UBC Theses and Dissertations
Cross-directional processes : modeling, identification and robust control Ammar, Mohammed E.
The aim of this work is to improve the identification of cross-directional (CD) models as well as to simplify the robust control design problem. Providing computationally efficient techniques for identification and robust control will facilitate the implementation of an autonomous CD control system. These are challenging problems as CD processes are large scale distributed parameter systems. The conventional model for a CD process is a spatial interaction matrix cascaded by a low order transfer function in the temporal domain. This representation results in a large dimensional multi-variable model. Model uncertainties in the process are inevitable and rise from several sources. As the CD process models are usually identified by input-output data from bump tests, there is a demand for better identification techniques that minimizes the uncertainties in CD mapping and response shape models. Mapping and misalignment detection are problems that are specific to CD processes due to the configuration of the paper machine and its unconventional scanning method. These problems are of great practical importance for industrial implementations. This work proposes modeling the CD process as a two-dimensional (2D) system that is spatially noncausal. The spatial noncausal transfer functions facilitate input design and identification in the spatial domain. Both noncausal finite impulse response (FIR) models and rational transfer functions are used to model the CD response. The FIR model representation is convenient for input design and identification in the CD while the spatial noncausal rational transfer function is more suitable for robust control design. The 2D representation for the plant and the controller is convenient for implementation in an autonomous control scheme with iterative feedback tuning or adaptive control. Robust stability criteria are developed to investigate the stability of the process under feedback. Employing the 2D representation results in criteria that are computationally efficient as the 2D stability conditions are replaced by a set of simple 1D problems. A robust stability criterion that is based on the v-gap stability criterion provides bounds for robust stability against perturbations in the plant or the controller. This feature permits designing a two-dimensional controller in an adaptive control scheme or a simple re-tuning of an existing controller through iterative feedback tuning. This property is convenient when switching between different grades of paper. Another stability criterion based on the concept of phase margins is developed to determine the closed-loop’s tolerance to misalignment uncertainties. Finally, a simple loop-shaping technique using spatial transfer functions is proposed to shape the closed-loop’s two-dimensional frequency response. The noncausal spatial transfer function provides a convenient tool for improving the closed-loop’s performance at low temporal frequencies. An adaptive control scheme is implemented to retune the system after a grade change. The developed techniques for identification and robust control can be used as a part of a more sophisticated autonomous control system.
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