Studies On Inverted Pendulum System By The Fuzzy Control

Inverted pendulum system is a typical multivariable,nonlinear,strong-coupling with fast motion and natural instability system.So the research of inverted pendulum has many important realistic meaning in the areas such as,the walking of biped robot,the posture adjustment in launching process of rocket,and the flying control of helicopter.Many correlative productions have applications in many fields of technology of spaceflight and subject of robot.Fuzzy control theory is introduced to study simulation and the simulation and the controlling problem in inverted pendulum in this paper.Success of simulation proves that the designed fuzzy controller has very good stability.Main research work is declared below:1) The Newton's mechanics and Lagrange Equation is used to drive the mathematical model of inverted pendulum and the transfer function as well as the state-space equation of inverted pendulum is deduced.2) Take a research on mathematical fundament and methods of fuzzy control theory:Fuzzy subset,fuzzy relations,as well as fuzzy reasoning,other related knowledge is introduced.Based on that further study on the structure and component of controller of single inverted pendulum are made and the precise amount of fuzzy,the design method of fuzzy control algorithm and fuzzy output ruling are introduced.3) The simulation of fuzzy control of inverted pendulum system.It is introduced how to realize the simulation of the inverted pendulum system by the SIMULINK toolbox.Especially the MASK packaging function enables the simulation model flexibility,which facilitates the simulation work.4) Design and simulation for controller of single inverted pendulum:considering simultaneous control four state variables x,x,θ,θdefinitely makes fuzzy control rules complicated and huge(the so-called rules explosion).Two fuzzy control design,that is location fuzzy controller and angle fuzzy controller,in tandem control.Take the output of the location fuzzy controller as a virtual angle plus a parameter which adds to the real angle of the swing pole to form a generalized angle. Take the generalized angle and the angular velocity as the input into the angle fuzzy controller to control the angle of the swing pole.Simulation experiment of the fuzzy control of inverted pendulum is very well implemented by using MATLAB SIMULINK.The result shows that it not only has quite good stability,but also is able to make the cart of the pendulum moving to the place where it is appointed by us in advance,along the orbit.5) The idea of layered fuzzy control solves the problem of rules explosion on double inverted pendulum.Simulation results show the better control effect.