Nonconservative Robust Control: Optimized and Constrained Sensitivity Functions

Abstract

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

Control System Loop-Shaping as a Mathematical Optimization Problem: An Ensemble of Models

“…If a discrete set with size m is used to represent each uncertain parameter, then a plant with n uncertain parameters gives rise to a set of n × m combinations, and the QFT controller must be able to stabilize the system for all these combinations. QFT is augmented with Horwitz-Sidi bounds in [18]. High order models feature more plant parameters, with possibly larger uncertainty ranges.…”

“…(17), which can be perceived as the mean error over the period of integration: OP-BW, described by Eq. (18). Therefore, both representations of OP-BW are worth investigation.…”

B-spline parametrized solution of robust PID control using the generalized KYP lemma

“…Due to the extensive developments in modern and robust control theory over the last decades, control synthesis based on loop shaping has become semi-or fullyautomated [1], [2]. However, H ∞ synthesis based on the KYP lemma is not widely applied in practice, since it is difficult to consider frequency-domain inequalities (FDIs) in finite frequency range directly.…”

Genetic Algorithm Tuning PID Control of Magnetic Powder Clutch

“…The present reports for PID control parameter optimization reflect the robust PID controller with parameter self-tuning [7][8][9], the PID controller with fuzzy algorithm tuning parameter [10][11][12] , the PID controller with neural networks tuning parameter [13][14][15] and the PID controller with genetic algorithm tuning parameter [16][17], et al…”