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Multivariable three-term optimal controller design for large-scale systems
Edward J. Davison, Daniel E. Davison, and Simon Lam
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.
