欠驱动基准系统的约束控制

Constrained control for the underactuated benchmark system

针对一种欠驱动基准系统,具有旋转激励的平移振荡器(translation oscillators with rotating actuator,TORA)系统,本文首次提出了一种具有约束的控制方法.该方法不仅可以保证闭环系统的稳定性,而且能够保证旋转小球在预设的范围内转动.相比已有控制方法,本文所提方法可以预设小球的转动范围以避免不理想的"循环"行为.具体而言,首先对系统的总机械能进行了详细分析;随后在其总机械能的基础上通过能量整形构造出一个新颖的能量函数;最后基于所构造的能量函数提出了一种具有约束的控制器,采用Lyapunov方法及La Salle不变性原理证明了相应闭环系统的稳定性.通过与已有方法进行仿真对比可知,本文方法在镇定控制与约束控制方面均表现出良好的控制性能.

For the first time, we propose a constrained control method for an underactuated benchmark system, the translation oscillators with rotating actuator （TORA） system. This method guarantees both the stability of the closed-loop system and the actuator rotation in a preset range. Compared with the existing available methods, the proposed method can preset the rotating range of the actuator to avoid the undesired unwinding behavior. Specifically, the total mechanical energy of the TORA system is analyzed firstly. Then, based on the total mechanical energy, a novel energy function is obtained via energy shaping. Finally, a constrained control method is proposed on the basis of the constructed energy function; and the stability of the corresponding closed-loop system is proved by using Lyapunov techniques and LaSalle invariance theorem. Simulation results show that, in comparison with existing methods, the proposed method achieves superior control performance in stabilization control and constraint control.