ℋ∞ control for uncertain plants using Horowitz bounds

A procedure is presented for optimizing weight functions, when determining ℋ_∞ controllers by loop shaping for SISO plants with model uncertainty. The optimization is combined with an evaluation method to give a final tuning of the controller. The basic idea of both the optimization and the parameter tuning is to formulate separate criteria for low, mid and high frequency closed loop properties. By doing so, the trade off between stability margins, high frequency robustness and low frequency performance is elucidated and, hence, the final choice of parameters is facilitated. The resulting controller has the inherent optimality features of ℋ_∞ controllers as well as a robustness to explicit plant uncertainties, guaranteed by the use of Horowitz bounds. In the procedure, low frequency performance is optimized subject to these bounds and a restricted high frequency loop gain. The method is applied to two different uncertain plants, and the results are evaluated in terms of robust performance and evaluated against optimized PID controllers. The comparison shows that with identical tuning parameters and for a given control activity the ℋ_∞ controllers achieve better low frequency performance at the same time as the maximum sensitivity is superior