Use of Passivity for Analysis and Tuning of PIDs: Two Practical Examples

This chapter aims to illustrate with two practical applications – control of induction motors and regulation of the air supply of a fuel cell system – how the property of passivity can be used to select the gains of the proportional‐integral‐derivative without appealing to linearization‐based techniques. It provides the theoretical justification to the scheme, proving that this output variable has the remarkable property that the linearization of the input‐output map is strictly passive. The chapter discusses the linearization of the model and some useful structural properties. In view of the complexity of the nonlinear model – even the reduced third order system‐most of the controllers for this application are designed based on its linear approximation. The chapter examines a theoretical justification has been given to the common practice of regulating the air supply system of a proton exchange membrane fuel cell with a simple PI controller around the compressor flow.