Discrete-Time System Conditional Optimization in the Parameter Space with Nonzero Initial Conditions

Abstract

The paper presents a new approach to the design of the classical PD controller for the plant in the closed loop control system. Proposed controller has two unknown adjustable parameters which are designed by the algebraic method in the two dimensional parameter space, by using the newly discovered characteristic polynomial of the row nondegenerate full transfer function matrix. The system relative stability, in regard to the chosen damping coefficient is achieved. The optimality criterion is the minimal value of the performance index and sum of squared error is taken as an objective function. The output error used in the performance index is influenced by all actions on the system at the same time: by nonzero initial conditions and by nonzero inputs. In the classical approach the output error is influenced only by nonzero inputs. Experimental results confirm that by taking into account nonzero initial conditions, an optimal solution is obtained, which is not the case with the classical method where optimization is performed at zero initial conditions.