Stabilizing Control Of A Single Inverted Pendulum System Based On Feedback Linearization

The phenomenon of non-linearity exists in nature and engineering technology, so the research of non-linear problems is particularly important. As a typical unstable nonlinear system, inverted pendulum system has simple structure, low cost and it can be controlled by a variety of methods. Therefore, it is often used to test various control methods to evaluate their performance. The inverted pendulum control is not only a typical non-linear control problem in the field of automatic control, it has also been widely used in aerospace, aviation, navigation, industrial processes and other fields. It is a hot spot in the field of non-linear control research. However, classical control theory and modern control theory need making approximation of nonlinear term, therefore classical control theory and modern control theory only can control the inverted pendulums in a certain extent, and there are certain disparity between the test results and engineering applications, teaching and scientific research.Recently, many researchers and control engineers show great interest in the development and application of nonlinear control methodologies. The impetus behind their research enthusiasms is that various advantages can be obtained by using nonlinear control. For instance, by using nonlinear control, the performance of existing control systems can be greatly improved, hard nonlinearities can be analyzed, modeling uncertainty can be dealt with more easily, and most systems can be designed in a simple way. Feedback linearization is a more advanced theory of non-linear control methods, it does not need to neglect any higher-order nonlinear term. Therefore, the model is closer to the actual system after making feedback linearization, and this method has better performance in the actual control.The paper mainly aims at applying feedback linearization to stabilizing control of a single inverted pendulum system. The single inverted pendulum system as control object is selected, and present research condition and studying significance of single inverted pendulum system are described. The mathematical model of the inverted pendulum is established by the method of Newton mechanics in the analytical mechanics. According to the linear system theory, we make a qualitative analysis of this model after linearizing the model, and the results of the analysis show the non-stability, controllability, observability of this model. After that, this paper designs a controller based on LQR theory, and carries out simulation. The simulation results show the controller is effective and efficient. In particular, it has a smaller control range, a longer response time and larger overshoot.In order to improve control efficiency, the paper describes in detail related theory of feedback linearization, and derives design steps of stabilizing controller based on related theory of feedback linearization. Then, according to this method, the paper incorporates non-linear feedback, and puts the non-linear pendulum system into a linear system. Then. according to modern control theory, the paper designs the inverted pendulum controller based on feedback linearization. In order to simulate the system better, this paper introduces the simulation software for the control system simulation, and makes the module simulation using this software based on the controller. The simulation results show the effectiveness of thecontroller. In particular, the controller has a larger control range, i.e., -68°≤θ≤68°.At last, the paper analyses two control methods of simulation results. According to comparing between the two results of controllers, the paper indicates that feedback linearization control of an inverted pendulum has the advantages of a low response time, small overshoot and a larger control range. However, in the controller design process, we have also seen this method has some disadvantages, e.g, a large amount of design steps, large amount of calculation.