Date of Award
Doctor of Philosophy (PhD)
Michael A. Henson
Two widely studied control techniques which compensate for process nonlinearities are feedback linearization (FBL) and nonlinear model predictive control (NMPC). Feedback linearization has a low computational requirement but provides no means to explicitly handle constraints which are important in the chemical process industry. Nonlinear model predictive control provides explicit constraint compensation but only at the expense of high computational requirements. Both techniques suffer from the need for full-state feedback and may have high sensitivities to disturbances. The main work of this dissertation is to eliminate some of the disadvantages associated with FBL techniques. The computation time associated with solving a nonlinear programming problem at each time step restricts the use of NMPC to low-dimensional systems. By using linear model predictive control on top of a FBL controller, it is found that explicit constraint compensation can be provided without large computational requirements. The main difficulty is the required constraint mapping. This strategy is applied to a polymerization reactor, and stability results for discrete-time nonlinear systems are established. To alleviate the need for full-state feedback in FBL techniques it is necessary to construct an observer, which is very difficult for general nonlinear systems. A class of nonlinear systems is studied for which the observer construction is quite easy in that the design mimics the linear case. The class of systems referred to are those in which the unmeasured variables appear in an affine manner. The same observer construction can be used to estimate unmeasured disturbances, thereby providing a reduction in the controller sensitivity to those disturbances. Another contribution of this work is the application of feedback linearization techniques to two novel biotechnological processes. The first is a mixed-culture bioreactor in which coexistence steady states of the two cell populations must be stabilized. These steady states are unstable in the open-loop system since each population competes for the same substrate, and each has a different growth rate. The requirement of a pulsatile manipulated input complicates the controller design. The second process is a bioreactor described by a distributed parameter model in which undesired oscillations must be damped without the use of distributed control.
Kurtz, Michael James, "Feedback Linearizing Control Strategies for Chemical Engineering Applications." (1997). LSU Historical Dissertations and Theses. 6576.