Modelling of piezoelectric actuating systems subjected to variable loads and frequencies and applications to prescribed performance control

Abstract

Piezoelectric actuators can offer micro/nano-level precision actuating ability and have been employed in different applications. For the piezoelectric actuating systems, the output actuating performance is affected not only by the internal non-smooth hysteresis but also by the operating load and the excitation frequency. To improve the actuating precision, predicting the nonlinear behaviour of the piezoelectric actuating system is essential for effective designs of control approaches. In this paper, a modified rate-dependent Prandtl–Ishlinskii model is presented to explore the coupling effects analytically between the internal hysteresis and the operating frequency with the external loads and predict the output behaviour of the piezoelectric actuating system accurately. The proposed modelling method is testified on a piezoelectric actuating platform under broad ranges of excitation frequencies (1–80 Hz) and external loads (0–0.5 kg), and the comparison results using the rate-dependent Prandtl–Ishlinskii (RDPI) model are also provided to prove the precision of the proposed method. Combining with the modified RDPI model, a guaranteeing preselected tracking controller is developed to ensure the output performance, and a set of tracking experiments under different frequencies with load is performed. The experimental results compared with PID control performance validate the effectiveness of the proposed prescribed performance control method and its high actuating performance against the adverse effects from the external hysteresis nonlinearities and external loads.