A Delay-based Nonlinear Controller for Nanopositioning of Linear Ultrasonic Motors

This work introduces a delay-based nonlinear controller aimed at position control of linear ultrasonic motors (LUMs), which is termed the cascade nonlinear proportional integral retarded (CNPIR) control law. This new controller incorporates a time delay in its structure, composed of two nested loops. The inner velocity loop is regulated through an integral retarded (IR) controller that contains a time delay in its structure. The outer position loop resorts to a nonlinear proportional (NP) controller endowed by a saturation function. A tuning procedure for the CNPIR controller is also proposed, and it is based on the placement of multiple dominant roots. The inner loop is tuned by assigning a dominant triple root, whereas a method based on solving a transcendental equation allows tuning the outer loop and assigns two dominant roots. Moreover, pole dominance is assessed through the argument principle. Experimental results on a linear ultrasonic motor allow assessing the real-time performance of the proposed controller to achieve high precision and fast response in spite of the effects of inner disturbances, hysteresis, and friction phenomena.