Design of Optimal Feedback Controller Based on Impulse Response

Abstract

This paper proposes a method of designing an optimal IFIR (Integrated Finite Impulse Response) controller which minimizes the weighted mean square value of both output error and control input based only on systems impulse response. Since the controller is constructed as a FIR filter, the computation for designing the optimal one is reduced to solving a discrete-time Wiener-Hopf equation. This equation can be solved recursively by increasing the order of the system via a type of Levinson's algorithm. Hence, the order of the controller can be estimated by evaluating the power of the output error and control input. At first the optimal design of controller is treated for an uncorrelated reference output. Next, the design method is extended to the case of colored reference output, which yields a model matching method in frequency domain. Finally, the effectiveness of the proposed method is demonstrated by computer simulations.