Robust PID controller tuning with specification on modulus margin

An iterative controller tuning method based on a frequency criterion is proposed in this paper. The frequency criterion is defined as the weighted sum of squared errors between the desired and actual value of the modulus margin (inverse of the infinity norm of the sensitivity function), phase margin and crossover frequency. The criterion is minimized using the iterative Gauss-Newton algorithm. The gradient and Hessian of the criterion can be expressed in terms of the derivatives of the open-loop system with respect to the frequency. These derivatives, as well as the robustness margins and the related frequencies are computed using a plant model. Simulation examples illustrate the effectiveness and the simplicity of the proposed method for controller tuning.