Mismatch and the optimal control of linear systems with series time delays

• Main Author: Hocken, R. D.
• Published: University of Bath 1983
• Subjects: 629.8; Control systems & control theory
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.347038

A feature common to predictor control schemes for plants with time delays is the use of a plant model. Any difference between plant and model is referred to as mismatch. The presence of mismatch introduces extra parameters which in a parametric optimisation problem may be exploited to produce performance improvement. A study is undertaken of the mechanism and opportunities for such improvement. When the cost functional is quadratic a matched predictor control scheme is known to be optimal. However, it is important to determine a relationship between mismatch and degradation in performance. This will indicate the amount by which plant and model may differ before the performance of the control scheme becomes unacceptable. With this aim, algebraic expressions are obtained for the mismatched input and output. An examination of these expressions shows how mismatch effects the stability and performance of the control scheme. When the plant contains measurement delays, the optimal matched control scheme requires prior knowledge of an initial state. An alternative control scheme operating without this prior knowledge is suboptimal and may be improved by mismatch. The types of mismatch that could produce improvement are determined.