Modeling and Stabilization of Cart Triple Link Inverted Pendulum using LQR Controller Incorporating Degree of Stability

In this paper a mathematical model for the cart triple inverted pendulum system is first presented using Lagrange equation in details. This model is then used to design a controller based on the LQR method to maintain the triple inverted pendulum on a cart around its unstable equilibrium position using single control input. The stability, controllability and observability are investigated and the choice of weights in LQR also discussed. Main focus is to introduce how to build the mathematical model and the analysis of the system's performance. The system is simulated in MATLAB environment and the simulation results establish the satisfactory performance of LQR controller in stabilizing the system.