Discrete-time system conditional optimisation in the parameter space via the full transfer function matrix

Abstract

Dynamic systems operate under the simultaneous influence of both the initial conditions and the input vector. There is neither physical nor mathematical justification for ignoring the initial conditions, e.g., in the control optimisation. This paper gives a response to the following question: Is a set of controller parameters which is optimal for the operation of a control system under zero initial conditions also optimal for its operation under non-zero initial conditions? The paper presents a new approach to the design of a classical proportional-differencesum (PDS) controller for a plant in a closed loop control system. The system relative stability with respect to a desired damping coefficient is accomplished. The minimal value of the performance index in the form of the sum of squared errors is the optimality criterion. Unlike the classical approach, the output error used in the performance index is influenced by all actions performed on the system at the same time.