A polynomial approach to minimax frequency domain optimization of multivariable feedback systems

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Abstract
The properties of a feedback system where the plant has rational transfer matrix H and the compensator has transfer matrix G can be characterized through the system functions S:=(I +HG)− and T:= G(I+HG)−1. Good disturbance attenuation, robustness, limited bandwidth and compensator roll-off may be obtained by minimizing a criterion of the form ||Z||∞, where Z:= V∗(S∗T∗W1∗WlS + T∗W2∗W2T)V, with respect to the compensator transfer matrix G. Here V, W1, and W2 are suitable rational weighting matrices. The solution of the problem can be reduced to a pair of matrix polynomial equations. Since the optimal solution is highly non-unique, special solutions with additional optimality properties are considered as well. The paper includes a discussion of the numerical solution of the polynomial equations and of the question how to choose the weighting matrices to ensure required feedback system properties. An example illustrates the results.

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