## 1 Introduction
The Ziegler-Nichols tuning method to design PI-PD controllers and performance has been evaluated based on the settling time, overshoot, and integral absolute error (IAE) [18]. Several studies were conducted using vector tuning, and trial-and-error approaches tuned fractional-order PI-PD controllers for a DC motor in the frequency frame and assessed performance based on steady-state errors [19]. [PERSON] et al., in [20], used the PSO algorithm to tune a fractional-order PI-PD controller for position control in a magnetic levitation system, evaluating overshooting and settling time performance. In another study [21], the Ziegler-Nichols method is used to design a PI-PD controller for voltage regulation of building-integrated photovoltaic and wind turbine systems, with the performance based on voltage. Similarly, in [22], the authors used the Ziegler-Nichols method to tune their PI-PD and I-PD controllers for speed control of DC motors and evaluated their performance based on the ISE and settling time. The study conducted in [23] used the Ziegler-Nichols method to tune a PI-PD controller for unstable control systems using sampled data and compared its performance in terms of ISE, overshoot, and settling time with that of the PID controller. Recent studies emphasize the importance of a rigorous performance assessment to evaluate the efficacy of PI-PD controllers due to their potential for better performance and stability. Researchers used specific performance measures tailored to the system's characteristics to quantify the PI-PD controller's performance and compare it with other controller types [1; 2; 12; 24]. Some performance measures used in the reviewed studies include settling time, overshoot, rise time, peak time, load disturbance, absolute error, phase and gain margins, ISE, ITSE, IAE, ITAE, and time response. These measurements evaluated different aspects of controller performance, including stability, speed of response, accuracy, ability to reject interference, and robustness. The choice of tuning method has been crucial in optimizing the PI-PD controller's performance. The results of the reviewed studies highlighting the versatility of PI-PD controllers in controlling different types of systems and processes are summarized and given in Table 1.  
\begin{table}
\begin{tabular}{l l c c c c c c} \hline
**Ref. ** & **Controller** & **Tuning Technique** & **No. of Parameters** & **System** & **Comparing Controllers** & **Performance Measure** \\ \hline
[2] & PI-PD & Auto tuning & 4 & First and second-order unstable & PID & Peak time, IAE, Settling time, & Verschow, Note time \\  & & & system with time delay & & & Settings time, Peak overshoot, Peak \\
[12] & PI-PD & Ziegler-Nichols & 4 & First-order plus dead time (stable & & Settling time, Peak overshoot, Peak \\  & & & and unstable system) & I, PI, and PID & undershoot (*ve), IAE, ISE, ITAE, & undershoot (*ve), IAE, ISE, ITAE, & undershoot (*ve), IAE, ISE \\  & & & & & & & \\  & & & & & & & \\  & &  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline
**Ref. ** & **Controller** & **Tuning Technique** & **No. of Parameters** & **System** & **Comparing Controllers** & **Performance Measure** \\ \hline \multirow{3}{*}{[15]} & \multirow{3}{*}{Cascode PI-PD} & Stochastic fractal search & \multirow{3}{*}{4} & \multirow{3}{*}{Plug-in Electric Vehicles} & \multirow{3}{*}{PI and PID} & \multirow{3}{*}{Settling time, IAE, ISE, ITAE, TISE} \\  & & and Pattern search & & & & & \\  & & algorithm & & & & & \\ \cline{4-7} \cline{8-9} \cline{  
The reviewed studies demonstrated different tuning methods to determine appropriate controller parameters, including automatic optimization [2], the Ziegler-Nichols method [5; 12; 33], and PSO algorithms [24; 31; 34]. Automated optimization techniques aim to simplify the controller design process for practitioners by automating the parameter tuning process.