Integral terminal sliding-mode-based adaptive integral backstepping control for precision motion of a piezoelectric ultrasonic motor

Abstract

The versatile and effective piezoelectric ultrasonic motor (PUM) has been widely used in many significant industrial and scientific applications, including precision positioning systems and surgical devices. However, the inherent friction, hysteresis nonlinearity, model uncertainties as well as various invariably presented external disturbances bring great challenges on the precision motion of PUM. In this development, a novel integral terminal sliding-mode-based adaptive integral backstepping control (ITSMAIBC) is formulated to accommodate theses adverse impacts and retain high tracking precision. In particular, the second-order auxiliary differential equations based on the integral terminal sliding-mode surface are constructed to obtain the property of finite-time convergence and desired steady-state performance. Through employing integral backstepping methodology with the auxiliary equations, the asymptotic stability is guaranteed and a high-order sliding-mode control (SMC)-like performance is also achieved to relieve the chattering phenomenon. An adaptive law is further incorporated into the proposed controller to estimate the upper bound of the total disturbance. The robust stability is proven by the Lyapunov theory. Moreover, the implementation of ITSMAIBC is simple without any high-order derivative or observer. The actual experiments on a PUM verify the effectiveness of the controller through tracking continuous sinusoidal waves and discontinuous triangular waves with different frequencies and amplitudes, and the proposed scheme achieves the best tracking performance in comparison with three benchmark controllers. A surgical operation on a mock membrane experimental system is also performed to validate the practical application of the proposed method on ear surgery.