基于改进PID的压电微定位平台反馈控制
|
摘要
为使压电微定位平台具有良好的性能,采用改进PID控制器对其进行反馈控制。首先,对压电执行器机电特性及平台动力学特性进行分析,建立并辨识出了平台动力学模型;其次,采用非饱和积分和钝化微分分别改进PID控制器中的常规积分和常规微分,以减小平台响应的超调量以及对干扰的敏感性;最后,对平台控制系统进行了仿真并实验验证了其有效性,结果表明,平台对5μm阶跃目标位移的响应为0.3 s,且无超调,稳态误差中线由无控制时的0.57~0.66μm减小为几乎为0;在跟踪由正弦信号、常值信号、斜坡信号所组成的目标位移时,跟踪误差几乎为0。改进PID控制器可消除平台的定位误差,并使平台具有较快的响应,且无超调。
To guarantee good performances for the piezoelectric micro-positioning stage,an improved PID controller is used to realize feedback control of the platform. To begin with,the dynamic model is derived and identified based on the electromechanical and the dynamic characteristics of the platform. Then,the conventional integral and differential terms of the PID controller are improved by means of the unsaturated integral and the passivation differential. The integral term can reduce the overshoot and the sensitivity for disturbances. Finally,the control system of the platform is simulated and the effectiveness is verified by experiments. The results show that the response of the stage to the step target displacement of 5 μm is 0. 3 s with no overshoot,and the steady state error is reduced to almost 0 from 0. 57 ~ 0. 66 μm in the case without control. When tracking the target displacement composed of sine signal,constant signal and slope signal,the tracking error is still almost 0. It can be found out that the improved PID controller can eliminate the positioning error,and obtain a faster response with no overshoot.
To guarantee good performances for the piezoelectric micro-positioning stage,an improved PID controller is used to realize feedback control of the platform. To begin with,the dynamic model is derived and identified based on the electromechanical and the dynamic characteristics of the platform. Then,the conventional integral and differential terms of the PID controller are improved by means of the unsaturated integral and the passivation differential. The integral term can reduce the overshoot and the sensitivity for disturbances. Finally,the control system of the platform is simulated and the effectiveness is verified by experiments. The results show that the response of the stage to the step target displacement of 5 μm is 0. 3 s with no overshoot,and the steady state error is reduced to almost 0 from 0. 57 ~ 0. 66 μm in the case without control. When tracking the target displacement composed of sine signal,constant signal and slope signal,the tracking error is still almost 0. It can be found out that the improved PID controller can eliminate the positioning error,and obtain a faster response with no overshoot.
引文
[1]SUMET H,EBERHARD B.Design and characterzation of a PZT driven micromachining tool based on single-point tool tip geometry[J].Precision Engineering,2009,33(4):387-394.
[2]王海涛,李世杰,张艳蕊.基于压电陶瓷的微进给平台的实验研究[J].机械设计与制造,2015,38(7):30-32.WANG H T,LI SH J,ZHANG R Y.Studies and experiment of micro-feeding table based on piezoelectric ceramic[J].Machinery Design&Manufacture,2015,38(7):30-32.
[3]TING Y,LI C C,LIN C M.Controller design for for high-frequency cutting using a piezo-drivenmicrostage[J].Precision Engineering,2011,35(3):455-463.
[4]洪涛,王佳,刘秀梅,等.用于扫描探针显微镜的复合型三维压电扫描器[J].压电与声光,2000,22(1):30-32.HONG T,WANG J,LIU X M,et al.Compound threedimensional piezoelectric scanner used in scanning probe microscopy[J].Pieoelectrics&Acoustooptics,2000,22(1):30-32.
[5]SALAPAKA S M,SALAPAKA M V.Scanning probe microscopy[J].Control Systems IEEE,2008,28(2):65-83.
[6]李源,孙薇斌,邵力,等.基于MEMS微触觉测头和纳米测量机的扫描测量平台[J].仪器仪表学报,2009,30(3):580-585.LI Y,SUN W B,SHAO L,et al.Scanning test pplatform based on MEMS micro tactile probe and nanomeasuring machine[J].Chinese Journal of Scientific Instrument,2009,30(3):580-585.
[7]刘锦勇,杨湛,陈涛,等.面向三维组装的微纳平台设计与研究[J].压电与声光,2016,38(4):548-552.LIU J Y,YANG ZH,CHEN T,et al.Design and research of the micro-nano system for 3D micro-assembly[J].Piezoelectric&Acoustooptics,2016,38(4):548-552.
[8]于志亮,刘杨,王岩,等.基于改进PI模型的压电陶瓷迟滞特性补偿控制[J].仪器仪表学报,2017,38(1):129-135.YU ZH L,LIU Y,WANG Y,et al.Hysteresis compensation and control of piezoelectric actuator based on an improved PI model[J].Chinese Journal of Scientific Instrument,2017,38(1):129-135.
[9]CHIEN H L,WEN Y J,YEAU R J.Design and control of a long-traveling nano-positioning stage[J].Precision Engineering,2010,34(3):497-506.
[10]蔡成波,崔玉国,蔡永根,等.压电微动平台的改进PID控制[J].压电与声光,2016,38(3):441-444.CAI C B,CUI Y G,CUI Y G,et al.Improved PID control of piezoelectric micro-positioning stage[J].Piezoelectrics&Acoustooptics,2016,38(3):441-444.
[11]WANG F C,TSAI Y C,HSIEH C H,et al.Robust control of a two-axis piezoelectric nano-positioning stage[J].World Congress,2011:3539-3544.
[12]ZHU W,YANG F F,RUI X T.Robust independent modal space control of a coupled nano-positioning piezostage[J].Mechanical Systems and Signal Processing,2018,106:466-478.
[13]LEON C,BIJAN S,UMESH B,et al.Development and control of a two DOF linear-angular precision positioning stage[J].Mechatronics,2015,32:34-43.
[14]张栋,张承进,魏强,等.压电工作台的神经网络控制[J].光学精密工程,2012,20(3):587-596.ZHANG D,ZHANG CH J,WEI Q,et al.Modeling and control of piezo-stage using neural networks[J].Optics and Precision Engineering,2012,20(3):587-596.
[15]LI L L,LI CH X,GU G Y,et al.Positive acceleration,velocity and position feedback based damping control approach for piezo-actuated nanopositioning stages[J].Mechatronics,2017,47:97-104.
[16]CAI K H,TIAN Y L,WANG F J,et al.Development of a piezo-driven 3-DOF stage with T-shape flexible hinge mechanism[J].Robotics and Computer-Integrated Manufacturing,2016,37(3):125-138.
[2]王海涛,李世杰,张艳蕊.基于压电陶瓷的微进给平台的实验研究[J].机械设计与制造,2015,38(7):30-32.WANG H T,LI SH J,ZHANG R Y.Studies and experiment of micro-feeding table based on piezoelectric ceramic[J].Machinery Design&Manufacture,2015,38(7):30-32.
[3]TING Y,LI C C,LIN C M.Controller design for for high-frequency cutting using a piezo-drivenmicrostage[J].Precision Engineering,2011,35(3):455-463.
[4]洪涛,王佳,刘秀梅,等.用于扫描探针显微镜的复合型三维压电扫描器[J].压电与声光,2000,22(1):30-32.HONG T,WANG J,LIU X M,et al.Compound threedimensional piezoelectric scanner used in scanning probe microscopy[J].Pieoelectrics&Acoustooptics,2000,22(1):30-32.
[5]SALAPAKA S M,SALAPAKA M V.Scanning probe microscopy[J].Control Systems IEEE,2008,28(2):65-83.
[6]李源,孙薇斌,邵力,等.基于MEMS微触觉测头和纳米测量机的扫描测量平台[J].仪器仪表学报,2009,30(3):580-585.LI Y,SUN W B,SHAO L,et al.Scanning test pplatform based on MEMS micro tactile probe and nanomeasuring machine[J].Chinese Journal of Scientific Instrument,2009,30(3):580-585.
[7]刘锦勇,杨湛,陈涛,等.面向三维组装的微纳平台设计与研究[J].压电与声光,2016,38(4):548-552.LIU J Y,YANG ZH,CHEN T,et al.Design and research of the micro-nano system for 3D micro-assembly[J].Piezoelectric&Acoustooptics,2016,38(4):548-552.
[8]于志亮,刘杨,王岩,等.基于改进PI模型的压电陶瓷迟滞特性补偿控制[J].仪器仪表学报,2017,38(1):129-135.YU ZH L,LIU Y,WANG Y,et al.Hysteresis compensation and control of piezoelectric actuator based on an improved PI model[J].Chinese Journal of Scientific Instrument,2017,38(1):129-135.
[9]CHIEN H L,WEN Y J,YEAU R J.Design and control of a long-traveling nano-positioning stage[J].Precision Engineering,2010,34(3):497-506.
[10]蔡成波,崔玉国,蔡永根,等.压电微动平台的改进PID控制[J].压电与声光,2016,38(3):441-444.CAI C B,CUI Y G,CUI Y G,et al.Improved PID control of piezoelectric micro-positioning stage[J].Piezoelectrics&Acoustooptics,2016,38(3):441-444.
[11]WANG F C,TSAI Y C,HSIEH C H,et al.Robust control of a two-axis piezoelectric nano-positioning stage[J].World Congress,2011:3539-3544.
[12]ZHU W,YANG F F,RUI X T.Robust independent modal space control of a coupled nano-positioning piezostage[J].Mechanical Systems and Signal Processing,2018,106:466-478.
[13]LEON C,BIJAN S,UMESH B,et al.Development and control of a two DOF linear-angular precision positioning stage[J].Mechatronics,2015,32:34-43.
[14]张栋,张承进,魏强,等.压电工作台的神经网络控制[J].光学精密工程,2012,20(3):587-596.ZHANG D,ZHANG CH J,WEI Q,et al.Modeling and control of piezo-stage using neural networks[J].Optics and Precision Engineering,2012,20(3):587-596.
[15]LI L L,LI CH X,GU G Y,et al.Positive acceleration,velocity and position feedback based damping control approach for piezo-actuated nanopositioning stages[J].Mechatronics,2017,47:97-104.
[16]CAI K H,TIAN Y L,WANG F J,et al.Development of a piezo-driven 3-DOF stage with T-shape flexible hinge mechanism[J].Robotics and Computer-Integrated Manufacturing,2016,37(3):125-138.