Modeling and Output-Feedback Control of Systems with Netushil Rate-Dependent Hysteresis Nonlinearties

We propose a rate-dependent hysteresis model constructed with a Netushil operator for modeling hysteresis nonlinearities. This hysteresis operator is constructed with an ordinary differential equation and a positive perturbation constant. We show that the positive perturbation constant in Netushil operator captures the rate-dependency in hysteresis loops when a harmonic input is applied. Furthermore, a linear combination of Netushil operators are proposed to model current-to-displacement hysteresis loop of a magnetostrictive actuator over different operating conditions. We further consider the problem of output-feedback tracking control of a class of mechanical systems that include rate-dependent hysteresis nonlinearities. In particular, we take an iron pendulum in a magnetic field system as a case study. We show that, in this case, an extended high-gain observer-based feedback linearizing control can be employed to solve the problem. The proposed control system has a number of features; namely, (i) it can guarantee ultimate boundedness of the tracking error, where the ultimate bound can be made arbitrarily small, for any given initial conditions and for bounded unknown exogenous inputs and modeling parameters, and (ii) it provides the possibility of shaping the transient response of the closed-loop system as desired. Simulation results are provided to verify the effectiveness of these results.