Robust PID Design Based on QFT and Convex–Concave Optimization

This paper presents an automatic loop-shaping method for designing proportional integral derivative controllers. Criteria for load disturbance attenuation, measurement noise injection, set-point response and robustness to plant uncertainty are given. One criterion is chosen to be optimized with the remaining ones as constraints. Two cases are considered: M-constrained integral gain optimization and minimization of the cost of feedback according to quantitative feedback theory. Optimization is performed using a convex-concave procedure (CCP). The method that relies on solving a sequence of convex optimization problems converges to a local minimum or a saddle point. The proposed method is illustrated by examples.