A Composite Controller for Piezoelectric Actuators Based on Action Dependent Dual Heuristic Programming and Model Predictive Control
Piezoelectric actuators (PEAs) have been widely applied in nanopositioning applications due to the advantages of the rapid response, large mechanical force and high resolution. However, due to the inherent hysteresis nonlinear property, the high-precision control of PEAs is challenging. To achieve the goal of high-precision motion control, various control methods have been reported in the literature. Recently, adaptive dynamic programming (ADP) has gained much attention to solve optimal control problems. Action dependent dual heuristic programming (ADDHP) is one of the effective structures of ADP, which can estimate the gradient of the cost function by using both the control action and the state as the input of the critic networks. In addition, model predictive control (MPC) is a form of control that uses the current state and the model predicted states to obtain the control action. In this paper, a composite controller is designed for the tracking control of PEAs with ADDHP and MPC. A multilayer feedforward neural network (MFNN) is proposed to model PEAs and is then instantaneously linearized for real-time finding the solutions to the optimization problem in MPC. Experiments are designed to verify the effectiveness of the proposed control method and some comparative experiments with other control methods are also conducted to show that the proposed method can achieve a better tracking performance.
KeywordsAction Dependent Dual Heuristic Programming (ADDHP) Model Predictive Control (MPC) Instantaneous linearization Piezoelectric Actuators (PEAs)
This work was supported in part by the National Nature Science Foundation under Grant 61873268, Grant 61421004, and Grant 61633016, in part by the Research Fund for Young Top-Notch Talent of National Ten Thousand Talent Program, in part by the Beijing Municipal Natural Science Foundation under Grant L182060, and in part by the Major Science and Technology Fund of Beijing under Grant Z181100003118006.
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