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This paper derives a minimal representation of linear multivariable systems on the basis of input and output records. Two optimal-control algorithms are established from the minimal structure. The algorithms generate a minimum-time response and a general-optimal response, respectively. The latter is based on minimisation of a quadratic cost criterion. A description of an online implementation of the minimum-time controller is presented. A 4th-order servo system is used for the study. A recursive least-squares procedure is applied to model process dynamics for controller design. It is demonstrated that incorporation of auxiliary error feedback reduces the requirement for accurate knowledge of process parameters.