Adaptive process control: Modelling, estimation, and control of constrained multivariable systems

This thesis presents new methods for process modelling, parameter estimation, and constrained multivariable predictive control for adaptive control systems. We have developed a new model applicable to open-loop stable systems which eliminates the problem of unstable pole-zero cancellations, which often cause instabilities in the closed-loop adaptive system. The new model is well suited for systems with large deadtimes, as well as for multivariable systems with large dispersions in the time constants. Simulation studies are presented which demonstrate the performance of an adaptive, predictive controller which uses the new model. We have also designed an adaptive deadzone which can be used to regulate the adaptation mechanism. This algorithm is able to eliminate bursting phenomena which result from lack of excitation to the system. Global stability results have been obtained for pole-placement control of an adaptive system which uses a least squares estimator with an adaptive deadzone. Simulation studies show that the adaptive deadzone performs well, even in the presence of unmodelled dynamics and unmeasured disturbances. A modification to the recursive least squares algorithm is presented which guarantees that the condition number of the covariance matrix remains bounded. Also, a linear programming approach to parameter estimation is presented. The estimation problem is cast as a constrained minimization problem, which allows us to restrict the parameter estimates to a bounded solution space. In order to handle process constraints in an optimal fashion, one can treat the control objective as a constrained optimization problem. We implement a control algorithm which is based on a constrained minimization of a linear objective function. The control objective is then formulated as a linear programming problem, and is solved using the simplex method. Several control objectives are considered, and the algorithm is demonstrated using simulations of a constrained multivariable fractionation process