Optimal Synchronization Control Of A Class Of Underactuated Lagrangian Systems

Many control schemes have been applied to the synchronous control system design. However, synchronization control methods are still in the process of development and perfection. In order to ensure the performance of tracking and synchronization, it is important to properly select output functions and to transform system states. For different synchronization control issues, different methods are used to select output functions and to transform states. The Lagrangian equation is widely used in many fields to establish dynamics equations, especially in electrical and mechanical control systems. There always exists a synchronization control strategy in general for typical Lagrangian systems. We can try to find the most extensive application of synchronization control.A partially linearized model for underactuated Euler-Lagrangian systems is obtained based on the feedback linearization method. Then, the small deviation linearization technique is applied to the partially linearized model to obtain a linear model. For the completely controllable linear system, a linear quadric optimal synchronization controller is proposed. Using the proposed methods, we design a synchronous motion system composed of two single linear inverted pendulums. The experimental results show that the optimal synchronization control system has realized a stable balance of the two inverted pendulums and a precise location of the two cars while they move synchronously. The effect of the optimal synchronization control scheme is better than the usual master-slave synchronization scheme.Under consideration of the existed friction or other uncertainties that disturb the synchronous system, an adaptive optimal synchronization controller is designed to attenuate the disturbances. Simulation results show that the proposed adaptive optimal synchronization controller can offset the outside disturbance, and improve the tracking and synchronization performances.