In this paper proposed PID Controller Tuning Method with a new equation of state by adding a new Integral Element to the Output Variable with the PID Controller Design Method using LQR Method in order to make sure the Robust and Stable Control performance of the Inverted Pendulum System which is suitable for evaluating the effectiveness of Control Theory due to its Unstable with Strong Nonlinearity. Then the research could confirm the excellent stability and excellent control performance of the Inverted Pendulum System through the simulation of Inverted Pendulum.