Non-conservative robust control: Optimized and constrained sensitivity functions
Artikel i vetenskaplig tidskrift, 2009

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 controller based on loop-shaping achieve approximately the same low-frequency performance.

optimization methods

Control systems

optimal control

proportional control


convergence of numerical methods


process control


Carl-Magnus Fransson

Chalmers, Signaler och system

Torsten Wik

Signaler och system, System- och reglerteknik, Reglerteknik

Bengt Lennartson

Signaler och system, System- och reglerteknik, Automation

Michael Saunders

Stanford University

Per-Olof Gutman

Technion - Israel Institute of Technology

IEEE Transactions on Control Systems Technology

1063-6536 (ISSN)

Vol. 17 298-308



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