Design of first-order inverted pendulum state feedback control system

Inverted pendulum control system is a complex,unstable,nonlinear system,the study of inverted pendulum system can effectively reflect many typical control questions.For a first-order linear inverted pendulum,first use Newton's laws to set up inverted pendulum motion equations,then calculate the system's state space expression,get the mathematical model.Suppose the cart displacement,velocity,the pendulum angle and the angle velocity as the four state variables,according to the control requirements,use of state feedback pole assignment method we can get the state feedback gain matrix,then we can deploy the poles in the right positions.In addition,taking into account some of the states of the system like the pendulum angle velocity are not easy to direct measurement,this paper,based on the subsystem of the vehicle and the pendulum,design two full-order observers to reconstruction the states and give the analysis of the simulation results.