Linear Inverted Pendulum Mechanism Model And Control Performance

The inverted pendulum system is characterized as a fast multi-variable nonlinear essentially unsteady system. The research on precise control of the inverted pendulum is of great practical engineering value for control problems of complicated industrial objects. This dissertation, based on the linear inverted pendulum of Googol Company, has made the modelings, control algorithm simulations and experiments on the 1-stage inverted pendulum and 2-stage inverted pendulum models and reached corresponding conclusions.The clssification, features, control targets,control methods , the development of the research on inverted pendulum control and its research status have been talked about in this dissertation. The dynamic model of linear 1-stage inverted pendulum has been deduced by means of Newton mechanics and its transfer function & state space equation have been obtained. The mathematic model has been attained by the Lagrangian Equation in analytical mechanics, the Lagrangian operator has been obtained through focusing on the analysis of kinetic energy and potential energy. The features of stability, contollability and observability of linear inverted pendulum system have been analyzed through MATLAB programs and modern control theories.The control stategies of inverted pendulum system have been studied on the basis of building system model. By taking classic control methods to the linear 1-stage inverted pendulum, designed have been the conventional PIDcontroller and double closed loop controller and the PID controller based on state space equation of inverted pendulum system. And by making MATALAB/Simulink simulation, different effects have been acquired. By taking modern control methods to the linear 2-stage inverted pendulum, the LRQ controller has been devised. By taking advantage of Googol MATLAB real-time control software, the LRQ control simulation figure of the linear 2-stage inverted pendulum has been obtained. And by altering the parameters of Simulink LRQ model and state space model, the best control result has been achieved.With the help of Googol MATLAB real-time control software experiment platfrom, conducted have been the online real-time simulation experiments on the linear 1-stage inverted pendulum systems and linear 2-stage inverted pendulum systems respectively by means of PID and LRQ control methods. In the experiment, the system can soon regain blanace even though the positions of the cart were changed and the system was given perturbations. Thus it can be seen that it has got a fairly good real-time control effect.