Journal
ULTRASONICS
Volume 124, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.ultras.2022.106727
Keywords
Piezoelectric actuators; Hysteresis; Koopman predictor; Global linearization; model predictive control (MPC)
Funding
- National Natural Science Foundation of China [51905131]
- Natural Science Foundation of Heilongjiang Province [LH2020E040]
- National Major Scientific Instruments and Equipment Development Special Funds [2018YFF01012003]
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This paper proposes a linear model predictive control scheme for compensating the nonlinearity of piezoelectric actuators (PEAs). The proposed scheme includes a global linearization predictor based on Koopman theory and a linear MPC optimization problem. The validity of the proposed scheme is demonstrated by experiments, showing a small steady-state error and improved computational efficiency.
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 mu m. 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 mu m, 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.
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