Research On Control Of Single Inverted Pendulum System

The rotary inverted pendulum system is an multivariable,nonlinear,strongly coupling and unstable system with single input and multiple output,whose stability control of inverted pendulum is the concrete application of control theory,it provides a good experimental platform for the verification and evaluation of control theory and methods.In the past,researchers mainly studied the vehicle inverted pendulum system with linear track,compared with the linear inverted pendulum system,the rotary inverted pendulum system has more degrees of freedom and larger control difficulty,and can overcomes the travel limits,so it provides a more satisfactory experimental platform for the verification of various control theories.Firstly,this paper introduces the research background and significance of inverted pendulum system,which including the classifications,the significance on aspects of education and teaching,scientific research,engineering application practice,and the domestic and foreign research situation of inverted pendulum system.Secondly,the paper uses the Lagrange equation to establish the dynamic model of the rotary single inverted pendulum system.Afterwards,it analyzes the performance of the the inverted pendulum system based on the definition and criterion of stability,controllability and observable property in the theory of linear system,then use the MATLAB function to calculate.It is demonstrated from the calculation results that the system is open-loop unstable,can be controlled and observed.Hence the system needs to design an external controller to keep it stable.And the paper controls the rotary single inverted pendulum system by two methods—the LQR control and the PID control,then compare them to each other and find that both of them can control the system effectively,but the stable adjustment time of connecting rod and pendulum rod is shorter and the overshoot of oscillation is smaller when the system is under PID control.As we all known,the key of PID controller design lies in how to select a set of optimal controller parameters quickly,that means,to adjust the PID control parameters.In order to solve the question of the repetition and tediousness by using a cut-and-trial method to adjust the PID controller parameters,the paper brings in the particle swarm optimization(PSO)algorithm,which is based on the standard PSO algorithm,and make improvements including inertia weight coefficient,learning factor and fitness function.The particle swarm optimization(PSO),which has characteristics of strong global searchingability,simple concept,easy parameter adjustment and fast rate of convergence,can be used to adjust the parameters of PID controller.Given the rotary inverted pendulum system is a multivariable complex system,where the ordinary PID is prone to integral saturation,the PID control based on particle swarm optimization(PSO-PID)need to be improved the structure.Hence,this paper adopt a strategy that improves the integral term and the proportional term,bring in two continuous variable functions as the proportion and integral term coefficients respectively to prevent the integral saturation.At last,the paper use the PSO-PID control and the improved variable-speed integral PSO-PID control to make simulations on the single rotary inverted pendulum in MATLAB.The results indicates that under the improved variable-speed integral PSO-PID control the overshoot of connecting rod and pendulum rod in the system is reduced to 0 and the adjusting time is shortened to 0.8s and 0.9s respectively.So the control strategy designed in this paper can effectively make the rotary single inverted pendulum system stable in a short time and provide a reference for the control of inverted pendulum system and other nonlinear system.