The Application Of Adaptive Sliding Mode Variable Structure Control To Linear Inverted Pendulum System

As the verification experiment platform for effective control method, the inverted pendulum system is a typical representative of a high order, multi-variable, nonlinear and naturally unstable system. So, it has have all kinds of connections with control theory and deep origin, the validity and practicability of the control method inverted is able to be verified by pendulum system, the pendulum system can also reflect some industrial control problems, such as nonlinear, high order and high instability. So, we can say that the inverted pendulum system is a bridge for control theory to industrial control from the laboratory. At present, the domestic and international research on the stabilization control of inverted pendulum system has entered a deep detail circumstance, including the emergence of control methods to it. Such as classic control, nonlinear control and intelligent control, the latest research results have been emerged in an endless stream. under such background, innovation to achieve the control method of the inverted pendulum is a certain difficulty.Sliding mode variable structure control theory is produced in solving nonlinear problem under the background, it has fast and strong external robustness, due to the sliding mode can be designed, so it has brought great convenience and flexibility to study the control problem. At the same time, the sliding mode control also has some shortcomings, such as the chattering caused by switching control problem of the system, it must be solved in the use of sliding mode control. In this paper, the work content and some innovation points are:1. In the first, the analysis of the structure and characteristics of the inverted pendulum is did, mathematical model is then established for the linear one and double inverted pendulum, and the controllability and observability of the system are analyzed based on modern control theory.2. It is a pair of contradiction for the robustness of sliding mode control and chattering phenomenon. For this, robust state feedback control of sliding mode based on LMI is given, and it is optimized by the linear matrix inequality algorithm, and then this control method is used in the linear one and two inverted pendulum system. Control effect is obvious, the robustness of the system is greatly improved and the chattering phenomenon is also improved.3. For the model reference adaptive control, the system reference model for there is difficult to certain, especially when the controlled object is a high order system, manual trial method to certain system reference model is incapable of action. This paper presents a model reference adaptive control method based on pole placement control, then the ideal reference model of linear one and two inverted pendulum was calculated easily, and the system was controlled steadily.4. When the system becomes very complex, it is very difficult to get the accurate mathematical model of the system. Based on this, this paper proposes an adaptive sliding mode control without physical parameters, and it is applied in the inverted pendulum system successfully.5. According to the method of control designed, in the MATLAB environment, the one and two level inverted pendulum systems are controlled steadily.