Adaptive Control for x Inverted Pendulum Utilizing Gain Scheduling Approach

The traditional type $x$ inverted pendulum is highly unstable, nonlinear and challenging system. The paper stabilizes the $x$ inverted pendulum through adaptive gain scheduling PID algorithm. The $x$ inverted pendulum is modeled based on Lagrange's approach. The performance of proposed controller is verified via various simulation works, which include disturbance and variation of parameters with time. The proposed controller is benchmarked with a conventional PID controller. It's found that the gain scheduling PID controller reduces the transient response 15.5% with respect to the traditional PID controller.