Data-driven controller tuning based on a frequency criterion

An iterative controller auto-tuning method 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. A relay feedback test is used to automatically obtain a non-parametric model of the open-loop system in a very important region for control design. The gain and phase margins as well as the crossover frequency are estimated with the non-parametric model using interpolations. The gradient and Hessian of the frequency criterion can be expressed in terms of the derivatives of the open-loop system with respect to the frequency. These derivatives can also be estimated with a good accuracy thanks to the non-parametric model. Since no assumptions are made on the plant, the method is valid for a very wide class of linear systems. Simulation examples illustrate the effectiveness and simplicity of the proposed method.