Nonconservative Robust Control: Optimized and Constrained Sensitivity Functions

An automated procedure for optimization of proportional-integral-derivative (PID)-type controller parameters for single-input, single-output (SISO) plants with explicit model uncertainty is presented. Robustness to the uncertainties is guaranteed by the use of Horowitz-Sidi bounds, which are used as constraints when low-frequency performance is optimized in a nonconvex but smooth optimization problem. In the optimization (and hence the parameter tuning), separate criteria are formulated for low-, mid-, and high-frequency (HF) closed-loop properties. The tradeoff between stability margins, control signals, HF robustness, and low-frequency performance is clarified, and the final parameter choice is facilitated. We use a combination of global and local optimization algorithms in the TOMLAB optimization environment and obtain robust convergence without relying on good initial estimates for the controller parameters. The method is applied to a controller structure comparison for a plant with an uncertain mechanical resonance and a plant with uncertain time delay and time constants. For a given control activity, stability margin, and HF robustness, it is shown that a PID controller with a second-order filter and an
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controller based on loop-shaping achieve approximately the same low-frequency performance.