Doctoral Dissertations

Daniel Rangel

Date of Award

5-1992

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Chemical Engineering

Major Professor

T. W. Wang

Committee Members

John D. Birdwell, Charles Moore, Duane Bruns

Abstract

The focus of this dissertation is the development of an efficient controller for nonlinear systems that handle constraints explicitly without requiring excessive computation time. The algorithm developed uses the input-output linearization technique (Isidori (1989) [35]) to extend the application of the Dynamic Matrix Control (DMC) algorithm (Cutler (1983) [16]) to nonlinear systems. Transformation methods based on differential geometry have been the only techniques that successfully extend some of the linear control theory to nonlinear systems. There has been no attempt to use the differen­tial geometry techniques to extend the application of the DMC to nonlinear systems with constraints, mainly because of the difficulty in handling the constraints after the transformation. The method presented in this work uses the input-output linearization technique to transform the original nonlinear process model into a pseudo-linear one. The obtained model is valid for the entire region of operation. Unconstrained DMC is then applied to the linear system. Constraint violations are then handled by a pointwise optimization method that computes a modified input such that, at each sampling time, this modified input would satisfy the system constraints and at the same time would be "closest" to the optimum input as dictated by DMC. In this work, we will refer to this controller as the Exact-Linearized-Constraint Controller (ELCC).

The feasibility and effectiveness of the ELCC is demonstrated through computer simulation of three processes: a Continuous Stirred Tank Bioreactor (CSTBR), an exothermic Continuous Stirred Tank Reactor (CSTR) and a catalytic reactor. In the first two processes, it is desirable to operate as close to the optimal point (a singular point) as possible, at the same time maintaining closed-loop stability in the face of disturbances and model uncertainties. Traditional linear control strategies cannot simultaneously satisfy these demands.

The combination of exact linearization with linear DMC presented in this work allows the selection of an arbitrary set point, regardless of its feasibility. When the stipulated set point becomes unachievable due to model parameter variations and disturbances, the ELCC will still operate the system in a stable manner, and at the same time drive the system to a steady-state level very close to the new maximum achievable point.

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