Combined Adaptive Backstepping and LQR Control for Inverted Pendulum

In this paper, a control strategy using adaptive backstepping control combined with optimal control is proposed to solve the problem of stable control of a linear inverted pendulum in the presence of external disturbances. The kinematic model of a one-stage linear inverted pendulum is derived using Lagrange’s theorem, and then a disturbance is introduced to establish a suitable Lyapunov function to design an adaptive update control rate to control the pendulum angle and attenuate the effect of the disturbance. Then the optimal controller is designed to control the trolley position, and the LQR is optimized by a genetic algorithm to form the controller of the whole linear inverted pendulum. Finally, the effectiveness and anti-disturbance capability of the method are verified by Simulink simulation.