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Stabilising a cart inverted pendulum system using pole placement control method

机译：使用杆子放置控制方法稳定推车倒立摆系统

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A cart inverted pendulum system is one of the most common case to be considered for testing many control algorithms, since it has some challenging problems associated with non linearity, complexity and underactuated system model. In fact, non-linearity behaviour of the inverted pendulum can be observed easily. Different pendulum angle response can be obtained by giving the same velocity in the cart. The cart inverted pendulum can be understood as an under actuated system since the system has a lower number of actuator than the degrees of freedom. One of the most convenient method to model the inverted pendulum system is to use Lagrange's equation. However, at present, many presented inverted pendulum models have been derived using simplified physical model. This simplified model may lead to problems for the implementation of the control algorithm in a real physical inverted pendulum system. In this paper, an inverted pendulum system model is presented, where a mechanical transmission system and a motor models have been included in the derivation of the inverted pendulum model. Hence, the problems for the control implementation in a real system can be minimized. The mathematical model of the inverted pendulum was derived using Lagrange's equation. The determination of the pole zero of the system is discussed. A simple method of pole placement is proposed to stabilise the pendulum at the desired position of the cart. Matlab simulation results show the effectiveness of the proposed method. And yet, this intuitive approach can lead to better understanding of the control behaviours.
机译：推车倒置摆动系统是用于测试许多控制算法的最常见情况之一，因为它具有与非线性，复杂性和欠扰系统模型相关的一些具有挑战性的问题。事实上，可以容易地观察倒置摆的非线性行为。通过在推车中具有相同的速度，可以获得不同的摆角响应。推车倒置摆可以被理解为致动系统，因为系统具有比自由度的致动器数量较少。模拟倒立摆系统的最方便的方法之一是使用拉格朗日的等式。然而，目前，已经使用简化的物理模型导出了许多呈现的反相摆模型。该简化模型可能导致在真实物理倒立摆系统中实现控制算法的问题。在本文中，提出了一种倒摆系统模型，其中机械传输系统和电动机模型已被包括在倒摆型模型的推导中。因此，可以最小化真实系统中控制实现的问题。使用拉格朗日的等式导出倒立的摆锤的数学模型。讨论了系统的杆零的确定。提出了一种简单的杆子放置方法，以在推车的所需位置稳定摆锤。 MATLAB仿真结果表明了该方法的有效性。然而，这种直观的方法可能导致更好地了解控制行为。

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