Time Optimal Swing-Up Control of Single Pendulum
Time Optimal Swing-Up Control of Single Pendulum
复制标题
单摆时间最优摆动控制
DOI：
10.1115/1.1383027
复制
发表时间：
2001
影响因子：
1.7
通讯作者：
K. Furuta
中科院分区：
文献类型：
--
作者：
Yongcai Xu;M. Iwase;K. Furuta
旋转式摆从悬垂状态到倒立状态的摆动被认为是最困难的控制问题之一，因为系统是非线性的、欠驱动的并且具有不可控状态。本文研究了使用有界输入的摆锤时间最优摆动控制。非线性系统的时间最优控制可以通过庞特里亚金极大值原理来表述，但实际上很难计算。在本文中，提出了一种新的计算方法来获得时间最优摆动问题的数值解。时间最优控制问题被描述为在有界输入幅度下达到最终状态的可实现时间的最小化，尽管已知解决该问题的算法很复杂。因此，在本文中，展示了如何将最佳时间上摆控制公式化为辅助问题，其中搜索最小输入幅度，使得终端状态在给定时间满足规范。通过所提出的方法，可以通过非线性优化来解决时间最优控制。通过简化摆模型的数值模拟对其方法进行了评估，检查其是否满足最大原理的必要条件，并使用旋转式摆进行了实验验证。
Swing-up of a rotating type pendulum from the pendant to the inverted state is known to be one of most difficult control problems, since the system is nonlinear, underactuated, and has uncontrollable states. This paper studies a time optimal swing-up control of the pendulum using bounded input. Time optimal control of a nonlinear system can be formulated by Pontryagin’s Maximum Principle, which is, however, hard to compute practically. In this paper, a new computational approach is presented to attain a numerical solution of the time optimal swing-up problem. Time optimal control problem is described as minimization of the achievable time to attain the terminal state under the bounded input amplitude, although algorithms to solve this problem are known to be complicated. Therefore, in this paper, it is shown how the optimal time swing-up control is formulated as an auxiliary problem in that the minimal input amplitude is searched so that the terminal state satisfies a specification at a given time. Through the proposed approach, time optimal control can be solved by nonlinear optimization. Its approach is evaluated by numerical simulations of a simplified pendulum model, is checked satisfying the necessary condition of Maximum Principle, and is experimentally verified using the rotating type pendulum.