Parameterized Bilinear Matrix Inequality Techniques in ${\cal H}_{\infty}$ Fuzzy PID Control Design
For control engineers working with fuzzy PID controllers, this work addresses the challenge of H-infinity design but offers an incremental approach by reformulating existing BMI techniques.
This paper develops a parameterized bilinear matrix inequality (PBMI) characterization for H-infinity fuzzy PID control design, relaxing it into a bilinear matrix inequality (BMI) optimization problem and proposing computational procedures. The algorithms are demonstrated on benchmark examples, but no concrete numerical results are provided.
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.