Revisiting Ziegler-Nichols. A fractional order approach

PID controllers are largely used in industry. Auto-tuning methods for these controllers have emerged over the years, including the well-known Ziegler-Nichols method. Several extensions and improvements to this early autotuning method have been proposed throughout the years. A new method is introduced in this manuscript suitable for fractional order PIDs. The "direction" of the loop frequency response in the critical Ziegler-Nichols point is shaped using the the fractional order. The numerical results show that better closed loop performance is achieved. Different case studies are considered to validate the proposed method and demonstrate its advantage compared to the standard method.