压电纳米运动系统的迟滞补偿与迭代学习分数阶滑模控制

Hysteresis compensation and iterative learning-based fractional order sliding mode control for piezoelectric nano motion systems

中文关键词  压电执行器  分数阶  迟滞补偿  迭代学习干扰观测器  滑模控制

英文关键词  piezoelectric actuator  fractional order  hysteresis compensation  iterative learning disturbance observer  sliding mode control

中文摘要

      针对压电纳米运动系统的轨迹跟踪问题, 本文提出了一种自适应迟滞补偿的迭代学习分数阶滑模控制方 法. 引入Prandtl-Ishlinskii模型描述压电纳米运动系统的迟滞非线性, 借助一种新的自适应滤波辨识方法获得其参 数, 设计逆控制器对迟滞非线性进行前馈补偿. 将外部扰动和未建模动力学视为集总干扰, 使用迭代学习方法设计 一种观测器对干扰进行估计与补偿. 在此基础上, 引入双曲正切函数, 构造分数阶滑模控制器. 通过李雅普诺夫方 法证明了参数估计误差的全局收敛性和闭环系统的稳定性. 最后, 将迭代学习分数阶滑模控制方法应用在压电纳 米运动系统中, 实验验证了该方法具有较强的抗干扰能力和较高跟踪精度.

英文摘要

      This paper proposes an iterative learning-based fractional-order sliding mode control scheme with adaptive hysteresis compensation to address the problem of trajectory tracking for piezoelectric nano motion systems. The Prandtl-Ishlinskii model is introduced to describe the hysteresis nonlinearity of the piezoelectric nano motion system. A new adaptive filtering identification method is employed to identify its parameters, and an inverse controller is designed to compensate the hysteresis nonlinearity of the piezoelectric nano motion system. Both external disturbances and unmodeled dynamics are treated as a lumped disturbance, an observer with iterative leaning is developed to estimate and compensate the total disturbance. On this basis, the hyperbolic tangent function is introduced to construct a fractional-order sliding mode controller. The global convergence of the parameter estimation error and the stability of the closed-loop system are proved by the Lyapunov method. Finally, the fractional-order iterative learning sliding mode control algorithm is applied to the piezoelectric nano motion system. The experimental results are provided to verify that the proposed algorithm has strong anti-disturbance ability and high tracking accuracy.