Two degree-of-freedom control design with improved H ∞ LMI representation

Chao Peng,Hongbing Xu,Jian Zhang

doi:10.1186/1029-242x-2012-147

Abstract

This paper focuses on the two degree-of-freedom (2DOF) control design problem for high-speed and precision tracking system. The requirements for tracking resolution, bandwidth are transformed to the H ∞ norm minimizing problem of tracking error. A 2DOF control design approach based on an improved H ∞ linear matrix inequalities (LMI) representation is proposed. The design approach offers a new LMI to obtain the feedforward controller and feedback controller in 2DOF control scheme. The results of simulation experiment demonstrates the proposed approach could obtain a better tracking performance compared with conventional H ∞ 2DOF design based on bounded real lemma.

Highlights

1 Introduction It is well known that two degree-of-freedom ( DOF) control design which combines the feedforward control and feedback control to achieve the desired tracking performance has been widely applied in trajectory tracking control system [ – ]
The DOF control system combined with inversion feedforward controller and high-gain feedback controller could achieve high-precision high-speed positioning in piezoactuators [ ]
By the DOF control design based on bounded real lemma (BRL) [ ], the minimum value of Wp(s)ε DOF(s) ∞ is . which is larger than the proposed design approach

Summary

Introduction

It is well known that two degree-of-freedom ( DOF) control design which combines the feedforward control and feedback control to achieve the desired tracking performance has been widely applied in trajectory tracking control system [ – ]. The DOF control system designed by solving the minimizing problem of the H∞ norm of weighted function is utilized to enhance the tracking performance of an atomic force microscope [ ]. Several robust DOF control design approaches take account into H∞ performance specification in worst system uncertainties and solve the H∞ optimization problem to improve the tracking performance and robustness.

Results

Conclusion