Study On The Modeling And Stability Control Of Inverted-pendulum System Based On Linear Motor

As a typical unstable non-linear system with the characteristics of simple structure, lowcost and easy to control, inverted pendulum is capable of manifesting many of the abstractcontrol concepts intuitively. Therefore, it is often used as the control object to test theperformance of various control methods. By using inverted pendulum, new control theoriesand approaches are developed continually, which are widely used in the field of aerospaceand robots. In this dissertation, we mainly focus on the stable control problem of the singlelinear motor inverted pendulum with the experimental platform provided by WinnerCompany. The main achievements are as follows:(1) Based on the intensive study on the structure of inverted pendulum and the extensiveanalysis of the latest research results in this field, system modeling and characteristic analysisof inverted pendulum is carried out. First, the mathematical model of single invertedpendulum is established through its dynamics equation and Lagrange equation and its transferfunction and state space equation are then deduced. In addition, the controllability,observability and frequency domain response characteristic of inverted pendulum areanalyzed, which reveals that the open-loop state of inverted pendulum is unstable, but it canbe controlled and observed in the equilibrium point.(2) According to the principle of “standing up pendulum and stabilizing cart”, combinedwith the characteristic that the variation of winding rod is small and easy to adjust, we adoptthe approach which first adjusts the angle of swinging rod, then control the position of thecart, and the fuzzy control algorithm, T-S fuzzy control algorithm and networked controlalgorithm of single inverted pendulum based on linear motor are designed. Moreover, weextend the results to the control of flexible connection inverted system and the triple PDcontroller and networked controller are devised. Finally, off-line simulation experiment isperformed in Matlab/Simulnik and the simulation results indicate that the effectiveness of thiscontrol scheme is acceptable.(3) After the off-line simulation, together with the off-line simulation and on-line realtime control, the hardware-in-the-loop simulation is carried out on the simulation platform provided by Winner Company. Simulink block diagram is used as the console of the invertedpendulum control system and we mainly concentrate on the controller structure design andparameter adjustment. The history curve is feasible to the analysis of the whole controlprocess. By adjusting the control parameter in real time, the inverted pendulum is balancedby the output torque of linear motor. Experimental results show reliability and effectivenessof the control algorithm and simulation platform.