MIMO System Identification for H(Infinity) Robust Control: A Frequency DomainApproach with Minimum Error Bounds

摘要

A frequency domain system identification procedure for MIMO systems that yields amodel with a bounded unstructured model error is presented. The disturbances on the input and output of the process are assumed to be bounded in the frequency domain, which implies that there exist bounding functions for the absolute value of the discrete Fourier transform of the noise signals. The identification of a SISO process is considered. Uncertainty regions for the process dynamics are derived and an optimal model by H(sub infinity) fitting is found. The identification method is extended to MIMO systems and various model error structures are considered. It is shown that for a fixed model the true model error can be expressed as a function of a known matrix G(z) and an unknown diagonal matrix Q(sub t)(z). An upper bound for the largest singular value of the model error is derived. The theory of structured singular values and of the so called Redheffer star products are used. The upper bounds for the model error are minimized in some norm sense. The choice of a linear parametrization leads to a convex optimization problem and the algorithms are robustly convergent. A case study, where a laboratory process with 2 inputs and 2 outputs is identified and a model with a bound on the model error, is derived.