LMI-based design of linear controllers for a magnetic shape memory push-push actuator

This paper proposes a design strategy of PID controllers for a positioning system based on magnetic shape memory alloys affected by a large hysteresis. The strategy is based on the reformulation of the control design as the stability of a linear parameter-varying system, and the subsequent use of linear matrix inequalities to perform the numerical synthesis of the controller. The design tool is applied to a positioning system in which two magnetic shape memory elements work in an antagonistic way, one being the load of the other. In the analysis of the experimental results, the paper also provides some considerations on the integrator reset to exploit the particular hysteresis shape and thus improve the energy efficiency of the controllers.