A fast relay feedback auto-tuning tilt-integral-derivative (TID) controller method with the fractional-order Ziegler-Nichols approach

The relay feedback auto-tuning method, which was an early commercialized approach, has maintained its popularity due to its simplicity and robustness. However, the classical proportional integral derivative (PID) controller auto-tuning method often results in unacceptable overshoot, especially for integrating and higher-order processes. By integrating the TID controller with the relay feedback technique, we significantly enhance dynamic control performance without relying on prior knowledge of the system. However, the direct application of the classical auto-tuning method to the TID controller encounters challenges due to the additional 1 fractional-order transfer function s - n . Therefore, we have developed a fractional-order Ziegler-Nichols (FOZ-N) approach, specifically designed to adjust the parameters of the TID controller. The proposed FOZ-N method is fast, simple, and capable of achieving the desired performance. In contrast to the previous Ziegler-Nichols tuning method, the TID controller parameters K t and K i are determined to shift the critical point (-1/ K u , j 0) to the FOZ-N point (-0 . 5 , - j 0 . 7) on the Nyquist curve, ensuring system robustness and dynamic performance. 1 The impact of the fractional order parameter s - n and ratio r is explored through time-domain analysis, where these parameters are determined to ensure optimal dynamic performance. Additionally, we provide a detailed tuning procedure along with a helpful example. To demonstrate the advantages of the proposed auto-tuning TID controller over the Ziegler-Nichols PID controller, Optimal PID controller, simple internal model control (SIMC) PID controller, and Ziegler-Nichols FOPID controller, we present a simulation illustration involving multiple different systems. To validate the practical outcomes of this paper, we present experimental results on the temperature control of a Peltier cell.