H∞Optimal Inversion Feedforward and Robust Feedback Based 2DOF Control Approach for High Speed-Precision Positioning Systems

Abstract

This paper proposed a novelH∞optimal inversion feedforward and robust feedback based two-freedom-of-freedom (2DOF) control approach to address the positioning error caused by system uncertainties in high speed-precision positioning system. To minimize theH∞norm of the positioning error in the presence of model uncertainty, a linear matrix inequality (LMI) synthesis approach for optimal inversion feedforward controller design is presented. The specification of position resolution, control width, robustness, and output signal magnitude imposed on the entire 2DOF control system are taken as optimization objectives of feedback controller design. The robust feedback controller design approach integrates with feedforward controller systematically and is obtained via LMI optimization. The proposed approach was illustrated through a simulation example of nanopositioning control in atomic force microscope (AFM); the experiment results demonstrated that the proposed 2DOF control approach not only achieves the performance specification but also could improve the positioning control performance compared withH∞mixed sensitivity feedback control and inversion-based 2DOF control.