Parameterized Bilinear Matrix Inequality Techniques in ${\cal H}_{\infty}$ Fuzzy PID Control Design

TL;DR

This paper introduces a new parameterized bilinear matrix inequality approach for designing ${ m H}_ ext{infty}$ fuzzy PID controllers, making the control design more practical and computationally feasible.

Contribution

It develops a novel bilinear matrix inequality characterization and relaxation method for ${ m H}_ ext{infty}$ fuzzy PID control, along with computational algorithms for solving the resulting nonconvex optimization.

Findings

Algorithms successfully applied to benchmark examples.

Enhanced practicality and tractability in fuzzy PID control design.

Demonstrated effectiveness of the proposed methods.

Abstract

Proportional-integral-derivative (PID) structured controller is the most popular class of industrial control but still could not be appropriately exploited in fuzzy systems. To gain the practicability and tractability of fuzzy systems, this paper develops a parameterized bilinear matrix inequality characterization for the ${\cal H}_{\infty}$ fuzzy PID control design, which is then relaxed into a bilinear matrix inequality optimization problem of nonconvex optimization. Several computational procedures are then developed for its solution. The merit of the developed algorithms is shown through the benchmark examples.