Reduction and controller design for fractional order Spherical tank system using GWO

In this paper the PID controller is designed to control the liquid level in the Spherical tank system (STS). The STS is modeled in fractional order and is approximated to an integer order by using oustaloup's approximation algorithm. The higher order integer system is reduced to a 2nd order by using Balanced Truncation (BT) method. The PID controller is designed for this reduced order model and the parameters of the PID controller are primarily tuned via trial and error (T&E) method and afterward these parameters are optimized using Grey Wolf Optimizer (GWO). The results of the GWO algorithm are compared with the T&E method of PID controller.