Composite Data Driven-Based Adaptive Control for a Piezoelectric Linear Motor

Piezoelectric linear motors play an important role in ultra-precision manufacturing technology. However, the complex nonlinear relationship between the input and output of the piezoelectric linear motors limits their further application. In this paper, to achieve precise motion control for a piezoelectric linear motor, a composite data driven-based adaptive control method is proposed, consisting of a correction controller, model free adaptive controller (MFAC), and low pass filter. The proposed control method addresses the demand for a precise model of the piezoelectric linear motor and solely relies on the linear model and input/output measurement data. First, an experimental test is implemented to analyze the complex nonlinearity between input and output signals of the controlled system, and a correction control is employed based on the dynamic linear sub-model of the piezoelectric linear motor to improve its dynamic and static characteristics. Then, to avoid the influence of unmodeled dynamics, such as inherent nonlinearity and external vibration, a MFAC is established as a feedback controller using data driven technology. In addition, a low pass filter is incorporated into the feedback loop to eliminate high frequency measurement noise in the system, thus improving the transient response of the MFAC method. Finally, the theoretical analysis of the error convergence is presented. The effectiveness of the proposed method is verified via comparisons with a correction control method, correction control-based digital sliding-mode control method, and correction control-based MFAC method. The experimental results indicate that the proposed control method is suitable for engineering applications. In particular, the root-mean-square error (RMSE) for the third-order S-curve tracking using the proposed is reduced by more than 15%, compared with the RMSEs for the cases with contrast control methods.