Tracking and Resonance Control for a Three-Degree-of-Freedom Compliant Tip-Tilt-Piston Stage Driven by Voice Coil Motors Based on Recursive Positive Position Feedback

The paper designs a composite controller, including a recursive positive position feedback (RPPF) controller and a feedforward-feedback controller, to suppress resonance and eliminate lag effects when controlling the three-degree-offreedom compliant tip-tilt-piston stage. Firstly, the structural configuration of the large-stroke compliant tip-tilt-piston stage was introduced. Then, the open-loop transfer function of each voice coil motor (VCM) acting individually on the stage was obtained using MATLAB’s System Identification toolbox. Next, using the $H_{2}$ norm, Laplace transform, and discretization processing to design recursive positive position feedback (RPPF) controllers and feedforward feedback controllers. Finally, bandwidth testing and triangular wave tracking experiments were conducted to verify the effectiveness of the proposed control scheme based on the maximum absolute error ($e_{m}$) and root mean square error ($e_{\text {rms }}$). Experimental results show that the closedloop system bandwidth using PI + RPPF + FF controller can be increased by $1130 \%$ and $26.8 \%$, respectively, compared to proportional-integral (PI) and PI+RPPF controllers. With PI + RPPF + FF controller, it can largely enhance the tracking performances of the stage.