Title :
Nonconservative Robust Control: Optimized and Constrained Sensitivity Functions
Author :
Fransson, Carl-Magnus ; Wik, Torsten ; Lennartson, Bengt ; Saunders, Michael ; Gutman, Per-Olof
Author_Institution :
Dept. of Signals & Syst., Chalmers Univ. of Technol., Goteborg
fDate :
3/1/2009 12:00:00 AM
Abstract :
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 H infin controller based on loop-shaping achieve approximately the same low-frequency performance.
Keywords :
Hinfin control; approximation theory; closed loop systems; concave programming; control system synthesis; convergence of numerical methods; robust control; three-term control; uncertain systems; Hinfin loop-shaping controller design; Horowitz-Sidi bound; PID controller; TOMLAB optimization environment; approximation theory; constrained sensitivity function; frequency closed-loop property; nonconservative robust control; nonconvex optimization problem; proportional-integral-derivative type controller; robust convergence; single-input single-output plant; uncertain system; ${cal H}_infty$ control; Control systems; convergence of numerical methods; optimal control; optimization methods; process control; proportional control; robustness;
Journal_Title :
Control Systems Technology, IEEE Transactions on
DOI :
10.1109/TCST.2008.924564