Stability Analysis and State Feedback Stabilization of Inverted Pendulum?

An inverted pendulum fitted on the moving cart (IPMC) represents a class of nonlinear system and is inherently unstable. Stabilizing such nonlinear systems is still a challenging objective for control engineers. It is very difficult to keep the pendulum always in upright position as it is highly sensitive to even a small disturbance and tend to fall down. Hence, the objective of the control mechanism is to maintain the pendulum up right position always by moving the cart back and forth, as long as the angle of deviation from upright position is within the admissible range. Several strategies such as Model Reference Control, Adaptive control, Sliding mode control, state feedback control etc., have already been proposed with reasonable accuracy for the control of IPMC problem. In the first part the mathematical model has been derived using fundamental principles, the controller has been designed using state feedback control technique and the entire system has been simulated using MATLAB-Simulink. The simulated results show that the performance of IPMC is satisfactory with state feedback control.