非线性机器人的智能反演滑模控制研究
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摘要
机器人是由机械本体、控制器、伺服驱动系统和检测传感器装置构成的，一种能仿人操作、可自动控制、重复编程、并能在三维空间完成各种作业的机电一体化设备。机器人的应用是潜力无限的，所有人类所从事的领域机器人基本都可以从事，从人们的日常生活、工农业生产到海洋探测、太空探测，机器人都发挥着越来越重要的作用。多关节机器人也称为机械臂、机械手，是指一端与基础固定的一系列具有空间运动能力的刚体的连接组合。根据其运动方式，多关节机器人是一个十分复杂的多输入多输出非线性系统，具有时变性、耦合性和非线性等动力学特征。其控制问题就是要使机器人的各关节或末端执行器位置能够以理想的动态品质跟踪给定的轨迹或稳定在指定的位置上。针对具有建模误差和不确定干扰的机器人控制，目前主要有：（1）PID控制；（2）自适应控制；（3）鲁棒控制；（4）变结构控制；（5）智能控制；(6)反演控制等等。本文主要研究了基于反演的滑模控制与模糊控制、神经网络控制相结合的控制方法，主要有以下研究成果。
（1）针对具有建模误差和不确定干扰的机器人轨迹跟踪问题，分别研究了反演线性滑模控制、反演非线性终端滑模控制和反演准滑模控制，并利用李亚普诺夫稳定性定理证明了系统的稳定性。反演的线性滑模控制采用传统的线性滑模面，其缺点无法在有限时间内收敛到平衡点。反演非线性终端滑模控制采用非线性终端滑模面，使得系统状态在滑模面上能够在有限时间内到达平衡点零。反演准滑模控制是在反演滑模控制律的基础上将符号函数改为饱和函数，即变成准滑模控制律。最后通过仿真实验验证了上述控制方法的有效性。
（2）将模糊控制、反演控制和滑模控制相结合，针对有建模误差和干扰的的多关节机器人轨迹跟踪控制问题，研究了全局PID模糊滑模控制、PID反演自适应模糊滑模控制、基于模糊补偿的反演滑模控制和反演非奇异终端模糊滑模控制，并利用李亚普诺夫稳定性定理证明了系统的稳定性。前两种控制方法利用自适应模糊控制器在线估计不确定性上界值，实现对建模误差和干扰的自动跟踪，削弱了抖振。模糊补偿的反演滑模控制通过设计模糊补偿器逼近建模误差和外界干扰，减弱干扰的影响，从而削弱控制器的抖动。反演非奇异终端模糊滑模控制采用非线性终端滑模面，克服了终端滑模面存在奇异点的缺点，基于反演方法设计控制系统，为了削弱抖振设计了模糊控制器对建模误差和干扰的自动跟踪。最后通过仿真实验验证了上述控制方法的有效性。
（3）将反演控制、滑模控制和神经网络相结合，针对有建模误差和干扰的的多关节机器人轨迹跟踪控制问题，研究了RBF神经滑模控制、全局PID神经滑模控制、积分反演神经滑模控制、反演非奇异终端神经滑模控制和反演非奇异快速终端神经滑模控制，并基于Lyapunov理论证明了系统的稳定性。RBF神经滑模控制是将切换函数作为RBF神经网络的输入，利用RBF神经网络直接作为滑模控制器，实现多入多出的神经滑模控制。全局PID神经滑模控制设计了全局PID滑模面，用RBF神经网络调节滑模控制的切换增益，通过在线调整控制器参数，实现对建模误差和干扰的自动跟踪，从而消除了抖动。积分反演神经滑模控制采用了RBF网络在线估计不确定性上界值，并且设计了网络权值的自适应律。反演非奇异终端神经滑模控制采用非线性终端滑模面，设计了神经网络控制器在线估计不确定性上界值，削弱了抖动。为了进一步减少系统收敛时间，设计了反演非奇异快速终端神经滑模控制。最后通过仿真实验验证了上述控制方法的有效性。
Robot consists of mechanical body,controller,servo driving system andsensor device,which has characteristics of human-simulated operation, auto-matic control and reprogrammability.It is an electromechanical equipmentthat can complete various operations in three dimensions.The use of robotshas become increasingly prevalent and far reaching.Robots almost can do allof what the human do. Robots are playing a more and more important role indaily life,industrial-agricultural production,ocean probe and spaceresearch.Multilink robot is also called mechanical arm or mechanical hand.Itis connection of rigid bodys with an end fixed which characterized by spacemovement. Based on the movement,Multilink robot is a complicated MIMOnonlinear system and has the nonlinear dynamics characteristics ofnonlinearity,time varying and coupling.The aim of the control strategy is tomake the output of the rigid robot tracking a desired trajectory in perfectdynamic quality.For tracking control of multilink robot manipulators withmodeling error and external disturbance,Now the following popular methodsare used:(1)PID Control;(2)Adaptive Control;(3)Robust Control;(4)variablestructure control;(5)intelligent control;(6)Backstepping Control.This paperput forward controlling methods,which combine backstepping sliding-modecontrol,fuzzy control and neural network.Main achievements are given asfollows in this paper.
(1)For tracking a desired trajectory of multilink robot manipulators withmodeling error and external disturbance,Backstepping linear sliding modecontrol,backstepping nonlinear sliding mode control and backsteppingquasi-sliding mode control are studied respectively.The system stability isproved by Lyapunov Principle.The traditional linear sliding surface is used inbackstepping linear sliding mode control which can't converge to itsequilibrium point in finite time.A terminal sliding mode (TSM) surface is used in backstepping nonlinear sliding mode control.Compared with linearhyperplane-based sliding modes, TSM offers the superior property of finitetime convergence.Based on backstepping sliding mode control,backsteppingquasi-sliding mode Control is obtained by converting sign function intosaturation funtion.Finally,simulation results verify the validity of the controlschemes as above.
(2)For tracking a desired trajectory of multilink robot manipulators withmodeling error and external disturbance,we studied new control methods inthis paper by combining fuzzy control,backstepping control and sliding modecontrol as follows:1.Global PID Fuzzy Sliding Mode Control;2.PIDBackstepping and adaptive Fuzzy Sliding Mode Control;3.BacksteppingSliding Mode Control with Fuzzy Compensation;4.Nonsingular TerminalFuzzy Sliding Mode Control Based on Backstepping.The stability of controlsystem is analyzed by Lyapunov Principle.A properly adaptive fuzzycontroller is designed to estimate uncertain upper boundary on line and trackthe modelling error and disturbance automatically in the first twomethods.Fuzzy compensation is designed to compensate the modelling errorand external disturbance in the backstepping sliding mode control with fuzzycompensation.So it weaken the disturbance and reduces chattering. Accordingto sliding mode control theory, backstepping is used to design nonsingularterminal sliding mode controller.So it overcomes disadvantage of singularpoint In order to reduces chattering a proper fuzzy controller is designed toestimate uncertain upper boundary on line and track the modelling error anddisturbance automatically. Finally,simulation results verify the validity of thecontrol schemes as above.
(3)For tracking a desired trajectory of multilink robot manipulatorswith modeling error and external disturbance,new control methods werestudied in this paper by combining backstepping control, sliding mode controland neural network control as follows:1.RBF Neural Network Sliding-modeControl;2.Global PID Neural Network Sliding Mode Control;3.IntegralBackstepping Sliding Mode Control;4.Backstepping Nonsingular Terminal Neural Network Sliding Mode Control;5.Backstepping Nonsingular FastTerminal Neural Network Sliding Mode Control.The system stability isproved by Lyapunov Principle.A switching function is used as input of RBFneural network in the RBF neural network sliding mode control. RBF neuralnetwork is treated as sliding mode controller directly.So MIMO neuralnetwork sliding mode control is implemented.Global PID sliding modesurface is designed in the global PID neural network sliding modecontrol.RBF neural network is used to adjust switching gain.Controllerparameters are tuned to estimate uncertain upper boundary on line.Sochattering is reduced.In order to estimate uncertain upperboundary,Self-adaptation principle of weight is designed in the integralbackstepping sliding mode control. Nonlinear terminal sliding mode surface isused in the backstepping nonsingular terminal neural network sliding modecontrol.RBF neural network sliding mode controller is designed to estimateuncertain upper boundary to reduce chattering.In order to further minimizeconvergence time, we design fast terminal neural network sliding modecontrol.Finally,simulation results verify the validity of the control schemes asabove.
（1）针对具有建模误差和不确定干扰的机器人轨迹跟踪问题，分别研究了反演线性滑模控制、反演非线性终端滑模控制和反演准滑模控制，并利用李亚普诺夫稳定性定理证明了系统的稳定性。反演的线性滑模控制采用传统的线性滑模面，其缺点无法在有限时间内收敛到平衡点。反演非线性终端滑模控制采用非线性终端滑模面，使得系统状态在滑模面上能够在有限时间内到达平衡点零。反演准滑模控制是在反演滑模控制律的基础上将符号函数改为饱和函数，即变成准滑模控制律。最后通过仿真实验验证了上述控制方法的有效性。
（2）将模糊控制、反演控制和滑模控制相结合，针对有建模误差和干扰的的多关节机器人轨迹跟踪控制问题，研究了全局PID模糊滑模控制、PID反演自适应模糊滑模控制、基于模糊补偿的反演滑模控制和反演非奇异终端模糊滑模控制，并利用李亚普诺夫稳定性定理证明了系统的稳定性。前两种控制方法利用自适应模糊控制器在线估计不确定性上界值，实现对建模误差和干扰的自动跟踪，削弱了抖振。模糊补偿的反演滑模控制通过设计模糊补偿器逼近建模误差和外界干扰，减弱干扰的影响，从而削弱控制器的抖动。反演非奇异终端模糊滑模控制采用非线性终端滑模面，克服了终端滑模面存在奇异点的缺点，基于反演方法设计控制系统，为了削弱抖振设计了模糊控制器对建模误差和干扰的自动跟踪。最后通过仿真实验验证了上述控制方法的有效性。
（3）将反演控制、滑模控制和神经网络相结合，针对有建模误差和干扰的的多关节机器人轨迹跟踪控制问题，研究了RBF神经滑模控制、全局PID神经滑模控制、积分反演神经滑模控制、反演非奇异终端神经滑模控制和反演非奇异快速终端神经滑模控制，并基于Lyapunov理论证明了系统的稳定性。RBF神经滑模控制是将切换函数作为RBF神经网络的输入，利用RBF神经网络直接作为滑模控制器，实现多入多出的神经滑模控制。全局PID神经滑模控制设计了全局PID滑模面，用RBF神经网络调节滑模控制的切换增益，通过在线调整控制器参数，实现对建模误差和干扰的自动跟踪，从而消除了抖动。积分反演神经滑模控制采用了RBF网络在线估计不确定性上界值，并且设计了网络权值的自适应律。反演非奇异终端神经滑模控制采用非线性终端滑模面，设计了神经网络控制器在线估计不确定性上界值，削弱了抖动。为了进一步减少系统收敛时间，设计了反演非奇异快速终端神经滑模控制。最后通过仿真实验验证了上述控制方法的有效性。
Robot consists of mechanical body,controller,servo driving system andsensor device,which has characteristics of human-simulated operation, auto-matic control and reprogrammability.It is an electromechanical equipmentthat can complete various operations in three dimensions.The use of robotshas become increasingly prevalent and far reaching.Robots almost can do allof what the human do. Robots are playing a more and more important role indaily life,industrial-agricultural production,ocean probe and spaceresearch.Multilink robot is also called mechanical arm or mechanical hand.Itis connection of rigid bodys with an end fixed which characterized by spacemovement. Based on the movement,Multilink robot is a complicated MIMOnonlinear system and has the nonlinear dynamics characteristics ofnonlinearity,time varying and coupling.The aim of the control strategy is tomake the output of the rigid robot tracking a desired trajectory in perfectdynamic quality.For tracking control of multilink robot manipulators withmodeling error and external disturbance,Now the following popular methodsare used:(1)PID Control;(2)Adaptive Control;(3)Robust Control;(4)variablestructure control;(5)intelligent control;(6)Backstepping Control.This paperput forward controlling methods,which combine backstepping sliding-modecontrol,fuzzy control and neural network.Main achievements are given asfollows in this paper.
(1)For tracking a desired trajectory of multilink robot manipulators withmodeling error and external disturbance,Backstepping linear sliding modecontrol,backstepping nonlinear sliding mode control and backsteppingquasi-sliding mode control are studied respectively.The system stability isproved by Lyapunov Principle.The traditional linear sliding surface is used inbackstepping linear sliding mode control which can't converge to itsequilibrium point in finite time.A terminal sliding mode (TSM) surface is used in backstepping nonlinear sliding mode control.Compared with linearhyperplane-based sliding modes, TSM offers the superior property of finitetime convergence.Based on backstepping sliding mode control,backsteppingquasi-sliding mode Control is obtained by converting sign function intosaturation funtion.Finally,simulation results verify the validity of the controlschemes as above.
(2)For tracking a desired trajectory of multilink robot manipulators withmodeling error and external disturbance,we studied new control methods inthis paper by combining fuzzy control,backstepping control and sliding modecontrol as follows:1.Global PID Fuzzy Sliding Mode Control;2.PIDBackstepping and adaptive Fuzzy Sliding Mode Control;3.BacksteppingSliding Mode Control with Fuzzy Compensation;4.Nonsingular TerminalFuzzy Sliding Mode Control Based on Backstepping.The stability of controlsystem is analyzed by Lyapunov Principle.A properly adaptive fuzzycontroller is designed to estimate uncertain upper boundary on line and trackthe modelling error and disturbance automatically in the first twomethods.Fuzzy compensation is designed to compensate the modelling errorand external disturbance in the backstepping sliding mode control with fuzzycompensation.So it weaken the disturbance and reduces chattering. Accordingto sliding mode control theory, backstepping is used to design nonsingularterminal sliding mode controller.So it overcomes disadvantage of singularpoint In order to reduces chattering a proper fuzzy controller is designed toestimate uncertain upper boundary on line and track the modelling error anddisturbance automatically. Finally,simulation results verify the validity of thecontrol schemes as above.
(3)For tracking a desired trajectory of multilink robot manipulatorswith modeling error and external disturbance,new control methods werestudied in this paper by combining backstepping control, sliding mode controland neural network control as follows:1.RBF Neural Network Sliding-modeControl;2.Global PID Neural Network Sliding Mode Control;3.IntegralBackstepping Sliding Mode Control;4.Backstepping Nonsingular Terminal Neural Network Sliding Mode Control;5.Backstepping Nonsingular FastTerminal Neural Network Sliding Mode Control.The system stability isproved by Lyapunov Principle.A switching function is used as input of RBFneural network in the RBF neural network sliding mode control. RBF neuralnetwork is treated as sliding mode controller directly.So MIMO neuralnetwork sliding mode control is implemented.Global PID sliding modesurface is designed in the global PID neural network sliding modecontrol.RBF neural network is used to adjust switching gain.Controllerparameters are tuned to estimate uncertain upper boundary on line.Sochattering is reduced.In order to estimate uncertain upperboundary,Self-adaptation principle of weight is designed in the integralbackstepping sliding mode control. Nonlinear terminal sliding mode surface isused in the backstepping nonsingular terminal neural network sliding modecontrol.RBF neural network sliding mode controller is designed to estimateuncertain upper boundary to reduce chattering.In order to further minimizeconvergence time, we design fast terminal neural network sliding modecontrol.Finally,simulation results verify the validity of the control schemes asabove.
引文
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