An Integrator-Backstepping-Based Dynamic Surface Control Method for a Two-Axis Piezoelectric Micropositioning Stage
ABSTRACT In this paper, an integrator-backstepping-based dynamic surface control method for a two-axis piezoelectric micropositioning stage is proposed. First, according to the dynamics of motion of a mechanical mass-spring system, mathematical equations that contain a linear viscous friction, a varied elasticity with cross-coupling effect due to mechanical bending, and dynamics of a hysteresis variable is proposed to describe the motion dynamics of the two-axis piezopositioning stage. Next, from the equations, a state-space model in which the applied voltage to the stage is defined as an output of an integrator is derived. On the basis of this state-space model, the integrator-backstepping-based dynamic surface control is proposed. By using the proposed control method to trajectory tracking of the two-axis piezopositioning stage, the dynamic performance, robustness to parameter variations, and trajectory tracking error can be improved. Experimental results of the time responses from the computer-controlled two-axis piezopositioning stage illustrate the validity of the proposed control method for practical applications in trajectory tracking.
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ABSTRACT: The XY table is composed of two piezo electric actuators (PEA) and a positioning mechanism (PM). Due to existence of hysteretic nonlinearity in the PEA and the friction in the PM, the high precision control for the XY table is a challenging task. This paper discusses the high precision adaptive control for the XY talbe, where the hysteresis is described by Prandtl-Ishlinskii model. The proposed control law ensures the global stability of the controlled stage, and the position error can be controlled to approach to zero asymptotically. Experimental results show the effectiveness of the proposed method.
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ABSTRACT: In this paper, a novel robust nonlinear sliding mode generator excitation controller for single machine infinite bus(SMIB) with parameter uncertainty and disturbance is proposed. The controller is designed in a backstepping manner, proportional-integral-derivative(PID) stabilizing signal of the virtual error is introduced in the design procedure. First according to the backstepping approach, series Lyapunov functions are constructed step by step, the adaptive law of damping coefficient is given in the second step, and finally, a novel sliding surface is designed. The whole control law is obtained by applying the sliding mode control theory, so the disturbance is attenuated. To validate the control law, some simulations were carried on in case of two faults, the results showed that the proposed control method is able to achieve a quite satisfactory control effect.
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