Fault Diagnosis Based On Observer For Inverted Pendulum System

Now, the study of fault detection and diagnosis is a hot research topic in the field of control. When the parameters of the model are known, we will use the method of observer firstly. Although this method needs a higher requirement of the system model, the method of the observer-based fault detection is more reliable and more effective, it also have a better performance of robustness.This article is aim at studying the inverted pendulum system, considering the method of observer for fault diagnosis. Then we can get the theorem of the fault diagnosis of the inverted pendulum system based on model. The main contents are as follows:Firstly, we mainly studied fault diagnosis method based on reduced-order observer of inverted pendulum system. We know that the inverted pendulum system has four variables, such as the displacement of the car, the speed of the car, the angle of swinging rod and angular velocity of swinging rod, and the displacement of the car and angle of swinging rod is measurable. In this case, if we use the full state observer for fault diagnosis, it may cause waste in engineering project. So we use the method of reduced-order observer for fault diagnosis. The advantages of this method are that it can make the structure simple and save cost. Thus, we use the adaptive method to control the system with fault diagnosis and get the observer gain matrix L by solving the linear matrix inequality. At last, we use MATLAB simulation to verify this theory. And the result of the simulation reflect the effectiveness of using the method of reduced-order observer to solve fault diagnosis problem of inverted pendulum system.Secondly, we mainly studied fault diagnosis method based on reduced-order sliding mode observer of inverted pendulum system. As the inverted pendulum system is a kind of strong coupling nonlinear system, there must be exist the deviation between the linear model and the original system after the linearization of the inverted pendulum system. So this article uses the uncertain linear model to describe the inverted pendulum system. In addition, we consider two cases as follows: Firstly, the fault is bounded and the boundary is known. We use the sliding mode observer to solve the problem of fault diagnosis. Secondly, the fault is bounded and the boundary is unknown. In this case, we consider the sliding mode switching function, using the time-varying sliding mode observer gain matrix, which can be more effective to identify fault. At last, in view of the inverted pendulum system, use MATLAB simulation to verify this theory. It is effective to use the method of reduced-order sliding mode observer to solve fault diagnosis problem of inverted pendulum system.Thirdly, as the inverted pendulum system is a nonlinear system, this article studied the nonlinear model of inverted pendulum system for fault diagnosis. Considering the interference and fault at the same time, we use fault diagnosis method to control the inverted pendulum system based on reduced-order sliding mode observer. Under this circumstance, consider two kinds of faults: the actuator fault and sensor fault. Then design the sliding mode observer respectively. At last, use MATLAB simulation to verify this theory. As a result, it shows that using the method of sliding mode observer is more effectively to diagnose the fault of nonlinear system and can resist the interference at the same time.