基于RBF神经网络的迟滞非线性模型预测控制

Nonlinear model predictive control of hysteresis based on RBF neural network

压电执行器具有响应快、质量比大、刚度高等特点,在纳米技术领域得到了广泛的应用。迟滞特性作为一种固有的非线性特性,极大地影响了迟滞控制的性能。本文提出了一种非线性模型预测控制(NMPC)方法来解决压电执行器的位移跟踪问题。首先,利用RBF神经网络实现了压电执行器的"外源输入非线性自回归移动平均"(NARMAX)模型;其次,利用NMPC原理将跟踪控制问题转化为优化问题,然后采用梯度下降算法求解。为验证所提出的建模和控制方法的有效性,并进行了MATLAB与COMSOL仿真实验。结果表明,所提出的RBF预测模型具有令人满意的精度,NMPC方法跟踪所得期望位移与实际位移绝对误差值最大达到0.016μm,平均绝对误差达到0.0121μm,具有较高的精度。

Piezoelectric actuators have the characteristics of fast response,large mass ratio,high rigidity,etc.,and have been widely used in the field of nanotechnology.As a kind of inherent nonlinear characteristic,hysteresis characteristic greatly affects the performance of hysteresis control.This paper proposes a nonlinear model predictive control(NMPC)method to solve the displacement tracking problem of piezoelectric actuators.First,the RBF neural network is used to realize the"external input nonlinear autoregressive moving average"(NARMAX)model of the piezoelectric actuator;secondly,the NMPC principle is used to transform the tracking control problem into an optimization problem,and then the gradient descent algorithm is used to solve it.In order to verify the effectiveness of the proposed modeling and control methods,MATLAB and COMSOL simulation experiments were carried out.The results show that the proposed RBF prediction model has satisfactory accuracy,the maximum absolute error between the expected displacement and the actual displacement obtained by the NMPC method tracking is 0.016μm,and the average absolute error is 0.0121μm,which has high accuracy.