Robust ultra-precision motion control of linear ultrasonic motors: A combined ADRC-Luenberger observer approach

Abstract

This work introduces an output feedback Active Disturbance Rejection Control scheme applied to the nanoposition control of uncertain Linear Ultrasonic Motors. The proposed algorithm, which is termed as the ADRC-Luenberger Observer Controller (ADRC-LOC), is composed of a Proportional Derivative controller plus a Disturbance Observer, the latter producing an estimate of the unknown disturbances affecting the ultrasonic motor to counteract their effects. A Luenberger Observer, which is designed using the disturbance-free model of the ultrasonic motor, produces velocity and acceleration estimates from position measurements. The velocity estimate is used in the derivative action of the Proportional Derivative controller whereas the acceleration estimate feeds the Disturbance Observer. The stability analysis of the closed-loop system shows that its solutions are Uniformly Ultimately Bounded. The effectiveness of the proposed approach is tested by means of real-time experiments. These outcomes show that the position errors obtained with the proposed ADRC-LOC are in the range of 50–100 nm. A recently proposed Sliding Mode Controller is also tested for comparison purposes. The proposed approach may be applied to linear uncertain perturbed systems of arbitrary order.