Linear Control Systems with Pointwise-in-Time Constraints: What Do We Do About Them?

Pointwise-in-time contraints are inherent in almost all practical control systems. They appear most commonly as actuator bounds on control variables, but physical limits on state variables are ubiquitous too. Neglecting such constraints in controller design and implementation can drastically degrade system performance or, worse, lead to catastrophic failures. Contemporary design procedures for multivariable systems often exacerbate these problems: saturation of the output control vector induces direction changes which severely damage required cancellations between controller and plant dynamics. Over the years many schemes have been proposed for dealing with pointwise-in-time constraints. Although the schemes may be formally classified according to their underlying methodologies (anti-windup, predictive models, Lyapunov functions, optimal control, ...) they are more often characterized by their diversity and speciality. Most of the schemes can only be applied to systems of relatively low order where performance demands are modest and process characteristics are benign. In current engineering practice the extensive theoretical literature plays a small role. The most common approach is to use a variety of special fixes, for example: simple anti-windup strategies, tuning of controller designs with constraint verification by simulation, increased actuator performance. With growing sophistication of controller designs, greater emphasis on improved performance and lower costs, and concern for reliable operation, it is unlikely that these simple fixes will suffice in the future. Systematic methodologies for designing and implementing relatively complex nonlinear controllers will be needed. The lecture explores bases for such methodologies It includes a broad review of prior literature.