Structural parameter design method for a fast-steering mirror based on a closed-loop bandwidth

doi:10.1007/s11465-019-0545-y

Front. Mech. Eng.

2020, Vol. 15

Issue (1) : 55-65 https://doi.org/10.1007/s11465-019-0545-y

RESEARCH ARTICLE

Structural parameter design method for a fast-steering mirror based on a closed-loop bandwidth

Guozhen CHEN, Pinkuan LIU(

), Han DING

School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

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Abstract

When a fast-steering mirror (FSM) system is designed, satisfying the performance requirements before fabrication and assembly is vital. This study proposes a structural parameter design approach for an FSM system based on the quantitative analysis of the required closed-loop bandwidth. First, the open-loop transfer function of the FSM system is derived. In accordance with the transfer function, the notch filter and proportional-integral (PI) feedback controller are designed as a closed-loop controller. The gains of the PI controller are determined by maximizing the closed-loop bandwidth while ensuring the robustness of the system. Then, the two unknown variables of rotational radius and stiffness in the open-loop transfer function are optimized, considering the bandwidth as a constraint condition. Finally, the structural parameters of the stage are determined on the basis of the optimized results of rotational radius and stiffness. Simulations are conducted to verify the theoretical analysis. A prototype of the FSM system is fabricated, and corresponding experimental tests are conducted. Experimental results indicate that the bandwidth of the proposed FSM system is 117.6 Hz, which satisfies the minimum bandwidth requirement of 100 Hz.

Keywords fast-steering mirror structural parameter PI controller bandwidth notch filter

Corresponding Author(s): Pinkuan LIU

Just Accepted Date: 26 June 2019 Online First Date: 25 July 2019 Issue Date: 21 February 2020

Cite this article:

Guozhen CHEN,Pinkuan LIU,Han DING. Structural parameter design method for a fast-steering mirror based on a closed-loop bandwidth[J]. Front. Mech. Eng., 2020, 15(1): 55-65.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-019-0545-y
https://academic.hep.com.cn/fme/EN/Y2020/V15/I1/55

Fig.1 Mechanical design of the FSM. MCM: Monolithic compliant mechanism; VCA: Voice coil actuator.

Fig.2 (a) Monolithic compliant mechanism; (b) elastic kinematic chain.

Fig.3 Block diagram of the closed-loop control system.

Fig.4 Parameter optimization of the gains of the PI controller gains.

Fig.5 Effects of variables on the bandwidth of the closed-loop control system. Effects of (a) rotational stiffness and (b) rotational radius.

Fig.6 Local coordinate frames of the (a) translational and (b) rotational plates.

Fig.7 Coordinate frames of the compliant mechanism.

Fig.8 Coordinate frame of the FSM.

Fig.9 Rotational motion of the FSM.

Fig.10 Simulation results of (a) open-loop and (b) closed-loop frequency responses.

Fig.11 Experimental setup of the stage: (a) Motion control system; (b) fast steering mirror stage.

Fig.12 Stiffness of the FSM around (a) x-axis and (b) y-axis.

Fig.13 Open-loop system identification of the FSM.

Fig.14 Experimental results of the (a) open-loop frequency response around the x-axis; (b) closed-loop frequency response around the x-axis; (c) open-loop frequency response around the y-axis; (d) closed-loop frequency response around the y-axis.

Fig.15 Sinusoidal signal responses of the FSM around (a) the x- and (b) the y-axes.

Fig.16 Motion resolution of the FSM.

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