小车倒立摆的自适应动态面控制
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摘要
针对一类含有参数扰动和外部扰动的不确定欠驱动系统提出了一种改进自适应动态面控制方法.首先通过坐标变换,小车倒立摆模型转换成部分反馈形式,由半严格形式模型设计动态面控制器.利用模糊逻辑处理系统不确定性的能力设计自适应控制器,然后在传统动态面控制器设计中采用跟踪微分器来得到原稳定化函数的精确微分,解决传统反步法的"微分爆炸",显著提升闭环系统的性能.采用李雅普洛夫方法,设计适当的参数,系统跟踪误差能收敛到原点,仿真结果验证了该方法的有效性.
A modified adaptive dynamic surface control was proposed for a typical underactuated mechanical system.With the help of coordinate transformation, the cart-pole model was transformed to a partially feedback form. Based on semistrict feedback form, a dynamic surface controller(DSC) was designed. An adaptive-based controller is constructed using the capability of fuzzy logic to tackle the uncertainties and then, by introducing tracking differentiator(TD), the‘explosion of complexity' problem in traditional backstepping technique was eliminated. TD was incorporated into the traditional DSC design procedure to obtain the precise original intermediate control signals and its derivative signals.Accordingly, the closed-loop control performance can be improved significantly. Based on the Lyapunov theorem, it was proved that appropriate parameter selection guaranteed that the tracking errors could converge to a compact set around zero.Simulation results confirmed the effectiveness of the proposed method.
A modified adaptive dynamic surface control was proposed for a typical underactuated mechanical system.With the help of coordinate transformation, the cart-pole model was transformed to a partially feedback form. Based on semistrict feedback form, a dynamic surface controller(DSC) was designed. An adaptive-based controller is constructed using the capability of fuzzy logic to tackle the uncertainties and then, by introducing tracking differentiator(TD), the‘explosion of complexity' problem in traditional backstepping technique was eliminated. TD was incorporated into the traditional DSC design procedure to obtain the precise original intermediate control signals and its derivative signals.Accordingly, the closed-loop control performance can be improved significantly. Based on the Lyapunov theorem, it was proved that appropriate parameter selection guaranteed that the tracking errors could converge to a compact set around zero.Simulation results confirmed the effectiveness of the proposed method.
引文
[1] MUSKINJA N, TOVORNIK B. Swinging up and stabilization of a real inverted pendulum. IEEE Transactions on Industrial Electronics,2006, 53(2):631–639.
[2] KHAZAEE M, MARKAZI A H D, RIZI S T, et al. Adaptive fuzzy sliding mode control of input-delayed uncertain nonlinear systems through output-feedback. Nonlinear Dynamics, 2017, 87(3):1943–1956.
[3] OH S R, SUN J, LI Z. Path following control of underactuated marine vessels via dynamic surface control technique. ASME 2008 Dynamic Systems and Control Conference. Ann Arbor, Michigan, USA:American Society of Mechanical Engineers, 2008:529–536.
[4] FANG Yiming, XU Yanze, LI Jianxiong. Adaptive dynamic surface control for electro-hydraulic servo position system with input saturation. Control Theory&Applications, 2014, 31(4):511–518.(方一鸣,许衍泽,李建雄.具有输入饱和的电液伺服位置系统自适应动态面控制.控制理论与应用, 2014, 31(4):511–518.)
[5] OLFATI-SABER R, MEGRETSKI A. Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles. Cambridge:Massachusetts Institute of Technology, 2001.
[6] HUANG J, RI S, LIU L, et al. Nonlinear disturbance observer-based dynamic surface control of mobile wheeled inverted pendulum. IEEE Transactions on Control Systems Technology, 2015, 23(6):2400–2407.
[7] LIU Y, YU H. A survey of underactuated mechanical systems. Iet Control Theory&Applications, 2013, 7(7):921–935.
[8] SUN G, REN X, LI D. Neural active disturbance rejection output control of multimotor servomechanism. IEEE Transactions on Control Systems Technology, 2015, 23(2):746–753.
[9] AZIMI M M, KOOFIGAR H R. Adaptive fuzzy backstepping controller design for uncertain underactuated robotic systems. Nonlinear Dynamics, 2015, 79(2):1457–1468.
[10] WANG Lixin. A Course on Fuzzy Systems and Control. Beijing:Tsinghua University Press, 2003.(王立新.模糊系统与模糊控制教程.北京:清华大学出版社, 2003.)
[11] HAN J. From PID to active disturbance rejection control. IEEE Transactions on Industrial Electronics, 2009, 56(3):900–906.
[12] WANG D. Neural network-based adaptive dynamic surface control of uncertain nonlinear pure-feedback systems. International Journal of Robust&Nonlinear Control, 2011, 21(5):527–541.
[13] ZHOU Tao. Tracking differentiator based on inverse hyperbolic sine function. Control and Decision, 2014, 29(6):1139–1142.(周涛.基于反双曲正弦函数的跟踪微分器.控制与决策, 2014,29(6):1139–1142.)
[14] HAN J, WANG W. Nonlinear tracking—differentiator. Journal of Systems Science&Mathematical Sciences, 1994, 14(2):177–183.(韩京清,王伟.非线性跟踪—微分器.系统科学与数学, 1994, 14(2):177–183.)
[2] KHAZAEE M, MARKAZI A H D, RIZI S T, et al. Adaptive fuzzy sliding mode control of input-delayed uncertain nonlinear systems through output-feedback. Nonlinear Dynamics, 2017, 87(3):1943–1956.
[3] OH S R, SUN J, LI Z. Path following control of underactuated marine vessels via dynamic surface control technique. ASME 2008 Dynamic Systems and Control Conference. Ann Arbor, Michigan, USA:American Society of Mechanical Engineers, 2008:529–536.
[4] FANG Yiming, XU Yanze, LI Jianxiong. Adaptive dynamic surface control for electro-hydraulic servo position system with input saturation. Control Theory&Applications, 2014, 31(4):511–518.(方一鸣,许衍泽,李建雄.具有输入饱和的电液伺服位置系统自适应动态面控制.控制理论与应用, 2014, 31(4):511–518.)
[5] OLFATI-SABER R, MEGRETSKI A. Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles. Cambridge:Massachusetts Institute of Technology, 2001.
[6] HUANG J, RI S, LIU L, et al. Nonlinear disturbance observer-based dynamic surface control of mobile wheeled inverted pendulum. IEEE Transactions on Control Systems Technology, 2015, 23(6):2400–2407.
[7] LIU Y, YU H. A survey of underactuated mechanical systems. Iet Control Theory&Applications, 2013, 7(7):921–935.
[8] SUN G, REN X, LI D. Neural active disturbance rejection output control of multimotor servomechanism. IEEE Transactions on Control Systems Technology, 2015, 23(2):746–753.
[9] AZIMI M M, KOOFIGAR H R. Adaptive fuzzy backstepping controller design for uncertain underactuated robotic systems. Nonlinear Dynamics, 2015, 79(2):1457–1468.
[10] WANG Lixin. A Course on Fuzzy Systems and Control. Beijing:Tsinghua University Press, 2003.(王立新.模糊系统与模糊控制教程.北京:清华大学出版社, 2003.)
[11] HAN J. From PID to active disturbance rejection control. IEEE Transactions on Industrial Electronics, 2009, 56(3):900–906.
[12] WANG D. Neural network-based adaptive dynamic surface control of uncertain nonlinear pure-feedback systems. International Journal of Robust&Nonlinear Control, 2011, 21(5):527–541.
[13] ZHOU Tao. Tracking differentiator based on inverse hyperbolic sine function. Control and Decision, 2014, 29(6):1139–1142.(周涛.基于反双曲正弦函数的跟踪微分器.控制与决策, 2014,29(6):1139–1142.)
[14] HAN J, WANG W. Nonlinear tracking—differentiator. Journal of Systems Science&Mathematical Sciences, 1994, 14(2):177–183.(韩京清,王伟.非线性跟踪—微分器.系统科学与数学, 1994, 14(2):177–183.)