Doctoral Dissertations

Chun-Yao Lien

Date of Award

5-1990

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Chemical Engineering

Major Professor

T. W. Wang

Committee Members

John Birdwell, Duane Bruns, Charles Moore, James Downs, Gang Qiu

Abstract

This dissertation presents a comprehensive study of using exact input-output linearization techniques for a nonlinear feedback controller design. A generic nonlinear continuous bioreactor is used as the benchmark test process for the feedback linearizing control strategies. The overall objective of this research is to investigate the applicability of the exact input-output feedback linearizing control scheme from both practical and theoretical aspects. For the controller design methodology, we use stable factorization theory to design a linear compensator for the exact input-output linearized system, obtained from applying geometric linearization methods. Thus, the overall controller structure is nonlinear and consists of a feedback linearizing transformation followed by a linear compensation scheme. For practical applications, in particular, we focus our attention on the singularity problem in the exact input-output linearization scheme. The existence of singular points, points at which inversion is not possible, renders the direct application of the standard exact input-output linearization method infeasible. In this study, we develop a new design scheme that allows one to approximately extend the feedback linearization algorithm smoothly to cover the singular points. The technique has been applied to the production rate control of a generic bioreactor system. The difficulty of the productivity control problem lies in the conflict between operating the reactor as close to its optimal point as possible, while at the same time maintaining the stability of the closed-loop system in the face of disturbances and culture parameter uncertainties, which at times, make the specified set-points unachievable. The feasibility and effectiveness of the new design algorithm has been demonstrated through computer simulation. The performance of the new control scheme is much superior to that of the linear controller based on locally linearized model in the following points: The closed-loop system will converge to the desired set-point regardless of the location of the initial steady state, i.e. at either side of the maximum productivity point. The nonlinear control scheme is able to operate the bioreactor at its largest possible optimal conditions when the desired set-point becomes unachievable due to culture parameter variations and disturbances. Though the geometric linearization methods provide a great potential to resolve non linear controller design problems, the big hurdle for its practical application is in the robustness considerations. In this research, we approach the robustness and sensitivity problems in the feedback linearizing control scheme from the geometric aspects. A robust exact input-output linearizing control algorithm for the single-input/single-output case is developed based on Lyapunov stability theory, which guarantees that the output of a nonlinear system will remain uniformly bounded in the presence of structure-matching plant uncertainties. Also developed is a parameter adaptive algorithm to compensate for the effect of linear parametric uncertainties on the exact input-output feedback linearizing control scheme for a nonlinear system that has a relative degree of one.

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