柔性机械手非奇异终端滑模控制方法的研究
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摘要
随着航天技术和机器人技术的发展,相对于传统的刚性机械手,柔性机械手以其高负载/自重比、低能耗、高速等优点,应用前景广阔。然而,由于结构柔性的存在、本身的非线性特性、模型参数不确定性、外部干扰等影响,柔性机械手成为一类复杂的非线性不确定系统,对其控制策略的研究不仅具有重要的理论价值,还具有较高的实际应用价值。
非奇异终端滑模是近来出现的一种新的滑模控制方法,它兼有传统线性滑模和终端滑模的优点,如强鲁棒性、有限时间收敛特性、高稳态精度等,同时还通过有目的地改变切换函数的形式,直接从滑模设计方面解决了现有终端滑模控制存在的奇异性问题,保证了控制系统的全局稳定性。然而,抖振问题是制约其实际应用的最大障碍。为此,本文从理论和柔性机械手的控制应用两方面,围绕非奇异终端滑模控制器的设计及抖振的消除问题进行了深入研究。
首先通过理论分析和仿真实验,将非奇异终端滑模与线性滑模和终端滑模进行对比,直观清晰地阐述了非奇异终端滑模的特性。然后,为解决抖振问题,提出了一种无抖振的二阶非奇异终端滑模控制方法,并将其应用于一类系统矩阵和输入矩阵皆存在不确定性的多变量不确定系统。详细探讨了如何从一个一般多变量系统经过非奇异状态变换和去耦合处理,变成一个由输入输出子系统和零动态子系统组成的解耦块能控标准型系统。之后,引入辅助系统,消除输入矩阵不确定项的影响,应用所提二阶非奇异终端滑模控制方法,保证输入输出子系统有限时间内跟踪上辅助系统,同时辅助系统有限时间内收敛到零,间接实现了输入输出子系统的有限时间收敛。最后,通过极点配置,使得零动态子系统的状态按递阶顺序渐近收敛到零,从而保证了整个系统的状态收敛。
以双臂柔性机械手为例,深入研究了其定点调节和轨迹跟踪控制问题。为解决柔性机械手非最小相位控制问题,实现末端定点调节,基于输出重定义方法,提出了一种基于遗传算法的非奇异终端滑模优化控制策略。设计思想为:首先将关节电机转角和柔性模态的线性组合定义为系统输出,通过输入输出线性化,将系统分解为输入输出子系统和内部子系统,使得系统在平衡点附近转变为易于控制的最小相位系统。针对输入输出子系统,设计非奇异终端滑模控制器,使系统有限时间内收敛到零,将内部子系统变为零动态子系统。利用作图法证明了重定义输出组合系数在保证零动态子系统稳定情况下的存在性和不唯一性,分析了不同输出组合系数对柔性机械手控制性能的影响,在此基础上,设计遗传算法优化组合输出系数,使得零动态子系统渐近收敛到零,最终实现柔性机械手末端位移的渐近收敛。此外,考虑到柔性机械手模型参数的不确定性,在给出系统不确定性描述基础上,推导了模型分解过程中原系统不确定性引入到分解后各子系统中的表达式,并根据Lyapunov稳定性理论算得由于系统参数不确定性引起的末端输出位移的误差范围。针对抖振问题,根据高阶滑模的去抖振原理,结合线性滑模和所提二阶非奇异终端滑模,对重定义后的输入输出子系统提出了一种三阶非奇异终端滑模控制方法,可保证输入输出子系统渐近收敛到零,同时对控制信号进行一次低通滤波作用,削弱了抖振对柔性机械手末端控制系统的影响,获得了明显的控制效果。
为实现柔性机械手的轨迹跟踪控制,同时削弱抖振现象,提出了一种基于模糊非奇异终端滑模的复合控制策略。设计思想为:首先利用奇异摄动方法和柔性机械手的双时间尺度特性,分别以关节电机转角和柔性模态偏差为变量,将双臂柔性机械手系统分解为慢变和快变两个子系统,以简化控制器设计。然后,针对慢变子系统,结合模糊控制和非奇异终端滑模控制方法,设计了复合控制器,其中非奇异终端滑模控制器用以保证慢变子系统的全局稳定性,提高系统的跟踪速度和精度,而模糊控制器用以根据系统状态距离滑模切换面的远近以及所设计的模糊规则,获得自适应的切换增益,削弱抖振对柔性模态的影响。最后,针对快变子系统,提出了一种基于观测器的状态反馈控制方法,设计了降维观测器估计不可测状态,即柔性模态偏差,然后基于重构的系统状态,设计了LQR控制器抑制快变子系统的弹性振动。
以上研究成果均基于非奇异终端滑模控制方法,且通过计算机仿真进行验证,仿真结果表明本文所提控制方法的有效性和可行性。
With the development of aeronautics and robotics, flexible manipulators exhibit wider application foreground in comparison with conventional rigid manipulators for their advantages, such as high load-to-weight ratio, low energy consumption, high speed and so on. However, structural flexibility, model parameter uncertainties, external disturbances combined with inherent nonlinear dynamics makes flexible manipulators a class of complicated nonlinear uncertain system. Thus, the control of flexible manipulators is of both theoretical and practical importance.
In the last decades, sliding mode control evolved into nonsingular terminal sliding mode (NTSM), which owns advantages of both traditional linear sliding mode (LSM) and terminal sliding mode (TSM), such as strong robustness, convergence in a finite time and high steady precision. Meanwhile, NTSM changes the mathematical form of switching surface, purposively avoids the singularity problem of TSM and makes the control signal globally nonsingular. However, chattering is the biggest drawback restricting the real application of NTSM. Thus, this thesis emphasizes on the NTSM controller design for flexible manipulator and chattering elimination.
This thesis firstly discusses distinctly the characteristics of NTSM by theoretical analyses and simulation comparison with LSM, TSM and NTSM. Then, in order to solve chattering problem, a free-chattering two-order NTSM control method is proposed and further applied into a class of multivariable system with uncertain systemic matrix and input matrix. This thesis discusses how to change the general multivariable system to decomposition block-controllable form after nonsingular state transformation and decomposition, which consists of an input-output subsystem and a zero-dynamics subsystem. Later, an auxiliary system is introduced to eliminate uncertainty of input matrix. By applying the proposed two-order NTSM control method, the input-output subsystem tracks the auxiliary system, and the auxiliary system converges to zero in a finite time, respectively. Therefore, the input-output subsystem indirectly realizes convergence in a finite time. Finally, by pole assignment, the zero-dynamics subsystem converges to zero asymptotically. Therefore, the proposed method guarantees the convergence of the whole system.
This thesis regards the two-link flexible manipulator as an example to research on its regulation and tracking control. In order to solve non-minimum phase control problem and realize end-point regulation of flexible manipulator system, a NTSM control strategy is proposed based on genetic algorithm (GA). Redefined system output as the combination of joint position and flexible modes, the flexible manipulator system is decomposed into input-output subsystem and internal subsystem. Therefore, the system is transformed into a minimum phase system around equilibrium point by input-output linearization. NTSM controller is designed to make the input-output subsystem converge to zero in a finite time. Moreover, the internal subsystem is transformed into zero-dynamics subsystem. The relationship between the zero dynamics and parameters of the redefined output is analyzed by graphic. Then GA is further adopted to optimize combined parameters, aimed to make zero-dynamics subsystem converge to zero. Meanwhile, the end-point of flexible manipulator converges to zero. Additionally, model parameter uncertainty is considered for flexible manipulators. By analyzing the uncertainties evolved from original system, the error range of end-tip output is calculated by Lyapunov stability theorem. In order to eliminate chattering, combining high-order sliding mode, LSM and the proposed two-order NTSM, a three-order NTSM control strategy is proposed for the redefined input-output subsystem to guarantee its convergence and elimination chattering by filtering. The validity of the proposed method is proved by theory analysis and simulation.
In order to deal with the problem of trajectory tracking control with oscillation elimination for flexible manipulators, a composite control strategy is proposed based on fuzzy NTSM. Based on the singular perturbation method and two time-scale decomposition, the flexible manipulator system is decomposed into two subsystems by modeling the joint angles and the corrected flexible modes as the slow and fast variables, respectively. For the slow subsystem, a composite controller is designed by combining NTSM and fuzzy control. NTSM controller is used to realize global stability, fast convergence and better tracking precision, while fuzzy controller is used to eliminate chattering phenomenon, according to the designed fuzzy rules and the distance from system states to switching surface. For the fast subsystem, an observer-based state-feedback control method is proposed. A reduced-order observer is proposed to estimate the corrected flexible mode variables that can not be measured directly. Therefore, the fast subsystem is stabilized by a simple LQR control around the equilibrium trajectory defined by the slow subsystem.
The above researches are all based on NTSM control, and the simulation results are presented to validate the design methods.
非奇异终端滑模是近来出现的一种新的滑模控制方法,它兼有传统线性滑模和终端滑模的优点,如强鲁棒性、有限时间收敛特性、高稳态精度等,同时还通过有目的地改变切换函数的形式,直接从滑模设计方面解决了现有终端滑模控制存在的奇异性问题,保证了控制系统的全局稳定性。然而,抖振问题是制约其实际应用的最大障碍。为此,本文从理论和柔性机械手的控制应用两方面,围绕非奇异终端滑模控制器的设计及抖振的消除问题进行了深入研究。
首先通过理论分析和仿真实验,将非奇异终端滑模与线性滑模和终端滑模进行对比,直观清晰地阐述了非奇异终端滑模的特性。然后,为解决抖振问题,提出了一种无抖振的二阶非奇异终端滑模控制方法,并将其应用于一类系统矩阵和输入矩阵皆存在不确定性的多变量不确定系统。详细探讨了如何从一个一般多变量系统经过非奇异状态变换和去耦合处理,变成一个由输入输出子系统和零动态子系统组成的解耦块能控标准型系统。之后,引入辅助系统,消除输入矩阵不确定项的影响,应用所提二阶非奇异终端滑模控制方法,保证输入输出子系统有限时间内跟踪上辅助系统,同时辅助系统有限时间内收敛到零,间接实现了输入输出子系统的有限时间收敛。最后,通过极点配置,使得零动态子系统的状态按递阶顺序渐近收敛到零,从而保证了整个系统的状态收敛。
以双臂柔性机械手为例,深入研究了其定点调节和轨迹跟踪控制问题。为解决柔性机械手非最小相位控制问题,实现末端定点调节,基于输出重定义方法,提出了一种基于遗传算法的非奇异终端滑模优化控制策略。设计思想为:首先将关节电机转角和柔性模态的线性组合定义为系统输出,通过输入输出线性化,将系统分解为输入输出子系统和内部子系统,使得系统在平衡点附近转变为易于控制的最小相位系统。针对输入输出子系统,设计非奇异终端滑模控制器,使系统有限时间内收敛到零,将内部子系统变为零动态子系统。利用作图法证明了重定义输出组合系数在保证零动态子系统稳定情况下的存在性和不唯一性,分析了不同输出组合系数对柔性机械手控制性能的影响,在此基础上,设计遗传算法优化组合输出系数,使得零动态子系统渐近收敛到零,最终实现柔性机械手末端位移的渐近收敛。此外,考虑到柔性机械手模型参数的不确定性,在给出系统不确定性描述基础上,推导了模型分解过程中原系统不确定性引入到分解后各子系统中的表达式,并根据Lyapunov稳定性理论算得由于系统参数不确定性引起的末端输出位移的误差范围。针对抖振问题,根据高阶滑模的去抖振原理,结合线性滑模和所提二阶非奇异终端滑模,对重定义后的输入输出子系统提出了一种三阶非奇异终端滑模控制方法,可保证输入输出子系统渐近收敛到零,同时对控制信号进行一次低通滤波作用,削弱了抖振对柔性机械手末端控制系统的影响,获得了明显的控制效果。
为实现柔性机械手的轨迹跟踪控制,同时削弱抖振现象,提出了一种基于模糊非奇异终端滑模的复合控制策略。设计思想为:首先利用奇异摄动方法和柔性机械手的双时间尺度特性,分别以关节电机转角和柔性模态偏差为变量,将双臂柔性机械手系统分解为慢变和快变两个子系统,以简化控制器设计。然后,针对慢变子系统,结合模糊控制和非奇异终端滑模控制方法,设计了复合控制器,其中非奇异终端滑模控制器用以保证慢变子系统的全局稳定性,提高系统的跟踪速度和精度,而模糊控制器用以根据系统状态距离滑模切换面的远近以及所设计的模糊规则,获得自适应的切换增益,削弱抖振对柔性模态的影响。最后,针对快变子系统,提出了一种基于观测器的状态反馈控制方法,设计了降维观测器估计不可测状态,即柔性模态偏差,然后基于重构的系统状态,设计了LQR控制器抑制快变子系统的弹性振动。
以上研究成果均基于非奇异终端滑模控制方法,且通过计算机仿真进行验证,仿真结果表明本文所提控制方法的有效性和可行性。
With the development of aeronautics and robotics, flexible manipulators exhibit wider application foreground in comparison with conventional rigid manipulators for their advantages, such as high load-to-weight ratio, low energy consumption, high speed and so on. However, structural flexibility, model parameter uncertainties, external disturbances combined with inherent nonlinear dynamics makes flexible manipulators a class of complicated nonlinear uncertain system. Thus, the control of flexible manipulators is of both theoretical and practical importance.
In the last decades, sliding mode control evolved into nonsingular terminal sliding mode (NTSM), which owns advantages of both traditional linear sliding mode (LSM) and terminal sliding mode (TSM), such as strong robustness, convergence in a finite time and high steady precision. Meanwhile, NTSM changes the mathematical form of switching surface, purposively avoids the singularity problem of TSM and makes the control signal globally nonsingular. However, chattering is the biggest drawback restricting the real application of NTSM. Thus, this thesis emphasizes on the NTSM controller design for flexible manipulator and chattering elimination.
This thesis firstly discusses distinctly the characteristics of NTSM by theoretical analyses and simulation comparison with LSM, TSM and NTSM. Then, in order to solve chattering problem, a free-chattering two-order NTSM control method is proposed and further applied into a class of multivariable system with uncertain systemic matrix and input matrix. This thesis discusses how to change the general multivariable system to decomposition block-controllable form after nonsingular state transformation and decomposition, which consists of an input-output subsystem and a zero-dynamics subsystem. Later, an auxiliary system is introduced to eliminate uncertainty of input matrix. By applying the proposed two-order NTSM control method, the input-output subsystem tracks the auxiliary system, and the auxiliary system converges to zero in a finite time, respectively. Therefore, the input-output subsystem indirectly realizes convergence in a finite time. Finally, by pole assignment, the zero-dynamics subsystem converges to zero asymptotically. Therefore, the proposed method guarantees the convergence of the whole system.
This thesis regards the two-link flexible manipulator as an example to research on its regulation and tracking control. In order to solve non-minimum phase control problem and realize end-point regulation of flexible manipulator system, a NTSM control strategy is proposed based on genetic algorithm (GA). Redefined system output as the combination of joint position and flexible modes, the flexible manipulator system is decomposed into input-output subsystem and internal subsystem. Therefore, the system is transformed into a minimum phase system around equilibrium point by input-output linearization. NTSM controller is designed to make the input-output subsystem converge to zero in a finite time. Moreover, the internal subsystem is transformed into zero-dynamics subsystem. The relationship between the zero dynamics and parameters of the redefined output is analyzed by graphic. Then GA is further adopted to optimize combined parameters, aimed to make zero-dynamics subsystem converge to zero. Meanwhile, the end-point of flexible manipulator converges to zero. Additionally, model parameter uncertainty is considered for flexible manipulators. By analyzing the uncertainties evolved from original system, the error range of end-tip output is calculated by Lyapunov stability theorem. In order to eliminate chattering, combining high-order sliding mode, LSM and the proposed two-order NTSM, a three-order NTSM control strategy is proposed for the redefined input-output subsystem to guarantee its convergence and elimination chattering by filtering. The validity of the proposed method is proved by theory analysis and simulation.
In order to deal with the problem of trajectory tracking control with oscillation elimination for flexible manipulators, a composite control strategy is proposed based on fuzzy NTSM. Based on the singular perturbation method and two time-scale decomposition, the flexible manipulator system is decomposed into two subsystems by modeling the joint angles and the corrected flexible modes as the slow and fast variables, respectively. For the slow subsystem, a composite controller is designed by combining NTSM and fuzzy control. NTSM controller is used to realize global stability, fast convergence and better tracking precision, while fuzzy controller is used to eliminate chattering phenomenon, according to the designed fuzzy rules and the distance from system states to switching surface. For the fast subsystem, an observer-based state-feedback control method is proposed. A reduced-order observer is proposed to estimate the corrected flexible mode variables that can not be measured directly. Therefore, the fast subsystem is stabilized by a simple LQR control around the equilibrium trajectory defined by the slow subsystem.
The above researches are all based on NTSM control, and the simulation results are presented to validate the design methods.
引文
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36张袅娜,张德江,冯勇.基于混沌遗传算法的柔性机械手滑模控制器优化设计.控制理论与应用. 2008,25(3):451~455
37张宇,杨唐文,孙增圻.基于神经滑模的柔性连杆机械手末端位置控制.机器人. 2008,30(5):404~409
38 D. Wang, M. Vidyasagar. Transfer Function for a Single Flexible Link. IEEE Int. Conf. of Robot, Scottsdale, AZ, 1989:1042~1044
39 S. K. Madhavan, S. N. Singh. Inverse Trajectory Control and Zero-Dynamics Sensitivity of an Elastic Manipulator. Int. J. of Robot Automatic. 1991,6(4):179~191
40 N. N. Zhang, Y. Feng and X. H Yu. Optimization of Terminal Sliding Control for Two-Link Flexible Manipulators. The 30th Annual Conf. of the IEEE Industrial Electronics Society, Busan, Korea, 2004:1318~1322
41 J. J. Shan, H. T. Liu and D. Sun. Modified Input Shaping for a Rotating Single-Link Flexible Manipulator. J. of Sound and Vibration. 2005,285(1)187~207
42 Z. Mohamed, J. M. Martins, M. O. Tokhi, et al. Vibration Control of a Very Flexible Manipulator System. Control Engineering Practice. 2005,13(3):267~277
43 J. Z. Xia, H. Meng. Real Time Estimation of Elastic Deformation for End-Point Tracking Control of Flexible Manipulators. ASME J. of Dynamics, Systems, Measurements and Control. 1993,115(3):385~393
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45 L. J. Ador, S. M. Rock. Experiments in Control of a Flexible Link RoboticManipulator with Unknown Payload Dynamics: an Approach. Int. J. of Robotics Research. 1994,13(6):481~495
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47 R. J. Wai, C. M. Lin and C. F. Hsu. Adaptive Fuzzy Sliding Mode Control for Electrical Servo Drive. Fuzzy Sets and Systems. 2004,143:295~310
48 C. L. Hwang, S. Y. Han and Y. S. Yu. A Network-Based Fuzzy Decentralized Sliding-Mode Control for Car-Like Mobile Robots. The14th IEEE Int. Conf. on Fuzzy Systems, Montreal, Canada, 2005:61~66
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50 J. J. Yan. Design of Robust Controllers for Uncertain Chaotic Systems with Nonlinear Inputs. Chaos, Solitons and Fractals. 2004,19(3):541~547
51王祝炯.滑模变结构控制系统设计方法研究.浙江工业大学硕士学位论文. 2003:1~30
52张昌凡.滑模变结构控制研究综述.株洲工学院学报. 2004,18(2):1~5
53高为炳.变结构控制的理论及设计方法.科学出版社. 1996: 26~59
54 V. I. Utkin, K. D. Young. Methods for Constructing Discontinuity Plans in Multidimensional Variable Structure Systems. Automatic Remote Control. 1979,13: 1466~1470
55 O. M. E. Ghezawi, A. S. I. Zinober and S. A. Billings. Analysis and Design of Variable Structure System Using Geometric Approach. Int. J. of Control. 1983,38(3): 657~671
56 K. K. D. Young. Design of Variable Structure Model Following Control Systems. IEEE Trans. on Automatic Control. 1978, AC(23): 385~400
57 C. M. Dorling. Two Approaches to Hyper-Plane Design in Multivariable Structure Control Systems. Int. J. of Control. 1986,44(1): 65~82
58 F. Chen, M. W. Dunnigan. A New Nonlinear Sliding-Mode Torque and Flux Control Method for an Induction Machine Incorporating a Sliding-Mode Flux Observer. Int. J. of Robust and Nonlinear Control. 2004,14(5):463~486
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