Research On Robust Control Of The Inverted Pendulum System

Based on math tool such as linear algebra and optimal method, modern control theories strictly depend on precise math model. The real process is accompanied by uncertainty widely, therefore the math model is not so precise. The controller designed by modern control theories is difficult to be implemented, to some extension, system's stability can't be guaranteed. So in modern control theory an important subject came out. Robust control, during establishing math model and designing the controller, considers the uncertainty, and based on the incomplete information of uncertainties designs a controller that is not based on uncertainties to make the system meet the desired performance.Inverted pendulum system is full of multivariable, high-order, unlinear, unstable characteristics, and its control process can effectively reflect many significant control problems, such as: stabilization problem, unlinear problem and robust problem. So usually inverted pendulum system is used to testify the effectivity of control theory. Research on it has not only meaningful theory worth, but also important engineering background and real significance.For the robust control of the inverted pendulum systems, in this paper the following content will be discussed:First, this paper makes a study of the constitution and work principle of the inverted pendulum system, re-computes the math model, and analyses the robustness, fragility and main disturbance sources.Second, this paper presents the application of the variable structure control (VSC) theory for the inverted pendulum system. Based on the linear quadratic optimal theory and poles place theory in the state-space equation mode, a sliding surface function is designed and the state-feedback controller using the VSC theory is got. In addition, the single and double inverted pendulum system are controlled successfully in the real equipment. Third, the H_∞control theory for the inverted pendulum system is studied in this paper and an H_∞output-feedback robust controller via DGKF method is designed. For the inverted pendulum system is a non-minimum phase and unstable system, this paper chooses a structure with two close-loops: an inner loop based on classical control theory to stabilize the unstable mode and the outer loop based on H_∞theory to control the whole system.Finally, after simulation on computer this paper uses MATLAB as control interface software. The researching results of this paper are applied to linear inverted pendulum experiment equipment produced by Googol Technology LTD. so as to verify the effectiveness of the control laws. During the experiments, the control parameters are adjusted and how the parameters effect on the performance is concluded. The results of experiments prove that each of the controllers has a good control effect.