Research On Mathematical Model And Control Strategy For Rotary Inverted Pendulum

Inverted pendulum system is a typical nonlinear,higher order, uncertain and fast-moving nature unstable system,control goal is to achieve a stable equilibrium,and the inverted pendulum system in an uncertain disturbances can quickly restore stable equilibrium state.Inverted pendulum as a test platform to validate the correctness and feasibility of a practical application of control theory,also to compare the merits of the algorithms through experimental results,which has great significance for the study of control theory.Therefore,this paper study on rotary inverted pendulum control system design and simulation under the experimental environmental,also have control experiments for rotary inverted pendulum.The main works in this paper are the following:Firstly,the paper analysis the characteristics of the rotary inverted pendulum system,and set up the mathematical model by using Lagrange equation.The stability,control ability of rotary inverted pendulum system are analyzed around equilibrium point,As a result,the rotary inverted pendulum system is verified as a natural unstable but controllable system.Secondly, mainly focus first order, double order rotary inverted pendulum system studied LQR control method. Carried out in MATLAB simulation environment, complete the stability control of the rotary inverted pendulum simulation and obtain good control effect. In addition, the use of genetic algorithms in LQR parameter optimizing, get the optimal control parameters. On this basis, build a first order, double order rotary inverted pendulum control module in real time, to verify at the material object, and proof of correctness and realizability of the algorithm.Finally,the paper uses the super-twisting sliding control method for first order rotary inverted pendulum simulation experiment,select the sliding function and the design parameters,while improve the controller, to achieve the first order rotary inverted pendulum simulation model of a stable control.In addition, the use of genetic algorithm for optimization parameters and the improve of sliding mode function for getting the optimal simulation parameters,it can effectively reduce the chattering of sliding mode control and other issues arising.Based on the theory, to build real-time control module based on sliding mode control algorithm, implemented the rotary inverted pendulum real-time control.