Extended state observer with FOF-PID controller design: implementation on a cart-pendulum system

The extended state observer (ESO) associated with a fractional-order-filter-PID controller (FOF-PID) is the foundation for the proposed control approach described in this study. Using the ESO and the FOF-PID controller, respectively, the issues of disturbance rejection and set-point tracking are resolved. The suggested control technique is applied to a cart-pendulum system’s real-time position control. Set-point tracking and disturbance rejection tests are conducted in the experiment to assess the performance of the controller in the structures with one and two degrees of freedom, referred to as 1DOF-ESO-FOF-PID and 2DOF-ESO-FOF-PID, respectively.