单级倒立摆系统角运动控制方案建模及仿真

The Movement Modeling and Simulation of the Scheme of Angle Movement Controlling of the Simple Inverted Pendulum

单级倒立摆系统是一种广泛应用的物理模型。控制单级倒立摆载体的运动是保证倒立摆稳定性的关键因素。为了避免常用的物理反馈分析方法和运动轨迹摄像制导控制方法的某些缺点,本文从力学的角度提出对倒立摆的运动进行纯角度制导分析,完成了对倒立摆载体的角度制导运动微分方程的数学建模,根据应用背景,设计了该模型的模糊控制系统,并利用Matlab软件的Simulink工具对倒立摆的运动进行了计算机仿真。实验表明,这种模糊控制配合代数解析方法的运算速度和计算机仿真的效果均较物理反馈和运动轨迹摄像制导控制方法有了一定的提高,仿真结果与其相当。该方法容易向二级甚至三级倒立摆控制系统推广。该方法可以有效地改善单级倒立摆控制系统的性能。

The simple inverted pendulum is a kind of physical model with broad application fields. The control of the carrier of the simple inverted pendulum is the pivotal factor to guarantee the stability of the pendulum. To avoid some disadvantages of the schemes commonly used such as physical feedback analysis and movement trace navigation by camera, we provide a scheme from the view of mechanics by using the pure angle disturbance navigation and the modeling of movement differential equation is described in this paper. We also design the model抯 fuzzy logical control system by consulting the inverted pendulum抯 background of application. This paper also gives a simulation model and result by using the Matlab and its toolbox Simulink. The actual simulative experiments show that the method of fuzzy logical control co-operates with algebra analysis and is of better effect and higher efficiency than the physical feedback analysis and movement trace navigation by camera. This method can also be extended to the two-level or three-level inverted pendulums easily. This control scheme can ameliorate the performances of simple inverted pendulums effectively.