Modeling and optimal control for a smart structure with stress-dependent hysteresis

The stress-dependent hysteresis existing in giant magnetostrictive materials impeded applications of magnetostrictive smart structures (MSS) under different mechanical loads. In this paper we propose a stress-dependent model for the hysteresis in a giant magnetostrictive actuator (GMA). Based on the proposed model, a finite horizon optimal control problem is studied for the system taking account of stress-dependent hysteresis without constructing the inverse operator extensively used. By dynamic programming method and the viscosity solutions theory, we derive the first order discontinuous Hamilton-Jacobi-Bellman (HJB) equation, and further prove that the value function is the unique viscosity solution of the HJB equation. Moreover, a discrete approximation scheme is adopted for the application of the control method. Simulation results verify the effectiveness of both the modeling and the control method.