多维磁悬浮隔振系统动力学模型与控制策略
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摘要
磁悬浮隔振系统具有非线性、强耦合、高响应、宽频带等特点,系统的隔振控制目标与其定子和浮子之间的位置约束相互制约,这对系统的精密控制提出了较大的挑战。为解决该问题,建立了面向控制的六自由度磁悬浮隔振系统非线性动力学模型,并提出了双闭环控制策略,使系统在低频到中高频带内实现隔振控制,在极低频带内实现跟踪控制。采用PD定点控制算法,在MATLAB/Simulink环境中开发了控制系统仿真程序,通过分析不同扰动频率下浮子的绝对运动响应以及定子与浮子之间的相对运动响应,获得了系统的隔振控制与跟踪控制仿真结果。搭建了磁悬浮隔振平台样机测试系统,验证了动力学模型的正确性和控制策略的有效性。
The maglev vibration isolation system has the characteristics of nonlinearity,coupling,high response and wide band.The vibration isolation control target and the position constraint between the stator and the floater is restricted by each other,which brings a great challenge on precision control.To solve the problem,a six degrees-of-freedom nonlinear dynamic model of the maglev vibration isolation system for control is established and a double-closed-loop control strategy is put forward.Through that,the system can achieve vibration isolation control in low and medium frequency band and achieve motion tracking control in the very-low frequency band.PD fixed-point control algorithm is adopted and a control system simulation program is developed in MATLAB/Simulink environment.By analyzing the absolute motion response of the floater and the relative motion response between the stator and the floater for different disturbance frequencies,the simulation results of isolation control and the tracking control are obtained.A test system of the maglev vibration isolation platform prototype is setup,and the correctness of the dynamic model and the validity of the proposed control strategy are verified.
The maglev vibration isolation system has the characteristics of nonlinearity,coupling,high response and wide band.The vibration isolation control target and the position constraint between the stator and the floater is restricted by each other,which brings a great challenge on precision control.To solve the problem,a six degrees-of-freedom nonlinear dynamic model of the maglev vibration isolation system for control is established and a double-closed-loop control strategy is put forward.Through that,the system can achieve vibration isolation control in low and medium frequency band and achieve motion tracking control in the very-low frequency band.PD fixed-point control algorithm is adopted and a control system simulation program is developed in MATLAB/Simulink environment.By analyzing the absolute motion response of the floater and the relative motion response between the stator and the floater for different disturbance frequencies,the simulation results of isolation control and the tracking control are obtained.A test system of the maglev vibration isolation platform prototype is setup,and the correctness of the dynamic model and the validity of the proposed control strategy are verified.
引文
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[2]李伟鹏,黄海,边边.精密跟瞄Hexapod平台研制及其振动控制[J].航空学报,2009,30(2):259-264.LI W P,HUANG H,BIAN B.Design and vibration control of precision pointing Hexapod[J].Acta Aeronautica et Astronautica Sinica,2009,30(2):259-264(in Chinese).
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[13] ZHU W H,TRYGGVASON B,PIEDBOEUF J.On active acceleration control of vibration isolation systems[J].Control Engineering Practice,2006,14(8):863-873.
[14] HU Y,CHEN C,WU H,et al.Study on structural optimization design and cascade PID control of maglev actuator for active vibration isolation system[J].Journal of Vibration and Control,2018,24(10):1829-1847.
[15] LIU J,LI Y,ZHANG Y,et al.Dynamics and control of aparallel mechanism for active vibration isolation in space station[J].Nonlinear Dynamics,2014,76(3):1737-1751.
[16] LI Y,HE L,SHUAI C G.Nonlinearity of maglev actuator and adaptive vibration control using improved FxLMS algorithm[J].Applied Mechanics&Materials,2013,390:434-439.
[17] YANG B J,CALISE A,CRAIG J,et al.Adaptive control for a microgravity vibration isolation system:AIAA-2005-6071[R].Reston,VA:AIAA,2005.
[18] HAMPTON R D,KNOSPE C,GRODSINSKY C,et al.Microgravity vibration isolation:Optimal preview and feedback control:NASA Technical Memorandum 105673[R].Washington,D.C.:NASA,1992.
[19] KIM Y K,WHORTON M S.Equations of motion for the g-LIMIT microgravity vibration isolation system:NASA/TM 211301[R].Washington,D.C.:NASA,2001.
[20] BEECH G,HAMPTON R.A simplified model of ARIS for optimal controller design:AIAA-2001-1138[R].Reston,VA:AIAA,2001.
[21] HAMPTON R,QURAISHI N.A state-space model of ARIS for optimal controller design:MATLAB implementation:AIAA-2004-0786[R].Reston,VA:AIAA,2004.
[22] HAMPTON R,RAO N S,KIM Y,et al.A high-fidelity dynamic model for the active rack isolation system:AIAA-1998-0458[R].Reston,VA:AIAA,1998.
[2]李伟鹏,黄海,边边.精密跟瞄Hexapod平台研制及其振动控制[J].航空学报,2009,30(2):259-264.LI W P,HUANG H,BIAN B.Design and vibration control of precision pointing Hexapod[J].Acta Aeronautica et Astronautica Sinica,2009,30(2):259-264(in Chinese).
[3] COBB R G,SULLIVAN J M,DAS A,et al.Vibration isolation and suppression system for precision payloads in space[J].Smart Materials and Structures,1999,8(6):798-812.
[4] WHORTON M.Robust control for microgravity vibration isolation[J].Journal of Spacecraft&Rockets,2005,42(1):152-160.
[5] GRODSINSKY C M,WHORTON M S.Survey of active vibration isolation systems for microgravity applications[J].Journal of Spacecraft and Rockets,2000,37(5):586-596.
[6] WINTHROP M F,COBB R G.Survey of state-of-the-art vibration isolation research and technology for space applications[J].Smart Structures and Materials,2003,5052:13-26.
[7] ZHU T,CAZZOLATO B,ROBERTSON W S,et al.Vibration isolation using six degree-of-freedom quasi-zero stiffness magnetic levitation[J].Journal of Sound&Vibration,2015,358:48-73.
[8]张军,谌勇,骆剑,等.整星隔振技术的研究现状和发展[J].航空学报,2005,26(2):179-183.ZHANG J,CHEN Y,LUO J,et al.Review of the whole-spacecraft isolation techniques[J].Acta Aeronautica et Astronautica Sinica,2005,26(2):179-183(in Chinese).
[9] KIM M H,KIM H C,HONG D P,et al.Design of a VCM actuator using Halbach magnet array for active vibration isolation system[J].Advanced Materials Research,2014,945-949:1465-1469.
[10] TRYGGVASON B,STEWART B,DECARUFEL J.The Microgravity vibration Isolation Mount(MIM):Development and flight test results[C]∥48th International Astronautical Congress,1997.
[11] TRYGGVASON B,STEWART W,JEAN D,et al.Acceleration levels and operation of the Microgravity vibration Isolation Mount(MIM)on the shuttle and the Mir space station:AIAA-1999-0578[R].Reston,VA:AIAA,1999.
[12] FENN R C,DOWNER J R,GONDHALEKAR V,et al.An active magnetic suspension for space-based microgravity vibration isolation[J].Active Noise and Vibration Control,1990,8:49-56.
[13] ZHU W H,TRYGGVASON B,PIEDBOEUF J.On active acceleration control of vibration isolation systems[J].Control Engineering Practice,2006,14(8):863-873.
[14] HU Y,CHEN C,WU H,et al.Study on structural optimization design and cascade PID control of maglev actuator for active vibration isolation system[J].Journal of Vibration and Control,2018,24(10):1829-1847.
[15] LIU J,LI Y,ZHANG Y,et al.Dynamics and control of aparallel mechanism for active vibration isolation in space station[J].Nonlinear Dynamics,2014,76(3):1737-1751.
[16] LI Y,HE L,SHUAI C G.Nonlinearity of maglev actuator and adaptive vibration control using improved FxLMS algorithm[J].Applied Mechanics&Materials,2013,390:434-439.
[17] YANG B J,CALISE A,CRAIG J,et al.Adaptive control for a microgravity vibration isolation system:AIAA-2005-6071[R].Reston,VA:AIAA,2005.
[18] HAMPTON R D,KNOSPE C,GRODSINSKY C,et al.Microgravity vibration isolation:Optimal preview and feedback control:NASA Technical Memorandum 105673[R].Washington,D.C.:NASA,1992.
[19] KIM Y K,WHORTON M S.Equations of motion for the g-LIMIT microgravity vibration isolation system:NASA/TM 211301[R].Washington,D.C.:NASA,2001.
[20] BEECH G,HAMPTON R.A simplified model of ARIS for optimal controller design:AIAA-2001-1138[R].Reston,VA:AIAA,2001.
[21] HAMPTON R,QURAISHI N.A state-space model of ARIS for optimal controller design:MATLAB implementation:AIAA-2004-0786[R].Reston,VA:AIAA,2004.
[22] HAMPTON R,RAO N S,KIM Y,et al.A high-fidelity dynamic model for the active rack isolation system:AIAA-1998-0458[R].Reston,VA:AIAA,1998.