欠驱动Lagrange系统的同步控制
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摘要
在当前的生产生活过程中,许多任务对于单个系统是无法独立承担的,从而就需要多个系统进行协调配合完成。欠驱动系统是控制输入数目少于系统自由度个数的控制系统,它广泛存在于机器人、交通运输和航空航天等各个领域。由于系统驱动器的减少,从而具有质量轻、成本低和能量消耗少等众多优点,因此研究多个欠驱动系统的协调同步控制具有很重要的意义。而欠驱动Lagrange系统是所有欠驱动系统的典型代表,所以本论文针对多个欠驱动Lagrange系统构成的同步运动系统,研究其同步控制问题。
首先,基于部分反馈线性化和线性二次型最优控制理论,设计了多个欠驱动Lagrange系统的协调同步控制器。控制器的设计过程中不仅对系统的跟踪误差进行了加权评价,同时也将同步误差变量引入到所设计的线性二次型性能指标函数中进行加权调节。通过调节加权矩阵中权值项的大小,从而达到同时改善系统跟踪性能和同步性能的目的。所设计的最优同步控制器不仅能够保证系统的跟踪误差有界,而且同时保证了系统运动的协调同步性,通过数值仿真和实时控制实验也验证了此结论。
其次,应用聚合式结构双层递阶滑模控制理论,设计了多个单输入欠驱动Lagrange系统的滑模同步控制律。根据系统的同步控制目标,定义了系统的同步误差,并结合交叉耦合控制策略定义了包含系统位置跟踪误差和同步误差的耦合状态变量。由耦合状态变量设计的第一层滑模面构造系统的第二层滑模面,通过设计系统的同步控制律,保证系统的轨线在有限时间内到达滑模面,并沿着滑模面趋向原点。仿真和实验结果表明,所设计的递阶滑模同步控制器不仅实现了对指令信号的精确跟踪,同时也实现了系统在运行过程中运动的协调同步。
然后,针对两个无输入耦合的欠驱动Lagrange系统,设计了系统的递推反步同步控制律。采用可逆坐标变换将系统动力学模型转化成规范形式后,定义系统的广义同步误差作为系统独立的状态变量,与欠驱动子系统联立设计了系统的同步控制律。另外,为了进一步实现对多个无输入耦合的欠驱动Lagrange系统的同步控制,定义系统的耦合误差状态变量,得到系统的耦合状态方程,进而采用递推反步设计方法,设计了适用于包含多个欠驱动Lagrange系统的同步运动系统的反步同步控制律,保证了系统的跟踪性能和同步性能。通过数值仿真和实验结果验证了该方法的有效性。
最后,研究了多个欠驱动Lagrange系统的无源化同步控制策略。通过设计闭环系统期望的能量函数,使闭环系统具有端口受控制哈密尔顿方程的形式,并将定义的同步误差变量引入到所设计的闭环系统期望的能量函数中,采用互联阻尼配置无源化控制方法,通过求解匹配条件得到了系统的同步控制器。数值仿真和实时控制实验结果表明,所设计的无源化同步控制器不仅实现了对指令信号的精确跟踪,而且保证了系统具有良好的同步性能。
In modern manufacture and life, many tasks can’t be accomplished independentlyby a single system. Multiple systems are usually coordinated to complete some missions.Underactuated systems are control systems with fewer control inputs than the number ofthe configuration variables. There exist such systems widely in robotics, transportation,aerospace vehicles and many other fields. Underactuated systems have the advantage inlight weight, low cost and less energy consumption due to the reduction of the systemdrivers. The synchronization of multiple underactuated systems is very important andnecessary. As the underactuated Lagrange systems are the typical systems of the wholeunderactuated systems, this dissertation is devoted to the synchronization control of mo-tion systems consisting of multiple underactuated Lagrange systems.
Firstly, the synchronization controller of multiple underactuated Lagrange systems isdesigned based on partial feedback linearization technology and linear quadratic optimalcontrol theory. During the controller design, not only the tracking errors are evaluated,but also the synchronization error variables are introduced into the quadratic performanceindex function. The weight matrix can be easily adjusted to improve the tracking andsynchronization performance. The designed optimal synchronization controller can guar-antee that the tracking error is bounded and meanwhile maintain the synchronization ofthe motion systems. Numerical simulation results and real-time control experiments vali-date the e?ectiveness of the proposed controller.
Secondly, the hierarchical sliding mode control theory is employed to design thesliding-mode synchronization control law for multiple single-input underactuated La-grange systems. Synchronization errors of the motion systems are defined according tocontrol objectives. The coupled state variables composed of position tracking errors andsynchronization errors are defined by using the cross-coupling control strategy. The sec-ond layer sliding surface is formed by the first layer sliding surfaces, which are designedwith the the coupled state variables. The designed synchronization control law can ensurethat the system trajectories reach the sliding surface in finite time, and tend to the originalong the sliding surface. Simulation and experimental results show that the proposed hi-erarchical sliding-mode synchronization controller can guarantee that the motion systemstrack command signals accurately and move in synchronization.
Then, the recursive backstepping synchronization control law is proposed for twounderactuated Lagrange systems without input coupling. A reversible coordinate trans-formation is used to transform the system dynamics model into a canonical form. Gen-eralized synchronization errors are defined as independent state variables to design thesynchronization controller. In addition, to realize synchronization control for multipleunderactuated Lagrange systems without input coupling, coupling state equations are ob-tained to propose the synchronization controller by using backstepping method. The syn-chronous motion of multiple underactuated Lagrange systems is achieved with the de-signed synchronization controller. Simulations and experimental results demonstrate theeffectiveness of the synchronization method.
Finally, the passivity-based synchronization control of multiple underactuated La-grange systems is studied. The closed-loop system is designed to have a port-controlledHamilton form with a desired energy function. The defined synchronization errors areintroduced into the desired energy function, which is the closed-loop Lyapunov func-tion. By solving the matching conditions, a passivity-based synchronization controller isobtained with interconnection and damping assignment passivity-based control method.Simulations and experimental results show that the proposed approach realizes a precisetrajectory-tracking control and good synchronization performance of the systems.
首先,基于部分反馈线性化和线性二次型最优控制理论,设计了多个欠驱动Lagrange系统的协调同步控制器。控制器的设计过程中不仅对系统的跟踪误差进行了加权评价,同时也将同步误差变量引入到所设计的线性二次型性能指标函数中进行加权调节。通过调节加权矩阵中权值项的大小,从而达到同时改善系统跟踪性能和同步性能的目的。所设计的最优同步控制器不仅能够保证系统的跟踪误差有界,而且同时保证了系统运动的协调同步性,通过数值仿真和实时控制实验也验证了此结论。
其次,应用聚合式结构双层递阶滑模控制理论,设计了多个单输入欠驱动Lagrange系统的滑模同步控制律。根据系统的同步控制目标,定义了系统的同步误差,并结合交叉耦合控制策略定义了包含系统位置跟踪误差和同步误差的耦合状态变量。由耦合状态变量设计的第一层滑模面构造系统的第二层滑模面,通过设计系统的同步控制律,保证系统的轨线在有限时间内到达滑模面,并沿着滑模面趋向原点。仿真和实验结果表明,所设计的递阶滑模同步控制器不仅实现了对指令信号的精确跟踪,同时也实现了系统在运行过程中运动的协调同步。
然后,针对两个无输入耦合的欠驱动Lagrange系统,设计了系统的递推反步同步控制律。采用可逆坐标变换将系统动力学模型转化成规范形式后,定义系统的广义同步误差作为系统独立的状态变量,与欠驱动子系统联立设计了系统的同步控制律。另外,为了进一步实现对多个无输入耦合的欠驱动Lagrange系统的同步控制,定义系统的耦合误差状态变量,得到系统的耦合状态方程,进而采用递推反步设计方法,设计了适用于包含多个欠驱动Lagrange系统的同步运动系统的反步同步控制律,保证了系统的跟踪性能和同步性能。通过数值仿真和实验结果验证了该方法的有效性。
最后,研究了多个欠驱动Lagrange系统的无源化同步控制策略。通过设计闭环系统期望的能量函数,使闭环系统具有端口受控制哈密尔顿方程的形式,并将定义的同步误差变量引入到所设计的闭环系统期望的能量函数中,采用互联阻尼配置无源化控制方法,通过求解匹配条件得到了系统的同步控制器。数值仿真和实时控制实验结果表明,所设计的无源化同步控制器不仅实现了对指令信号的精确跟踪,而且保证了系统具有良好的同步性能。
In modern manufacture and life, many tasks can’t be accomplished independentlyby a single system. Multiple systems are usually coordinated to complete some missions.Underactuated systems are control systems with fewer control inputs than the number ofthe configuration variables. There exist such systems widely in robotics, transportation,aerospace vehicles and many other fields. Underactuated systems have the advantage inlight weight, low cost and less energy consumption due to the reduction of the systemdrivers. The synchronization of multiple underactuated systems is very important andnecessary. As the underactuated Lagrange systems are the typical systems of the wholeunderactuated systems, this dissertation is devoted to the synchronization control of mo-tion systems consisting of multiple underactuated Lagrange systems.
Firstly, the synchronization controller of multiple underactuated Lagrange systems isdesigned based on partial feedback linearization technology and linear quadratic optimalcontrol theory. During the controller design, not only the tracking errors are evaluated,but also the synchronization error variables are introduced into the quadratic performanceindex function. The weight matrix can be easily adjusted to improve the tracking andsynchronization performance. The designed optimal synchronization controller can guar-antee that the tracking error is bounded and meanwhile maintain the synchronization ofthe motion systems. Numerical simulation results and real-time control experiments vali-date the e?ectiveness of the proposed controller.
Secondly, the hierarchical sliding mode control theory is employed to design thesliding-mode synchronization control law for multiple single-input underactuated La-grange systems. Synchronization errors of the motion systems are defined according tocontrol objectives. The coupled state variables composed of position tracking errors andsynchronization errors are defined by using the cross-coupling control strategy. The sec-ond layer sliding surface is formed by the first layer sliding surfaces, which are designedwith the the coupled state variables. The designed synchronization control law can ensurethat the system trajectories reach the sliding surface in finite time, and tend to the originalong the sliding surface. Simulation and experimental results show that the proposed hi-erarchical sliding-mode synchronization controller can guarantee that the motion systemstrack command signals accurately and move in synchronization.
Then, the recursive backstepping synchronization control law is proposed for twounderactuated Lagrange systems without input coupling. A reversible coordinate trans-formation is used to transform the system dynamics model into a canonical form. Gen-eralized synchronization errors are defined as independent state variables to design thesynchronization controller. In addition, to realize synchronization control for multipleunderactuated Lagrange systems without input coupling, coupling state equations are ob-tained to propose the synchronization controller by using backstepping method. The syn-chronous motion of multiple underactuated Lagrange systems is achieved with the de-signed synchronization controller. Simulations and experimental results demonstrate theeffectiveness of the synchronization method.
Finally, the passivity-based synchronization control of multiple underactuated La-grange systems is studied. The closed-loop system is designed to have a port-controlledHamilton form with a desired energy function. The defined synchronization errors areintroduced into the desired energy function, which is the closed-loop Lyapunov func-tion. By solving the matching conditions, a passivity-based synchronization controller isobtained with interconnection and damping assignment passivity-based control method.Simulations and experimental results show that the proposed approach realizes a precisetrajectory-tracking control and good synchronization performance of the systems.
引文
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