Synchronizaiton Control For Underactuated LAGRANGE Systems

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.