Multivariable three-term optimal controller design for large-scale systems

Abstract

Abstract-This paper deals with the design of controllers for large-scale linear time-invariant multi-input multi-output systems, such as those that often arise in process control. We focus on two standard controller objectives: (i) asymptotic regulation subject to unmeasurable constant disturbances, and/or (ii) asymptotic tracking of constant set-points. In either case, standard output-feedback controller design methodologies typically result in controllers that have order at least as large as that of the plant; for large-scale systems, the controller order can consequently be impractically large. The purpose of this paper is to introduce, for the subclass of plants that are open-loop stable, a low-order three-term (i.e., PID) multivariable control design approach that is practical to compute numerically, even for large-scale systems. A design algorithm and existence results to construct such a controller are given, and the approach is applied to several examples. Remarkably, at least for the examples considered, the three-term controller's performance is quite similar to that achieved by the standard (much higher order) controller that solves the servomechanism problem.

Controller design of multivariable LTI unknown systems

“…This performance index measures the "average cost" of (2.47) over all initial conditions y 0 uniformly distributed on a unit disk ball [31]. Likewise, we can define the following performance indices:…”