FIR-based phase matching for robust Retrospective-Cost Adaptive Control

In this paper we develop frequency-domain methods for approximating IIR plants with FIR transfer functions. The underlying goal is to increase the performance and robustness of Retrospective-Cost Adaptive Control (RCAC), which is applicable to MIMO possibly nonminimum-phase (NMP) plants without the need to know the locations of the NMP zeros. The only required modeling information is an FIR approximation of the plant, which may be based on a limited number of Markov parameters, or possibly noisy frequency response data. In this paper we investigate the resulting phase mismatch between the true plant and the FIR approximation obtained through linear and nonlinear approximation methods. We consider degradation in the phase mismatch due to uncertainty in the frequency response data.