UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Estimation and identification of moisture content in paper Jonsson, Ivar Mar 1991

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1991_A7 J66.pdf [ 17.89MB ]
Metadata
JSON: 831-1.0098468.json
JSON-LD: 831-1.0098468-ld.json
RDF/XML (Pretty): 831-1.0098468-rdf.xml
RDF/JSON: 831-1.0098468-rdf.json
Turtle: 831-1.0098468-turtle.txt
N-Triples: 831-1.0098468-rdf-ntriples.txt
Original Record: 831-1.0098468-source.json
Full Text
831-1.0098468-fulltext.txt
Citation
831-1.0098468.ris

Full Text

Estimation and Identification of Moisture Content in Paper by Ivar Mar Jonsson B.A.Sc. University of Iceland, Reykjavik, 1988. t A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF ELECTRICAL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August 1991 © Ivar Mar Jonsson, 1991 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. The University of British Columbia Vancouver, Canada Department DE-6 (2/88) Abstract The purpose of this thesis is to summarize some results obtained for an improved moisture estimation and identification algorithm which extracts, the cross direction (CD) moisture profiles and machine direction (MD) moisture variations from the composite measured profile, in the presence of noise. The objective is to use the algorithm as part of a paper machine control system to maintain the moisture content of the sheet at a target value and keep a uniform cross-sectional profile shape. The estimation and identification scheme is based upon a nonlinear model, and consists of a modified least squares algorithm for estimating cross direction profile deviations and a Kalman filter for estimating machine direction variations and disturbances. The scheme, when tested on simulated data where the true profiles are known, is shown to give robust and effective results. Off-line testing of the algorithm on industrial data is also presented. Results from the on-line application of the algorithm working in closed loop in the industry are also included. Future work will consist of further industrial testing along with fine-tuning. The final objective is then to have this algorithm integrated in an overall paper machine control system, where other variables, such as basis weight and caliper, are estimated and controlled. ii Table of Contents Abstract ii List of Tables v List of Figures .- vi Acknowledgments x 1 Introduction 1 1.1 Description of the prior art 3 1.2 Motivation for this work 4 1.3 Outline of the thesis 5 2 The Moisture Variation Model 6 2.1 Underlying theory and assumptions 6 2.2 The Moisture Variation Model's structure 7 3 The Estimation and Identification Procedure 10 3.1 Exponential multiple scan trending 10 3.2 Previous EIMC algorithm and results 10 3.3 The Exponential Forgetting and Resetting Algorithm 12 3.4 Diverse calculation issues on EFRA matrices „ 13 3.5 Extraction of the nonlinear term 14 3.6 The Kalman filter 16 3.7 The EIMC algorithm structure 17 4 Results using Simulated Data 19 4.1 The setup of EIMC 19 4.2 Results using EIMC ' 19 4.3 EIMC versus exponential multiple scan trending 25 iii 5 Industrial Implementation Issues 29 5.1 Knowledge of the moisture target value 29 5.2 Spikes in autocorrelation 31 5.3 Scan direction 32 5.4 Effect of sensor time constant, r 33 5.5 Timing of measurements and scan speed 34 5.6 Paper sheet movement 35 5.7 Diverse issues 35 5.7.1 Bounds on parameters and states 35 5.7.2 Computation time 35 6 Analysis of Industrial Data 36 6.1 Moisture control systems in both automatic and manual mode 36 6.2 Moisture control system in manual mode 40 6.3 On-line testing at a mill 46 7 Conclusions 70 References 72 iv List of Tables 5.1 Effect of different time constants on the estimated CD profile amplitude 0 List of Figures 1.1 Typical water/fiber ratios . 1 1.2 The scanning process 2 2.3 Zig-zag measurement path due to the sensor and paper sheet movement 8 3.4 Structure of the old EIMC algorithm 11 3.5 Overall structure of the improved EIMC algorithm 17 4.6 Raw data for the simulated data 20 4.7 Estimated CD profiles for the simulated data 21 4.8 Raw CD profile and estimated CD profile at scan #30 22 4.9 Estimated it for the simulated data 23 4.10 Estimated B for the simulated data 23 4.11 The coefficient of determination r 2 for the estimated B 24 4.12 Autocorrelation for the simulated data 24 4.13 The MD variations out of EIMC and EXPO for the simulated data 25 4.14 CD profile at scan #150 for EIMC and EXPO for the simulated data 26 4.15 Standard deviation for EIMC and EXPO for the simulated data 26 4.16 Residuals from EIMC for the simulated data 27 4.17 Residuals from EXPO for the simulated data 27 4.18 Autocorrelation of the residuals from EXPO for the simulated data 28 5.19 Estimated CD profile shape with different target values for simulated data 29 5.20 Estimated B with different target values for simulated data 30 vi 5.21 Estimated u with different target values for simulated data 30 5.22 Explanation of the spikes in the autocorrelation function . . . 31 5.23 Residuals from simulated data with wrong time sequence 32 5.24 Estimated CD profile, r = 0.2seconds 33 5.25 Estimated CD profile, r = 0.5 seconds 34 6.26 Raw moisture data for control in both automatic and manual mode 37 6.27 Estimated CD profiles for control in both automatic and manual mode 38 6.28 Estimated €, for control in both automatic and manual mode 39 6.29 Estimated B for control in both automatic and manual mode .39 6.30 Image of raw moisture data for control in manual mode 41 6.31 Image of the estimated CD profiles for control in manual mode 42 6.32 Raw profile and estimated CD profile at Scan #25 for CD for control in manual mode. (Note, that u « 0) 43 6.33 Data box #20. Bump detection with two different settings of EFRA for CD control in manual mode 43 6.34 Estimated S for control in manual 44 6.35 Estimated B for control in manual 44 6.36 Autocorrelation of residuals for control in manual 45 6.37 Image of raw moisture data, Mil l Trial 48 6.38 Time-sequence of the raw moisture for Period 4, Mill Trial 49 6.39 Power Spectrum of the raw moisture for Period 4, Mil l Trial 50 6.40 Image of the actuators settings (Devronizer), Mill Trial 51 6.41 Estimated MD variations using EIMC and EXPO, Mill Trial 52 vii 6.42 Time-sequence of the raw moisture, the scan average, and the estimated MD variations from EIMC for Period 4, Mil l Trial .52 6.43 Power Spectrum of the estimated fast MD variations using EIMC for Period 4, Mil l Trial 53 6.44 Image of the estimated CD profiles using EIMC, Mill Trial 54 6.45 Image of the estimated CD profiles using EXPO, Mill Trial 55 6.46 Estimated B, Mil l Trial 56 6.47 Composite raw profile (2a = 0.353) for scans 46-70, Mil l Trial 57 6.48 Composite raw profile (2a = 0.307) for scans 306-330, Mil l Trial 57 6.49 2cr of the raw moisture for each scan, Mill Trial 58 6.50 2cr of the estimated CD profiles using EIMC and EXPO, Mil l Trial 58 6.51 MD variations in data box #157 of the estimated CD profile using EIMC, Mil l Trial . . . 59 6.52 MD variations in data box #282 of the estimated CD profile using EIMC, Mil l Trial . . . 60 6.53 Residuals for Period 4 using EIMC, Mill Trial 60 6.54 Residuals for Period 4 using EXPO, Mil l Trial 61 6.55 Autocorrelation of the residuals for Period 4 using EIMC, Mil l Trial 61 6.56 Autocorrelation of the residuals for Period 4 using EXPO, Mill Trial 62 6.57 Image of the basis weight, Mill Trial 63 6.58 Image of the dry weight, Mil l Trial 64 6.59 Image of the caliper, Mill Trial 65 6.60 Moisture at single point 66 6.61 Basis Weight at single point 67 6.62 Caliper at single point 68 viii 6.63 Power Spectrum of the moisture single-point measurement ix Acknowledgments I wish to thank my supervisor Prof. G.A. Dumont for his invaluable insight and assistance during my thesis work. I would also like to thank my co-supervisor Prof. M.S. Davies for his help and input. I would like to thank all my co-researchers in the Paper Machine Control group, Dr. C. Lindeborg, Mr. F. Ordubadi, Mr. K. Kristinsson, Mr. J. Ghofraniha, Mr. G. Wang, and Mr. S. Morgan, for their input and support for this research topic. I would especially like to thank Dr. Y. Fu for all his help. I am thankful for the good cooperation with the experienced staff of Devron-Hercules Inc., especially Mr. M . Heaven who was always available to give good answers. I would like to thank all my friends in the control group and the staff at the Pulp and Paper Centre. I would also like to thank all my friends and family who have been supportive through the ordeal of my educations era, especially my parents. At last I am most grateful to my wonderful wife, Iris, and my daughter Alma, for their dedicated support and patience during my graduate studies. x Chapter 1: Introduction Chapter 1 Introduction The moisture content of paper is the percentage ratio between the weight of water and the total weight of the paper sheet. This variable is of great importance to both the quality of the product and the energy consumed in the papermaking process. The moisture content of the paper sheet is typically Water removal on wire Pulp bales pick-up Slushing Refining Thick Thin stock stock cleaning etc. metering ' 0 o 0 o 8 D o § © R e e l u p Paper Presses Main machine bank dryers Size press After-bank dryers Figure 1.1: Typical water/fiber ratios [19] less than 10% at the end of the dryer section of the paper machine. In the dryers, the moisture ratio (water/fiber) is thus approximately reduced by a factor of eight, from its value at the wet presses (See Figure 1.1). The variations in the paper sheet properties are denned in four directions: Machine direction (MD); Cross direction (CD); Random or residual (R) and Vertical or thickness direction (ZD). The moisture variability is measured and controlled in two dimensions: the machine direction and the cross direction. MD variations occur with respect to time and are assumed independent of the cross-machine position. The CD profile is a variable both with respect to cross-machine position 1 Chapter 1: Introduction Figure 1.2: The scanning process and time [25] (See Figure 1.2). However, as the MD variations are much more rapid in the time domain than the CD profile variations, the CD profile can be considered nearly time-invariant. The ultimate objective of the control system is to successfully control the entire spectrum of moisture variations, from very narrow and short-term variations to the very broad and long-term. The main control unit for the moisture MD variations is the dryer steam pressure. For MD control, a control action is taken at least every scan. The CD profile can be controlled by various types of actuators, located at fixed intervals across the paper machine's width, such as steam boxes, remoisturizing showers or infrared heating boxes [24]. In practice, a CD control action is taken only every 2-4 scans. To operate these actuators so that the moisture content of the whole sheet can be controlled at a uniform target level, knowledge of the moisture content is needed. It is (clearly) impossible to measure 100% of the sheet; only a portion of the sheet is "sampled" and presumed to represent the entire product. The moisture sensor is a single infrared scanning gauge mounted on a frame at the dry end. As the sensor slowly traverses the moving paper sheet, it continuously traces a diagonal path, measuring a distorted profile that includes both MD variations and CD profiles as well as random variations (See Figure 1.2). Improved measurement techniques now enable measurements at fixed intervals, as fine as 1 cm. wide [25]. The speed of the paper sheet is much higher than the speed of the scanning device so that the angle of the path of the gauge relative to the MD as it crosses the sheet is very shallow, typically less than 1 deg. [7]. Therefore the signal contains mainly the MD component, and 2 Chapter 1: Introduction the problem is then to retrieve the true CD profile from this raw composite signal. The problem of estimating and controlling CD profiles on paper machines is the topic of an extensive literature. 1.1 Description of the prior art Due to the complex nature of paper variations, extensive research and experience have led to a number of papers in the paper machine control area. In [2], Bialkowski defines and gives a good and the most recent survey of various terms, concepts and the behaviour of paper variables, such as moisture, basis weight and caliper. Cutshall et. al. ([5], [4]) present a number of "Useful Methods" for measurement and analysis of grammage variations. These methods are as well suitable for moisture variations. Statistical measurement tools used in the paper industry are explained, the variations dimensions described and the problem of measuring "true" CD profiles is discussed. Smith [24] gives a survey of cross-direction paper machine control of moisture, basis weight, and caliper. The benefits of CD control are listed and reveal that nothing but economical benefits are gained with installation of a CD control system. A CD control system is made up of three components: a scanning gauge for measuring, a process control computer and a actuator system. Moisture CD profile control is most commonly accomplished with segmented steam boxes, sheet rewetting sprays, and infrared drying systems. Wilhelm discusses in [26] the controllability of CD variations and the analysis of paper sheet characteristics, using data gathered from paper machines. A wet end moisture control system has been on the research agenda since the early sixties, e.g. in [11] a patent is claimed for a cross machine moisture control system for the wet end of a paper machine. An on-line cross-machine moisture profile is obtained and a number of actuators is used to adjust the profile to a desired shape. Lindeborg has published a number of articles about modeling, estimation and control of moisture variations. The Drying Curve Model (DCM) is the underlying model for his research and is presented in [13]. The model describes the evaporation-rate profile after the press section. In [15] it is 3 Chapter 1: Introduction experimentally verified that the measured composite moisture profile is a nonlinear function of the CD profile and the MD variations. The Moisture Variation Model (MVM) for dry end variations, describing this nonlinear relationship is also presented. In [16] and [17] a simulation system is developed to better understand the influence of selected design factors, such as measurement box size, measurement noise, sensor-actuator misalignment, sensor response speed etc., on the performance of a cross-direction moisture control system in papermaking. Situations are pointed out where the measurements can give misleading conclusions. Lindeborg develops in [12] a nonlinear algorithm to estimate the moisture variation character-istics, based on his M V M . In [3] dual Kalman filter configuration is applied to sheet measurement, by using models stated to be reasonably valid. In [7], Dumont discusses the overall control of the web processes, and gives an overview of the paper machine models, the profile estimation and the MD and CD control. The conventional procedure to remove unwanted MD variability from the profile is referred to as exponential multiple-scan trending. It is simply described as weighting the measurement at each cross-direction position relative to the long-term historical value. The random variation is estimated by subtracting the MD variation and the CD profile from the total variation. The sum is called the residual (R) and contains all measurement and analysis error. This method is slow, not optimal, and will give a biased estimate of the moisture profile because of the inherent process nonlinearity. This will be verified in Section 3.1. To effectively measure and control cross-direction moisture variations, MD variability must be quickly and thoroughly removed from control profiles. In [20] a new approach, to separate the CD profile and the MD variation from the zig-zag pattern of moisture measurements, is presented by Natarajan et. al. This algorithm, the Estimation and Identification of Moisture Content (EIMC), is based on the M V M in [15] and has some new attractive features such as more frequent estimates of MD variations and increased accuracy and convergence rate. 1.2 Motivation for this work In this thesis improvements to the EIMC method are presented. The previous EIMC [20] was found to give biased estimates of a nonlinear coefficient in the nonlinear moisture model. The 4 Chapter 1: Introduction extraction of this coefficient is now carried out after each scan. A modified least squares algorithm for the CD profile estimation has been implemented instead of the classical least squares algorithm. With these changes the EIMC is robust and gives unbiased results when tested on simulated data, as shown later in this thesis. An extensive industrial database consisting of moisture measurements from various paper machines has been used to test the EIMC algorithm. The results of this off-line testing are promising as shown later. The improved EIMC algorithm has been tested on-line in industry and these results are presented here with the system working both in open-loop and closed-loop. The EIMC is now in the final evaluation stage and will be implemented as part of the moisture content paper machine control system in an Canadian paper mill for continuous testing in the very near future. 1.3 Outline of the thesis In Chapter 2 the Moisture Variation Model is described and some terms explained. The state-space format of the model is presented. The algorithm structure is put forward in Chapter 3 and the components of the algorithm are discussed. The problems encountered in the development of the algorithm are described along with their solution. The behavior of the algorithm is first tested in Chapter 4 with data generated by using the Moisture Variation Model. The settings of various variables for the algorithm are as well described. The results show excellent correlation between the simulated true variations and the estimates. The algorithm is then compared to the conventional identification approach. In Chapter 5 some industrial implementation issues of the EIMC are discussed. Results from the analysis of industrial data are shown in Chapter 6. On-line testing of the algorithm is also presented along with some results. The evaluation of the real data led to a number of conclusions and new aspects. Finally, in Chapter 7, the overall conclusions are drawn and suggestions for further work are given. 5 Chapter 2: The Moisture Variation Model Chapter 2 The Moisture Variation Model 2.1 Underlying theory and assumptions The main goal of Lindeborg's research is to describe the moisture content D% at the dry end in a certain CD position n and at a certain time k. D% is composed of [15]: the CD profile component pu; a variation u'£ in the MD; and a component v% representing the error between the true moisture content and its mathematical description. His starting point is the process model for the multicylinder dryer section derived in [13]. By using a Taylor series expansion in [14], Lindeborg shows that the final moisture content D can be described as the sum of the content at a working point and a factor, representing the sum of; the changes in the process variables (evaporation rate, oven dry weight, machine speed and press moisture content), and the product of these process variables changes, a nonlinear term B and the deviation of the CD profile from the reference level MT. The basic formulation of the model for one working point is D = (Mr + p) + u * (1 4- Bp) + error term (2.1) In [14] it is shown that the error term in Equation 2.1 is small enough to justify the model structure for the normal working region of the paper machine and that the model has the following properties: Property 1. The CD profile elements, Pn = Mr+pn, change only slowly with time, due to infrequent and small control actions in cross-direction. Lindeborg's study of cross-direction drying performance also reveals that the evaporation-rate profile shape is approximately constant over long periods of time (e.g. weeks) [13]; Property 2. The variations in MD are synchronous in all CD profile positions, due to multiple factors such as an imperfect consistency control system, variations in the headbox pressure, pulses from pumps, oscillations in the steam system, etc.; Property 3. The CD profile will be deformed when the average level is changed, e.g. at low moisture levels, the water is bound within the fibres to a greater extent, which makes water 6 Chapter 2: The Moisture Variation Model transport more difficult. Different parts of the sheet will therefore react differently to the same change depending on whether they have a high or a low moisture content; Property 4. The amplification factor (1 + Bp) implies that MD variations have high amplitudes in those positions where P" has a large value; Property 5. The model parameter B with the dimension (moisture content)-1 is approximately constant for a certain reference level Mr and the parameter changes only slowly with time. For clarification of whether changes in the moisture of the paper sheet are due to the CD profile or to the MD variations, two definitions are made in [15]. Definition 1. The CD profile whose elements have the chosen reference value Mr as their average is called the basic cross-machine profile. Definition 2. The basic machine-direction variation uk is the variation which can be measured in a position where the profile element p" — 0. 2.2 The Moisture Variation Model's structure From Equation 2.1 and the M V M assumptions, the M V M for dry-end variations is presented in [20] as follows: y'k' = Dl - Mr = pn + (1 + Bp")uk + vk (2.2) where: y'kl is the measured profile deviation from the reference level, at CD position n and time instant kT; Dkl is the measured profile; MT is the MD target value (setpoint); p" is the CD profile deviation at position n; B is the nonlinear term coefficient; uk is the MD variation at time kT; and 7 Chapter 2: The Moisture Variation Model o o Scan m o o Scan m-1 n+1 -n — n-1 -— o < 1 — o o CD (Sensor movement) PAPER SHEET I o O o Scan m-2 o o (k-l)T kT (k+l)T MD (Sheet movement) Figure 2.3: Zig-zag measurement path due to the sensor and paper sheet movement vk models both sensor noise and neglected higher order terms in the model, and is assumed to be a Gaussian white noise process with known variance R. The moisture sensor moves only in the cross direction while the paper moves in the machine direction. The combination of the two movements leads to a zig-zag set of measurements, as can been seen in Figure 2.3. In Equation 2.2 n indicates the cross direction position (1 < n < N), at time instant kT (See Figure 2.3). N is the total number of measurements points taken in CD and T is the time period between measurements and k is an integer which increases with time. Due to the zig-zag measurement pattern, n (the space variable), either increases or decreases by one depending upon whether the sensor movement is from front to back or from back to front of the machine. This relationship must be kept in mind throughout the thesis. The MD variations are described as: (2.3) where: u is the mean moisture content in the MD; and £jt is a zero mean stochastic process. Note that with good MD control, u should be zero. According to [20] £ can be modelled as a first-order process, £ f c + l = a f Jfc + w f c (2.4) Chapter 2: The Moisture Variation Model where: a is a known constant; and wk is a zero mean Gaussian white noise process with known variance q. Collecting Equations 2.2-2.4 into a state-space form, gives: xjt+i = Axk + Wk „,ri _ n i / w „ I „ . Vk=P +C Xk + Vk (2.5) (2.6) u "1 0' ' 0 " xk = Ah. A = 0 a .wk. where: (2.7) Cn = [(l + Bp") (1 + Bp")] Equations 2.5 and 2.6 are the fundamental equations on which the design of the EIMC algorithm is based. Equations 2.5 and 2.6 could as well be looked at as a stochastic bilinear state-space form. If a bilinear state-space form of the M V M were to be used, a different design approach would have to be taken. A number of bilinear estimation techniques are given in [21]. 9 Chapter 3: The Estimation and Identification Procedure Chapter 3 The Estimation and Identification Procedure 3.1 Exponential multiple scan trending The conventional way to extract the CD profile and the MD variations from the composite profile is done with the Exponential Multiple Scan Trending algorithm (EXPO). In [6] EXPO is presented simply as: D"(m) is the measured moisture content, at scan m and CD position n; Y(m) is the scan average at scan m; iV is the total number of data boxes in CD; s"(m) is the filtered CD profile deviation at position n; and p is the exponential filter weighting factor, 0 < p < 1. To effectively eliminate the MD variations from the CD profile a small weighting factor, in the region p < 0.3, is usually chosen. The EXPO algorithm has been considered to give an adequate performance, according to industrial experience. 3.2 Previous EIMC algorithm and results In [20], a recursive algorithm is developed, with the measured profile deviation at CD position n, ykl, as the input, to estimate the profile moisture value, pn, the nonlinear term B, the MD upset £jt, and the MD average u at each time instant k. The main assumption in the development is that the CD quantities vary slowly in comparison with the MD quantities. The algorithm is based on a bootstrap approach combining a Kalman filter and a least squares algorithm, both derived from the state-space model Equations 2.5 and 2.6. The Kalman filter predicts (3.8) s"(m) = p{Dn(m) - Y(m)) + (1 - p)sn(m - 1) where: 10 Chapter 3: The Estimation and Identification Procedure Least Squares Parameter Identifier for CD Quantities p« g Measurement Prediction Kalman filter for MD quantities •y'k Figure 3.4: Structure of the old EIMC algorithm u and £fc by using the present estimates of p" and B. The prediction from the Kalman filter is then used together with ykl+\ in the recursive least squares algorithm to update p"^ 1 and B. The alternating estimation of MD and CD quantities is continued recursively. The block diagram of this first version of EIMC is shown in Figure 3.4. The equations of the first version of EIMC corresponds basically to Equations 3.30-3.38 with the exception of the least squares equations which were previously based on an Recursive Least Squares algorithm. This version of the EIMC algorithm has been proven to give reasonable results when tested with generated data where the profiles and process values are known. The predicted output was accurate i.e. yk fa yk and therefore small residuals were detected. The estimation of u was unbiased. The shape of the estimated CD profile was correct but the overall amplitude of the profile was wrong. The estimation of the nonlinear term B was clearly biased. It is clear from Equations 2.5-2.6 that the model has a product term involving p, u and B. In [1] it is shown that such a product term can lead to biased estimation. The conclusion drawn from this, is that indeed it can be proved both experimentally and theoretically that B and pn are biased and therefore a new approach is needed. The Kalman filter is kept intact, as its performance is fully satisfactorily. Because of the product term involving both the parameters an independent approach must be taken for the estimation of B. 11 Chapter 3: The Estimation and Identification Procedure To ensure a better estimation of the time-varying parameter pn a modified least squares algorithm will be implemented instead of the classical recursive least-squares algorithm. 3.3 The Exponential Forgetting and Resetting Algorithm It is known that the basic Recursive Least Squares (RLS) algorithm has optimal properties when the parameters are time invariant. The basic approach is however unsuitable for tracking time-varying dynamics as the gain vector converges to zero [23]. With modified versions of the algorithm the gain can be prevented from going to zero. The size of the gain at which the algorithm settles will be a compromise between tracking ability and noise sensitivity [18]. The Exponential Forgetting and Resetting Algorithm (EFRA) [23] has been shown to have superior performance when tracking time-varying parameters. In [23], the EFRA is presented as follows 9(t)=9(t-l) + L(t)e(t), L(t) = aP(t - 1)^(<)[1 + rl>T(t)P(t - l)m]~\ P(t) = jP(t - 1) - aP{t - l)tf>(t) [1 + ^ T(t)P(t - l)^(t)]' (3.9) x ipT(t)P(t -l) + 3I- SP2(t - 1) This algorithm contains four adjustable parameters, but according to [23] it is relatively straightfor-ward to select these constants in practice. The general guidelines are as follows: 1. a adjusts the gain of the estimators, typically a G [0.1, 0.5]; 2. f3 small, directly related to the smallest eigenvalue of P, f3 G [0, 0.01]; 3. A the forgetting factor, A G [0.9, 0.99]; and 4. 6 small, inversely proportional to the maximum eigenvalue of P, 8 G [0, 0.01]. From Equation 3.9 and [8], the identifier for pn is given by (3.10) TVu , (3.11) fc dp A l + * f V M * J + < 3 ' 1 2 ) 12 Chapter 3: The Estimation and Identification Procedure where: ' denotes the estimate of the corresponding quantity; Pk is a N x 1 vector with pk = [p1 p2 • • • pN]T\ and Vfc is the N x N covariance matrix at instant k, with initial value Vq (likewise, po is an initial value for the CD profile). In reading the above equations, the connection between n and k should not be invoked when n does not appear as an explicit superscript. In all such variables all iV (or N x N) cross direction quantities are simultaneously updated from the scalar measurement y\l and its estimate. 3.4 Diverse calculation issues on EFRA matrices In a typical industrial environment, N might be 400 or higher and with a sampling period T = 0.1 second. To reduce the complexity in such an environment, the identifier described in Equations 3.10-3.12 is not used directly. Instead, we reduce its size in order to update pk and Vk locally using only the element corresponding to the CD position n associated with k. Such a local update can be achieved if we place restrictions on Vq and The restriction on Vq is that it should be a diagonal and positive semidefinite matrix. Physically this implies that we assume that adjacent profile points are not correlated. The restriction on will be developed next. From Equations 3.10-3.12 and 2.6, with the understanding that the right hand side of Equation 3.10 is evaluated at pk, we have [20]: where: T" is a N x 1 vector with all elements zero except the element n which is 1. M " is a N x 2 matrix with all elements zero except that in the row n. The non-zero row is given by the matrix $: (3.13) $ = [5 B] (3.14) 13 Chapter 3: The Estimation and Identification Procedure From Equation 3.13, it is apparent that the first two terms have the structure that we seek. However, the third term does not satisfy our requirements since the 2 x N matrix can, in general, have non-zero elements throughout. This is best seen by examining the form of the recursive equation for ^Xfc [9] for the conditions of our problem. In view of this we neglect the third term in Equation 3.13. Simulation results show that this approximation is tolerable. Since we will now be dealing only with the local versions of Equations 3.10-3.12, we introduce some additional notation. V" denotes the entry in Vk corresponding to the covariance of pn while the corresponding entry of is given by: A practical difficulty that arises is that of distinguishing between the target moisture level, and u, the mean machine direction offset. To increase the robustness of the algorithm the following heuristic modification is implemented [20]. At the end of each scan we compute the average of the N values of pn estimated during the scan. This average is subtracted from each pn (to ensure p" = 0) and finally added to the currently estimated u. Intuitively, the above can be seen by 71 = 1 the fact that if the right hand side of Equation 2.2 is averaged over a scan, with P" = 0> w e have u as the approximate result. Note that if the target moisture level is chosen appropriately, the long term average of u should be zero. 3.5 Extraction of the nonlinear term B is estimated separately using the relation between the variance in the moisture level and the moisture level itself at each CD position [12]. For each scan, a least squares fit of the variance for the set of CD positions is made, and a value of the parameter B is calculated. Due to the instrumentation limitations in the industry the measurement data can currently only be provided at the end of a scan so that a precalculated B, based on the latest scan, can be used for the next profile estimation. (3.15) n = l 14 Chapter 3: The Estimation and Identification Procedure From [12], we have, for each CD position n: ay{n) = [1 + Bpn]au(n) (3.16) where c y(n) and cru(n) are the standard deviations of yn and u at CD position n. Using the least-squares method on Equation 3.16, with n = 1,2,..., N, and assuming that au(n) is constant for the cross-section of the paper sheet, i.e. au = cru(n) V n = 1,2,..., N, we can write: • • "I *y(2) = 1 P(2) .*y(N). .1 p(A0-Let C = BCTU, and with summation of Equation 3.17 N E E P(«Vy W iV AT Ar E P(») E P\n) n=l Ar As E P(N) = 0, Equation 3.18 becomes n = l Ar E °"yH H=l Ar E P(n)<r„(n) AT 0 Ar o E P 2 or 1 A ' n=l Ar E P ( " K ( « ) n = l  E P2(«) n = l Thus we obtain: AT £ P ( " K W ° « _ n = l  Q ~~ N N E ay(n) E P 2(") where: <7„(n) = y/(l- - & f + A<(n) - (1 -(3.17) (3.18) (3.19) (3.20) (3.21) (3.22) (3.23) 15 Chapter 3: The Estimation and Identification Procedure and $ = ( 1 - ^ + ^ - 1 (3-24) In Equation 3.22 * indicates the estimate of the corresponding quantity. In Equation 3.23, Oy{n), denotes the variance value from the previous scan at CD position n. Here \i is the exponential forgetting factor in the recursive updating of uy{n) and y'kl. A negative value of B is physically impossible as that would indicate high variance for low moisture content, which is against the assumptions of the model, see property 3 and 4 in section 2.1 and [12]. As well, a negative B would indicate that o-y(n) < au(n). This violates as well the physical properties of the M V M as the process (composite) variations can not be smaller than the MD variations at position n. Thus the nonlinear term can only be defined as B > 0. 3.6 The Kalman filter The Kalman filter gives a minimum variance estimate of the states as the noise terms in Equations 2.5 and 2.6 are assumed to be gaussian. In [9] the Kalman filter is presented as follows: x(t + 1) = Ax(t) + K{t)[y{t) - Cx(t)] + Bu(t) x(t0) = x0 K(t) = [AE(t) + S] [CE(i )CT + R]_1 E(t) 4 E{[x(t) - x(t)][x(t) - x(t)]T\y(t - 1), y(t - 2),. • ,y(to)} (3.25) (3.26) (3.27) (3.28) E(r) denotes the state error covariance and K(t) is the filter gain. The Kalman filter design used for EIMC, for estimating xk, is based on Equations 3.25-3.28. Note that in Equation 2.6, the covariance of Wk is given by Q in the following equation with q\ = 0. Q = (3.29) " 9 1 0" .0 q\ However, with q\ = 0, the gain for u will asymptotically go to zero. To avoid this a small value of q\ is used, g = 9M£»(l — a2) where qMD is the MD variance and a is the constant from Equation 2.3. 16 Chapter 3: The Estimation and Identification Procedure yjj (Raw Data) Extraction of B Least Squares Parameter Identifier for CD Quantities £n Measurement Prediction Kalman filter for MD quantities (Estimated Data) Figure 3.5: Overall structure of the improved EIMC algorithm 3.7 The EIMC algorithm structure The overall structure of the modified algorithm is shown in Figure 3.5. Finally, the improved version of the algorithm is given in Equations 3.30 through 3.38 following the evaluation order. On the first pass through these equations, all variables not defined earlier are to be provided as initial estimates. When the same variable appears on both sides of an equation, the current value of the variable is to be used in evaluating the right hand side. The averaging operations on p" and the calculation of new B at the end of each scan are not shown in the equations below. h V" l + Bh —Vn -A 1 + Vn(ift)' + (3- 6(V"Y Pn = p" + C" 1+ (</>£) ( l + 5p")[ l 1] AZCnT C"EC» T + R (3.30) (3.31) (3.32) (3.33) (3.34) (3.35) 17 Chapter 3: The Estimation and Identification Procedure F E C«EC» r + R in E C " T C " E (3.36) (3.37) Fxk^+Kk{yl-pn) (3.38) In the equations above " indicates the estimate of the corresponding quantity. V " is the covariance matrix at instant k. a, 8, 8 are constants of EFRA, controlling the performance the algorithm, and A is the forgetting factor of EFRA. E and K are the covariance and the gain respectively of the Kalman filter. The algorithm requires considerable computation, however the local update procedure means that a minimum number of calculations needs be carried out at each stage. The most complex set of calculations is carried out at the edge of the sheet at the end of a scan. In practice, extra time is available at the conclusion of each scan since the sensor spends some period off-sheet. 18 Chapter 4: Results using Simulated Data Chapter 4 Results using Simulated Data In simulations, where both the process and the measurement procedures are simulated, we have knowledge of the true profiles and other parameters estimated by the EIMC. Thus the performance of EIMC can be evaluated and as well compared to the results from the EXPO algorithm. 4.1 The setup of EIMC A sine wave with amplitude one is used as the simulated profile. The process (measurement) is modelled by Equations 2.2-2.4 with the simulated sine wave as the true CD profile shape. The settings for the process data, for 200 scans with target (setpoint) value 5.0, is N = 50, a = 0.85, q = 0.04, R = 0.005, u = 0.50 and B = 0.40. The initial parameters and states for the algorithm are chosen as: pn = yn, l<n<N (first scan) B = 0.50, (scan one to five) '0" '0.30 0 " X = E = 0 0 0.40 Vn = 1000, 1 < n < N As the EIMC algorithm needs to be initialized, the first estimate B is available at scan five, n is chosen as 0.95 in the recursive updating of o-y(n) and ykl for the least squares extraction of B (Equation 3.22). E is the covariance matrix of the Kalman filter. Vn is the covariance scalar of EFRA. In [23], the choice of the EFRA constants a, 3 and 8 is discussed. The constants which give the most desirable features for EIMC in the following simulations are a = 0.5, (3 = 0.05 and 8 = 0.00005. The forgetting factor of EFRA is chosen as A = 0.95. 4.2 Results using EIMC The simulation results are shown in Figures 4.6-4.12. Note that for all 3-dimensional profile plots that follow, the MD axis (Scan) is greatly compressed compared to the CD axis (Data box). 19 Chapter 4: Results using Simulated Data Figure 4.6: Raw data for the simulated data 20 Chapter 4: Results using Simulated Data Figure 4.7: Estimated CD profiles for the simulated data 21 Chapter 4: Results using Simulated Data The raw measured data (the input) from the simulated sensor is shown in Figure 4.6 and the estimated CD profiles (the output) are shown in Figure 4.7. The sine wave profile is successfully extracted from the noisy input after about five scans. In Figure 4.8 the raw profile and the estimated CD profile at scan #30 are compared, the noise has been removed and the shape of the estimated CD profile corresponds well to the original sine wave profile. „ r Raw CD prof i le „ c Est imated CD prof i le 2.5 l 1 j 2.5 l " ' Figure 4.8: Raw CD profile and estimated CD profile at scan #30 U (Figure 4.9) converges to the correct process value of 0.50. B (Figure 4.10) converges to the correct process value of 0.40 as well. B is extracted by a least-square method so the coefficient of determination [22], r 2 , can be used as a performance meter of the extraction. A value of the coefficient of determination close to one would indicate a nearly perfect correlation of the variables used for the extraction. Figure 4.11 shows that the coefficient of determination is close to one which indicates a good confidence in the extraction of the B term. Figure 4.12 shows the autocorrelation of the residual sequence out of the Kalman filter and indicates that all the information about the states and parameters has been successfully extracted by EIMC, since the autocorrelation is nearly white. By using the modified version of EIMC, the algorithm now gives unbiased results for the key process parameters B and u in about ten to twenty scans. As the initial pn values are equal to the initial measured profile deviations, ykl, the estimation of the CD profile converges quickly to the correct profile. 22 Chapter 4: Results using Simulated Data 1.0 0.8 0.2 0.0 True MD variations Estimated MD variations -0.2 —1 L_ 50 100 Scan 150 200 0.60 Figure 4.9: Estimated u for the simulated data 0.50 E-i 0.40 0.30 0.20 0.10 True B Estimated B 0.00 50 100 Scan 150 200 Figure 4.10: Estimated B for the simulated data 23 Chapter 4: Results using Simulated Data Measurement Lag Figure 4.12: Autocorrelation for the simulated data 24 Chapter 4: Results using Simulated Data Other simulations with different initial conditions and diverse simulated profiles give the same results of convergence and robustness of EIMC. It should be mentioned here that without knowledge of the target value, the estimated parameters and states becomes biased, and depend on what the assumed target value is. In industry the objective is to keep the moisture content at a given target value so the target value will always be known in industrial application of EIMC. 4.3 EIMC versus exponential multiple scan trending Here the same simulated data set is used as in section 4.2. In Figure 4.13 it can been seen that the behaviour of the estimated MD variations, u, is similar for both methods, although EIMC has clearly a smaller variance of the estimate. In Figure 4.14 the CD profile at scan #150 is shown Scan Figure 4.13: The MD variations out of EIMC and EXPO for the simulated data both for the EXPO method with p = 0.2 (a conservative weighting value) and EIMC with (3=0.05. The true CD profile shape is included as well. It is quite obvious that the CD profile estimated by EXPO has wrong profile amplitude and is distorted, which is caused by the inability to detect the nonlinear behavior in the data. From Figure 4.15 it can be seen that there is an off-set in the standard 25 Chapter 4: Results using Simulated Data •1.5 —i—i—i—i—r 10 True CD profile Estimated EIMC CD profile Estimated EXPO CD profile 20 30 Scan 40 50 Figure 4.14: CD profile at scan #150 for EIMC and EXPO for the simulated data 1.0 0.4 0.2 0.0 fV Is • • • a of sinusoidal profile a of EIMC CD profile a of EXPO CD profile 50 1 • i i 100 Scan _i 1 1 i 150 200 Figure 4.15: Standard deviation for EIMC and EXPO for the simulated data deviation from the "true" value of 0.707 for the EXPO method, but with EIMC a fairly good value of standard deviation is achieved. Figures 4.16-4.17 show the residual sequences out of both algorithms. The variance of the residuals are o\XPO = 0.045 and o\1MC = 0.040, thus the variance out of EIMC is smaller. 26 Chapter 4: Results using Simulated Data 2000 4000 6000 Measurement number 8000 10000 Figure 4.16: Residuals from EIMC for the simulated data 2000 4000 6000 Measurement number 8000 10000 Figure 4.17: Residuals from EXPO for the simulated data Figure 4.18 shows that the autocorrelation of the residuals of EXPO contains some low frequency harmonics. The conclusion regarding the performance of EXPO in estimating simulated data is that EXPO is insufficient in estimating the true CD shape as EXPO does not take into account the inherent process 27 Chapter 4: Results using Simulated Data 1.0 I 1 1—' 1 1 1 1 1 1 1 1 1 1 1 ' 1 1 1 ' — 0.8 -0.6 -0.4 -0.2 --0.2 L i , i i , i , i , 0 200 400 600 800 1000 Measurement Lag Figure 4.18: Autocorrelation of the residuals from EXPO for the simulated data nonlinearity. The EIMC algorithm clearly outperforms EXPO in extracting the correct states and parameters for simulated data. The next step is to evaluate the performance of EIMC for industrial data sets, but first various industrial implementation issues need to be clarified. 28 Chapter 5: Industrial Implementation Issues Chapter 5 Industrial Implementation Issues Before applying the EIMC algorithm, to a real paper machine, a few practical problems have to be studied. The main and most important problems that affect the performance of EIMC will be discussed individually in the following sections. 5.1 Knowledge of the moisture target value It should be mentioned here that without knowledge of the "true" moisture target (setpoint) value, Mr, the estimated parameters p" and the nonlinear term B become biased. This depends on the assumed target value. The distortion of a sinusoidal profile estimated by EIMC with different target values can been seen in Figure 5.19. The same simulated data set as in section 4.2 is used. It can be seen that the amplitude of the distortion increases as a function of the target value mismatch. Figure 5.20 shows how biased B becomes with wrong target values, u + M , (See Figure 5.21) reveals the true MD variations of 5.50 thus u is independent of the target value. 1.5 - i — I — I — i — I — r — Target = 6.0 Correct Target = 5.0 Target = 4.5 Figure 5.19: Estimated CD profile shape with different target values for simulated data 29 Chapter 5: Industrial Implementation Issues 0.60 0.50 En 0.40 '— 0.30 0.20 0.10 0.00 True B Correct Target = 5.0 - Target = 6.0 -• Target = 4.5 50 100 Scan 150 200 Figure 5.20: Estimated B with different target values for simulated data 'o True MD Correct Target Target = 6.0 Target = 4.5 5.0 50 100 Scan 150 200 Figure 5.21: Estimated u with different target values for simulated data It can be stated that in industry the objective is to keep the moisture content at a given target value. The target value will thus always be known in an on-line industrial application of EIMC and the estimated parameters and states will then reveal the true variations trends. 30 Chapter 5: Industrial Implementation Issues 5.2 Spikes in autocorrelation The general formulation of the autocorrelation function is, Ryy(k) = ^ y y ^ , where: 1 JV-fc Cyy(k) = -Y,{yT-yT){yT+k-yT+k) k = 0,1,2,..., K (5.40) The periodic spikes in the autocorrelation of the residuals out of EIMC (see Figure 4.12 and later, Figures 6.36 and 6.55) can be explained as a cause of the measurement process. The scanning device traverses back and forth over the paper sheet and to reveal an equal distance time-lag (see Figure 5.22) between two measurement points, the sensor has to traverse back and forth at least once. Al l the measurements taken at scan #4 in Figure 5.22 have the same time-lag to corresponding measurements taken at scan #2, thus every 2JV point in the measurement sequence is correlated. The periodic spikes in the autocorrelation correspond to multiples of 2N. CD (sensor) Time Figure 5.22: Explanation of the spikes in the autocorrelation function 31 Chapter 5: Industrial Implementation Issues 5.3 Scan direction Another issue is the scan direction and how wrong knowledge about the scan direction affects the time and calculation sequences. At this time and during the mill trial this issue was important, but in an overall integrated estimation system which should be designed in such a way that all relevant variables, such as time stamps and scan direction, were accessible this problem would not arise. It is hard to detect the true scan direction sequence just by looking at the data sequence. By analyzing the simulated data set in section 4.2 in both the true time sequence and the wrong time sequence, at least a slight indication of the effect of wrong time sequence can be revealed. Figure 5.23 shows the residuals out of EIMC when the wrong time-sequence is used. 2000 4000 6000 Measurement number 8000 10000 Figure 5.23: Residuals from simulated data with wrong time sequence There is a slightly higher variance value for the wrong direction, a2 = 0.042 compared to aElMC = 0040 (from Figure 4.16) for the correct scan direction. The autocorrelation of the residuals does not show any difference. There is no noticeable difference in the estimation of u and B. The profile shape is the same in both cases, but just with a slight amplitude difference. Note here that the only variable that is directly time dependent is £k-32 Chapter 5: Industrial Implementation Issues For the industrial data analysis the initial scan direction is always chosen the same i.e. from the left side (L) to right side (R) of the paper machine and thus the next scan direction will be from R to L and son on. In the mill trial the scanner was always started and restarted from the left side of the paper machine. Thus the mill data is very close to a true scan direction sequence. 5.4 Effect of sensor time constant, r The filtering effect of a sensor is modelled by [16]: y(n, k) = (1 - d)ym(n, k) + dym(n ± 1, k - 1) (5.41) where: y(n, k) is the filtered value that represent the composite measurement; ym(n, k) is the measured value; ym(n ± 1, k — 1) is the measured value at the previous sampling instant (fc — 1). n i l denotes the CD-position of the sensor head at (k — 1); d is the combination of the measurement circuit time constant, r, and the scan speed. The effect of the time constant is tested on data simulated by using the M V M with a uniform profile shape with two symmetrical unit impulses instead of the sinusoidal profile shape used in section 4.1. The estimated profile is shown in Figures 5.24-5.25 for two different time constants. 1.0 0.5 0.0 -0.5 -1.0 0 10 20 30 40 50 Figure 5.24: Estimated CD profile, r = 0.2seconds 33 Chapter 5: Industrial Implementation Issues i . o l ! -ml I 0 10 20 30 40 50 Figure 5.25: Estimated CD profile, r = 0.5 seconds Time constant, r Impulse #1, Amplitude = 1.0 Impulse #2, Amplitude = -1.0 0.0 0.953 -0.970 0.1 0.947 -0.957 0.2 0.902 -0.876 0.5 0.707 -0.651 1.0 0.498 -0.467 Table 5.1 Effect of different time constants on the estimated CD profile amplitude Here it is assumed that the measurement time is T = 0.4 second so d = e - 0 4 / T . The effect of the time lag cancels out because of the L to R, R to L measurements, but the amplitude of the CD profile impulses decreases. The estimates of u and B behaves well. Table 5.1 shows the amplitude change of the estimated CD profile for different r's. For a longer time lag the amplitude is lower. These results shows that the EIMC is not dependent on the sensor time constant beside the CD profile shape. It could be possible to implement some sort of compensation of the wrongly estimated CD profile amplitude, if the time constant were known. 5.5 Timing of measurements and scan speed An important issue in the industrial data collection is to keep track of the measurement times. There can be different scan speeds from R to L and from L to R of the paper machine. Both these 34 Chapter 5: Industrial Implementation Issues effects can cause wrong estimates and control action. The scanning device is not a continuously running system, so the sampling rate at the edges of the paper machine is nonuniform due to calibration breaks. As the scan speed can be different we could experience nonuniform sampling depending on the scan direction. The nonuniform sampling rate of the raw composite data should be kept in mind when frequency analysis are done in section 6.3. 5.6 Paper sheet movement Paper sheet movement can both cause a distorted data box frame i.e. misalignment between the sensors and actuators, and loss of databoxes at the edges. The EIMC algorithm should thus only use measurements from valid data boxes which if possible should have a time and a space stamp for accurate estimation. 5.7 Diverse issues 5.7.1 Bounds on parameters and states So far it has not been necessary to put bounds on the parameters and the states except for a lower limit of the nonlinear term B. In the industry reasonable bounds will have to be implemented as safety limits. 5.7.2 Computation time The new modified version requires less calculations than its predecessor as the updating is done locally and is therefore easier to implement in the industry. A real time version of EIMC, using the QNX operating system, is already available on a portable computer for on-line testing in the paper industry. Although the EIMC needs considerable computation, preliminary tests on the portable computer implies that a 20MHz 80386-based computer should give adequate response speed. 35 Chapter 6: Analysis of Industrial Data Chapter 6 Analysis of Industrial Data The development of EIMC is a part of a collaborative research project between The University of British Columbia (UBC), Devron Hercules Inc. (DHI), and The Pulp and Paper Research Institute of Canada (PAPRICAN). The industrial partner, DHI, has been providing industrial data collected from a variety of paper machines. These various industrial data sets [10] have been used to validate the modified EIMC algorithm off-line. The data sets presented here were obtained from two paper machines with the moisture control systems in automatic and manual mode respectively. Furthermore, extensive field test of the EIMC took place in June 1991 and the results from those tests have been thoroughly analyzed and will be presented here as well. The initial states, parameters, the covariance matrices and the settings of EFRA are the same as for the simulated data in chapter 4. The process values, q = 0.40, R = 0.01 and a = 0.85, will be used to describe the moisture variations for a paper machine [20]. On industrial data, there is no knowledge of the true MD variations and CD profiles (such knowledge would make the EIMC redundant) and so the results obtained for industrial data sets cannot be verified as on simulations. 6.1 Moisture control systems in both automatic and manual mode This data set were collected on a paper machine manufacturing fine grade paper with 3.4% moisture content to be either used as photo copying paper or base coat paper. The 7-meter wide headbox is from Valmet and the design speed is at 968 m/minute. The CD moisture control system is a Devronizer (steam box actuator control system from DHI) with 46 actuators, each with a width of 15.24 cm. The speed of the scanning device across the sheet is 45 seconds. Figures 6.26-6.28 show the results when the EIMC is applied to the data set with both the MD and the CD moisture control systems in automatic mode. At scan #25 the pressure to the steam boxes is set to 50% of full scale. At scan #36 a step-change of the pressure from 50% to 100% is given. The number of CD points (N) is 113 and the number of scans is 60. 36 Chapter 6: Analysis of Industrial Data 6 f Figure 6.26: Raw moisture data for control in both automatic and manual mode Figure 6.27 shows the estimated CD profiles obtained from the raw moisture data in Figure 6.26. The CD profile converges rapidly to a constant shape which corresponds well to the assumption of slow CD variations [15]. The streak at databoxes 40-45 in the CD profile is easily detected. The estimation of u (Figure 6.28) detects the process upsets in the MD approximately 10 scans after the second bump test. This delay is due to a long process response. Note although that the first changes of the pressure at scan #25 does not show up either in the raw moisture data nor in the u state. At scan 51 the MD variation is at it's peak level and after that the MD controller actions alter the trend towards the setpoint value of zero MD variations. As the actuators change is the same across the paper machine, the CD profile should not change which is correctly revealed 37 Chapter 6: Analysis of Industrial Data Chapter 6: Analysis of Industrial Data Scan Figure 6.29: Estimated B for control in both automatic and manual mode 39 Chapter 6: Analysis of Industrial Data 6.2 Moisture control system in manual mode This data set were collected on a pulp machine manufacturing thick pulp (target grammage 640.6 g/m2) with a wide 15 cm. slice lip opening at the headbox. The 4.42 m wide counter flow headbox is from Beliot and the design speed is at 184 m/minute. The manufacturing target per day is 905 metric tons of pulp. The CD moisture control system is again a Devronizer with 25 actuators, each with a width of 15.24 cm. The scanning device in this case traverses two times across the sheet before it updates, every 68 second, the measured raw profile. Figure 6.30 shows the image of the raw moisture data for this pulp machine with the moisture control system in manual mode with two actuators bumps. The horizontal axis of the image shows CD position and the vertical axis corresponds to the scans, with scan #4 at the bottom. In the color history plots, the variation in each profile (image) is quantized into 256 levels and each level is assigned a color value. See as well the explanatorily color bar beside the image. The moisture variation varies from a low of 2.90% (dark blue) to a high of 10.70% (white). The number of CD points (N) is 118 and the number of scans is 60. The bumps at scan #25 are easily detected by the algorithm, with the EFRA constant (3 = 5.0, as can been seen in Figures 6.31, 6.32 and 6.33. Figure 6.31 shows the image of the estimated CD profiles obtained from the raw moisture data in Figure 6.30. The light areas are high moisture values and the dark areas are low moisture values. Figure 6.32 shows a horizontal cross-section of Figure 6.31. The deviations around databoxes 20 and 87 shows the bumps in the moisture CD profile. From Figure 6.33, which shows a vertical cross-section of Figure 6.31, the bump detection in MD is shown for two different settings of the parameters in EFRA. /3 is changed to 5.0 (increasing the lower limit of EFRA's covariances matrix) to make EIMC more sensitive to CD profiles changes, but the cost of this is a more noise-sensitive algorithm. The estimation of u (Figure 6.34) detects the process variations in the MD due to the bump tests at the beginning of the scanned data. The estimated value of B is shown in Figure 6.35. B reaches its lower limit between scans 18 and 20 where the upsets in MD are most severe (Figure 6.34) i.e. where iik is changing rapidly during the scan and thus violating the assumptions of the M V M . 40 Chapter 6: Analysis of Industrial Data 12 8 6 -, 1 • 1 1 • i i i i i . i , • • i • i i Row CD profile — — — - Estimated CD profile — ft ' v A I ~ \}\A \\ A . ,i\kMh AI A r A XJ }Y / ^ / i \ 1 Ni V \ <N-" » v J \ r\ ki'\i ' V -i \\A / i . . . i 0 20 40 60 80 100 120 Databox Figure 6.32: Raw profile and estimated CD profile at Scan #25 for CD for control in manual mode. (Note, that u « 0) Scan Figure 6.33: Data box #20. Bump detection with two different settings of EFRA for CD control in manual mode 43 Chapter 6: Analysis of Industrial Data 0.50 0.40 F-0.30 0.20 E-0.10 o.oo E Scan Figure 6.34: Estimated u for control in manual Scan Figure 6.35: Estimated B for control in manual 44 Chapter 6: Analysis of Industrial Data 1.0 0.8 -0.6 0.4 0.2 0.0 -0.2 -0.4 0 200 400 600 Measurement Lag 800 1000 Figure 6.36: Autocorrelation of residuals for control in manual The autocorrelation, shown in Figure 6.36, of the residuals confirms that useful data is extracted, with the exceptions of the periodic spikes in the correlations corresponding to multiples of the scan average period and some indication of colored noise. The residuals could be whiter by fine tuning the a parameter. The fine tuning of EFRA is still under investigation, but so far the algorithm has been robust under extreme industrial conditions. 45 Chapter 6: Analysis of Industrial Data 6.3 On-line testing at a mill This section describes the results obtained using the EIMC on a modern newsprint machine for both open-loop and closed-loop, cross-machine control of a profiling Devronizer (steam box actuator control system from DHI). The trial was performed in cooperation between UBC and DHL The objectives of the Control Trial where; to evaluate the EIMC performance at estimating the machine direction and cross-machine direction moisture variation using on-line composite moisture profiles, and to evaluate the EIMC ability to detect cross-machine moisture changes caused by manual changes in the profiling Devronizer's set points. The performance of the EIMC was assessed when used for closed-loop CD control of the Devronizer compared to the performance achieved with a conventional CD estimation system (EXPO). During the mill trial other paper machine variables, such as basis weight and caliper, where collected and for comparative purposes, to the moisture, the analysis of these variables is included here as well. Finally, for further insight into the behaviour of the various paper machine variables, single point data are analyzed. The single point data where collected from the same newsprint machine (as where the Control Trial took place) but at an earlier date. The mill, chosen for the control trial, is designed for an annual newsprint production of 220 000 tonnes per year. The paper machine is a Voith 8.4-metre-trim, twin-wire machine with a design speed of 1150 m/min. The speed of the scanning device across the sheet is 48 seconds. The CD moisture control system is again a Devronizer with 88 actuators, each with a width of 10 centimeters. During the mill trial, the EIMC algorithm was run on a portable computer (the industrial version of EIMC has been implemented by Mr. Fariborz Ordubadi) connected to the main Devron control computer. The EIMC received raw moisture composite profiles and returned the estimated CD moisture profile and an estimate of the MD variation each scan. The EIMC was first run in parallel with the standard Devron control system during standard closed-loop control and during the bump tests. Finally, the system was switched to control the Devronizer while using the estimated CD profiles obtained from the EIMC algorithm. 46 Chapter 6: Analysis of Industrial Data The data used in this section consists of 334 scans which have been patched together from five different test periods taken from the mill trial. The data set has minimal sheet breaks. The total number of data boxes (N) is 480. Period 1. Scan #0-59. Automatic control with estimates from the conventional algorithm (/9=0.2) and with conventional control tuning parameters. Period 2. Scan #60-108. Automatic control with estimates from the EIMC algorithm (settings as in section 6.1) with 0=5.0) and the control tuning parameters the same as for Period 1. Period 3. Scan #109-170. Manual control with estimates from the EIMC algorithm and the control tuning parameters the same as for Period 1. Steam boxes bumps were introduced at scan #133. Period 4. Scan #171-234. Automatic control with estimates from the EIMC algorithm and the control tuning parameters the same as for Period 1. Period 5. Scan #235-333. Automatic control with estimates from the EIMC algorithm and with new control tuning parameters based on the bump test during Period 3. Due to other test that were performed on the paper machine by other vendors the data collected from the edges of the paper machine is here discarded. The data box range used in the analysis is therefore from data box #40 to data box #430, i.e. N = 391. During the mill trial, the extraction of the nonlinear term B was confined to data boxes 22-430. Figure 6.37 provides a color history of the unfiltered, raw moisture variations over the 334 scans. The data set has here been greatly compressed and the real ratio of paper passed during one scan versus paper sheet is 960 m:8.4 m or 115:1. This means that the true scan axis in the color images should be 7.6 km. The actual length of paper evolved during the 334 scans is 321 km and the weight is 135 tons. The dark blue/purple color corresponds to low moisture content (dry paper) and the light green/white corresponds to high moisture content (wet paper). In Figure 6.37, the moisture variation varies from a low of 4.95% (dark blue) to a high of 9.49% (white). See as well the explanatorily color bar beside the image. The color contour plot clearly shows stable streaks in the MD direction present over the entire set of scans (i.e. at data boxes 98, 291, 397, 410 etc.). Figure 6.37 also shows 47 m Chai 'P'er 6 . mm W moistur 4S o Q Chapter 6: Analysis of Industrial Data 9 I ' ' ' ' 1 ' ' ' ' r Measurement point (*103) Figure 6.38: Time-sequence of the raw moisture for Period 4, Mill Trial some significant MD upsets occurring between scans 190 and 266. The upsets are across the entire machine and show a transition from dry to wet and back to dry before the upset recovers. During this MD upset, which is approximately 2 percent peak-to-peak, the variation trend in the paper sheet is not continuously going upwards or downwards. Instead the large swings in reel moisture oscillates with a periodicity of a little more than two scans which can be implicitly seen in Figure 6.38, which shows the time-sequence of the raw moisture variation for Period 4 (scans 181-230). Figure 6.39 shows the power spectrum of the raw moisture variation for Period 4. This analysis separates the variation into its component sinusoidal frequencies and determines how much each component contributes to the total variation. There is a clear spike in the spectra at frequency 1.22 * 10~3 Hz which correspond to the time-period of 81.9 second. The time-period for the scanner to go back and forth is 78.2 second, thus the spike almost reveals the scanning process. A possible source for this spike is that the MD controller only takes control action at the end of each scan and if the controller is badly tuned or poorly designed the response to the control signal will be slow and reveal a trend as can be seen in Figure 6.38. So the low frequency reflects the poor MD control performance. Figure 6.37 also shows the results of six Devronizer bumps (of ±50%) introduced at scan 133. Increasing the Devronizer set points cause the sheet to become dryer (i.e. data boxes 145-160) while decreasing the set points 49 Chapter 6: Analysis of Industrial Data Hz Figure 6.39: Power Spectrum of the raw moisture for Period 4, Mill Trial cause the sheet to become wetter (i.e. data boxes 335-360). Figure 6.40 shows the color image of the Devronizer set points over the 334 scans. This Figure 6.40 clearly shows regions of automatic control (scans 0-100 and 180-334) and as well the Devronizer bumps introduced at scan 133. Figure 6.41 provides a trend of the raw moisture scan averages compared to the estimates of the MD moisture variation obtained from the Kalman filter. The algorithm clearly tracks the MD variation even through the large upsets at scans 210 and 260. The EIMC MD estimates are available at a much faster pace than on a scan interval basis. Figure 6.42 shows the time-sequence of the estimated MD variations from the EIMC for Period 4 (scans 181-230). Here the large swings in reel moisture, from Figure 6.38, can be clearly seen. The EIMC estimate tracks the upsets implicitly and reveals the trend of MD variation on a measurement point basis. Figure 6.42 shows as well the time-sequence of the estimated MD variation out of the exponential filter. The information content of the EXPO MD estimates is quite low in Figure 6.42 as high frequency variations have been filtered 50 Chapter 6: Analysis of Industrial Data 1.0 I—'—'—'—'—i—'—1—'—'—r~'—'—1—•—i—1—1—1—1—i—1—1—1—1—i—1—1—•—1—r Measurement point (*103) Figure 6.42: Time-sequence of the raw moisture, the scan average, and the estimated MD variations from EIMC for Period 4, Mill Trial out. EIMC clearly outperforms the exponential filtering method as the conventional filter can only provide an MD estimate at the end of each scan. Figure 6.43 shows the power spectrum of the estimated MD variation out of EIMC for Period 4. There is a clear spike in the spectra at frequency 52 Chapter 6: Analysis of Industrial Data K M 10-3 10-2 io-i 1Q0 Hz Figure 6.43: Power Spectrum of the estimated fast MD variations using EIMC for Period 4, Mill Trial 1.22 * 1 0 - 3 Hz which corresponds to the time-period of 81.9 second. This frequency is the same as was detected for the raw moisture variations (See Figure 6.39) and the shapes of the power spectra of the raw moisture data and the estimated MD variations is the same for the low frequency range. Thus EIMC is fully capable of extract the MD variation from the composite signal. Figure 6.44 provides a color image of the estimated CD moisture variation from EIMC. The stable MD streaks are still present and more evident than in Figure 6.37 as the raw data is filtered. The random, scan-to-scan variation has been considerably reduced. The Devronizer bumps after scan 133 are clearer and better denned than in Figure 6.37. Also, the EIMC has prevented the MD upsets between scans 190 and 266 from affecting the CD profiles (i.e. the MD variations has been truly separated from the CD profiles). Here the estimated CD profile varies from a low of about 5.7% (blue) to a high of approximately 8.5% (white). In Figure 6.45, the EXPO estimated CD profile varies from the same low and high values as for the EIMC estimated CD profile. The main differences 53 Chapter 6: Analysis of Industrial Data 0.50 F-1—'—'—'—i—'—'—'—'—i—1—'—1—'—i—1—'—1—1—i—'—1—'—1—i—'—1—'—'—i—'—'—'—1 -0 50 100 150 200 250 300 350 Scan Figure 6.46: Estimated B, Mill Trial between the estimated CD profiles is that the exponential filter clearly picks up the MD variations as CD variations. This can been clearly seen in the period (scan 190-270) where the MD upsets occurs. If the high and low values for this region (scan 190-270) are investigated further it reveals higher variance for the exponential filter as that filter picks up the MD variations. The high and low values of the estimated CD profile are about 50% higher in magnitude than for the estimated CD from EIMC. Figure 6.46 shows the estimation of the nonlinear term B. The B term reveals the MD variation trend and the average value is around 0.11. This data set unveils the limitation of EIMC. As a result of the big MD upsets the extraction of B becomes negative. For those regions where B becomes negative the approximation is made that there is no nonlinearity in the process and thus 5 = 0 (See section 3.5). For other data sets, where MD was more stable, for the same paper machine the value B = 0.13 was also the average. Thus it can be stated that this particular paper machine has a process value of B around 0.13. Figures 6.47-6.48 show a composite raw moisture profile, obtained by averaging, over 25 scans (taken from period 1) for the Devronizer under control based on estimates from the exponential filter and when using estimates from* the EIMC (25 scans, taken from period 5). The average moisture profile shows a reduction in variation when under control based on the EIMC estimate. 56 Chapter 6: Analysis of Industrial Data 8.0 I — 1 — 1 — i — 1 — 1 — i — ' — ' — i — 1 — 1 — i — ' — 1 — i — ' — 1 — i — ' — 1 — i — 1 — ' — i — ' — ' — i — ' — ' — i — ' — ' — i — 1 — ' — r 7.5 <t> 3 o 7.0 6.5 6'°40 70 100 130 160 190 220 250 280 310 340 370 400 430 Data box Figure 6.47: Composite raw profile (la = 0.353) for scans 46-70, Mill Trial 8.0 7.5 -6.0 - i — i — i — | — i — i — | — i — i — | — i — i — r — > — . — | — . — i — | — • — i — | — i — i — | — i — i — | — i — i — i — i — i — r _J—i i i i i i i i i i i i . i i i i i i i i i i i i . i . . i . . i 40 70 100 130 160 190 220 250 280 310 340 370 400 430 Data box Figure 6.48: Composite raw profile (2<r = 0.307) for scans 306-330, Mill Trial This improvement may be a result of better control or just a reduction in the residual component over the data set. Standard deviation is one indicator of the variability of the data set. Figure 6.49 provides a plot of the instantaneous 2a (calculated on each scan) for the overall data set for the raw moisture. The 57 Chapter 6: Analysis of Industrial Data 0.6 0.4 -0.2 -0.0 50 100 150 200 Scan 250 300 350 Figure 6.49: 2a of the raw moisture for each scan, Mill Trial 1.4 1.2 1.0 -- i 1 1 1 r -EIMC estimate EXPO estimate 0.2 0.0 50 100 150 200 Scan 250 300 350 Figure 6.50: 2a of the estimated CD profiles using EIMC and EXPO, Mill Trial 2a is calculated for the data box region 40-430 for each scan. The raw moisture profile exhibits considerable scan-to-scan variability as a result of the random components. The 2a for the exponential filtered and the EIMC CD estimated profiles, shown in Figure 6.50, exhibit less variations than for the raw moisture. The 2a of the CD moisture profiles from the exponential filter is higher than that 58 Chapter 6: Analysis of Industrial Data 50 50 100 150 200 250 300 350 Scan Figure 6.51: MD variations in data box #157 of the estimated CD profile using EIMC, Mill Trial of the estimation from EIMC and clearly shows the effect of the MD upsets between scans 190 and 266. The EIMC 2a is both smoother and lower than for the exponential filter and shows only a high 2a during the bump tests between scans 133 and 170. Thus EIMC reflects the true CD variations better than the exponential filter. Figures 6.51-6.52 shows how the EIMC tracks changes in CD moisture in a given data box corresponding to changes introduced by the Devronizer bumps (introduced at scan 133). The raw moisture measurements in a given data box show considerable random variation. In contrast, the estimated CD variation shows much less random variation while still closely tracking the bumps. The speed at which the EIMC follows CD changes depends on the 3 EFRA value and must be traded-off against the ability of the EIMC to reject random variations. In this case, fairly good CD tracking has been achieved with an acceptable reduction in the random moisture variation. Figures 6.53-6.54 shows the residuals (composite estimated profile - measured profile) from both the filtering methods for Period 4. The residuals from EIMC are smaller in magnitude (cr2 = 0.0315) and more random than the residuals {a2 = 0.0885) from the exponential filter. As well, Figures 6.55-6.56 shows the autocorrelation of the residuals shown in Figures 6.53-6.54. The characteristics of the EIMC autocorrelation function is clearly more random than for the exponential 59 Chapter 6: Analysis of Industrial Data — i r — i r— Raw data Estimated EIMC dat<p 50 100 150 200 Scan 250 300 350 Figure 6.52: MD variations in data box #282 of the estimated CD profile using EIMC, Mill Trial 10 15 20 Measurement point (*103) Figure 6.53: Residuals for Period 4 using EIMC, Mill Trial filter which reveals a low frequency content. The EIMC residual indicates that more information has been extracted from the data than in the case of the exponential filter. As part of the overall analysis of this specific paper machine and to reveal a better insight into the interconnection of the moisture content to other descriptive paper machine variables, such as 60 Chapter 6: Analysis of Industrial Data 1.5 1.0 0.8 0.6 0.4 0.2 10 15 Measurement point (*105) Figure 6.54: Residuals for Period 4 using EXPO, Mill Trial o.o t^^|4^^.^vn 20 -0.2 200 400 600 Measurement Lag 800 1000 Figure 6.55: Autocorrelation of the residuals for Period 4 using EIMC, Mill Trial basis weight, dry weight and caliper, some analysis results for these variables will be presented here. Figure 6.57 shows a color image of the basis weight variations over the 334 scans. The stable streaks evident in the raw moisture (Figure 6.37) are also present in the basis weight. The MD variations in the basis weight are also clearly evident (i.e. at scans 135 and 214-233). Figure 6.58 provides 61 Chapter 6: Analysis of Industrial Data 400 600 800 1000 Measurement Lag Figure 6.56: Autocorrelation of the residuals for Period 4 using EXPO, Mill Trial the color history of the dry weight variations. Here too, the MD streaks present in the moisture are clearly evident in the dry weight for the entire data set. Figure 6.58 shows significant MD variations in the dry weight over the whole data set and especially at scans 135 and 240. Figure 6.59 shows the image of the raw caliper profile variation over the 334 scans. Caliper cannot be measured as an absolute value as it is impossible to caliber the sensor. So the caliper measurement is a relative value. There are stable streaks in the caliper over the 334 scans but not at the same data box location as the streaks in the other variable's profiles. The streak strongly present in the moisture and weight profiles at data box 291, for example, is not present at all in the caliper profile image. There appears to be regions of fairly evenly spaced streaks towards the front of the paper machine (i.e. between data boxes 110 to 160) and regions where the evenly spaced streaks are not apparent. There are major changes in the average MD caliper over the data set at scans 44 and 237. These changes cannot be directly attributed to changes in other variable's profiles but could be assigned to calendar stack changes, or to problems of caliper measurement. The streak present in the moisture and weight profiles can be attributed to "hardware" problems of the paper machine such as clogged valves, etc. Single point data analysis determines the variation present in a single point. The collection of this data set took place three months before the mill trial. The single point data were sampled at 62 Chapter 6: Analysis of Industrial Data •BBS - r - r i r o CO o o o co o CO o CO o CO CO PQ CO CV M c 02 CO CO CO o o CO CD CD CV2 CO CO C\2 o o CO CD CO CO o o CD CO CO SUBOg Figure 6.57: Image of the basis weight, Mill Trial o CD O CO O C O o III 1 03 CO id o" LO C5 CD A m 'S CO ra 63 Chapter 6: Analysis of Industrial Data T i -i r i r CO CO CO o o CO CD CO CD CO oa c\2 o o CO CD CO CO o o CD CO CO SUBOg Figure 6.58: Image of the dry weight, Mill Trial 64 Chapter 6: Analysis of Industrial Data 3 s 5 10 15 20 25 30 35 40 45 50 Time (seconds) Figure 6.60: Moisture at single point 60 samples per second for a time-period of 200 seconds (i.e. 12000 samples). The scanner was stationary on the sheet at a single location during the 200 second time-period thus the whole paper machine control system was in manual. Figures 6.60-6.62 shows the moisture, basis weight and caliper data for the first 50 second time-period. Apparently there is a significantly high correlation between the moisture (Figure 6.60) and the basis weight variation (Figure 6.61) while the caliper (Figure 6.62) is relatively uncorrelated to the moisture and the basis weight. The 2a values are 1.44 % for the moisture; 1.14 g/m 2 for the basis weight ; and 1.52 microns (/an) for the caliper. The 2a value for the moisture can be compared to the 2a value of the residuals component shown in Figures 6.53-6.54, which shows that all the random components in the moisture profiles are also present when the scanner is stationary. This indicates that the random moisture profile variation is due to real, short-term MD variation in the sheet moisture. Figure 6.63 shows the power spectrum of the single-point moisture measurement for the whole time-period of 200 seconds. This analysis 66 Chapter 6: Analysis of Industrial Data 48 I 1 1 1 1 1 1 1 1 r 43 -42' 1 1 1 1 ' ' 1 1 1  0 5 10 15 20 25 30 35 40 45 50 Time (seconds) Figure 6.61: Basis Weight at single point separates the single-point variation into its component sinusoidal frequencies and determines how much each component contributes to the total variation. The moisture variation is dominated by low frequency components. The largest component correspond approximately to a 18 second period. The Kalman filter of EIMC has proven to be fully capable to track down these short-term MD variations e.g. Figure 6.42. The EIMC removes more of the random, scan-to-scan moisture variations than the standard exponential filter. EIMC provides superior separation of CD profile variation from MD upsets. The conventional algorithm would in the case of MD upsets assign those upsets to CD variations and thus would the CD controller wrongly chase apparent CD variation caused by MD upsets. The EIMC accurately tracks MD changes in the reel moisture on a scan-to-scan basis and reveals the trend of MD variation on a data box basis. Narrow streaks in the CD moisture profiles are clearly exposed and CD changes introduced by Devronizer bumps are tracked, by EIMC. The overall conclusion from 67 Chapter 6: Analysis of Industrial Data 80 | 1 1 1 1 1 1 1 1 r ? 4 0 5 10 15 20 25 30 35 40 45 50 Time (seconds) . Figure 6.62: Caliper at single point the mill trial is that the EIMC can provide the operator with a view of the true CD and MD variations in the sheet which could lead to a better CD and MD control. The EIMC should be tested further on-line for sensitive analysis of the tuning parameters. Both the CD profile estimates and the partial scan MD estimates provided by the EIMC should be used both for the CD and MD control and the performance of the overall system (i.e. the EIMC estimate system and the control system) assessed with a conventional system. Further field trips will hopefully provide more knowledge and lead to more improvements on the EIMC. Finally, as more components become available for an overall integrated paper machine estimation and control system the smoothness of the EIMC can be better ensured. 68 69 Chapter 7: Conclusions Chapter 7 Conclusions Modifications to the Estimation and Identification of Moisture Content (EIMC) algorithm have been presented in this thesis, along with estimation results both for simulated and industrial data. It has been demonstrated that, the EIMC algorithm can be successfully used for estimation and identification of moisture content when tested with simulated data, and with both off-line and on-line industrial data. • A second-order nonlinear model is used to describe the moisture variations of the paper. This process model has been validated experimentally with industrial data by Lindeborg [15] • The two key assumptions in the development of the EIMC algorithm are; nearly time invariant Cross Direction profile elements changes, and synchronous variation in the Machine Direction in all CD profile elements. • The EIMC design was tested by simulations of the moisture variations process where the convergence rate to the correct states and parameters was measured and proved to be fast. The EBMC's response to simulated process step-changes in both MD and CD is good and EIMC performed well at various levels of introduced noise. • Further, the sensitivity of the EIMC with respect to the changes in process parameters assumptions such as the magnitude of noise and the location of the parameter a of the first-order model of MD variations where thoroughly investigated. EIMC proved to be robust and insensitive to changes within reasonable bounds. The main contributions of this work to the area of Paper Machine Control are outlined as: • One of the states in the model describes MD variations. The estimate of this state enables much faster MD variation detection, i.e. at each CD element, when compared to the conventional update of MD variations as scan averages. • The estimate of the MD variations during the scanning process allows MD control at an increased rate. As well the MD variations can reveal frequencies much higher than scanning frequency. 70 Chapter 7: Conclusions • Adequate estimation of CD profiles, where any MD variation is extracted. • The EIMC shows better extraction of the MD variations and the CD profiles from the composite profile than EXPO. • New insight of paper variations with colour image rastering of various process variables of a paper machine. The EIMC algorithm is not computationally intensive as the experience from the mill trial revealed, so it will be relatively straightforward to include EIMC in a paper machine control system. Future studies along these lines could include: • Further sensitivity analysis of EIMC and validation of the EIMC performance at a mill site. • Off-line tests at exactly the same points on the sheet at which the parameters and states are estimated on-line to reveal the true MD variations and CD profiles. This kind of coordinated off-line tests, while providing the best method of checking the performance of the EIMC algorithm, are difficult and time consuming to perform. • On-line identification of the a parameter. • Improve the extraction method of the nonlinear term B, where fast MD upsets will be taken into account. • Adaptive tuning of the various tuning parameters such as (3 of EFRA. • Estimation Trending before process changes, i.e. implement a simulation device of the process parallel to the control system. • Assess the amount of energy consumed in the drying process when using EIMC along with tighter control to the conventional energy consumption. • Evaluate the likelihood of paper rejection when using EIMC. • Optimization of the computational speed of the EIMC before the final industrial implementation. 71 References [I] M . S. Ahmed. On bootstrap estimation of system parameters and states. IEEE Trans. Automat. Contr., AC-28(7), 1983. [2] W. Bialkowski. Newsprint uniformity and process control - the untapped competitive edge. In CPPA Conference, pages A255-A269, Montreal, 1990. [3] S.-C. Chen. Kalman filtering applied to sheet measurement. In 7th American Control Conference, pages 643-647, Atlanta, Georgia, 1988. [4] K. Cutshall. The nature of paper variation. Tappi Journal, June 1990. [5] K. Cutshall, G. Ilott, and J. Rogers. Grammage Variation — Measurement and Analysis. Technical Section CPPA monograph, Canadian Pulp and Paper Association, Montreal, 1988. [6] E. Dahlin. Computational methods of a dedicated computer system for measurement and control on paper machines. In 24th Engineering Conference, TAPPI, pages 62.1-62.42, San Francisco, California, Sept. 1969. [7] G. A. Dumont. Control techniques in the pulp and paper industry. In Control and Dynamic Systems, volume 37, pages 65-114. Academic Press, Inc., 1990. [8] G. A. Dumont, M . S. Davies, K. Natarajan, C. Lindeborg, F. Ordubadi, Y. Fu, K. Kristinsson, and I. Jonsson. An improved algorithm for estimating paper machine moisture profiles using scanned data. 30th. IEEE CDC, Brighton, England, Dec. 1991. [9] G. Goodwin and K. Sin. Adaptive Filtering, Prediction and Control. Prentice Hall Inc., 1984. ISBN 0-13-004069-X. [10] M . Heaven and et. al. U.B.C. data files. Technical report, Devron-Hercules Inc., 500 Brooksbank Avenue, North Vancouver, B.C. Canada V7J 3S4, Oct. 1990. [II] M . A. Keyes. Cross machine moisture control system for the wet end of a paper machine. U.S. Pat. no. 3,619,359, Beloit Corporation, 1971. 72 [12] C. Lindeborg. A nonlinear algorithm for the estimation of moisture variation characteristics in the paper process. In Proc. of 17th Int. Conf. BIAS-81, Control of Industrial Processes, volume 3, pages 139-158, Milan, Italy, Oct. 1981. [13] C. Lindeborg. A method for analysis of cross-direction drying performance in a paper machine. The Journal of the Technical Association of the Pulp and Paper Industry (TAPPI), 65(10): 119-122, Oct. 1982. [14] C. Lindeborg. A process model for the moisture variations at the dry end of a paper machine. Technical report, Control Engineering Laboratory, Chalmers University of Technology, Gothenborg, Sweden, 1983. [15] C. Lindeborg. A process model of moisture variations. Pulp and Paper Canada, 87(4):T142-147, 1986. [16] C. Lindeborg. Simulation of cross-direction moisture control. Pulp and Paper Canada, 90(12):T470-475, 1989. [17] C. Lindeborg. Modelling and simulation of the cross-direction moisture control. In New Available Techniques and Current Trends, 24th EUCEPA Conference, May 1990. [18] L. Ljung and T. SOderstrom. Theory and Practice of Recursive Identification. The MIT Press, Cambridge, Massachusetts, 1983. [19] R. J. McGill. Measurement and Control in Papermaking. Adam Hilger Ltd, Bristol, England, 1980. [20] K. Natarajan, G. A. Dumont, and M . S. Davies. An algorithm for estimating cross and machine direction moisture profiles for paper machines. In IFAC/IFORS Symposium, pages 27-31, Beijing, PRC, Aug. 1988. [21] M . B. Priestley. Non-Linear and Non-Stationary Time Series Analysis. Academic Press Limited, London, 1988. [22] E. W. Ramsdell. The Practical Application of Statistical Analysis in the Industrial Process. TAPPI Press, Atlanta, 1981. [23] M . E. Salgado, G. C. Goodwin, and R. H. Middleton. Modified least squares algorithm incorpo-rating exponential resetting and forgetting. International Journal of Control, 47(2):477-491, 1988. [24] K. E. Smith. Cross-direction control is still top process automation trend. Pulp and Paper, 59(21):72-76, Feb. 1985. [25] B. Taylor. Optimum separation of machine-direction and cross-direction product variations. Tappi Journal, pages 87-92, Feb. 1991. [26] R. G. Wilhelm Jr. On the controllability of cross-direction variations of sheet properties. In TAPPI Engineering Conference, pages 621-629, 1984. 74 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0098468/manifest

Comment

Related Items