On PID control of dynamic systems with hysteresis using a Prandtl-Ishlinskii model

This papers deals with PI and PID control of second order systems with an input hysteresis described by a modified Prandtl-Ishlinskii model. The problem of the asymptotic tracking of constant references is re-formulated as the stability of a polytopic linear differential inclusion. This offers a simple linear matrix inequality condition that, when satisfied with the chosen PI or PID controller gains, ensures the tracking of constant reference and also allows the designer to establish a performance index. The validation of the approach is performed experimentally on a Magnetic Shape Memory Alloy micrometric positioning system.