Research On Modeling And Control Of Linear Inverted Pendulum Based On Matlab

The stability control of the inverted pendulum is a typical problem in control theory.So far,classical control theory,modern control theory and various intelligent control theory have been used to achieve the stability control of inverted pendulum,which greatly promotes the development of control theory.The stability control of inverted pendulum has many practical applications.All of the control problems with center of gravity up and fulcrum down are very similar to the control of inverted pendulum,such as the stability control of offshore drilling platform,the stability control of satellite launch pad,and the safe landing of aircraft.The research on the stability control of inverted pendulum is always one of the hot topics in the control field.This paper takes the primary inverted pendulum and the secondary inverted pendulum as the research object,and study the realization and improvement of control performance of multiple control methods on the inverted pendulum.In this paper,a mathematical model of the inverted pendulum in the form of differential equation and state space equation is established based on the Newtonian mechanic’s law and the Lagrange method.Then the Simulink simulation model and the Simscape simulation model of the inverted pendulum are built in Matlab software platform.Then,state feedback control,PID control,fuzzy PID control and reinforcement learning based on DDPG agent are used to control the inverted pendulum.Finally,the control performance of different control methods is compared and analyzed.The main research results and innovations of this paper are as follows:(1)In this paper,the mathematical model and control technology of the inverted pendulum are reviewed and summarized.Then,the basic knowledge of this paper is introduced.This theoretical knowledge is the theoretical basis for the establishment of inverted pendulum simulation model,the control simulation of inverted pendulum and the analysis of the results,which provides important theoretical guidance for the research content and the analysis of the results of this paper.(2)The mathematical model of the inverted pendulum is the basis of controller design.In this paper,the structure composition and parameters of the primary inverted pendulum and second inverted pendulum are introduced,and then the differential equation and state space equation of the inverted pendulum are established by the Newton’s laws of mechanics and the Lagrange’s method.These equations take the force acting on the trolley as the input,and the angle of the pendulum and the trolley displacement as the output.The state variables are the displacement and velocity of the trolley and the angular displacement and velocity of the pendulum.Then the Simulink simulation models and the Simscape simulation models of the inverted pendulum are built in the Matlab software platform.The Simscape simulation models of the primary inverted pendulum and second inverted pendulum body are created,and the simulation model of the primary inverted pendulum system containing the driving motor is the innovation of this paper.The Simscape simulation model of the inverted pendulum is more intuitive than the Simulink model,and it can animate the movement process of the inverted pendulum.Compared with the primary inverted pendulum,the mathematical model of the second inverted pendulum is more complex,with two state variables of the second pendulum rod angle and angular velocity,which makes it more difficult to control.(3)PID control method,state feedback control method,fuzzy PID control method and reinforcement learning control method are used as control methods.All the four control methods can make the primary inverted pendulum body(without driving motor)stable.The control performance of the first three control methods is the same,in which the angle overshoot is 0.0086rad and the adjustment time is 4s.The trolley displacement overshoot and steady-state error are the smallest under the fuzzy PID control,and the trolley displacement overshoot and steady-state error are the largest under the state feedback control.The angle overshoot of the pendulum rod under the reinforcement learning method is 0.0057rad,and the adjustment time is 3s,which is better than the first three control methods,while the steady-state error of the trolley displacement and the adjustment time are worse than the first three control methods.When there is a driving motor,the control performance of the inverted pendulum system deteriorates,the angle overshoot of the pendulum rod is larger,and the displacement overshoot and steady-state error of the trolley are larger.The innovation of this paper lies in the application of reinforcement learning control method based on DDPG agent on inverted pendulum.In the control of the second inverted pendulum body(without driving motor),the PID control,state feedback control and fuzzy PID control can make the second inverted pendulum stable,among which the fuzzy PID control has the best control effect,the adjustment time is the smallest,which is 4s,the car displacement steady-state error is the smallest,which is 0.019m.The angle overshoot of the first inverted pendulum rod and the second inverted pendulum rod are 0.004rad and 0.006rad respectively.The state feedback control has the worst control effect,the trolley displacement overshoot and steady-state error are the largest,and the angle overshoot of the first inverted pendulum rod is the largest.