Control of Systems Subject to Constraints

Citation

Kothare, Mayuresh V. (1997) Control of Systems Subject to Constraints. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/anhq-xj51. https://resolver.caltech.edu/CaltechETD:etd-01162008-153136

Abstract

Every operating control system must deal with constraints. On the one hand, the range and rate of change of the input or manipulated variable is limited by the physical nature of the actuator (saturation limits). On the other hand, process state variables or outputs (pressures, temperatures, voltages) may not be allowed to exceed certain bounds arising from equipment limitation, safety considerations, or environmental regulations.

A rich theory exists for designing controllers - both linear (H₂/H_∞, LQG, LTR, pole-placement) and nonlinear (nonlinear H_∞, control, feedback linearization, sliding mode control, gain scheduling). However, none of these popular and fashionable controller design techniques account for the presence of input or output constraints. Although occasionally these constraints may be neglected, in general, they lead to design and operating problems unless they are accounted for properly.

In traditional control practice, overrides or mode selection schemes are used to deal with output constraints: they switch between a "bank" of controllers, each of which is designed to achieve a specific objective. In both cases (saturation limit and mode selection), a control input nonlinearity is introduced into the operating system.

Despite its significance, the study of the constrained control problem has received far less attention than the traditional unconstrained (linear and nonlinear) control theory. With few exceptions, most of the controller design techniques for constrained systems are by-and-large ad-hoc, with very little guarantees of stability, performance and robustness to plant model uncertainty.

The objective of this thesis is to take a broad approach towards the constrained control problem. One part of the thesis is devoted to the development of a systematic and unifying theory for studying the so-called Anti-Windup Bumpless Transfer (AWBT) problem. The other part aims towards the development of a general novel approach for the synthesis of a robust model predictive control (MPC) algorithm.

Thesis Files