Date of Award
Doctor of Philosophy (PhD)
Professor John F. MacGregor
This thesis presents new results in the research area of multiple input/multiple output(MIMO) controller design for chemical processes. The topics considered in this work are: robustness properties of linear MIMO controller designs; the design of approximate inverses for linear MIMO controllers; disturbance prediction in model predictive controller designs; and the development of a nonlinear inferential feedback control strategy for semi-batch copolymerization processes.
A review of robustness analysis procedures based on the use of norm bounded mismatch regions in the frequency domain is presented. These theories are considered for use in the assessment of the relative robustness trends of different MIMO Internal Model Controller designs. Based on these theories, three approaches to analyzing robustness properties are considered: the use of a condition number and singular value analysis on the approximate model inverse; singular value analysis assuming unstructured norm bounded uncertainty; and new procedure based on disk uncertainties in each element of the transfer function matrix that requires the use of structured singular value theory. The problems of conservatism with each approach as a result of unrealistic uncertainty characterizations is discussed, and new results are provided. The approaches are compared and evaluated with different MIMO Internal model controller designs. Compared to previously proposed procedures for relative robustness assessment, new proposed procedure based on disk uncertainties in each element of the transfer is shown to reduce conservatism in analyzing controller design robustness trends.
A general method for obtaining least squares optimal inverses for multivariable Internal Model Controllers (IMCs) is presented. An analytical solution is arrived at using a well known method for optimally factorizing discrete transfer function matrices. The procedure automatically handles unbalanced, noninvertible, and nonsquare systems, and provides controllers with excellent performance and robustness properties. These IMC designs are compared with some of the more traditional IMC designs where tunable diagonal filters are combined with fixed but usually suboptimal inverses. Robustness properties are investigated in simulated mismatch case studies, and with the robustness assessment procedures described above.
A general procedure is proposed for improving disturbance regulation in MlMO Dynamic Matrix Controllers (DMC). The method makes use of autoregressive, integrated moving average disturbance models to provide disturbance predictions, and requires only a simple modification to the DMC algorithm. The method proposed is far more computationally efficient and simple to apply relative to other procedures proposed. Examples are presented were the proposed modification leads to a substantial improvement in DMC disturbance regulation.
A strategy is proposed for estimating and controlling properties of styrene/butadiene rubber (SBR) latex produced in a semi-batch reactor. The nonlinear control strategy features a nonlinear state estimator, a nonlinear open-loop feedforward compensator, and a linear feedback controller to correct for errors in the feedforward control actions. In arriving at a nonlinear state estimator, three approaches, extended Kalman filtering, extended Kalman filtering with global reiteration, and a nonlinear optimization approach were considered. The second approach was found to be most effective and was therefore adopted. The importance of introducing sufficient meaningful nonstationary states is discussed in order to have biased-free state estimates when nonideal conditions exist. Using the knowledge of modelled chemical reaction mechanisms, open-loop feedforward actions are proposed based on establishing conditions for maintaining fixed instantaneous copolymer properties. These open-loop/feedforward policies establish quasi-steady state conditions on the instantaneous copolymer properties to be controlled. This allows for the application of simple feedback control strategies to correct for errors remaining after the open-loop/feedforward actions. The approaches considered for feedback controller design were conventional paired PI, a decoupling and linearizing mullivariable transfonnation approach, and model-based optimal controller design. The second approach was found to be the most convenient for use in the nonlinear inferential feedback control scheme. The performance of the overall nonlinear inferential feedback design strategy proposed in this work is demonstrated to be robust to model mismatch, disturbances, and state initialization errors. In all cases investigated, copolymer properly control is greatly improved over a fixed operating policy determined off-line. The proposed strategy is simple and effective alternative to computationally intensive on-line optimization procedures, and has the potential for greatly improving product reproducibility and quality control in polymer manufacturing industries.
Kozub, Derrick John, "Multivariable Control: Design, Robustness, And Nonlinear Inferential Control For Semi-Batch Polymerization Reactors" (1989). Open Access Dissertations and Theses. Paper 1871.