Piezoelectric actuators (PEAs) are widely applied in precision positioning. However, the nonlinear characteristics such as hysteresis and creep limit the ultra-precision applications. This paper proposes a linear model predictive control (MPC) scheme for compensating the nonlinearity of PEA. Firstly, a global linearization predictor is constructed based on Koopman theory to represent the hysteresis behavior of PEA. The high-precision predictor is implemented by a novel memory related neural network (NN), and the prediction error reaches only 0.002 μm. Then the tracking control problem is transformed into a linear MPC optimization problem, thereby avoids the sophisticated nonconvex optimization problem. In practice, the constrained MPC problem is rewritten into a dense form, and solved by quadratic programming technique. Finally, the validity of the proposed scheme is demonstrated by experiments. The short-term steady-state error of the proposed scheme is 0.002 μm, which is far less than that of the inversion method; the long-term steady-state performance also indicates its effectiveness in compensating creep. Further, the excellent frequency-dependent results show that the proposed scheme is superior to the existing control method. Especially, the computational efficiency can be improved by 20%. The proposed predictor and control method are of great significance for the tracking control of PEA.
Keywords: Global linearization; Hysteresis; Koopman predictor; Piezoelectric actuators; model predictive control (MPC).
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