Robust proportional integral derivative controller tuning with specifications on the infinity-norm of sensitivity functions

An overview of the recent works on proportional integral derivative (PID) controller tuning methods based on specifications on the infinity-norm of the sensitivity functions is presented. The presented approach is very flexible relative to the controller structure and the a priori knowledge about the process. It can be applied to plants described by parametric models, frequency domain non-parametric models as well as in a model-free framework. For the latter, procedures for measuring the design parameters values are described. The problem is then solved by minimising iteratively a frequency criterion, defined as the weighted sum of squared errors between the actual values and desired values of the design parameters. If the plant is described by a parametric model, model uncertainty can be handled to guarantee stability and performance robustness of the designed closed-loop system. Simulation examples are provided to compare the results obtained with the proposed approach to those resulting from well-accepted PID controller tuning methods. An application of the proposed method to a double-axis permanent-magnet synchronous motor illustrates the effectiveness of the approach to control of systems with large uncertainties.