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

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.

Relative vibration identification of cutter and workpiece based on improved bidimensional empirical mode decomposition

In the process of cutting,the relative vibration between the cutter and the workpiece has an important effect on the surface topography.In this study,the bidimensional empirical mode decomposition(BEMD)method is used to identify such effect.According to Riesz transform theory,a type of isotropic monogenic signal is proposed.The boundary data is extended on the basis of a similarity principle that deals with serious boundary effect problem.The decomposition examples show that the improved BEMD can effectively solve the problem of boundary effect and decompose the original machined surface topography at multiple scales.The characteristic surface topography representing the relative vibration between the cutter and the workpiece through feature identification is selected.In addition,the spatial spectrum analysis of the extracted profile is carried out.The decimal part of the frequency ratio that has an important effect on the shape of the contour can be accurately identified through contour extraction and spatial spectrum analysis.The decomposition results of simulation and experimental surface morphology demonstrate the validity of the improved BEMD algorithm in realizing the relative vibration identification between the cutter and the workpiece.