Nonlinear control for rotational movement of cart-pendulum system using homoclinic orbit
Nonlinear control for rotational movement of cart-pendulum system using homoclinic orbit
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DOI：
10.1007/s12555-015-0255-0
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发表时间：
2016-09
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影响因子：
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通讯作者：
Hiroya Oka;Yuji Maruki;H. Suemitsu;T. Matsuo
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文献类型：
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作者：
Hiroya Oka;Yuji Maruki;H. Suemitsu;T. Matsuo
在本文中，我们讨论使用分立面来控制摆旋转运动的方法。我们设计了一个控制器，通过使用一种前向控制设计来实现摆的同宿运动或异宿运动以及小车的渐近稳定性。首先，我们推导出一个通过摆子系统的李亚普诺夫函数收敛到同宿轨道的控制器。接下来，我们通过购物车子系统的另一个 Lyapunov 函数给出非线性稳定控制器。此外，使用第三个李亚普诺夫函数并添加补充控制输入，我们保证摆收敛到同宿轨道并且小车稳定。最后利用基于MATLAB/Simulink的快速控制器原型系统进行了仿真和实验，演示了摆锤向前向上旋转和巨大摆动的过程。
In this paper, we deal with the control method for rotational movements of a pendulum using a separatrix. We design a controller that attains a homoclinic motion or a heteroclinic motion of the pendulum and the asymptotic stability of the cart by using a kind of forwarding control design. First, we derive a controller that converges to a homoclinic orbit via a Lyapunov function of the pendulum subsystem. Next, we give a nonlinear stabilizing controller via another Lyapunov function of the cart subsystem. Moreover, using the third Lyapunov function and adding a complementary control input, we guarantee that the pendulum converges to the homoclinic orbit and the cart is stabilized. Finally, the simulation and the experiment using the rapid controller prototyping system based on MATLAB/Simulink are performed to demonstrate the forward upward circling and the giant swing of the pendulum.