Global Linearized Sparse Prediction and Adaptive Dead Zone Compensation for a Piezoelectric Actuator

A piezoelectric actuator (PEA) is a fundamental part of a high-precision motion system, yet its performance is critically constrained by inherent nonlinearities such as the velocity dead zone and hysteresis. To overcome these limitations and the associated time-varying dynamics, this study introduces a novel control framework for a dual-mode standing wave PEA. The framework integrates a Global Linearized Sparse Prediction (GLSP) model with an Adaptive Kalman Observer-based Model Predictive Control (AKOBMPC) strategy, specifically designed for velocity dead-zone compensation. The GLSP model employs Koopman operator theory to lift the complex, nonlinear electromechanical and contact dynamics into a linear invariant subspace. Incorporated with a deep learning-based structured pruning mechanism, the model achieves an effective balance between prediction accuracy and computational efficiency, facilitating real-time implementation. Leveraging this high-fidelity model, the AKOBMPC algorithm is developed to estimate unmeasurable disturbances and optimize the control sequence for precise velocity tracking. Experimental results demonstrate the GLSP model's accurate prediction of system behavior under varying loads and excitation frequencies. The proposed controller effectively suppresses the velocity dead zone, achieving tracking errors within ±0.35 mm/s for a 40.00 mm/s trapezoidal reference and within ±0.50 mm/s for sinusoidal tracking. These results confirm the superior performance of the AKOBMPC scheme over conventional methods, offering a robust solution for high-precision velocity regulation in PEA system and contributing to the advancement of next-generation precision actuator.