Design of Linear Flexible Two Inverted Pendulum Control System Based on LQR

Since linear flexible double inverted pendulum closed loop system is unstable, and the spring of flexible joint has effect on the frequency response of the system. The flexible two inverted pendulum mathematical modeling was built based on Lagrange method. According to the optimal control theory, a system of optimal liner quadratic regulator was designed. Using MATLAB to calculate the state feedback vector and then feed back to the equation of state, the obtained simulation curve reached the desired effect. The compiled programs in MATLAB and VC succeed in achieving the stability of liner spring double inverted pendulum stability controlling.