Swing-up And Stability Control Of The Circular Inverted Pendulum

In this paper,the method of automatic swing up and stability control of the ring inverted pendulum is studied,which is based on the real experiment of realizing swing up of the single stage ring inverted pendulum inverse system by LABVIEW programming controller.First of all,the mathematical models of the single and second-order ring inverted pendulum are established by using Lagrange equation,and the qualitative analysis of the system is carried out.Secondly,based on LQR control method,the stability control simulation experiment of the ring inverted pendulum is completed.Then,the energy method swing controller is used to realize the automatic swing up experiment of the single stage ring inverted pendulum.However,due to the disadvantages of the energy method swing up,such as long response time and multi-user energy is not easy to control,and so on,the inverse system based swing up controller is further proposed.Finally,the control experiment based on the inverse system control strategy is realized by LabVIEW,which fills up the blank of the application of the inverse system control strategy in the inverted pendulum experiment in China.The main contents of this paper are as follows:1.Based on the in-depth study of the inverted pendulum system structure and extensive reading of references at home and abroad,the Lagrangian modeling method is used to build the mathematical models of the first and second stage ring inverted pendulum.The performance of the ring inverted pendulum system is analyzed.It is proved that the ring inverted pendulum system model has the characteristics of open-loop instability,controlling and immovability.2.The LQR controller is constructed to control the stability of the first and second inverted pendulum system near the equilibrium point.The simulation results show that LQR controller has good control effect and can realize the stable control of inverted pendulum.The energy method control strategy is used to complete the simulation experiment of the automatic swing up control of the first stage ring inverted pendulum.According to the problem that the rotating bar of the real object has a dead zone and cannot rotate 360 °,the sign function is introduced to transform the original controller to ensure the safe use of the equipment to the maximum extent.The experimental results show that although the energy method can realize the automatic swing up of the inverted pendulum system,the response speed of the system is slow,and it is not suitable for the higher-order inverted pendulum system.Therefore,the inverse system control strategy is proposed to complete the automatic swing up control of the system and complete the simulation experiment.3.This paper proposes to build the physical experiment control platform of the invertedpendulum by LABVIEW programming software,and realize the physical experiment of automatic swing up and stability control of the ring-shaped inverted pendulum system based on the inverse system control strategy.By using the interp1 difference function,the reference trajectory and the feedback gain data are processed linearly,so that the reference trajectory,the feedback gain and the feed-forward control data obtained from the simulation experiment are consistent with the sampling frequency of the real-time control,and the simulation experiment is closely combined with the real experiment.The experimental results show that the inverse system control strategy has the advantages of fast response and high stability.