Operator-Based Vibration Control System Design of a Flexible Arm Using an SMA Actuator with Hysteresis

: This paper presents a method of operator-based nonlinear vibration control for a flexible arm using a Shape Memory Alloy (SMA) actuator with hysteresis. SMA actuators have hysteretic characteristic and so it is di ffi cult to design a controller which satisfies desired performance. In order to eliminate the e ff ect of the hysteresis, a nonlinear compensator is designed by using a hysteresis model, which is described by an operator-based Prandtl-Ishlinskii (PI) hysteresis model. Based on the concept of the Lipschitz operator and the robust right coprime factorization condition, nonlinear vibration controllers are designed, and robust stability of the closed-loop system with unconsidered vibration modes of the flexible arm as perturbation is guaranteed. Moreover, a tracking operator is designed to ensure the output tracking performance. Finally, numerical simulation and experimental results are presented to show the e ff ectiveness of the proposed design method.

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