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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 two-degree-of-freedom under-driven mechanical system. To solve the problem that Acrobot system needs to design a pendulum controller and a balance controller respectively, and the controller design is complicated, a new type of stabilization control strategy is proposed Control Strategy Just design a controller to get the Acrobot up and down from a stable equilibrium point downwards and up and down to an unstable equilibrium point up and down. First, the Euler-Lagrange equation is used to establish the dynamic model for the system. Then, a closed-loop global coordinate transformation scheme is proposed based on partial feedback linearization, which converts the Acrobot system dynamics model into a strict feedback cascade standard model. Finally, the system is divided into several subsystems by using the backstepping method. Lyapunov functions are constructed for each subsystem respectively, and the virtual control inputs are designed to achieve the system’s stabilization control. The simulation results show that the proposed control strategy is simple and effective and can be applied to a two-DOF underactuated system similar to the Acrobot system with high theoretical and practical value.