Memory related predictive compensation control of Piezoelectric actuators based on global linearization Koopman theory.

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.