Research On The Balance Control Of Single Linear Inverted Pendulum Based On Kalman Filter

Inverted pendulum system is a typically multi-variable, strongly coupling, nonlinear and self-instability system abstracted from rocket boosters. The research on such a complex system involves many important theory problems control, such as nonlinear problems, robustness, ability, and tracking problems. So the digital simulation and physical control of inverted pendulum system are applied as the typical schemes to check up a certain theory or a certain method of control in the field of control.The inverted pendulum system with rod angle measurd by potentiometer is taken as the research object and the problem of balancing it with big noise in the angle signal is studied. This work can give some help in solving related practical engineering problems.Firstly, a mathematical model of inverted pendulum is established by using the Lagrange method. Then a modeling method using conservation laws of physics is proposed and it is applied in mathematical modeling. The simulation model is built in MATLAB/Simulink simulation environment and the validity of the mathematical models that have been established is verified.Based on the basic principle of sliding mode control theory, a proper controller is designed for the inverted pendulum and its zero dynamic is analyzed. The method of designing the linear sliding mode face using Ackermann formula is introduced. Digital simulation results show the effectiveness of this controller.The signal noise of the rod angle is measured. According to the basic principle of the Kalman filter theory, a kalman filter is designed for the inverted pendulum system. Simulation results show that the Kalman filter have a stronger filtering capability on the signal noise of the rod angle of the system.Finally, with a PC monitoring program, physical experiments are taken on the physical platform of single linear inverted pendulum designed and manufactured by Lab for motion control of Harbin Institute of Technology. The experimental results show that the designed Kalman filter has a good filtering effectiveness on signal noise of the rod angle of the inverted pendulum, while the sliding mode controller can balance the inverted pendulum smooth and steady and has good robustness.