\(H_\infty\) optimal inversion feedforward and robust feedback based 2DOF control approach for high speed-precision positioning systems (Q5964367)

Summary: This paper proposes a novel \(H_\infty\) optimal inversion feedforward and robust feedback based 2-degrees-of-freedom (2DOF) control approach to address the positioning error caused by system uncertainties in high speed-precision positioning system. To minimize the \(H_\infty\) 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 is illustrated through a simulation example of nanopositioning control in Atomic Force Microscope (AFM); the experiment results demonstrate that the proposed 2-DOF control approach not only achieves the performance specification but also could improve the positioning control performance compared with \(H_\infty\) mixed sensitivity feedback control and inversion-based 2-DOF control.