Study On Swing-up Strategy Of Inverted Pendulum Based On Deviation Function

Inverted pendulum system is a complicate and unstable nonlinear system. It plays an important role in verifying control theories and algorithms. Research methods and thoughts of inverted pendulum are widely used in many important research directions, such as balance control of walking bipedal robots, launch control of multi-stage rockets, attitude control of satellites and so on. With the advantages of low cost, relatively simple structure, easy for parameter adjustion and so on, inverted pendulum system has been attracting people’s attention and study. How to swing the pendulum from the natural pendent position up to the inverted position rapidly and stabilize them in large angular range, is the key point in the research of inverted pendulum controlling. In this thesis, a kind of swing-up strategy based on deviation function is proposed, and the single and double inverted pendulums are swung up with this strategy respectively. The main works of this thesis are as follows:(1) The mathematical model of the inverted pendulum systems are established with Lagrange method. The relevant linearization models at the upright equilibrium point are obtained. The controllability, observability and stability of the inverted pendulum system at the equilibrium point are qualitative analysed separately.(2) For the single inverted pendulum system, a kind of swing-up control strategy based on the deviation function is designed and simulated. The method adjusts the controlled quantity mainly through the introduction of an angle feedback function. The advantages of this method is that the pendulum gains great controlled quantity in the natural sagging state, which makes the swing-up of the pendulum rapider and the adjustment of the control parameters much easier. The feedback function can be designed in various forms under the given conditions. Compared with the commonly used energy control, fuzzy control and Bang-Bang control method, the inverted pendulum based on the deviation function swings up with less time. With the same feedback function and initial controlled quantity, pendulums with different length are all swung up to the upright equilibrium position in quite short time. It indicates that swing-up control strategy based on deviation function is robust.(3) The deviation function method is applied to design controller for swinging up double inverted pendulum. Firstly, the step by step scheme is used. Three controllers are designed according to the process of swinging up. Then, the synchronization scheme is used. The control strategy of the synchronization scheme is same as that of the step by step scheme. The only difference is that they have different control parameter values. The simulation results show the success of swinging up double inverted pendulum with deviation function, and the control parameter adjustment is more convenient. Lastly, by changing the length of pendulums in two different conditions, the robustness of the feedback strategy is proved through simulation.(4) Finally, based on the above simulation work, experiment of single inverted pendulum swing up control is carried out, The effectiveness of the designed control strategy is verified through practical object.