基于非线性干扰观测器的一类欠驱动系统跟踪控制
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摘要
针对一类欠驱动系统的跟踪控制问题,提出一种基于非线性干扰观测器的控制策略.首先给出一种基于跟踪误差的输出函数,通过等式变形和Butterworth低通滤波器解决未知控制方向问题;其次,引入一种新型非线性干扰观测器,对系统未知模型进行补偿,使控制器的设计无需知道系统的结构和参数;再次,通过对系统的内部动态和外部动态的分析,证明闭环系统的输出收敛于原点,跟踪误差信号一致最终有界;最后,将该方法应用于小车倒立摆模型,仿真结果表明了所提出方法的有效性.
A nonlinear disturbance observer-based control scheme is proposed for the trajectory tracking of a class of underactuated systems. Firstly, a tracking error-based output function is proposed and the equation transformation and Butterworth low-pass filter are applied to solve the problem of unknown control directions. By introducing a novel nonlinear disturbance observer, which is used to compensate for unknown system model, the need to know the structure of the system and its parameters is obviated. The internal and external dynamics are rigorously analyzed, thereby proving the uniform ultimate boundedness of the error trajectory. Finally, the proposed method is applied to the cart-pole inverted pendulum, and the simulation results show its effectiveness.
A nonlinear disturbance observer-based control scheme is proposed for the trajectory tracking of a class of underactuated systems. Firstly, a tracking error-based output function is proposed and the equation transformation and Butterworth low-pass filter are applied to solve the problem of unknown control directions. By introducing a novel nonlinear disturbance observer, which is used to compensate for unknown system model, the need to know the structure of the system and its parameters is obviated. The internal and external dynamics are rigorously analyzed, thereby proving the uniform ultimate boundedness of the error trajectory. Finally, the proposed method is applied to the cart-pole inverted pendulum, and the simulation results show its effectiveness.
引文
[1] Liu Y, Yu H. A survey of underactuated mechanical systems[J]. IET Control Theory&Applications, 2013,7(7):921-935.
[2] Azimi M M, Koofigar H R. Adaptive fuzzy backstepping controller design for uncertain underactuated robotic systems[J]. Nonlinear Dynamics, 2014, 79(2):1457-1468.
[3] Hashem Ashrafiuon, R Scott Erwin. Sliding mode control of underactuated multibody systems and its application to shape change control[J]. Int J of Control, 2008, 81(12):1849-1858.
[4] Pathak K, Franch J, Agrawal S K. Velocity and position control of a wheeled inverted pendulum by partial feedback linearization[J]. IEEE Trans on Robotics, 2005,21(3):505-513.
[5] Esmaeili N, Alfi A, Khosravi H. Balancing and trajectory tracking of two-wheeled mobile robot using backstepping sliding mode control:Design and experiments[J]. J of Intelligent&Robotic Systems, 2017, 87(3):601-613.
[6] Cui R, Guo J, Mao Z. Adaptive backstepping control of wheeled inverted pendulums models[J]. Nonlinear Dynamics, 2015, 79(1):501-511.
[7] Mahjoub S, Mnif F, Derbel N, et al. Radialbasis-functions neural network sliding mode control for underactuated mechanical systems[J]. Int J of Dynamics&Control, 2014, 2(4):533-541.
[8] Yue M, Wang S, Sun J Z. Simultaneous balancing and trajectory tracking control for two-wheeled inverted pendulum vehicles:A composite control approach[J].Neurocomputing, 2016, 191(26):44-54.
[9] Mohammadi A, Tavakoli M, Marquez H J, et al. Nonlinear disturbance observer design for robotic manipulators[J].Control Engineering Practice, 2013, 21(3):253-267.
[10] Huang J, Ri S, Liu L, et al. Nonlinear disturbance observer-based dynamic surface control of mobile wheeled inverted pendulum[J]. IEEE Trans on Control Systems Technology, 2015, 23(6):2400-2407.
[11] Bu X W, Wu X Y, Chen Y X, et al. Design of a class of new nonlinear disturbance observers based on tracking differentiators for uncertain dynamic systems[J]. Int J of Control Automation&Systems, 2015, 13(3):595-602.
[12] Wang Y, Cao L, Zhang S, et al. Command filtered adaptive fuzzy backstepping control method of uncertain non-linear systems[J]. IET Control Theory&Applications, 2016, 10(10):1134-1141.
[13] Sui S, Tong S, Li Y. Adaptive fuzzy backstepping output feedback tracking control of MIMO stochastic pure-feedback nonlinear systems with input saturation[J].Fuzzy Sets&Systems, 2014, 254(6):26-46.
[14] Bu X, Wu X, Zhang R, et al. Tracking differentiator design for the robust backstepping control of a flexible air-breathing hypersonic vehicle[J]. J of the Franklin Institute, 2015, 352(4):1739-1765.
[15] Khalil H K. Nonlinear systems[M]. 3rd ed. Upper Saddle River:Prentice-Hall, 2002:521-530.
[16] Wang J J. Position and speed tracking control of inverted pendulum based on double PID controllers[C]. The34th Chinese Control Conf. Hangzhou:IEEE, 2015:4197-4201.
[2] Azimi M M, Koofigar H R. Adaptive fuzzy backstepping controller design for uncertain underactuated robotic systems[J]. Nonlinear Dynamics, 2014, 79(2):1457-1468.
[3] Hashem Ashrafiuon, R Scott Erwin. Sliding mode control of underactuated multibody systems and its application to shape change control[J]. Int J of Control, 2008, 81(12):1849-1858.
[4] Pathak K, Franch J, Agrawal S K. Velocity and position control of a wheeled inverted pendulum by partial feedback linearization[J]. IEEE Trans on Robotics, 2005,21(3):505-513.
[5] Esmaeili N, Alfi A, Khosravi H. Balancing and trajectory tracking of two-wheeled mobile robot using backstepping sliding mode control:Design and experiments[J]. J of Intelligent&Robotic Systems, 2017, 87(3):601-613.
[6] Cui R, Guo J, Mao Z. Adaptive backstepping control of wheeled inverted pendulums models[J]. Nonlinear Dynamics, 2015, 79(1):501-511.
[7] Mahjoub S, Mnif F, Derbel N, et al. Radialbasis-functions neural network sliding mode control for underactuated mechanical systems[J]. Int J of Dynamics&Control, 2014, 2(4):533-541.
[8] Yue M, Wang S, Sun J Z. Simultaneous balancing and trajectory tracking control for two-wheeled inverted pendulum vehicles:A composite control approach[J].Neurocomputing, 2016, 191(26):44-54.
[9] Mohammadi A, Tavakoli M, Marquez H J, et al. Nonlinear disturbance observer design for robotic manipulators[J].Control Engineering Practice, 2013, 21(3):253-267.
[10] Huang J, Ri S, Liu L, et al. Nonlinear disturbance observer-based dynamic surface control of mobile wheeled inverted pendulum[J]. IEEE Trans on Control Systems Technology, 2015, 23(6):2400-2407.
[11] Bu X W, Wu X Y, Chen Y X, et al. Design of a class of new nonlinear disturbance observers based on tracking differentiators for uncertain dynamic systems[J]. Int J of Control Automation&Systems, 2015, 13(3):595-602.
[12] Wang Y, Cao L, Zhang S, et al. Command filtered adaptive fuzzy backstepping control method of uncertain non-linear systems[J]. IET Control Theory&Applications, 2016, 10(10):1134-1141.
[13] Sui S, Tong S, Li Y. Adaptive fuzzy backstepping output feedback tracking control of MIMO stochastic pure-feedback nonlinear systems with input saturation[J].Fuzzy Sets&Systems, 2014, 254(6):26-46.
[14] Bu X, Wu X, Zhang R, et al. Tracking differentiator design for the robust backstepping control of a flexible air-breathing hypersonic vehicle[J]. J of the Franklin Institute, 2015, 352(4):1739-1765.
[15] Khalil H K. Nonlinear systems[M]. 3rd ed. Upper Saddle River:Prentice-Hall, 2002:521-530.
[16] Wang J J. Position and speed tracking control of inverted pendulum based on double PID controllers[C]. The34th Chinese Control Conf. Hangzhou:IEEE, 2015:4197-4201.