Experimental Study on Robust Nonlinear Forced Vibration Control for an L-Shaped Arm with Reduced Control Inputs

This paper presents an operator-based robust nonlinear control approach for an L-shaped arm vibration experimental system. The arm is driven by a linear pulse motor to move along a frame and controlled by a piezoelectric actuator in parallel. The aim of this paper is to allow the motor to move fast and reduce the arm vibration by controlling the motion of the motor and the piezoelectric actuator simultaneously. In detail, first, the vibration dynamics of the L-shaped arm is modeled based on the Euler-Bernoulli beam theory. The hysteresis of the piezoelectric actuator is modeled using a Prandtl-Ishlinskii hysteresis model. Second, by using operator-based robust right coprime factorization approach, the proposed control for the system is designed where the linear motor is optimally controlled to reduce the time consumption and the vibration at the vertical part of the arm. Meanwhile, with the hysteresis compensation, the piezoelectric actuator is used to further reduce the vibration at the horizontal part of the arm. Finally, the results of the experiment are demonstrated to verify the effectiveness of the proposed control scheme.