压电陶瓷驱动器的滑模观测器反演控制
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摘要
针对压电陶瓷驱动器中固有的迟滞非线性问题,设计基于滑模状态观测器的反演控制器对其进行输出跟踪控制。首先对压电陶瓷驱动的系统模型进行分析,将迟滞非线性部分视为有界干扰;在此基础上设计滑模状态观测器,对压电陶瓷驱动器的速度状态进行估计,整个系统仅需要测量输出位置信息。对采用滑模状态观测器的系统进行反演控制器设计,最后通过Lyapunov稳定性理论证明了闭环系统是稳定的,系统中的所有信号是一致最终有界的。仿真结果表明了方法的有效性。
For piezoelectric ceramic actuator with inherent hysteresis nonlinear,an output tracking control scheme using backstepping control on sliding-mode observer is designed. First of all,the analysis of piezoelectric ceramic actuator system model is conducted,hysteresis is considered as a generalized disturbance. Then sliding mode observer is designed to observe speed variable. The system only needs the measurement of output position information. The backstepping controller is dedigned for the system using sliding mode observer. Finally,it is proved that the closed-loop system is stable using Lyapunov stability theory. All the signals in the system are uniformly ultimately bounded. Simulation results show the effectiveness of the method.
For piezoelectric ceramic actuator with inherent hysteresis nonlinear,an output tracking control scheme using backstepping control on sliding-mode observer is designed. First of all,the analysis of piezoelectric ceramic actuator system model is conducted,hysteresis is considered as a generalized disturbance. Then sliding mode observer is designed to observe speed variable. The system only needs the measurement of output position information. The backstepping controller is dedigned for the system using sliding mode observer. Finally,it is proved that the closed-loop system is stable using Lyapunov stability theory. All the signals in the system are uniformly ultimately bounded. Simulation results show the effectiveness of the method.
引文
1 Chen C M,Hsu Y C,Fung R F.System identification of a ScottRussell amplifying mechanism with offset driven by a piezoelectric actuator.Applied Mathematical Modelling,2012;36(6):2788—2802
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3 王伟,刘向东.压电迟滞系统的3阶滑模跟踪控制器设计.控制理论与应用,2008;25(3):456—461Wang Wei,Liu Xiangdong.Design of third-order sliding-mode tracking controller for piezoelectric hysteretic systems.Control Theory&Applications,2008;25(3):456—461
4 Escareno J A,Rakotondrabe M,Habineza D.Backstepping-based robust-adaptive control of a nonlinear 2-DOF piezo-actuator.Control Engineering Practice,2015;41:57—71
5 屈百达,胥文涛.考虑压电陶瓷不确定性的鲁棒自适应控制.压电与声光,2014;(4):658—662Qu Baida,Xu Wentao.Roubust adaptive control of piezoelectric ceramics considering its uncertainty.Piezoelectrics&Acoustooptics.2014;(4):658—662
6 张利军,杨立新,郭立东,等.压电陶瓷驱动平台自适应输出反馈控制.自动化学报,2012;38(9):1550—1556Zhang Lijun,Yang Lixin,Guo Lidong,et al.Adaptive output feedback control for piezoactuator-driven stage.Acta Automatica Sinica,2012;38(9):1550—1556
7 Peng J Y,Chen X B.Integrated PID-based sliding mode state estimation and control for piezoelectric actuators.IEEE/ASME Transactions on Mechatronics,2014;19(1):88—99
8 Zhou J,Wen C,Li T.Adaptive output feedback control of uncertain nonlinear systems with hysteresis nonlinearity.IEEE Transactions on Automatic Control,2012;57(10):2627—2633
9 Ahmed-Ali T,Lamnabhi-Lagarrigue F.Sliding observer-controller design for uncertain triangular nonlinear systems.IEEE Tranctions on Automatic Control,1999:4(6):1244—1249
2 Gu G Y,Zhu L M,Su C Y,et al.Modeling and control of piezo-actuated nanopositioning atages:a survey.IEEE Transactions on Automation Science&Engineering,2016;13(1):313—332
3 王伟,刘向东.压电迟滞系统的3阶滑模跟踪控制器设计.控制理论与应用,2008;25(3):456—461Wang Wei,Liu Xiangdong.Design of third-order sliding-mode tracking controller for piezoelectric hysteretic systems.Control Theory&Applications,2008;25(3):456—461
4 Escareno J A,Rakotondrabe M,Habineza D.Backstepping-based robust-adaptive control of a nonlinear 2-DOF piezo-actuator.Control Engineering Practice,2015;41:57—71
5 屈百达,胥文涛.考虑压电陶瓷不确定性的鲁棒自适应控制.压电与声光,2014;(4):658—662Qu Baida,Xu Wentao.Roubust adaptive control of piezoelectric ceramics considering its uncertainty.Piezoelectrics&Acoustooptics.2014;(4):658—662
6 张利军,杨立新,郭立东,等.压电陶瓷驱动平台自适应输出反馈控制.自动化学报,2012;38(9):1550—1556Zhang Lijun,Yang Lixin,Guo Lidong,et al.Adaptive output feedback control for piezoactuator-driven stage.Acta Automatica Sinica,2012;38(9):1550—1556
7 Peng J Y,Chen X B.Integrated PID-based sliding mode state estimation and control for piezoelectric actuators.IEEE/ASME Transactions on Mechatronics,2014;19(1):88—99
8 Zhou J,Wen C,Li T.Adaptive output feedback control of uncertain nonlinear systems with hysteresis nonlinearity.IEEE Transactions on Automatic Control,2012;57(10):2627—2633
9 Ahmed-Ali T,Lamnabhi-Lagarrigue F.Sliding observer-controller design for uncertain triangular nonlinear systems.IEEE Tranctions on Automatic Control,1999:4(6):1244—1249