Fractional Modeling And Optimal Control Of Inverted Pendulum System

The synthesis of robot technology,control theory,computer control and other fields is inverted pendulum system.Its own characteristics and advantages can be regarded as a microcosm of the controlled object research in the field of typical control engineering,and it is convenient to test the feasibility of the control theory or method.The related research results of inverted pendulum system are widely used in industrial production engineering,such as robot control technology,electric balance vehicle research,vertical control in rocket launching,attitude control in satellite flight and manipulator.Therefore,the research of inverted pendulum system has important significance and unpredictable engineering application value.Aiming at the distortion of integer-order model and actual model of nonlinear system in engineering field,this paper takes inverted pendulum system as the research object,studies its non-linearity and multi-variable characteristics,establishes its fractional-order model by fractional-order theory,identifies the parameters of the model by several improved particle swarm optimization algorithms,and uses the probability function of t-test confidence interval and the fitness function of ITAE.By comparing the merits and demerits of various parameter identification algorithms,the optimal identification parameter group is determined,and the parameter identification of fractional order inverted pendulum system is completed.The simulation results show that the response curve of fractional order system model is closer to the actual output response curve of inverted pendulum system.On the basis of fractional order parameter identification and modeling of inverted pendulum system,a fractional order digital PID controller is designed.A particle swarm optimization algorithm,which combines chaotic search with adaptive inertia weight adjustment,is used to optimize the parameters of the inverted pendulum system.The problem that the optimization of particle swarm parameters easily falls into local optimum is solved and the parameter search is improved.The convergence accuracy of the optimal algorithm is obtained and the global optimal solution of the parameters is obtained.The dynamic response curves of fractional-order controller and integer-order PID controller optimized by CAPSO algorithm are compared by simulation with MATLAB/Simulink.The system has good stability,follow-up and anti-interference ability.Finally,using the inverted pendulum system of Googol Company,a hardware-in-the-loop simulation and verification platform is built under the software environment of Matlab and DOS to verify the effectiveness and feasibility of the fractional order modeling and parameter identification of the inverted pendulum system and the parameter optimization control algorithm of fractional order PID controller based on CAPSO.