Investigation of Legendre polynomials expanded adaptive controller with inverse compensation for high frequency tracking of electro-hydraulic force systems

Accurate force tracking of an electro-hydraulic force system (EHFS) is of great significance in various industrial applications. As the EHFS is inevitably confronted with hydraulic nonlinearities, dynamic variations and uncertain disturbances, the real-time force tracking performance is generally unsatisfactory, especially for high frequency command force signals. For reducing the force tracking error with relatively high frequency inputs, a Legendre polynomials expanded adaptive controller with inverse compensation is proposed in this paper. The proposed controller is constructed by introducing an offline designed inverse compensation (IC) controller and an online adaptive controller to the EHFS governed by traditional Proportional Integral (PI) controller, in which the former IC controller is acting as the inner loop controller and the latter adaptive controller is regarded as an outer controller. The inner loop IC controller with fixed control parameters is offline designed on the basis of traditional PI controller by means of the generalized projection identification algorithm and the zero magnitude error tracking technology, focusing on extending the real-time force tracking bandwidth of the EHFS. The outer loop online adaptive controller is developed by Legendre polynomials expanded adaptive filters with nonlinear mapping ability, whose weights are online updated by an adaptive tuning algorithm with the aim of handling system's dynamic variations, nonlinearities and uncertain disturbances. The proposed controller is implemented on a real EHFS test rig by the xPC/Target rapid prototyping technique, and comparative experimental results demonstrate that the proposed controller can achieve much higher high frequency tracking performance than the traditional PI and IC controller commonly used in industry.