Parameter optimized controller design based on frequency domain identification

Abstract

Recently, there has been a great tendency towards the development of iterative design methodologies combining identification with control in a mutually supportive fashion. In this thesis, we develop such an algorithm utilizing nonparametric frequency domain identification methods in order to realize the online iterative design of parameter optimized controllers for a system of unknown dynamics. The control design is based on the minimization of LQG (Linear Quadratic Gaussian) cost criterion with a two-degree of freedom control system. This is achieved by the approximation of an optimality relation, which is derived for a particular parametrization of one of the controllers, using the frequency domain transfer function estimates and application of this together with a numerical optimization algorithm. It is shown that, if the first controller is a FIR filter of length greater than or equal to two times the number of frequencies present in the reference input, the designed control system is optimal independent of the stabilizing second controller.