximize NOx conversion efficiency and minimize NH3 downstream of the SCRcatalyst. Compared with previous research, the proposed GS control method has a few advantages. Firstly,all gain-scheduling parameters are measurable, so there is no control performance degradation due to esti-mation or calculation error. Secondly, it is practically adoptable in industrial applications since the proposedmethod does not include complex algorithms such as a nonlinear observer. Finally, the proposed method fordetermining the engine operating region for each of LTI controllers can easily be adopted by SCR systemsthanks to the simplicity of the design procedure.The remainder of this section is organized as follows. In Section 3.2, a control-oriented SCR modelare briefly reviewed. Section 3.3 presents the motivation and the structure of the proposed GS controller.In Section 3.4, the design process of GS controllers is also described. In Section 3.5, for the proposed GScontroller, the simulation results are then demonstrated in transient conditions using experimental data ofNOx disturbance, exhaust gas temperature, and exhaust gas flow rate obtained over non-road-transient cyclemode from a heavy-duty diesel engine.3.2 PreliminariesIn this section, as a preparation for presenting our main results in Sections 3.3 and 3.4, the control-oriented3-state model studied in [36] will be reviewed.As discussed in Chapter 2, for model-based SCR controller design, a 3-state control-oriented SCR dy-namic model was derived in [36], by using the chemical reaction equations in the SCR catalyst, asx˙ = Ax+ f(x) +B wu . (3.1)263.2. PreliminariesHere, the state vector x, the input u, and the disturbance d are defined respectively asx :=CNOx,outCNH3,outθ , u := CNH3,in , d := CNOx,in . (3.2)The matrices A and B, and the nonlinear function f(x) in (3.1) are defined byA :=−Q¯ 0 00 −(kadsΩ + Q¯) kdesΩ0 kads −(kox + kdes) , (3.3)B :=Q¯ 00 Q¯0 0 , (3.4)f(x) :=−kredΩx1kadsΩx2−(kredx1 + kadsx2)x3, (3.5)with the notation xi for the i-th entry of x. In (3.3)–(3.5), the model parameters Q¯ [1/sec], Ω [mole/m3],and ki are respectively the normalized exhaust gas flow rate, the ammonia absorption capacity of the SCRcatalyst, and the chemical reaction constants given byki := αie− EiRT , i = red, ox, ads, des. (3.6)Here, αi [m3/mole], Ei [kJ/mole], and T [K] are respectively pre-exponential factors for i-th reaction, ac-tivation energies for i-th reaction, universal gas constant, and exhaust gas temperature in the SCR catalyst.The reaction rates containing each chemical reaction constant were described in Chapter 2.The model (3.1) is a nonlinear parameter-varying model. It is nonlinear due to the term f in (3.5), andit is parameter-varying because of the exponential dependence of ki in (3.6) on T . To design a controllerfor this nonlinear parameter-varying system, we will adopt a gain-scheduling control technique which willbe presented in the next section. We assume that NH3,in converted from the injected urea is the control273.3. GS H∞ SCR Controllerinput for simplicity, even though the urea injection is the actual manipulated variable in real SCR controlsystems [19, 32, 36].3.3 GS H∞ SCR ControllerIn this section, the operating range of the SCR system will be introduced based on exhaust gas temperature(T ) and NOx upstream of SCR catalysts (NOx,in). The motivation of GS controller will then be covered.The structure of the proposed GS controllers will also be explained.3.3.1 Operating rangeThe operating range of the SCR system is defined by the minimum and maximum input signal limits, for theexhaust gas temperature T [K] and the concentration of NOx entering the SCR catalyst NOx,in [moles/m3].During typical heavy-duty diesel engine operation, T and NOx,in can vary respectively between 430 and700 [K] and between 0 and 0.045 [moles/m3] as shown in Fig. 2.4. Note that the operating range is notalways the same, but it depends on the actual engines.3.3.2 Motivation of GS controllerAs one option to design an SCR controller, a linear time-invariant (LTI) controller can be considered. Thiscan be accomplished by linearizing a nonlinear SCR model (3.1) around an operating point. However, theoperating range of the SCR system is typically too broad for a signle LTI controller to perform well overthe entire operating range. Therefore, there is a limitation to implementing a functional LTI controller inindustry [63].Another option is a nonlinear technique due to the term f in (3.5). Successful results have been alreadyreported for designing nonlinear observers and nonlinear controllers for SCR systems [64–66]. Nonetheless,there are also drawbacks in terms of implementing nonlinear controllers in a practical SCR system due tocomplexity and computational cost.Rather than dynamic controllers, a map-based algorithm is normally adopted in commercial SCR systemssince it is easily adoptable. However, it is doubtful that the control performance by using a map-basedalgorithm would be satisfactory as the emission standard becomes increasingly stringent. This is becausethese maps must be filled by conducting a number of engine tests at a static mode, and it is unclear that283.3. GS H∞ SCR Controllerthe control systems developed based on engine tests at a static mode have desired control performance attransient modes.Based on the consideration above, a gain-scheduling (GS) controller which consists of multiple LTIcontrollers and a controller switching law will be appropriate as an SCR controller since the GS controllercontrols a system over the entire operating range with simpler control algorithms than nonlinear controllers.The control performance of the GS controller depends on the selection of a control system structure, GSparameters, and the switching law.3.3.3 Feedforward-feedback controlThe SCR control system structure proposed in this chapter is depicted in Fig. 3.1. The controller, denoted byK(r) in Fig. 3.1, is a feedforward-feedback (FF-FB) gain-scheduling (GS) controller. The controller K(r)is a feedforward controller as it receives the NOx sensor signal w (=NOx,in) upstream of the SCR catalystand determines NH3,in to effectively cancel out incoming NOx. Such feedforward control is helpful inimproving the disturbance rejection at the transient, since the rough amount of NH3,in can be determinedbased on NOx,in measurement, without waiting for receiving feedback signals.SCR catalyst𝑟Figure 3.1: FF-FB GS SCR controller structure (The controller, K(r), consists of the feedforward and feed-back controllers. Dotted arrows indicate gain-scheduling parameters.)In addition to the feedforward control, the controller K(r) is a feedback controller because it utilizesthe NOx and NH3 sensor signals after the SCR catalyst, x1(=NOx,out) and x2(=NH3,out). This feedbackpart is important to make the control system robust against errors of the model (3.1) used in the controllerdesign. Note that the ammonia coverage ratio θ is not used as a feedback signal because it is not measurablein practice.293.3. GS H∞ SCR Controller3.3.4 Gain-scheduling controlThe controller K(r) is gain-scheduled with the gain-scheduling parameter vector (r), indicated with dottedlines in Fig. 3.1 and defined byr :=NOx,inTNH3,out =wTx2 . (3.7)Note that the equilibrium point of the model (3.1) is determined by specifying these three variables to beconstant, as the three state equations have six variables (x ∈ R3, w, T , and u).The gain-scheduling parameters NOx,in, T , and NH3,out are selected by considering the system dy-namics and measurability. The measurable disturbance NOx,in affects the outputs, NOx,out and NH3,out.The system matrix (3.3) and the nonlinear function (3.5) have exponential dependence of ki on T . The NH3coverage ratio (θ) which affects the dynamics of the SCR system should be a GS parameter. However, θ isnot measurable, so NH3,out which is measurable and correlated with θ, can instead be selected.The gain-scheduling parameters and the multiple LTI controllers are illustrated in Fig. 3.2. For w andT , the sub-regions can be determined by dividing the entire operating range equally. In the entire operatingrange, if there is a specific operating range where SCR control systems mainly operate, then the sub-regionscan be determined by equally dividing that specific range. However, for NH3,out, the sub-regions can bedetermined by dividing the entire operating range based on the tuning parameters. The tuning parameters areTw (=𝑁𝑂𝑥,𝑖𝑛)𝑥2 (=𝑁𝐻3,𝑠𝑙𝑖𝑝)𝑆𝑆1𝑆𝑆𝐾−1𝐾111𝐾𝑖𝑗𝑘Figure 3.2: The gain-scheduling parameters and the multiple LTI controllers303.4. Design of SCR Control Gain-scheduled by Ammonia Slip Measurementreferred to as switching surfaces, denoted by SSi, i = 1, . . . ,K − 1 where K indicates the number of sub-regions in x2 axis. As shown in Fig. 3.2, the sub-regions are unequally divided by switching surfaces (SSi).The SSi can be determined using the proposed decision method which will be introduced in Section 3.4.2.The gain-scheduling controller consisting of each LTI controller is expressed asK(r) = Kijk, if r ∈ Rijk, (3.8)for i=1, . . . , I , j=1, . . . , J , and k=1, . . . ,K. Here,Rijk is the set of sub-regions depending on w, T , and x2.The switching among LTI controllers is performed by gain-scheduling parameters to select an LTI controllerin a sub-region where the engine is operating.3.4 Design of SCR Control Gain-scheduled by Ammonia Slip MeasurementIn order to design the FF-FB GS SCR controller (3.8), the design procedure consists of two parts: design ofLTI controller (Kijk) and design of sub-regions (Rijk).First, for designing an LTI controller, H∞ control law is employed in this section because it is easilyapplicable to control problems involving multivariate systems with cross-coupling between channels [67].Additionally, the frequency dependence of the disturbance signal can be considered by using H∞ controllaw. These traits suit an SCR control system well for two reasons.1. There is a trade-off relation between NOx,out and NH3,out, meaning that excessively injected NH3leads to low NOx,out and high NH3,out, and vice versa.2. The disturbance signal (NOx,in) should be attenuated over its own frequency band.Second, the sub-region (Rijk) is determined in a heuristic way by equally dividing the operating range ofT andw. See T -axis andw-axis as illustrated in Fig. 3.2. This is because these operating ranges are typicallyknown for a specific diesel engine. However, the sub-region for NH3,out is decided in a systematic way,because the operating range of NH3,out depends on the SCR control system. The method of determiningsub-regions for NH3,out is proposed in Section 3.4.2.313.4. Design of SCR Control Gain-scheduled by Ammonia Slip Measurement3.4.1 Design of LTI H∞ controllersIn order to design an LTI controller Kijk in (3.8), let us consider the block diagram depicted in Fig. 3.3.Note that this block diagram is the same as Fig. 3.1, except for the following modifications:G𝑖𝑗𝑘𝐾𝑖𝑗𝑘12𝛿𝛿𝛿𝛿WWFigure 3.3: Block diagram of the weighted control system1. There are no gain-scheduling parameter signals (dotted lines in Fig. 3.1).2. The GS controller K(r) is replaced by an LTI H∞ controller Kijk in (3.8).3. The SCR catalyst is replaced by a linearized SCR modelGijk at an operating point in sub-regionRijk.4. There are weighting function blocks, W1 and W2.5. The perturbation signals, δw, δu, δx1, δx2, xW1 , and xW2 from the linearization point are used insteadof the corresponding signals themselves.Based on Fig. 3.3, the H∞ controller design problem is formulated asminKijk‖T ‖∞ , (3.9)where T is the transfer function from NOx,in perturbation (δw) generated by diesel engines to the weightedperformance indices [xW1 xW2 ]T . Minimization of the H∞ norm of T implies that the variation of NOx,indoes not affect the minimized NOx,out and NH3,out.The design procedure of the proposed LTI H∞ control system is as follows:1. Derivation of a linearized model (Gijk) based on the selected operating point values.2. Design of an LTI H∞ controller (Kijk).323.4. Design of SCR Control Gain-scheduled by Ammonia Slip MeasurementIn the derivation procedure 1), the nonlinear SCR model (3.1) is linearized by using the selected operatingpoint values asδx˙ =(A+∂f∂x∣∣∣∣x=xoT=To)δx+B δwδu , (3.10)where xo and To represent operating point values. Here, these values are selected by specifying T , w,and x3 (=θ) to be constant, since three variables are useful to capture the range of operating conditions ofSCR systems. The values of T and w are selected by subdividing their respective operating ranges into equalsegments. The values of x3 are selected within the range of 0 to 1. The value of x3 influences the magnitudesof NOx,out and NH3,out, and should therefore be selected based on the desired controller behaviour. Forinstance, higher value of x3 will produce lower NOx,out and higher NH3,out.In the design procedure 2), an LTI H∞ controller is designed based on the linearized model (Gijk) andthe weighting functions (W1 and W2). The weighting functions are designed by following two guidelines.1. The frequency of disturbance signal (NOx,in) which depends on the specific diesel engine should befound by using the Fast Fourier Transform of the measurement data obtained over the full drivingcycle. The weights are then selected to reduce the influence of NOx,in perturbation on NOx,out andNH3,out perturbation over the frequency of the disturbance signal.2. The weights should be adjusted to take trade-off between NOx,out and NH3,out in an iterative way. IfNOx,out has to be decreased, then we can either increaseW1 or decreaseW2. BothW1 andW2 shouldbe tuned until the desired NOx,out and NH3,out are obtained. Note that W1 can be mainly tuned tominimize NOx,out here to guarantee prioritized low NOx,out compared to NH3,out.3.4.2 Design of sub-regionsThe sub-regions Rijk (3.8) are designed based on the characteristic of the gain-scheduling parameters: w,T , and x2 (NH3,out). Since w and T depend on the specific diesel engine, determining sub-regions is doneby dividing the entire operating ranges. However, x2 is determined by the SCR controller, and there isambiguity for determining segments for x2 prior to designing controllers. Therefore, the sub-regionsRijk isdesigned after the controller design, with the following steps:1. Design of multiple GS controllers.333.4. Design of SCR Control Gain-scheduled by Ammonia Slip Measurement2. Design of sub-regions.In the design step 1), the GS controllers, denoted by Kk(rˆ), k = 1, . . . ,K, consist of the multiple LTIcontrollers designed by following the design procedure introduced in Section 3.4.1. Each GS controllerKk(rˆ) can be gain-scheduled by using the gain-scheduling parameter vector defined byrˆ := NOx,inT = wT . (3.11)Each GS controller Kk(rˆ) consists of multiple LTI controllers asK1(rˆ) = Kij1, if rˆ ∈ Rˆij , (3.12)K2(rˆ) = Kij2, if rˆ ∈ Rˆij , (3.13)......KK(rˆ) = KijK , if rˆ ∈ Rˆij , (3.14)where Rˆij is the set of sub-regions depending on w and T . To design Kk(rˆ), we assign an operating pointvalue ranging between 0 and 1 to NH3 coverage ratio (θ) as visualized in Fig. 3.4. Then, the operating pointvalues for NH3,out and NOx,out are determined based on θ. Generally, NH3,out is increased and NOx,outis decreased as θ is increased. Based on this phenomenon, K1(rˆ) has the smallest values of θ and NH3,out,and the largest value of NOx,out. The GS controller KK(rˆ) is then designed assuming the largest values ofθ and NH3,out and the smallest value of NOx,out. All other controllers are based on intermediary valuesof θ, NH3,out, and NOx,out. For instance, referring to Fig. 3.4, Rˆ11 on K1(rˆ) has a LTI controller, K111,which was designed based on smaller θ, smaller NH3,out, and larger NOx,out, compared to K11K in Rˆ11on KK(rˆ).The number of GS controllers depends on the number of selected operating points θ. For instance, thedesign can be done by assuming a minimum value of θ (= 0.1), which is implemented on K1(rˆ), and amaximum value of θ (= 0.9), which is implemented on K9(rˆ). This process repeats for all intermediarycontrollers K2(rˆ) to K8(rˆ), which are designed assuming θ values of 0.2 through 0.8 at increments of 0.1.By designing multiple Kk(rˆ) based on the selected operating point values in the proposed method, theseGS controllers have different advantages. Namely, the behaviours of K1(rˆ), · · · ,KK(rˆ) differ depending343.4. Design of SCR Control Gain-scheduled by Ammonia Slip Measurementon NH3,out and NOx,out, and we can select one of them by using the switching surfaces which will beintroduced in the next step. In the design step 2), the sub-region is divided by switching surfaces SSk,k = 1, . . . ,K− 1, as introduced in Fig. 3.2. The Violation-Time-based Decision (VTD) method is proposedto determine switching surfaces. The violation time period, denoted by ∆V Ti, is defined as the time lengthover which NH3,out is greater than or equal to some specified NH3,out level (NH3,min) under the operationof i-th GS controller Ki(rˆ).∆V Ti =∫τdt, τ = {t : NH3,out = NH3,min} , (3.15)In other words, if the violation time corresponding to K1(rˆ), K2(rˆ), and K3(rˆ) have the following relation-ship:∆V T1 < ∆V T2 < ∆V T3, (3.16)then it means that NH3,out by K1(rˆ) exceeds the NH3,out level for a shorter period than NH3,out by K2(rˆ)andK3(rˆ). The following paragraph explains how to use violation time periods for procedurally determiningswitching surfaces. First, referring to Fig. 3.5 where the left plot shows NH3,out for three GS controllersK1(rˆ), K2(rˆ), and K3(rˆ), we start taking the violation time period from each curve above 0.1 [mole/m3] ofTw (=𝑁𝑂𝑥,𝑖𝑛)𝐾111𝐾𝐼𝐽1𝐾𝐼11𝐾1𝐽1Tw (=𝑁𝑂𝑥,𝑖𝑛)𝐾11𝐾𝐾𝐼𝐽𝐾𝐾𝐼1𝐾𝐾1𝐽𝐾𝑥𝑜3 (= 𝜃)𝑥𝑜2(= 𝑁𝐻3,𝑠𝑙𝑖𝑝)𝑥𝑜1(= 𝑁𝑂𝑥,𝑜𝑢𝑡)Figure 3.4: The gain-scheduling parameters and multiple GS controllers designed based on differently se-lected operating point values (θ, NH3,out, and NOx,out)353.5. Simulation ResultsNH3,out level.0 5 10Time [sec]0510NH3,slip [mole/m3 ]0 5 10NH3,slip [mole/m3]0510 VT [sec]SS1 2.5 VT 8.013SS2 6.2 VT 4.272Figure 3.5: Violation-Time-based Decision methodThe violation time periods, denoted by ∆V T , are drawn in the right plot. Second, by repeating thisprocess, up to 10 [mole/m3], we can construct the right plot in Fig. 3.5. Note that a shorter violation timeabove a certain NH3,out level means that the relevant GS controller reduces NH3 more than another GScontroller does. Therefore, this plot may then be used to identify the switching surfaces based on where thelowest violation time period curve generated byKi(rˆ) changes. For instance, from 0 to 2.5 [mole/m3],K1(rˆ)consistently yields the lowest violation time periods. Between 2.5 and 6.2 [mole/m3], K2(rˆ) consistentlydelivers the lowest violation time periods. Beyond, 6.2 [mole/m3], K3(rˆ) maintains the lowest violationperiods. We would therefore define the switching surfaces between controllers based on the regions whereeach controller minimizes violation time periods; that is, at SS1 = 2.5 and SS2 = 6.2 [mole/m3]. Theoperating point values used for controller desing are provided in Appendix B.3.5 Simulation ResultsIn order to validate the proposed controller design, we present closed-loop simulation results by using theproposed GS H∞ controllers. The simulation studies were pursued based on the control-oriented SCRmodel (3.1).363.5. Simulation Results3.5.1 Controllers for simulation testThe following four controllers were designed and their performances in reducing NOx and NH3,out werecompared.1. Feedforward controller: KFF2. GS PID controller: KPID3. Sliding mode controller: KSMC4. Proposed GS H∞ controller: KH∞Here, a feedforward controller, KFF , was designed based on the NOx sensor signal. Both GS controllers,KPID and KH∞ were designed based on the gain-scheduling parameters: NOx,in, T , and NH3,out. TheKPID consists of a feedforward controller and twenty-seven PID controllers controlling each sub-region, bydividing the entire operating region into 3 regions in each axis in Fig. 3.2. A sliding mode controller, KSMC ,was designed based on the method proposed in [68]. The switching surfaces of the KH∞ were determinedbased on the violation-time-based decision method as disscussed in Section 3.4.2.3.5.2 An SCR model for simulation testAs discussed in Chapter 2, for realistic simulations, the sensor data were measured over NRTC test mode asdepicted in Fig. 3.6.The tuning parameters for the controller design were obtained by following the proposed design proce-dure: SS1 = 0.0005, SS2 = 0.0009, W1 = 1.3s+0.5s+0.83 , and W2 =1.3s+0.07s+0.07 . For realistic simulations, 700msdelay of NOx sensor, and 1000ms delay of NH3 sensor were implemented during simulation testing.3.5.3 Control performanceThe simulation results show that the proposed KH∞ delivers better outcomes than other controllers. In thefirst plot in Fig. 3.7, which corresponds to NOx,out generated by each controller, the performance by theproposed controller yields a significant improvement over KFF and KPID. The desirable result obtained bythe proposed controller was expected since small NOx,out of an operating point value was selected for allsub-regions. Additionally, the NOx,out reduction was prioritized in tuning the weighting functions in the373.5. Simulation Results0 200 400 600 800 1000 120001000NOx,in [ppm]0 200 400 600 800 1000 1200400500600Temperature [K]0 200 400 600 800 1000 1200Time [sec]00.10.2Flow rate [m3 /s]Figure 3.6: Input signals to the SCR model for the simulation testLTI controller design. In the second plot, the results forNH3,out also show better performance byKH∞ thanthose by other controllers. The third plot shows that the NH3 coverage ratio level by the proposed controlleris relatively lower than those by other controllers. As listed on Table 3.1, the proposed KH∞ shows betterperformance than other controllers. Each value of NOx,out, NH3,out, and θ in Table 3.1 is obtained bydividing the sum of each result by total time. The NOx conversion efficiency (η) was used to compare theperformance asη =∫tNOx,in(t)dt−∫tNOx,out(t)dt∫tNOx,in(t)dt× 100. (3.17)Table 3.1: Comparison of control performanceControllerNOx,out[ppm]NH3,out[ppm]θ[-]η[%]KFF 128.8 9.9 0.06 80.6KPID 56.7 14.3 0.06 91.4KSMC 41.9 9.7 0.04 93.6KH∞ 40 9.8 0.04 94383.5. Simulation Results0 200 400 600 800 1000 12000200400NOx,out [ppm]0 200 400 600 800 1000 12000204060NH3,slip [ppm]0 200 400 600 800 1000 1200Time [sec]00.10.20.3 [-]Figure 3.7: Comparison of control performance amongKFF ,KPID,KSMC , and proposedKH∞ : The initialvalues are NOx,out = 58 ppm, NH3,out = 38 ppm, and θ = 0.23.5.4 Robustness analysis: model uncertaintyTo validate the proposed controller’s robustness, the most sensitive parameters were firstly identified byconducting the open-loop test with the SCR model. The model parameters, αi, Ei, i = red, ox, ads, des,and Ω were perturbed in the range of ±10%. As depicted in Fig. 3.8, the result shows that E1, E2, and E4are sensitive parameters affecting theNOx reduction. In other words, when the values of E1, E2, and E4 arechanged due to the system degradation or incorrect parameter identification, the control performance maybe degraded. The closed-loop simulation tests with the pertubed sensitive parameters were then performedto validate the proposed controller’s robustness.Referring to Fig. 3.9, the NOx conversion efficiency and NH3,out continued to degrade as parameterperturbation of E1 increased from 0 to 10%. On the other hand, the parameter perturbation decreased from 0to−10%, the better performance was observed since less activation energy for chemical reaction was needed.393.5. Simulation ResultsA1 A2 A3 A4 E1 E2 E3 E4Model parameters3456NOx,out [mole/m3 ] 10-3Figure 3.8: NOx,out change due to SCR model parameter perturbation (On each box, the red-horizontalline indicates the median, and the bottom and top edges of the box indicate the 25th and 75th percentiles,respectively. The blue-horizontal line out of the box represents the most extreme data points not consideredoutliers. The outliers are plotted individually using the ’+’ symbol)As listed on Table 3.2, most cases showed that the proposed controller did not degrade its performancewith low NH3,out. However, the performace with −10% parameter perturbation of E4 showed the worstdegradation. This result implies that the activation energy of NH3 desorption (E4) should be carefullyidentified in SCR modeling, or that a controller taking into account robustness against the uncertainty of E4needs to be designed.0 200 400 600 800 1000 1200020406080100 [%] -10% E1 perturbation -5% E1 perturbation 0% E1 perturbation 5% E1 perturbation 10% E1 perturbation0 200 400 600 800 1000 1200Time [sec]050NH3,slip [ppm] Figure 3.9: Performance with parameter perturbation (E1)403.6. SummaryTable 3.2: Performance with parameter perturbationsLevel[%]E1 E2 E4η NH3,out η NH3,out η NH3,out[%] [ppm] [%] [ppm] [%] [ppm]-10 97.2 8.3 92.8 8.9 76.4 31.7-5 96.1 8.8 93.7 9.5 88.4 15.6+5 91.2 15.6 94.0 9.8 97.4 7.5+10 84.8 17.7 94.0 9.9 98.8 6.93.5.5 Robustness analysis: sensor noiseTo investigate the proposed controller’s robustness against the sensor noises, we conducted the simulationtest using sensor noises assd = s(1 + rmδ), (3.18)where rm and δ represent the percentage of noises and uniformly distributed random numbers, respectively.Here, s and sd express sensor signal and sensor signal with noises. All sensor signals were replaced withsignals with noise. The results in Fig. 3.10, show that the designed controller is robust against even 15%sensor noise. For all level of sensor noise, the NOx conversion efficiency (η) was obtained larger than 90%with the desired NH3,out (< average 10ppm). This implies that the proposed controller can be adopted inthe SCR application with typical sensor noise.3.6 SummaryIn this study, the gain-scheduling controller with the measurable ammonia slip as one of the gain-schedulingparameters was proposed to minimize NOx and NH3 downstream of the catalyst over the transient drivingcycle mode. The proposed gain-scheduling controller is comprised of linear time-invariant H∞ controllersand their associated sub-regions depending on ammonia slip. For determining the sub-regions, a Violation-Time-based Decision method was proposed. The performance of the proposed gain-scheduling control sys-tem was assessed in simulations using experimentally obtained NOx disturbance, exhaust gas temperature,and exhaust gas flow rate. The results demonstrated that the proposed control design method is effective,413.6. Summary0 200 400 600 800 1000 1200050100 [%] 0% sensor noise: 94.0 %5% sensor noise: 94.1 %10% sensor noise: 93.6 %15% sensor noise: 93.1 %0 200 400 600 800 1000 1200Time [sec]01020NH3,slip [ppm]Figure 3.10: Performance with sensor noisecompared to a feed-forward, a gain-scheduling PID, and previously studied control methods using slidingmode control, and that the designed controller is robust against model uncertainty and sensor noise. Based onthe provided simulation results, it can be concluded that the capability of the proposed gain-scheduling H∞control system is sufficient for this application without the consideration of the estimation error in nonlinearobservers. The important future work will be the experimental validation of the proposed controller with realdiesel engines.42Chapter 4Linear Parameter-Varying SCR Control4.1 IntroductionThe results by the controller proposed in Chapter 3 demonstrate that the gain-scheduling H∞ controlleris effective, compared to a feed-forward, a gain-scheduling PID, and previously studied control methodsusing sliding mode control, and that the designed controller is robust against model uncertainty and sensornoise. Although the stability and the performance of the designed SCR controller were demonstrated insimulations, there was no theoretical guarantee at the controller design stage. It means that there is little doubtof stability in the environment with high uncertainties or sensor noises. Although the SCR system may notbe suddenly diverged with high uncertainties and sensor noise, the guaranteed stability is a significant issue.To systematically guarantee stability, using an alternative design method, a linear parameter-varying (LPV)gain-scheduling (GS) controller was proposed.As discussed in Chapter 1, the studies for the gain-scheduling controllers have been conducted in [36, 69].The feedback control approach using a gain-scheduling control strategy was proposed based on proportionaland integral gains, which depend on exhaust gas temperature and exhaust gas flow rate in [69]. Although theresult was demonstrated through simple simulations and transient tests, it is limited to only NOx reductionwithout any discussion of ammonia slip. A gain-scheduling SCR controller using exhaust gas temperatureand ammonia coverage ratio was also presented [36]. Simulation results were reasonable, but the methodin [36] has some drawbacks. Firstly, the ammonia slip sensor located at the downstream of the SCR catalystwas not used for feedback control. Secondly, only one quasi-LPV (qLPV) model was employed for controllerdesign, while there was another quasi-LPV model which has a potential benefit. Thirdly, the feedforwardcontroller and the feedback controller were designed separately. Lastly, there were no robustness analysesfor the designed LPV controller.In this chapter, we will present LPV approach to the SCR controller design. The approach covers thedrawbacks of the method in [36] mentioned above. To be more specific, our approach utilizes NH3 slip434.2. Control-oriented SCR modelsensor for feedback control, designs an LPV controller based on a new quasi-LPV SCR model having NOxand NH3 emissions out of the SCR catalyst as varying parameters, synthesizes feedforward and feedbackLPV controllers simultaneously, and analyzes controller robustness against model parameter variation andsensor noises.The content of this chapter is constructed as follows. Section 4.2 briefly introduces the control-orientedSCR model. In Section 4.3, qLPV models for the usage in controller design are derived. Based on thederived qLPV models, the proposed LPV control structure and controller design procedure are described inSection 4.4. Simulation results of the proposed controllers under a transient driving cycle and under modeluncertainty and sensor noises are presented in Section 4.5. Section 4.6 summarizes this chapter.4.2 Control-oriented SCR modelA control-oriented three-state model for the chemical reactions in the SCR catalyst was introduced in [37]as follows:x˙ = A(Q,T )x+ f(T, x) +Bd(Q)d+B(Q)u. (4.1)Here, the state vector x, the disturbance w, and the input u are respectively defined by5x :=CNOx,outCNH3,outθ , d := CNOx,in , u := CNH3,in . (4.2)The matrices A, Bd, B and the nonlinear function f are given byA(Q,T ) := −QV 0 00 kad(T ) +QV −kde(T )Ω0 −kad(T ) kde(T ) + kox(T ) ,Bd(Q) :=QV00 , B(Q) :=0QV0 ,5We assume that NH3,in converted from the injected urea is the control input for simplicity, even though the urea injection isthe actual manipulated variable in real SCR control systems [36, 37].444.3. Quasi-LPV (qLPV) SCR modelf(T, x) :=−kre(T )Ωx1kad(T )Ωx2−(kre(T )x1 + kad(T )x2)x3,where xi is the i-th component of the vector x. All the notations used in the model (4.1) and their meaningsare listed in Table 4.1.Table 4.1: Notations and their meaningsNotation [Unit] MeaningV [m3] Volume of the catalystΩ [mole/m3] NH3 adsorption capacityCx,in [mole/m3] Concentration of species x at inletCx,out [mole/m3] Concentration of species x at outletkad [m3/mole-s] Reaction constant for NH3 adsorptionkre [m3/mole-s] Reaction constant between NOx reductionkde [1/s] Reaction constant for NH3 desorptionkox [1/s] Reaction constant for NH3 oxidationT [K] Exhaust gas temperatureQ [m3/s] Exhaust gas flow rateθ [–] NH3 coverage ratioWe stress that the model (4.1) is a nonlinear parameter-dependent model. It is nonlinear because of thecoupling terms x1x3 and x2x3 in the function f , while it is parameter-varying due to the dependency of thematrices A, Bd and B and the function f on variables T and Q. Note that the variable T is measurable inreal time by the temperature sensor and the variable Q can be calculated with the temperature and the airmass flow sensors. Thus they can be exploited as gain-scheduling parameters for controller adaptation tovarying engine operations conditions.4.3 Quasi-LPV (qLPV) SCR modelThe nonlinear parameter-varying model (4.1) can be regarded as a quasi-LPV model when either (x1, x2)-pair or x3 in the function f is regarded as varying parameters, denoted by ρ. In both cases, the quasi-LPVmodel takes the following common form:Σ(Q,T, ρ) :x˙ = ALPV (Q,T, ρ)x+Bd(Q)d+B(Q)u,(4.3)454.3. Quasi-LPV (qLPV) SCR modelwhere the matrix ALPV is given byALPV (Q,T, ρ) := A(Q,T ) +Af (T, ρ). (4.4)In (4.4), the parameter-varying matrix Af comes from the function f by regarding some elements in x asvarying parameters.4.3.1 Regarding (x1, x2) as varying parametersIn this case, by denoting ρ := [ρ1, ρ2]T := [x1, x2]T in the function f , the matrix Af can be obtained asAf (T, ρ) :=0 0 −kre(T )Ωρ10 0 kad(T )Ωρ20 0 −(kre(T )ρ1 + kad(T )ρ2) . (4.5)Note that the varying parameters ρ in this case can be measured in real time with the NOx sensor andthe NH3 sensor at the outlet of the catalyst and thus they can be utilized as gain-scheduling parameters. Tothe best of our knowledge, the quasi-LPV SCR model with (4.5) was not used in controller design before.4.3.2 Regarding x3 as a varying parameterIn this case, by denoting ρ := x3 in the function f , the matrix Af can be derived asAf (T, ρ) :=−kre(T )Ωρ 0 00 kad(T )Ωρ 0−kre(T )ρ −kad(T )ρ 0 . (4.6)The quasi-LPV model with (4.6) was utilized in controller design in [36]. In contrast to the previouscase, the varying parameter ρ(= θ) in this case is not directly measurable and thus needs to be estimatedin real time for its usage in gain-scheduling control. The estimation methods for the ammonia coverageratio have been developed based on steady-state condition [36], extended Kalman filter [15], sliding modeobserver [16], Luenberger sliding mode observer [17], and nonlinear observer [70]. The ammonia coverageratio estimation is beyond the scope of this work, and we assume hereafter that the ammonia coverage ratioθ is accurately estimated and thus available for feedback control and gain-scheduling control purposes.464.4. Quasi-LPV SCR Controller Design4.4 Quasi-LPV SCR Controller DesignThis section presents the proposed LPV control structure and the LPV design procedure.4.4.1 Proposed control structureThe control structure proposed in this chapter is illustrated in Fig. 4.1. In the figure, the quasi-LPV modelof the SCR system is given by (4.3), and its dependency on varying parameters is indicated by the dashedarrow.Figure 4.1: Block Diagram of the Proposed LPV Control SystemA linear parameter-varying (LPV) controller, denoted by K(Q,T, ρ), determines the control input ubased on the feedforward signal d, the feedback signal (x1, x2), and the ammonia coverage ratio feedbackerror signale := r − θ, (4.7)where r is the reference signal for θ to be specified and offers an extra degree of freedom in controllerdesign. Feedforward control is employed since it is useful to achieve fast response to reject varying butmeasurable disturbance d, while feedback control is adopted to accomplish robust performance against themodel uncertainty and the sensor noises. The LPV controller is gain-scheduled with gain-scheduling (GS inFig. 4.1) parameters, which are again indicated with the dashed arrow in Fig. 4.1.474.4. Quasi-LPV SCR Controller Design4.4.2 LPV controller designFor designing the LPV controller in Fig. 4.1 using an existing LPV controller design technique [71], we firsttransform the block diagram in Fig. 4.1 into a linear fractional transformation (LFT) form in Fig. 4.2. Then,we attach weighting functions for signals to be minimized, and apply the existing LPV controller designmethod based on the linear matrix inequality (LMI).Figure 4.2: LFT RepresentationThe ‘Generalized plant’ block in Fig. 4.2 can be derived from the block diagram in Fig. 4.1 asx˙ = ALPV (Q,T, ρ)x+ [Bd(Q), 0]w +B(Q)u,z = C1x+D11w, dz = 01×3C1x+ [1 0]D11w,(4.8)where the vectors z and w and the matrices C1 and D11 are defined byz :=x1x2e , w := dr , (4.9)C1 :=1 0 00 1 00 0 −1 , D11 :=0 00 00 1 . (4.10)To balance the reductions of x1 = CNOx,out , x2 = CNH3,out and the tracking error e of ammonia484.5. Simulation Resultscoverage ratio, and to focus on the reductions over specific frequency ranges of the exogenous signals d andr, we introduce the weighted signal in the Laplace domain as shown in Fig. 4.2:zW (s) := W (s) 00 We(s) z(s), (4.11)where W (s) and We(s) are respectively 2 × 2 and scalar weighting transfer functions, to be tuned in thecontroller design. The derivation of the generalized plant by combining the ‘Generalized plant’ block andthe weighting functions in Fig. 4.2 is straightforward, and thus omitted here.Assume that we are given the generalized plant with the specified weighting functions, as well as theranges of values and rates of changes for the gain-scheduling parameters:Q ≤ Q ≤ Q, Qv≤ Q˙ ≤ Qv, (4.12)T ≤ T ≤ T , T v ≤ T˙ ≤ T v, (4.13)ρ ≤ ρ ≤ ρ, ρv≤ ρ˙ ≤ ρv, (4.14)where the notations for the upper bounds and the lower bounds are introduced. Under these assumptions,the LPV controller K(Q,T, ρ) can be designed such that the closed-loop system becomes asymptoticallystable, and the L2-gain from w to zW is minimized over all trajectories meeting (4.12)-(4.14) [71]. The L2-gain minimization leads to reduced NOx and NH3 emissions, with the appropriate tuning of the weightingfunctions in (4.11) and the reference r in (4.7).4.5 Simulation ResultsIn this section, we validate the designed LPV SCR controllers in simulations.4.5.1 Simulation settings: model parametersIn the simulation study, we took model parameter values from a real diesel engine with an SCR catalyst atDoosan Infracore Co. Ltd., with V = 19.87 · 10−3 [m3] and Ω = 158 [mole/m3]. The chemical reactionconstants were given byki(T ) = αie− EiRT , i = ad, re, de, ox, (4.15)494.5. Simulation Resultswhere the subscripts ad, re, de, and ox correspond to NH3 adsorption, NOx reduction, NH3 desorption,and NH3 oxidation, respectively, and the pre-exponential factor αi and the activation energy Ei [KJ/mol]were set as in Table 4.2.Table 4.2: Parameter values for chemical reaction constantsi ad re de oxαi 2.13 · 107 3.32 · 109 3.28 · 1011 4.33 · 106Ei 42 85 113 1124.5.2 Simulation settings: controller design parametersFor the model parameters above, weighting functions in (4.11) for LPV controller design were selected bytrial and error asW (s) = 0.1s+10s+1 00 0.1s+10.16s+2.031 , We(s) = 0.1s+ 9.962s+ 0.4812. (4.16)Here, these low-pass-filter weighting functions were tuned to suppress low-frequency components of thesignals CNOx,out , CNH3,out and e, and to take the trade-off between NOx emission and NH3-slip.In the design, the values Q and T were taken to be constant, i.e., the upper and lower bounds were set tothe same values and the rates of changes were zero:Q = Q = 0.231, Qv= Qv = 0, (4.17)T = T = 538.15, T v = T v = 0. (4.18)We designed two LPV controllers, denoted byKLPV1 andKLPV2 . The former and the latter respectivelycorrespond to the case when ρ = [x1, x2]T and to the case when ρ = x3 in (4.3). (See Section 4.3).) In eachdesign, the bounds for ρ in (4.14) were assumed to be as follows.• Design of KLPV1ρ = 10−4 × 11 , ρ = 10−4 × 22 , (4.19)ρv= −10−5 × 11 , ρv = 10−5 × 11 . (4.20)504.5. Simulation Results• Design of KLPV2ρ = 0, ρ = 1, ρv= −0.01, ρv = 0.01. (4.21)4.5.3 Simulation settings: exogenous signalsSimulation studies were conducted with the structure in Fig. 4.1, by replacing ‘Quasi-LPV model’ blockwith the original nonlinear model (4.1). Here, it was necessary that exogenous signals d, Q, T , and r bespecified.The signals d(= CNOx,in), Q and T were obtained by an open-loop experiment, with the Non-RoadTransient Cycle (NRTC) applied to an actual diesel engine, as shown in Fig. 4.3. Since NRTC contains mostof the transient driving conditions that real diesel engines experience, the validation with NRTC implies thepractical feasibility of the controller. The reference value r = 0.015 for the ammonia coverage ratio θ wasobtained by trial and error to achieve 10 [ppm] NH3,out in average. A rule of thumb for tuning r-value isthat the smaller the r-value is, the smaller NH3,out is but the larger NOx,out is.0 200 400 600 800 1000 120001000 d [ppm]0 200 400 600 800 1000 1200Time [sec]400500600 T [K]0 200 400 600 800 1000 120000.10.2 Q [m3 /s]Figure 4.3: Signals in an Experimental NRTC Test4.5.4 Performance analysisWith the designed two LPV controllers (KLPV1 and KLPV2), the NOx emission NOx,out and the ammoniaslip NH3,out are plotted in Fig. 4.4. In addition to these two controllers, a baseline proportional-integral-514.5. Simulation Resultsderivative (PID) gain-scheduled controller KPID was designed and its performance was plotted in the samefigure.0 200 400 600 800 1000 12000200400600NOx,out[ppm]0 200 400 600 800 1000 1200Time [sec]020406080NH3,out[ppm]KPIDKLPV1KLPV2Figure 4.4: Controller PerformanceThe quantitative evaluations of the performance are summarized in Table 4.3, where NOx,out andNH3,out were measured with the average value over all time. The NOx conversion efficiency denotedby η [%] is defined byη :=∫tNOx,in(t)dt−∫tNOx,out(t)dt∫tNOx,in(t)dt× 100. (4.22)Table 4.3: Comparison of control performanceController NOx,out [ppm] NH3,out [ppm] η [%]KPID 56.7 14.3 91.4KLPV1 44 9.7 93.3KLPV2 45 10.0 93.2In both Fig. 4.4 and Table 4.3, it can be observed that the designed LPV controllers outperform thebaseline gain-scheduling PID controller by increasing the NOx conversion efficiency and by reducing theammonia slip to an acceptable level 10 ppm.524.5. Simulation Results0 500 1000Time [sec]80859095100 [%]0% perturbation10% perturbation-10% perturbationFigure 4.5: Performance by KLPV1 with parameter perturbation4.5.5 Robustness analyses: model parameter variation and sensor noiseRobustness of the designed controllers is essential because the modeling error and the sensor noises are in-evitable in practice. To investigate the robustness of the proposed controllers KLPV1 and KLPV2 , robustnessanalyses were conducted in two scenarios. The first scenario is to change the reaction rate kre of the NOxreaction with ±10% perturbation. The second scenario is to add 10% sensor noises on all sensor signals.For model parameter variation, Figs. 4.5 shows the NOx conversion efficiency η when kre perturbs by±10%. It can be seen in the figure that the η-value improved most of the time slightly when kre increased by10%. This is because the chemical reactions for theNOx reduction occurred 10% more than the unperturbedcase. On the contrary, in the case of −10% perturbation of kre, the efficiency η got worse in general.However, it is still more than 92% efficiency. Table 4.4 gives the summary of the robustness analysis for kre-value perturbation. As seen in the table, the average value of NH3,out was not affected by the perturbationof kre. These observations imply the robustness of the designed KLPV2 .For the case of 10% sensor noises with uniformly-distributed random variables, η-value andNH3,out aredepicted in Figs. 4.6. In the η-plot, we can see that theNOx conversion efficiency continues to degrade as thesensor noise increases up to 10%, while NH3,out continues to decrease. It implies that the controller KLPV1534.6. SummaryTable 4.4: Robustness against model parameter variationController Perturbation NOx,out NH3,out η[%] [ppm] [ppm] [%]KLPV1 0 44 9.7 93.310 41.7 9.6 93.7−10 46.9 9.8 92.9KLPV2 0 45 10.0 93.210 42.5 10.0 93.5−10 48.3 10.1 92.7is more robust against sensor noises than the controller KLPV2 . Table 4.5 lists the quantitative evaluationsand shows η-value is greater than 91% with the average value of NH3,out less than 10 ppm.Table 4.5: Robustness against sensor noiseController Sensor noise NOx,out NH3,out η[%] [ppm] [ppm] [%]KLPV1 0 44 9.7 93.35 45.1 9.5 93.110 46.5 9.4 92.9KLPV2 0 45 10.0 93.25 51.6 9.3 92.210 57.7 8.7 91.3In summary, it was verified in simulations that the designed LPV controllers, KLPV1 , KLPV2 , are robustagainst both ±10% reaction rate difference and 10% sensor noises.4.6 SummaryThis chapter proposed linear parameter-varying (LPV) controller design for urea-based selective catalyticreduction (SCR) systems in heavy-duty diesel engines, in order to minimize the emissions of nitrogen oxides(NOx) and ammonia (NH3) downstream of the catalyst. The novelties in contrast to previous work on LPVSCR controller design are that our approach utilizes NH3 slip sensor for feedback control, designs an LPVcontroller based on a new quasi-LPV SCR model having NOx and NH3 emissions out of the SCR catalystas varying parameters, synthesizes feedforward and feedback LPV controllers simultaneously, and analyzescontroller robustness against model parameter variation and sensor noises. In simulations, it was demon-strated that the designed LPV controllers outperform a baseline proportional-integral-derivative (PID) con-544.6. Summary0 500 100080859095 [%]0% sensor noise5% sensor noise10% sensor noise0 500 1000Time [sec]0102030NH3,out [ppm]Figure 4.6: Performance by KLPV1 with sensor noisetroller and that the controllers work robustly against model parameter uncertainty and measurement noises.Therefore, it can be concluded that the proposed LPV SCR controllers are a viable alternative to existingSCR controllers. The important future work will be the experimental validation of the proposed controllerwith real diesel engines.55Chapter 5Discrete-time Preview-Feedback H∞Control for Selective Catalytic ReductionSystemsIn this chapter, a preview control strategy using previewed NOx disturbance will be presented. Section 5.1will briefly introduce a preview control. In Section 5.2, the proposed preview-feedback control apporach isintroduced. The design of discrete-time preview-feedback H∞ Controller is then described in Section 5.3.Section 5.4 demonstrates the control performance, robustness analysis, comprsion with MPC, and computa-tional requirement. Secion 5.5 summarizes conclusion and funture works.5.1 IntroductionAs disscussed in Chapter 1, a model predictive controller utilizing a prediction of the amount of NOx emis-sions reaching the catalyst in the future can be expected to improve NOx conversion efficiency with lowammonia slip. These MPC techniques were able to successfully bring down the levels of NOx and NH3emitted. However, the main drawback of MPC is high computational burden of on-board micro-controllerssince it solves optimization problems in real-time. Due to the limited computational resources in engineapplications, control methods which are simpler to implement than MPC are preferable. To cover the com-putational drawback of MPC, in this section, we will present another control method that has the capabilityof handling the predicted NOx information, called preview control. The performance of the preview con-trollers was investigated in many applications [53, 56, 57]. The primary difference of preview control fromMPC is that the preview controller is designed offline and that its implementation demands only simple alge-braic calculations (products of matrices and vectors), in contrast to real-time optimization required in MPC.565.2. Proposed Preview-Feedback Control ApproachFigure 5.1: Schematic of an SCR control system (EGR and VTG stand for exhaust gas recirculation andvariable turbine geometry, respectively)In particular, we employ theH∞ preview controller combined with the feedback controller, referred to as thepreview-feedback H∞ controller hereafter, which is the solution of an offline optimization problem to mini-mize the NOx amount and the ammonia slip leaving the SCR system. The designed preview-feedback H∞controller is validated in simulations with an experimentally-acquired NOx signal under a transient drivingcycle. It is demonstrated that the designed preview-feedback H∞ controller provides comparable perfor-mance to MPC, but with much less computational cost in its implementation. In addition, the robustness ofthe designed preview-feedback H∞ controller against NOx prediction error is confirmed in simulations.5.2 Proposed Preview-Feedback Control ApproachTo overcome the control challenges brought up in Chapter 1, the previewed NOx information as depicted inFig. 5.1 can be employed with the measurable NOx,out and NH3,out. Note that this diagram is the same asFig. 1.3, except the following modifications:1. There is previewed NOx information being input to an SCR controller.2. The diesel engine and the flow of NOx,in signal from the exhaust manifold is shown.3. For simplicity, DOC and DPF are omitted.575.3. Design of Discrete-time Preview-Feedback H∞ ControllerThe different colored circles on the disturbance signal graph represent different levels of NOx,in concen-tration at different timing (time step) in the exhaust manifold caused by changing operation of the dieselengine.Due to the slow dynamics of the SCR system, it is too late to inject NH3,in by looking at the “present”green circle (which is small amount of NOx), for efficient chemical reaction between NOx and NH3. Tomitigate this control challenge, we can inject NH3,in by looking at the “far future”, for example purple oryellow circle (which is large amount of NOx). This means that larger NH3,in will be injected because thecontroller knows that the NOx coming from the engine gradually increases up to the far future. This largerNH3,in will then increase the ammonia storage level in the catalyst, causing better performance than thecontroller without “far future” preview.Due to the time delay of the NOx sensor, it is also too late to inject NH3,in by looking at the “present”green circle. This green circle is the signal which is delayed about 700 [ms] due to the sensor delay. Thecomputed NH3,in based on green circle will be injected when the purple or yellow circle reaches the SCRcatalyst. This means that the chemical reactions will then happen with undesirable combination of chemicalcompounds (i.e. large NOx + small NH3). To alleviate this control challenge, again, the previewed NOxinformation including “far future” purple or yellow circle (which is large amount of NOx) can be used incontroller design where h denotes the preview length.In this section, we propose a preview-feedback H∞ controller based on previewed NOx,in information,capable of reducing NOx,out with low NH3,out. The proposed preview-feedback H∞ controller is designedbased on an H∞ control law to mitigate the control challenges consisting of the slow dynamics of the SCRsystem and the time delay of the NOx sensor. It is assumed that the NOx,in prediction signal is available.The method of predicting NOx disturbance has been studied in previous research based on virtual sensors,on-board monitoring equipment, and measurable signals relating to engine operating conditions [72–74].5.3 Design of Discrete-time Preview-Feedback H∞ ControllerIn order to present the design of the preview-feedback H∞ controller, its structure will first be introduced.The discrete-time controller design procedure based on a control-oriented SCR model will then be described.585.3. Design of Discrete-time Preview-Feedback H∞ ControllerSCR𝐾𝑃𝑉E𝑑(= 𝐶𝑁𝑂𝑥,𝑖𝑛)𝑥𝑑(previewed signal)𝑇(exhaust gas temperature)𝑄(exhaust gas flow rate)𝐾𝐹𝐵𝐾𝑃𝑉+𝐹𝐵𝑦 = 𝐶𝑁𝑂𝑥,𝑜𝑢𝑡𝐶𝑁𝐻3,𝑜𝑢𝑡𝑢(= 𝐶𝑁𝐻3,𝑖𝑛)Figure 5.2: SCR preview-feedback H∞ controller structure5.3.1 Structure of preview-feedback H∞ controllerThe controller, denoted by KPV+FB in Fig. 5.2, is a preview-feedback H∞ controller This controller com-putes the optimal amount of CNH3,in , denoted by u, to reduce CNOx,out and CNH3,out , denoted by y. Itconsists of two controllers, KPV and KFB . The controller KPV is a preview controller because it uti-lizes previewed CNH3,in [mole/m3] signals, denoted by a vector xd of length h, where h is the previewlength. Based on the previewed CNOx,in , KPV computes the optimal amount of CNH3,in to reduce CNOx,out[mole/m3] and CNH3,out [mole/m3] by injecting sufficient and optimal amounts of CNH3,in [mole/m3] inadvance for dealing with rapidly changing incoming CNOx,in . In addition to the preview controller, the con-troller KFB is a feedback controller using sensor signals CNOx,out and CNH3,out . This closed-loop feedbackstructure provides the benefit of robustness by adjusting the controller output in response to changing actualemissions of CNOx,out and CNH3,out . The block E, [I 0 . . . 0] is the extraction of the disturbance signalCNOx,in , denoted by d, from the previewed signals xd. The exhaust gas temperature T and the exhaust gasflow rate Q are the input signals of the SCR model.5.3.2 Control-oriented SCR modelTo design the preview-feedbackH∞ controller, we consider the dynamics of SCR systems studied in [37] forthe SCR-block in Fig. 5.2. In this SCR model, it is assumed that all injected urea is converted into CNH3,infor simplicity. This control-oriented nonlinear SCR model is derived based on chemical reactions: NOx595.3. Design of Discrete-time Preview-Feedback H∞ Controllerreduction, NH3 oxidation, NH3 adsorption, and NH3 desorption as discussed in Chapter 2.x˙ = Ax+ f(x) +B du , y = Cx, (5.1)whereA,B, andC represent the state matrix, the input matrix, and the output matrix which extractsCNOx,outand CNH3,out , respectively. Here, the state vector x, the disturbance d, and the input u are defined respec-tively asx :=CNOx,outCNH3,outθ , d := CNOx,in , u := CNH3,in , (5.2)where θ denotes the fractional surface coverage of ammonia related to NH3 adsorption and desorption,called ammonia coverage ratio. The matrix A and the nonlinear function f(x) contain the reaction rateconstants given byki := αie− EiRT , i = red, ox, ads, des. (5.3)Here, αi [m3/mole], Ei [kJ/mole], R, and T [K] represent respectively pre-exponential factors for i-th re-action, activation energies for i-th reaction, universal gas constant, and exhaust gas temperature in the SCRcatalyst (shown as an arrow in Fig. 5.2). The matrix B contains the normalized exhaust gas flow rate givenbyQ¯ =QV. (5.4)Here, Q [m3/sec] is the exhaust gas flow rate (shown as an arrow in Fig. 5.2) and V [m3] is the volumeof exhaust gas in the substrate channel. This control-oriented nonlinear SCR model (5.3.2) is a parameter-varying model because of the dependence of ki in (5.3) on the exhaust gas temperature T , and dependenceof normalized exhaust gas flow rate Q¯ (5.4) on exhaust gas mass flow rate Q. To evaluate a linear time-invariant controller to be designed for this parameter-varying system, we will perform the simulation testusing experimentally obtained exhaust gas temperature, exhaust gas flow rate, and NOx disturbance overthe transient driving cycle. The details of the control-oriented SCR model can be found in the previous605.3. Design of Discrete-time Preview-Feedback H∞ Controller𝑤[k] 𝑑[t]𝑢[k]𝑊H𝑥𝑑[k]Discrete-time generalized plant (𝑃𝐷) Continuous-time generalized plant (𝑃𝑐) ZOH𝑇𝑠ZOH𝐾𝑃𝑉+𝐹𝐵𝑢[t]𝑑[k]SCRE𝑇𝑠𝑇[t]𝑄[t]𝑧𝑊[t]𝑦[t] 𝑧𝑊[k]𝑦[k]Figure 5.3: Block diagram for SCR preview-feedback controller designwork [37].5.3.3 Derivation of the discrete-time generalized plantAs a preparation for a discrete-time preview-feedback H∞ Controller design, a discrete-time generalizedplant is derived in this section. To make use of the previewed NOx disturbance in controller design, theblock diagram for an SCR control system is introduced as depicted in Fig. 5.3. This block diagram is thesame as Fig. 5.2, except for the following modifications:1. The block H and the signal w are added to generate xd signal.2. The zero-order hold (ZOH) blocks and samplers with sampling time Ts are employed for bridgingdiscrete-time and continuous-time signals.3. The red dashed line indicates a continuous-time generalized plant, denoted by Pc.4. The blue dash-dotted line represents a discrete-time generalized plant, denoted by PD.5. The weighting function block, denoted by W , is added.Here,w[k] represents unpreviewedNOx disturbance (at time k+h+1) (see Fig.2) and xd[k] is the previewedNOx disturbance vector (at times k, . . . , k + h), d[k] is the NOx disturbance (at time k), u[k] is the controlinput (CNH3,in), y[k] represents the measured CNOx,out and CNH3,out , and zw[k] represents the weightedoutput to be kept small. The continuous-time state-space equations are obtained based on the continuous-615.3. Design of Discrete-time Preview-Feedback H∞ Controllertime linearized model of the nonlinear SCR model 5.1 with continuous-time W as˙¯x = A¯x¯+ B¯ du , zwy = C¯x¯, (5.5)where W (s) = Cw(SI −Aw)−1Bw +Dw. Here, x¯, A¯, B¯, and C¯ are defined asx¯ := xxw , A¯ := Aop 0BwCop Aw , B¯ := Bop0 , (5.6)C¯ := DwCop CwCop 0 . (5.7)Here, Here, Aop, Bop, and Cop represent the linearized A, B, C matrixes based on operating point valueswhich are CNOx,op, CNH3,op, and θop. The discrete-time state-space equations are obtained based on thecontinuous-time state space equations 5.5 by using the zero-order hold technique as˙¯x[k + 1] = Adx¯[x] +Bd d[k]u[k] , (5.8) zw[k]y[k] = Cdx[k], (5.9)where Ad := eA¯Ts , Bd := (∫ Ts0 eτdτ)B¯, Ts represents the sampling time, and Cd = C¯.Referring to Fig. 5.3, the previewed NOx disturbance is defined asxd[k] := [d[k] d[k + 1] · · · d[k + h]]T , (5.10)where h represents the preview length of NOx disturbance. The system H in Fig. 5.3 can be derived basedon xd[k] in 5.10 asH : XH [k + 1]xd[k] = AH BHI 0 xH [k]w[k] , (5.11)625.3. Design of Discrete-time Preview-Feedback H∞ Controller𝐾𝑃𝑉+𝐹𝐵𝑃𝐷𝑢[k]𝑤[k] 𝑥𝑑[k]𝑦[𝑘]𝑍𝑦[𝑘]Figure 5.4: SCR control system in LFT formwhere xH [k] denotes the state of the system H and AH , BH , and w[k] are defined asAH :=0 I · · · 00 0. . ....0. . . . . . I0 · · · 0 0, BH :=0...0I, (5.12)w[k] := d[k + h+ 1]. (5.13)In order to design the proposed preview-feedback H∞ controller based on the H∞ control technique, theSCR control system in Fig. 5.3 is represented in the linear fractional transformation (LFT) form, as depictedin Fig. 5.4. Based on this LFT representation, discrete-time generalized plant PD are derived based on thetechnique in [55] asΨ[k + 1] := Ad Bd1E0 AHΨ[k] + 0 Bd2EBH 0 w[k]u[k] , (5.14)zw[k] = [Cd1 0]Ψ[k], (5.15) xd[k]y[k] = 0 ICd2 0Ψ[k], (5.16)where Ψ[k] = [x¯[k] xH [k]]T . Here, the Bd1 and Bd2 represent the first and the second column of Bdmatrix, Cd1 abd Cd2 express the first and the second row of Cd matrix.635.4. Simulation Results5.3.4 Design of an H∞ controllerThe proposed preview-feedback H∞ controller is designed based on the SCR control system in LFT form inFig. 5.4. Thus, the proposed preview-feedback H∞ controller design problem is formulated asminKPV+FB‖T (KPV+FB)‖∞ , (5.17)where T (KPV+FB) is the transfer function from w[k] to zw[k]. The proposed controller is designed by min-imizing the H∞ norm of the transfer function from the unpreviewed NOx disturbance w[k] to the weightedoutput zw[k]. The control design parameter W in Fig. 5.3 can be selected by trial and error to take thetrade-off between two control objectives, i.e., CNOx,out and CNH3,out reduction.5.4 Simulation ResultsTo evaluate the proposed controller, we conducted the simulation tests. We basically followed the simulationsetup as discussed in Chapter 2. This section is organized as follows. Section 5.4.2 presents the controlperformance by the proposed controller. Comparison with MPC is then discussed in Section 5.4.3. Robust-ness analysis based on uncertainties is also covered in Section 5.4.4. Section 5.4.5 shows the computationalrequirement by the proposed controller.5.4.1 Simulation setupFor the realistic simulation environment, the input signals for the SCR model such as exhaust gas temperatureT , exhaust gas flow rate Q, and NOx disturbance d were experimentally measured under the non-roadtransient cycle (NRTC) mode, as depicted in Fig. 5.5. Although the time delay of sensor is not visible, eachsensor has approximately 700 ms time delay. The controller design parameter, weighting function W (s),was selected by trial and error asW (s) = 0.1s+9.98s+0.83 00 0.1s+10.09s+1.68 . (5.18)Here, these weighting functions were tuned to suppress low-frequency components of output signals to takethe trade-off between NOx,out and NH3,out.645.4. Simulation ResultsFigure 5.5: Experimental data measured under NRTC mode5.4.2 Control performanceTo demonstrate the effect of the preview length of the preview-feedback H∞ controller, the results of theproposed H∞ controllers with different preview lengths were compared. It can be seen in Fig. 5.6 that thepreview-feedbackH∞ controllers provide better performance with maintainedNOx level and reducedNH3level for larger preview lengths.Table 5.1: Comparison of control performance based on preview lengthPreview [ms] CNOx,out [ppm] CNH3,out [ppm] η [%]0 70.5 10.8 89.3400 66.4 10.5 90.0700 46.1 10.1 93.0The average amount of emissions for three preview lengths are summarized in Table 5.1, where wecan see the reduced emissions with 700 [ms] preview length. This implies that longer previewed NOxdisturbance leads to better performance under transient engine operating conditions. This is because thepreview controller utilizes the previewed NOx information to compute the amount of NH3 before the NOxdisturbance arrives at the SCR catalyst. Thus, the SCR control system can prepare optimal amount of NH3despite the slow system dynamics.655.4. Simulation ResultsFigure 5.6: The performance of the preview-feedback H∞ controllers with various preview lengthsFigure 5.7: Control performance of MPC and preview-feedback H∞ controllers5.4.3 Comparison with MPCAs a baseline controller, a model predictive controller (MPC) was designed based on the method in theprevious study [48]. In contrast to the MPC that solves an optimization problem in real-time, the proposedpreview-feedbackH∞ controller solves an optimization problem off-line. As depicted in Fig. 5.7, the resultsshow that the proposed controller with 700 [ms] preview length achieves comparable results to MPC with thesame prediction horizon. The relative reduction rates [%] in Table 5.2 then show that the proposed controllerdelivers better performance than the designed MPC does.665.4. Simulation ResultsTable 5.2: Quantitative comparison between MPC and preview-feedback H∞ controllersPerformance MPC Proposed controllerCNOx,out [ppm] 49.4 46.1(7% improvement)CNH3,out [ppm] 10.4 10.1(3% improvement)Figure 5.8: The structure of the simulation test with uncertain previewed signal x∆[k]5.4.4 Robsutness analysis based on uncertaintiesThe motivation of the robustness analysis is to investigate how much the CNOx,in prediction error degradesthe performance of the proposed controller. To investigate the robustness of the proposed controller, simula-tion tests were performed using previewed NOx disturbance with uncertainties as depicted in Fig.5.8. Thisdiagram is the same as Fig. 5.2, except for the red dashed block and x∆[k]. The red dashed block representsuncertainties and x∆[k] expresses previewed NOx disturbance with uncertainties. The uncertainty of thepreviewed NOx disturbance is implemented asx∆[k] = xd[k](1 + rmδ[k]), (5.19)where rm represents the percentag of uncertainty and δ expresses uniformly distributed random numbers,such that -1<δ[k]<0. This uncertainty in the previewed NOx disturbance can negatively affect the controllerwhile computing CNH3,in. In practice, the previewedNOx disturbance with uncertainties may happen whenthere is prediction error occurred due to inaccurate prediction model or the drifted NOx sensor signals.The preview-feedback H∞ controller will then exploit inaccurate NOx information, i.e., not the actual675.4. Simulation ResultsFigure 5.9: NOx disturbance signal with uncertaintiesone reaching the SCR catalyst. This difference in how the disturbance is considered between the preview-feedback H∞ controller and the SCR catalyst may cause issues for the preview-feedback controller. Priorto performing this simulation, the previewed NOx disturbance with uncertainties was prepared as shown inFig. 5.9. Each plot shows the NOx disturbance signal with different uncertainties. This means that the NOxdisturbance signal with 20% uncertainty is less predicted than other theNOx disturbance signals as depictedin Fig. 5.9.On the basis of the structure mentioned in Fig. 5.8, as well as the previewed NOx disturbance withuncertainties in Fig. 5.9, the simulation test for robustness was conducted. Referring to Fig. 5.10, on thetop plot, the CNOx,out reduction by the preview-feedback H∞ controller with 10% of uncertainties did notdegrade a lot, compared to that of the preview controller without uncertainties. In the second plot, theperformance continues to degrade as the uncertainties increase. However, the results do not show significantdifference up to 30% of uncertainties. The third plot shows much large difference of the result by thepreview-feedforward controller with 40% of uncertainties, compared to the controller without uncertainties.Since -1< δ[k] <0 causes less x∆[k] than actual one, these results were expected. Because of under-predictionof the NOx signal, the preview-feedback H∞ controller anticipates less CNOx,in amount coming from theengine than actual one and computes less CNH3,in amount than desired one. Thus, the control performancefor CNOx,out continues to decline as the uncertainties increase. On the other hand, CNH3,out decreases dueto less injected CNH3,in. The details of the robustness analysis are given in Table 5.3. The results imply thatthe prediction error should be within 30% to guarantee the performance of the proposed preview-feedback685.4. Simulation ResultsFigure 5.10: The robustness of the preview-feedback H∞ controllersH∞ controller. Otherwise, we need to design the robust preview-feedback H∞ controller which takes intoaccount the uncertainty.Table 5.3: Robustness analysisUncertainties [%] CNOx,out [ppm] CNH3,out [ppm] η [%]0 46.1 10.1 93.010 52.4 10.0 92.120 62.1 9.9 90.630 65.0 9.8 90.240 72.5 9.5 89.05.4.5 Computational requirementTo evaluate the computational requirement for the proposed controller implementation, the simulation wasperformed on an ordinary laptop computer with a 1.70 GHz CPU (Samsung/NT270E5J) and 8GB of RAM,with the MATLAB/SIMULINK Profiler activated. We found that 0.024 [ms] is needed for every functioncall of the proposed controller. Since a sampling interval of the proposed SCR control system is 100 [ms],0.024 [ms] is a small percentage of sampling update interval. In contrast to the proposed controller, an MPCcontroller needs 1.581 [ms] per function call. As a result, the proposed preview-feedback H∞ controllerdemonstrates much smaller computation time, along with better performance as discussed in Section 5.4.3.This reduced computational requirement in the preview-feedback H∞ controller will lead to outstanding695.5. Summaryadvantages over MPC when it comes to on-board microcontrollers in diesel engines.5.5 SummaryIn this chapter, the discrete-time preview-feedback H∞ controller for selective catalytic reduction systemsin diesel engines was developed to minimize NOx emissions with affordably low NH3 downstream of thecatalyst over the transient driving cycle mode. Under the assumption that the NOx disturbance is previewedby using various information such as the terrain, acceleration pedal position, and engine operating conditions,the SCR controller was designed with preview and feedback H∞ control schemes.The findings of this study are as follows. First, the advantage of the preview-feedback H∞ control strat-egy was shown by the simulation test using experimentally obtained input data such as NOx disturbance,exhaust gas temperature, and exhaust gas mass flow rate over the transient conditions. The simulation re-sult shows around 34% (NOx,out) and 6% (NH3,out) improvement delivered by the preview-feedback H∞controller with longer preview length compared to a non-preview SCR controller. Second, compared to theperformance yielded by an MPC controller, the proposed SCR controller delivered 7% and 3% improvementfor NOx and NH3 slip, respectively. Third, the simulation tests performed with previewed NOx distur-bance with uncertainties implied feasibility of the proposed method under an uncertain NOx environment.However, the 30% uncertainties started to negatively affect the performance. Finally, the proposed SCRcontroller yielded better performance with less computation time compared to an MPC controller.Potential areas of further research stemming from this work will be the validation of the proposed con-troller using experiments with real diesel engines and robust preview-feedback controller design for largeNOx prediction errors.70Chapter 6Conclusions6.1 ConclusionsThis thesis provided three contributions to selective catalytic reduction (SCR) Systems. The first one isan approach to designing a gain-scheduling (GS) controller with measurable GS parameters. The secondone is an alternative approach to designing a GS linear parameter-varying (LPV) controller with a guar-antee of stability and performance of the closed-loop system. The last one is to develop a discrete-timepreview-feedback SCR controller based on the state augmentation technique using previewed disturbanceinformation. Through these three contributions, the research objectives (O1), (O2), and (O3) discussed inSection 1.6 were achieved.Specifically, the SCR controller gain-scheduled by ammonia slip measurement was proposed to achievethe research objective (O1) by filling the research gap for the conservatism caused by large operating range.The proposed design method was a switching GS controller, in which we divided the operating range intosub-regions, designed a local GS controller for each sub-region, and switched those controllers by usingammonia slip measurement. The local GS controller is comprised of multiple linear time-invariant (LTI)H∞ controllers and their associated sub-regions depending on exhaust gas temperature and nitrogen ox-ides (NOx) disturbance. The multiple LTI H∞ controllers providing internal stability and satisfactory per-formance of the closed-loop system for each sub-region were developed. By using measurable GS parame-ters, the challenge for unmeasurable catalyst conditions was alleviated.A Violation-Time-based Decision (VTD) method was also proposed for determining the sub-regions andthus, the control performance of the proposed controller was improved. The performance of the proposedGS control system was assessed in simulations using experimentally obtainedNOx disturbance, exhaust gastemperature, and exhaust gas flow rate. The results demonstrated that the proposed control design methodis effective, compared to a feed-forward, a gain-scheduling proportional integral derivative (PID), and previ-ously studied control methods using sliding mode control, and that the designed controller is robust against716.1. Conclusionsmodel uncertainty and sensor noise. Based on the provided simulation results, it can be concluded that thecapability of the GS H∞ control system is sufficient for SCR applications.The GS LPV controller with the measurable NOx disturbance and NH3 slip as the GS parameters forthe SCR system was proposed to accomplish the research objective (O2) by overcoming the drawbacks ofthe existing LPV controller. The proposed controller was systematically designed based on linear parameter-varying techniques. To design the controller, the quasi LPV models were derived by selecting state variablesas gain-scheduling parameters. The proposed controllers were then designed based on quasi LPV modelswith internal stability and a guaranteed L2 gain bound of the closed-loop system. The novelties in contrastto previous work on LPV SCR controller design are that our approach utilizes NH3 slip sensor for feedbackcontrol, designs an LPV controller based on a new quasi-LPV SCR model having NOx and NH3 emis-sions out of the SCR catalyst as varying parameters, synthesizes feedforward and feedback LPV controllerssimultaneously, and analyzes controller robustness against model parameter variation and sensor noises.The findings of this study are as follows. Firstly, the proposed LPV SCR controllers showed superiorperformance to a GS PID controller over the simulation test using experimentally obtained input data suchas NOx disturbance, exhaust gas temperature, and exhaust gas flow rate over the transient conditions. Thesimulation result showed around 23% (NOx,out) and 33% (NH3,out) improvement delivered by LPV SCRcontrollers compared to the GS PID controller. Secondly, compared to the LPV SCR controller with θ asa gain-scheduling parameter, the LPV SCR controller with NOx,out and NH3,out as gain-scheduling con-trollers yielded comparable performance even with slightly better NOx conversion efficiency. This impliedfeasibility of the LPV SCR controller with measurable gain-scheduling parameters. Finally, the simulationtests under 10% parameter perturbation and sensor noise showed that the proposed controllers can yieldcomparable performance compared to the results without uncertainties. Based on the provided simulationresults, it can be concluded that the capability of the proposed LPV SCR controllers is sufficient for SCRapplication as alternatives.The discrete-time preview-feedback SCR controller was proposed to reach the research objective (O3) byaddressing the research gap for high computational requirement arose by on-line optimization. The proposeddiscrete-time preview-feedbackH∞ controller was designed based on the state augmentation technique withthe assumption that the NOx disturbance is previewed by using various information such as the terrain,acceleration pedal position, and engine operating conditions. Several findings are as follows. First, theadvantage of the preview-feedback H∞ control strategy was shown by the simulation test using experimen-726.2. Future Worktally obtained input data such as NOx disturbance, exhaust gas temperature, and exhaust gas mass flowrate over the transient conditions. The simulation result shows around 34% (NOx,out) and 6% (NH3,out)improvement delivered by the preview-feedback H∞ controller with longer preview length compared to anon-preview SCR controller. Second, compared to the performance yielded by an MPC controller, the pro-posed SCR controller delivered 7% and 3% improvement for NOx and NH3 slip, respectively. Third, thesimulation tests performed with previewed NOx disturbance with uncertainties implied feasibility of theproposed method under an uncertain NOx environment. However, 30% of uncertainties started to nega-tively affect the performance. Finally, the proposed SCR controller yielded better performance with lesscomputation time compared to an MPC controller.The proposed SCR controllers can be adopted in different SCR catalyst conditions since the robustnessanalyses showed their robustness against different parameter variations and sensor noises. The GS H∞controller and the GS LPV controller can be implemented in SCR systems withNOx andNH3 sensors. Thepreview-feedback SCR controller can be selected in SCR systems where the previewed NOx disturbance isavailable.6.2 Future WorkBased on the study for the SCR systems, the future work is summarized as below.1. The validation of the proposed controllers should be conducted by using either high fidelity modelsor actual engines. The model parameters such as pre-exponential factors and activation energies ofchemical reaction constants should be identified on the real SCR applications. All control designparameters such as weighting functions (W ), switching surface (SSi), and preview length (h) can alsobe tuned by following the proposed design method.2. Robust preview-feedback controller design for large NOx prediction errors can be conducted. Sincethere is a possibility of NOx prediction error in real SCR applications, it can be one of the interestingfuture research directions.3. Degradation of the SCR catalyst over the product lifetime is common because of high temperature andpoisoning. The advanced control strategies based on adaptive control [75] and robust control [76] willbe able to contribute the SCR systems with consistent performances under aged SCR conditions.73Bibliography[1] K. Reif. Diesel engine management: Systems and components. Springer Fachmedien Wiesbaden.Friedrichshafen, 2014.[2] J. B. Heywood. Internal Combustion Engine Fundamentals. TATA McGRAW-HILL, 1988.[3] J. E. Jonson, J. Borken-Kleefeld, D. Simpson, M. Posch, and C. Heyes. Impact of excess NOx emis-sions from diesel cars on air quality, public health and eutrophication in europe. Environmental Re-search Letters, 12(9), 2017.[4] T. V. Johnson. Review of diesel emissions and control. International Journal of Engine Research,10:275–285, 2009.[5] J.B. Dementhon, T. Colliou, B. Martin, M. Bouchez, M. Guyon, I. Messaoudi, R. Noirot, S. Michon,C. Gérentet, and L. Pierron. Application of NOx adsorber to diesel depollution: Performances anddurability. Oil and Gas Science and Technology, 58:129–149, 2003.[6] M. Hsieh, M. Canova, and J. Wang. Model predictive control approach for afr control during lean NOxtrap regenerations. SAE International Journal of Fuels and Lubricants, 2:149 – 157, 2009.[7] R. Mrad, A. Aissat, R. Cousin, D. Courcot, and S. Siffert. Catalysts for NOx selective catalytic reduc-tion by hydrocarbons (HC-SCR). Applied Catalysis A: General, 504:542–548, 2015.[8] S. Sasaki, J. Sarlashkar, G. D. Neely, J. Wang, Q. Lu, and H. Sono. Investigation of alternative combus-tion, airflow-dominant control and aftertreatment system for clean diesel vehicles. SAE Transactions,116:486–495, 2007.[9] N. Waldbuesser, J. Guenther, H. Hoffmann, O. Erlenmayer, F. Duvinage, C. Enderle, J. Schommers,and D. Waeller. Specifics of Daimler’s new SCR system (BLUETEC) in the diesel sprinter van -certified for NAFTA 2010. SAE International, 2:2010–01–1172, 2010.74Bibliography[10] K. Hirata, N. Masaki, H. Ueno, and H. Akagawa. Development of urea-SCR system for heavy-dutycommercial vehicles. SAE Transactions, 114:678–685, 2005.[11] J. Gieshoff, A. Shafer-Sindlinger, P. C. Spurk, J. A. Tillaart, and C. Garr. Improved SCR systems forheavy-duty applications. SAE World Congress, pages 2000–01–0189, 2000.[12] EPA. Air Pollution Control Technology Fact Sheet. EPA−452/F−03−032, United States Environmen-tal Protection Agency.[13] A. Grossale, I. Nova, E. Tronconi, D. Chatterjee, and M. Weibel. Study of a Fe–zeolite-based systemas NH3−SCR catalyst for diesel exhaust aftertreatment. Catalysis Today, 136:18–27, 2008.[14] S. Suárez, S. M. Jung, P. Avila, P. Grange, and J. Blanco. Influence of NH3 and NO oxidation on theSCR reaction mechanism on copper, nickel and vanadium oxide catalysts supported on alumina andtitania. Catalysis Today, 75:331–338, 2002.[15] M. F. Hsieh and J. Wang. An extended Kalman filter for ammonia coverage ratio and capacity es-timations in the application of diesel engine SCR control and onboard diagnosis. American ControlConference, pages 5874–5897, 2010.[16] M. F. Hsieh and J. Wang. Observer-based estimation of selective catalytic reduction catalyst ammo-nia storage. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of AutomobileEngineering, 224(9):1199–1211, 2010.[17] T. Zheng, W. Han, Y. Li, B. Yang, and L. Shi. Luenberger-sliding mode observer based ammoniaconcentration estimation for selective catalyst reduction system. 12th World Congress on IntelligentControl and Automation, pages 3021–3026, 2016.[18] J. N. Chi. Control challenges for optimal NOx conversion efficiency from SCR aftertreatment systems.SAE World Congress and Exhibition, pages 2009–01–0905, 2009.[19] D. Upadhyay and M. Nieuwstadt. Model based analysis and control design of a urea-SCR DeNOxaftertreatment system. ASME Journal of Dynamic Systems, Measurement, and Control, 14:641–653,2006.75Bibliography[20] F. Willems, R. Cloudt, E. V. D. Eijnden, B. D. Jager, W. Boomsma, and I. V. D. Heuvel. Is closed-loopSCR control required to meet future emission targets? SAE World Congress, pages 2007–01–1574,2007.[21] M. Devarakonda, G. Parker, J. Johnson, V. Strots, and S. Santhanam. Model-based estimation andcontrol system development in a urea-SCR aftertreatment system. SAE International Journal of Fuelsand Lubricants, 1:646–661, 2009.[22] M. F. Hsieh and J. Wang. An extended Kalman filter for NOx sensor ammonia cross-sensitivity elim-ination in selective catalytic reduction applications. American Control Conference, pages 3033–3038,2010.[23] P. S. Dhillon, M. P. Harold, D. Wang, A. Kumar, and S. Joshi. Hydrothermal aging of Pt/Al203monolith: Washcoat morphology degradation effects studied using ammonia and propylene oxidation.Catalysis Today, pages 20–29, 2019.[24] S. Dosda, D. Berthout, G. Mauviot, and A. Nogre. Modeling of a DOC, SCR−F, SCR exhaust linefor design optimization taking into account performance degradation due to hydrothermal aging. SAEInternational Journal of Fuels and Lubricants, pages 621–632, 2016.[25] C. Chen. Direct adaptive control of chemical process systems. Industrial and Engineering ChemistryResearch, 40:4121 – 4140, 2001.[26] Y. Ma and J. Wang. Control of aged automotive selective catalytic reduction systems for consistentperformances. Journal of the Franklin Institute, 354:8094–8116, 2017.[27] M. F. Hsieh. Control of Diesel Engine Urea Selective Catalytic Reduction Systems. PhD thesis, OhioState University, 2010.[28] K. Yang and P. Chen. Ammonia distribution control for a two-cell SCR system in a new configuration.American Control Conference, pages 282–287, 2020.[29] Q. Lin and P. Chen. Model-based analysis and control of SCR using NOx sensor measurements.American Control Conference, pages 5522–5527, 2018.76Bibliography[30] G. Pontikakis, G. Konstantas, and A. Stamatelos. Three way catalytic converter modeling as a modernengineering design tool. ASME Journal of Engineering for Gas Turbines and Power, page 906–923,2004.[31] B. Roduit, A. Baiker, F. Bettoni, J. Baldyga, and A. Wokaun. 3−D Modeling of SCR of NOx, by NH3on vanadia honeycomb catalysts. AIChE Journal, 44:2731–2744, 1998.[32] J. Johnson V. Strots M. Devarakonda, G. Parker and S. Santhanam. Adequacy of reduced order modelsfor model-based control in a urea-SCR aftertreatment system. 2008 World Congress, 2008-01-0617,2008.[33] C. Ericson, B. Westerberg, and I. Odenbrand. A state space simplified SCR catalyst model for real timeapplications. 2008 World Congress, 2008-01-0616, 2008.[34] C. M. Schär, C. H. Onder, H. P. Geering, and M. Elsener. Control-oriented model of an SCR catalyticconverter system. SAE Technical Paper, 2004.[35] C. M. Schär. Control of a selective catalytic reduction process. PhD thesis, ETH Zurich, 2003.[36] D. Upadhyay and M. Nieuwstadt. Modeling of a urea-SCR catalyst with automotive applications.ASME International Mechanical Engineering Congress and Exposition, pages 707–713, 2008.[37] M. N. Devarakonda. Dynamic Modeling, Simulation and Development of Model-based Control Strate-gies in a urea-SCR Aftertreatment System in Heavy-duty Diesel Engine. PhD thesis, Michigan Techno-logical University, 2008.[38] D. H. E. Seher, M. Reichelt, and S. Wickert. Control strategy for NOx emission reduction with SCR.SAE International Truck and Bus Meeting and Exhibition, pages 2003–01–3362, 2003.[39] J. N. Chi and H. F. M. DaCosta. Modeling and control of a urea-SCR aftertreatment system. SAE WorldCongress, 2005-01-0966, 2005.[40] C. M. Schar, C. H. Onder, and H. P. Geering. Control of an SCR catalytic converter system for a mobileheavy-duty application. IEEE Transactions on Control Systems Technology, 14(4):641–653, 2006.[41] C. Schar, C. Onder, and H. Geering. Mean value model of the SCR system of a mobile application.IFAC World Congress, July 2002.77Bibliography[42] D. Upadhyay and M. Nieuwstadt. Exhaust gas aftertreatment systems: US patent, US6928806B2. 2006.[43] Q. Song and G. Zhu. Model-based closed-loop control of urea SCR exhaust aftertreatment system fordiesel engine. SAE Transactions, 111:102–110, 2002.[44] M. Meisami-Azad, J. Mohammadpour, K. M. Grigoriadis, M. P. Harold, and M. A. Franchek. LPVgain-scheduled control of SCR aftertreatment systems. International Journal of Control, 85(1):114–133, 2012.[45] E. F. Camacho and C. Bordons. Model Predictive Control. Springer, 2004.[46] M. Nikolaou. Model predictive controllers: A critical synthesis of theory and industrial needs. Ad-vances in Chemical Engineering, 26:131–204, 2001.[47] Y. Ma and J. Wang. Model-based control of automotive selective catalytic reduction systems with roadgrade preview. In American Control Conference, pages 7–12, 2018.[48] C. Chiang, C. Kuo, C. Huang, and J. Lee. Model predictive control of SCR aftertreatment system.Proc. IEEE Conference on Industrial Electronics and Applications, page 2058–2063, 2010.[49] C. Ericson. Model-based Optimization of a Complete Diesel Engine/SCR System. PhD thesis, LundUniversity, 2009.[50] T. L. McKinley and A. G. Alleyne. Adaptive model predictive control of an SCR catalytic convertersystem for automotive applications. IEEE Transactions on Control Systems Technology, 20(6):1533–1547, 2012.[51] Y. Ma and J. Wang. A predictive control method for automotive selective catalytic reduction systems.American Control Conference, pages 1593–1598, 2019.[52] N. Planakis, V. Karystinos, G. Papalambrou, and N. Kyrtatos. Nonlinear model predictive control forthe transient load share management of a hybrid diesel-electric marine propulsion plant. AmericanControl Conference, pages 1955–1960, 2020.[53] T. Katayama and T. Hirono. Design of an optimal servomechanism with preview action and its dualproblem. International Journal of Control, 45(2):407–420, 1987.78Bibliography[54] Y. Fujisaki and T. Narazaki. Optimal preview control based on quadratic performance index. IEEEConference on Decision and Control, 4:3830–3835, 1997.[55] K. Takaba. A tutorial on preview control systems. SICE 2003 Annual Conference, 2:1388–1393, 2003.[56] S. Yim. Design of a preview controller for vehicle rollover prevention. IEEE Transactions on VehicularTechnology, 60:4217–4226, 2011.[57] T. Egami, H. Sasaki, and Y. Yatsuda. A digital nonlinear control of robot by means of real time previewdesired signal. Journal of Robotics Society of Japan, 14:406–414, 1996.[58] F. Wu, X. H. Yang, A. Packard, and G. Becker. Induced L2−norm control for LPV systems withbounded parameter variation rates. International Journal of Robust and Nonlinear Control, 6:983–998,1996.[59] M. Devarakonda, G. Parker, J. Johnson, and V. Strots. Model based control system design in aurea−SCR aftertreatement system based on NH3 sensor feedback. International Journal of AutomotiveTechnology,, 1:653–662, 2009.[60] C. D. Rakopoulos and E. G. Giakoumis. Diesel Engine Transient Operation. Springer, 2009.[61] S. Sasaki, J. Sarlashkar, G. Neely, J. Wang, Q. Lu, and H. Sono. Investigation of alternative combus-tion, air flow dominant control and aftertreatment systems for clean diesel vehicles. SAE TransactionsJournal of Fuel and Lubricants, (116):486–495, 2008.[62] X. Yuan, H. Liu, and Y. Gao. Diesel engine SCR control: current development and future challenges.Emission Control Science and Technology, page 121–133, 2015.[63] A. Hariharan, J. Watkins, and M.E. Sawan. Optimal control in selective catalytic reduction using linearquadratic regulator. IEEE 59th International Midwest Symposium on Circuits and Systems, 2016.[64] M. F. Hsieh and J. Wang. Nonlinear observer designs for diesel engine selective catalytic reductionammonia coverage ratio estimation. IEEE Conference on Decision and Control, pages 6596–6601,2009.79[65] H. Zhang, J. Wang, and Y. Wang. Robust filtering for ammonia coverage estimation in diesel engineselective catalytic reduction systems. ASME Journal of Dynamic Systems, Measurement, and Control,135:064504–1–064504–7, 2013.[66] M. F. Hsieh and J. Wang. Adaptive and efficient ammonia storage distribution control for a two-catalystselective catalytic reduction system. ASME Journal of Dynamic Systems, Measurement, and Control,134:011012–1–011012–11, 2012.[67] D. Gu, P. H. Petkov, and M. M. Konstantinov. Robust Control Design with MATLAB. Springer, 2013.[68] Y. Ma and J. Wang. Sliding-mode control of ammonia coverage ratio for automotive selective catalyticreduction systems. American Control Conference, pages 25–30, 2018.[69] C. Winkler, P. Flörchinger, M. D. Patil, J. Gieshoff, P. Spurk, and M. Pfeifer. Modeling of SCR DeNOxcatalyst - looking at the impact of substrate attributes. SAE Transactions, 112:691–699, 2003.[70] K. K. Jain, J. R. Hiremath, and P. H. Meckl. Term−by−Term observer design method to estimateammonia storage in SCR catalyst. American Control Conference, pages 4899–4904, 2020.[71] P. Apkarian and R. J. Adams. Advanced gain-scheduling techniques for uncertain systems. IEEETransactions on Control Systems Technology, 6(1):21–32, 1998.[72] J. Arregle, J. Lopez, C. Guardiola, and C. Monin. Automotive Model Predictive Control. Springer,Linz, 2010.[73] F. Lin. Control oriented NOx and soot emission estimation for diesel engine. Master Thesis, 2011.[74] O. Ozhkina and V. Lozhkin. Estimation of nitrogen oxides emissions from petrol and diesel passengercars by means of on-board monitoring: Effect of vehicle speed, vehicle technology, engine type onemission rates. Transportation Research Part D: Transport and Environment, 47:251–264, 2011.[75] G. C. Goodwin and K. S. Sin. Adaptive Filtering Prediction and Control. Prentice Hall, 2009.[76] S. Skogestadand and I. Postlethwaite. Multivariable Feedback Control. Wiley, 2005.80Appendix AOpen-loop simulation testsTo perform robustness analysis, we changed each model parameter with±2, ±4, ±6, ±8, and±10% pertur-bation under the open-loop simulations. The purpose of this open-loop simulations is to find how sensitivethe model parameters are. For this open-loop simulation tests,NOx,in,NH3,in, exhaust gas temperature (T ),and normalized exhaust gas flow rate (Q¯) should be specified. As shown in Fig. A.1, the constant and thestep signals were selected for NOx,in and NH3,in. The exhaust gas temperature and the normalized exhaustgas flow rate are fixed as 500 [K] and 9 [1/sec].0 100 200 300 400 500 600 700 800 900112711281129NOx,in [ppm]0 100 200 300 400 500 600 700 800 900Time [sec]05001000NH3,in [ppm]Figure A.1: Input signals for open-loop simulationsThe model parameters related to the chemical reaction constants were selected as follows.• Ered: activation energy of NOx reduction• Eox: activation energy of NH3 oxidation• Eads: activation energy of NH3 adsorption81Appendix A. Open-loop simulation tests• Edes: activation energy of NH3 desorptionThe perturbation of Ered affects both NOx,ou and NH3,out as depicted in Fig. A.2. The NOx,out andNH3,out continue to increase as Ered perturbs up to 10%. On the contrary, when Ered changes by -10%0 100 200 300 400 500 600 700 800 90005001000NOx,out [ppm]0 100 200 300 400 500 600 700 800 90001020NH3,out [ppm]0 % perturbation2 % perturbation4 % perturbation6 % perturbation8 % perturbation10 % perturbation-2 % perturbation-4 % perturbation-6 % perturbation-8 % perturbation-10 % perturbationFigure A.2: Parameter perturbation of Ered0 100 200 300 400 500 600 700 800 90005001000NOx,out [ppm]0 100 200 300 400 500 600 700 800 900Time [sec]0246NH3,out [ppm]0 % perturbation2 % perturbation4 % perturbation6 % perturbation8 % perturbation10 % perturbation-2 % perturbation-4 % perturbation-6 % perturbation-8 % perturbation-10 % perturbationFigure A.3: Parameter perturbation of Eoxperturbation, NOx,out and NH3,out decrease because NOx reduction can be occurred by less activationenergy.Figure A.3 shows thatNH3,out continues to decrease when the perturbation ofEox decreases up to -10%.82Appendix A. Open-loop simulation testsIt is also observed that NH3,out is mainly affected when Eox perturbs. However, the variation of NH3,outis smallest compared to other results by parameter perturbation. This implies that Eox is the least sensitiveparameter, and thus, it does not affect the performance degradation with ±10% parameter uncertainties.When the parameters (Eads) changes with 10% perturbation, the result demonstrates that NH3,outmainly increases. This is because NH3 adsorption less happens and results in an increase of NH3,out.On the other hand, -10% perturbation of Eads causes an increase of NH3 adsorption and thus NH3,outdecreases.0 100 200 300 400 500 600 700 800 90005001000NOx,out [ppm]0 100 200 300 400 500 600 700 800 900Time [sec]01020NH3,out [ppm]0 % perturbation2 % perturbation4 % perturbation6 % perturbation8 % perturbation10 % perturbation-2 % perturbation-4 % perturbation-6 % perturbation-8 % perturbation-10 % perturbationFigure A.4: Parameter perturbation of EadsThe NH3,out increases as Edes changes by -10% perturbation, as shown in Fig. A.5. The decrease ofEdes leads to more NH3,out compared to an unperturbed case. The results by Edes perturbation show anenormous variation of the performance.In summary, Ered perturbation affects both NOx,out and NH3,out performances, and Edes perturbationcauses an enormous degradation. Therefore Ered and Edes should be carefully considered in the controllerdesign procedure. Furthermore, both parameters perturbed can be utilized for the robust analysis of theproposed controllers.83Appendix A. Open-loop simulation tests0 100 200 300 400 500 600 700 800 90005001000NOx,out [ppm]0 100 200 300 400 500 600 700 800 900Time [sec]02040NH3,out [ppm]0 % perturbation2 % perturbation4 % perturbation6 % perturbation8 % perturbation10 % perturbation-2 % perturbation-4 % perturbation-6 % perturbation-8 % perturbation-10 % perturbationFigure A.5: Parameter perturbation of Edes84Appendix BOperating point valuesTable B.1 shows all operating point values selected to design each gain-scheduling controllers in Sec-tion 3.4.2 to help some readers understand.Table B.1: Operating points for controller designT NOx,in NOx,out NH3,out θ NH3,in Controller[K] [mole/m3] [mole/m3] [mole/m3] [-] [mole/m3]468 0.01042 0.00135 0.00016 0.35 0.00924 K1H∞(rˆ)468 0.01042 0.00129 0.00018 0.37 0.00932 K2H∞(rˆ)468 0.01042 0.00121 0.00021 0.40 0.00943 K3H∞(rˆ)468 0.02292 0.00171 0.00058 0.65 0.02181 K1H∞(rˆ)468 0.02292 0.00166 0.00064 0.67 0.02191 K2H∞(rˆ)468 0.02292 0.00159 0.00073 0.70 0.02207 K3H∞(rˆ)468 0.03542 0.00231 0.00095 0.75 0.03408 K1H∞(rˆ)468 0.03542 0.00225 0.00106 0.77 0.03424 K2H∞(rˆ)468 0.03542 0.00217 0.00127 0.80 0.03453 K3H∞(rˆ)538 0.00906 0.00018 0.00055 0.15 0.00957 K1H∞(rˆ)538 0.00906 0.00016 0.00063 0.17 0.00969 K2H∞(rˆ)538 0.00906 0.00014 0.00077 0.20 0.00989 K3H∞(rˆ)538 0.01994 0.00041 0.00055 0.15 0.02022 K1H∞(rˆ)538 0.01994 0.00036 0.00063 0.17 0.02038 K2H∞(rˆ)538 0.01994 0.00031 0.00077 0.20 0.02060 K3H∞(rˆ)538 0.03081 0.00038 0.00103 0.25 0.03171 K1H∞(rˆ)538 0.03081 0.00035 0.00114 0.27 0.03187 K2H∞(rˆ)538 0.03081 0.00032 0.00133 0.30 0.03212 K3H∞(rˆ)608 0.00802 0.00002 0.00322 0.15 0.01406 K1H∞(rˆ)608 0.00802 0.00002 0.00373 0.17 0.01496 K2H∞(rˆ)608 0.00802 0.00001 0.00455 0.20 0.01635 K3H∞(rˆ)608 0.01764 0.00004 0.00322 0.15 0.02366 K1H∞(rˆ)608 0.01764 0.00004 0.00373 0.17 0.02456 K2H∞(rˆ)608 0.01764 0.00003 0.00456 0.20 0.02596 K3H∞(rˆ)608 0.02727 0.00006 0.00322 0.15 0.03326 K1H∞(rˆ)608 0.02727 0.00006 0.00373 0.17 0.03416 K2H∞(rˆ)608 0.02727 0.00005 0.00456 0.20 0.03556 K3H∞(rˆ)85Appendix CParameter valuesThe gain of the feedforward controller (KFF ) is selected as 0.705 by trial and error. The Table C.1 showsthe parameter values of the gain-scheduling (GS) proportional-integral-derivative (PID) controller (KPID)in Section 3.5.Table C.1: Parameter values of KPIDSub-region Controller P I DRˆ111 K111PID(rˆ) –2 0.01 0Rˆ211 K211PID(rˆ) –3 0.01 0Rˆ311 K311PID(rˆ) –3 0.01 0Rˆ121 K121PID(rˆ) 21 –0.00045 535Rˆ221 K221PID(rˆ) 3.8 0 0Rˆ321 K321PID(rˆ) 3.8 0 0Rˆ131 K131PID(rˆ) –11 –0.016 533Rˆ231 K231PID(rˆ) 50 –0.5 108Rˆ331 K331PID(rˆ) 50 –0.5 108Rˆ112 K112PID(rˆ) –5 0.01 0Rˆ212 K212PID(rˆ) –5 0 0Rˆ312 K312PID(rˆ) –5 0 0Rˆ122 K122PID(rˆ) 16 –0.00045 535Rˆ222 K222PID(rˆ) 3 0 0Rˆ322 K322PID(rˆ) 3 0 0Rˆ132 K132PID(rˆ) 15 –0.016 533Rˆ232 K232PID(rˆ) –50 –0.5 108Rˆ332 K332PID(rˆ) –50 –0.5 108Rˆ113 K113PID(rˆ) –10 0.01 0Rˆ213 K213PID(rˆ) –10 0 0Rˆ313 K313PID(rˆ) –10 0 0Rˆ123 K123PID(rˆ) –2 –0.00045 535Rˆ223 K223PID(rˆ) –2 –0.00045 535Rˆ323 K323PID(rˆ) –2 0 0Rˆ133 K133PID(rˆ) 10 –0.016 533Rˆ233 K233PID(rˆ) –143 –0.5 108Rˆ333 K333PID(rˆ) –143 –0.5 10886Appendix C. Parameter valuesThe sliding mode controller (KSMC) was designed asu =(H + λ)(kadsQ¯(1− θ))(−θ˙ + γ(rθ − θ)),H = kred(CNOx θ˙ − Q¯CNOx − kredΩCNH3CNOx + Q¯d)θ+ koxθ˙ − kads(kdesΩθ − (kadsΩ + Q¯)CNH3 + kadsΩθCNH3 − θ˙CNH3 − θkdesΩθ+ θ(kadsΩ + Q¯)CNH3 − θkadsΩθCNH3) + kdesθ˙ − γθ˙.Here, the control design parameters, λ = 0.6 and γ = 0.4, and the reference value rθ = 0.023 for theammonia coverage ratio θ were selected by trial and error to minimize NOx,out with 10 [ppm] NH3,out inaverage.87
Thesis/Dissertation
eng
Mechanical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Gain-scheduling and preview control of selective catalytic reduction systems in diesel engines
Text