Research On Modeling And Control Methods Of Inverted Pendulum System

Inverted pendulum is a typical system and an important research object in control areas as amultivariable, nonlinear and unstable system, and is also an ideal model to verify many kinds of controlalgorithm. A lot of abstract control theories can be demonstrated intuitively through the control process ofinverted pendulum such as stability, controllability, robustness and anti-jamming of system, etc. Researchof control methods for inverted pendulum is significant, especially for development of the two-wheeledself-balancing vehicle and other similar experiment equipment.Fisrtly, based on analysis of the linear single and double inverted pendulum physical models,Lagrange mathematical modeling method is adopted to establish the inverted pendulums, and the pros andcons of this mathematical modeling methods are discussed; and then the another modeling method based onSimMehanics toolbox in MATLAB software is put forwards, and mechanism models of the linear singleand double inverted pendulum successfully are established. Compared with the Newtonian mechanicsprinciple and Lagrange method, the method is proved more convenient, accurate and faster..Based on SimMehanics model of linear double inverted pendulum, after introduces the differentcontrol methodes, a LQR control algorithm based on kalman filtering, which adopts kalman filter as thestate observer to observe the real-time status of system, and makes optimal estimation of the system outputs.Through experimental comparison, this compound control is better than LQR method, and can greatlyreduce the impact of the system noise and measurement noise on the stability of the inverted pendulum.In the control theory teaching process,the virtual reality technology can be used as auxiliary means torealized real-time control of inverted pendulum. The virtual reality scene of inverted pendulum system wasestablished by VRML.And it adopts the dynamics model to drive the virtual reality scene. After integrationwith the controller, it generates real-time simulation program by MATLAB/RTW toolbox,3D animation ofsystem is generated， and the original abstract， boring learning content can be display with images，animation，sounds，and other media forms in class. In addition to，it improves the teaching quality of thecontrol theory and promotes the reform of teaching.The modeling and control methodes are very similar for the linear single inverted pendulum system and two-wheeled self-balancing vehicle. we can apply the theory of linear inverted pendulum system on thetwo-wheeled self-balancing vehicle. A scheme of hardware modular design and control method is putforwards to verify the feasibility and validity in actual experiments.