基于级联标准型的Acrobot反步控制

Backstepping Control Strategy of Acrobot Based on Cascade Form

Acrobot是一种典型的二自由度欠驱动机械系统,针对Acrobot系统镇定控制中需要分别设计起摆控制器和平衡控制器,控制器设计复杂这一问题,提出一种新型的镇定控制策略,该控制策略仅仅需要设计一个控制器,就可以使Acrobot由竖直向下的稳定平衡点起摆,并稳定于竖直向上的不稳定平衡点。首先,采用欧拉-拉格朗日方程为系统建立动力学模型;然后,结合部分反馈线性化,提出一种闭环全局坐标变换方案,将Acrobot系统动力学模型转换为严格反馈级联标准型;最后,采用反步法将系统分为若干个子系统,分别为每个子系统构造Lyapunov函数,并设计虚拟控制输入,最终实现系统的镇定控制。仿真结果表明,所提出的控制策略简单有效,可以应用于与Acrobot系统类似的二自由度欠驱动系统中,具有较高的理论和应用价值。

Acrobot is a typical underactuated mechanical system with two degrees of freedom. It is complicated to design the swing-up and balance controller in the stabilization control of Acrobot. This paper presents a new control strategy that just one controller is needed to swing up the Acrobot from its stable downward position to its upward position and stabilize it. First, based on the Euler-Lagrangc equations, the dynamic model of Acrobot was established. Next, combining with the partial feedback linearization, the paper proposes a closed-loop global change of coordinates that allows to describe the dynamic model of the Acrobot in the strict feedback cascade ibrm. Then, the system was divided into several subsystems based on the backstepping method. The Lyapunov functions were constructed and the virtual control inputs were designed for each subsystem. The stabilization control of the system was achieved ultimately. Simulation results show that the proposed control strategy is simple and effective, which is of high theory and application value.