Iterative controller tuning using Bode's integrals

An iterative controller tuning based on a frequency criterion is proposed. The frequency criterion is defined as the weighted sum of squared errors between the desired and measured gain margin, phase margin and crossover frequency. The method benefits from specific feedback relay tests to determine the gain margin, the phase margin and the crossover frequency of the closed-loop system. The Bode's integrals are used to approximate the derivatives of amplitude and phase of the plant model with respect to the frequency without any model of the plant. This additional information is employed to estimate the gradient and the Hessian of the frequency criterion in the iterative controller tuning method. Simulation examples and experimental results illustrate the effectiveness and the simplicity of the proposed method to design and tune the controllers.