Arbitrary Order PID Controller Design for an Inverted Pendulum System

This paper presents a study on the design of arbitrary-order controllers for controlling an inverted pendulum system in two distinct targets: the angle of rotation of the pendulum and the position of the cart. A systematic and methodological approach, using cascade control, is used to tackle the non-linearity of the system. The behavior of the arbitrary-order integral and derivative parts of each controller is approximated through the Curve-Fitting approximation method. Numerical simulations were conducted within a Simulink/Matlab environment to demonstrate the improved performance of the transient response of the nonlinear system when it is compared to the traditional integer-order controllers.