The aim of this work is to find an adaptive control scheme to realize precise position tracking for a piezo-actuated stage, which is usually very difficult to control due to the essential nonlinearity and unknown uncertainty. Firstly, a proportional-integral-derivative (PID) sliding mode controller is designed based on the established model and the estimated parameters. Then, in order to reduce the influence of model error, a radial basis function (RBF) neural network is integrated to the controller to improve the control performance. Eventually, an adaptive RBF based PID-type sliding mode controller (RBF-PIDSMC) is proposed and its stability is derived mathematically based on Lyapunov theory. Simulation results of the proposed controller are compared with the PID sliding mode controller to verify its tracking performance. Positioning tracking experiments with two different trajectories are also conducted to verify the correctness and effectiveness of the proposed controller. We can conclude that the proposed controller can be used to track commanded position trajectory for the piezoelectric stage.

这项工作的目的是找到一种自适应控制方案，以实现对压电驱动平台的精确位置跟踪，由于固有的非线性和未知不确定性，通常很难控制该平台。首先，基于所建立的模型和估计的参数，设计了比例积分微分（PID）滑模控制器。然后，为了减少模型误差的影响，将径向基函数（RBF）神经网络集成到控制器中以提高控制性能。最终提出了一种基于RBF的自适应PID型滑模控制器（RBF-PIDSMC），并基于Lyapunov理论从数学上推导了其稳定性。将该控制器的仿真结果与PID滑模控制器进行比较，以验证其跟踪性能。还进行了两种不同轨迹的定位跟踪实验，以验证所提出控制器的正确性和有效性。我们可以得出结论，提出的控制器可用于跟踪压电平台的指令位置轨迹。