## 2 State of the Art  
The paper by [1] demonstrates the effectiveness of heuristic algorithms in tuning Fractional Order LQI (FOLQI) controllers for a highly interacting Multiple Input Multiple Output (MIMO) quadruple tank system. The study highlights the superior performance and robustness of the FOLQI controllers over traditional Integer Order LQI (IOLQI) controllers. This paper introduces a novel DualMode Adaptive Fractional Order PI controller with an Adaptive Feedforward controller for the Quadruple Tank Process, showcasing enhanced performance in reference signal tracking across all output ranges through numerical simulation and experimentation. The paper [2] presents a self-tuning Dual Mode Adaptive Fractional Order PI and Adaptive Feedforward controller for the Quadruple Tank Process, demonstrating superior performance. The paper by [3] proposes an optimum H-infinity norm-based controller for a Single Capacity (SC) tank system, demonstrating significant performance improvements over P, PI, and PID controllers, as well as a Grey Wolf Optimizer (GWO)-tuned PID controller, in terms of settling time, overshoot, and steady-state error. The paper by [4] uses a simplified genetic algorithm to tune PID controllers for a multipurpose water tank plant in Peru, showing superior performance over traditional methods in optimizing control parameters for flow, pressure, level, and temperature loops. Table 1 summarizes recent advancements in intelligent self-tuning PID controller methodologies applied to various nonlinear tank systems. The table highlights key research works, including self-tuning fuzzy PID controllers, meta-heuristic algorithms for PID tuning, and hybrid approaches for optimizing control performance. Each study demonstrates the application of different optimization techniques, such as genetic algorithms, particle swarm optimization, and cuckoo search optimization, to improve the efficiency and robustness of PID controllers. The table also indicates whether the studies involved a mathematical tank model and the PID methodology, showcasing a comprehensive overview of the latest trends in advanced control strategies for nonlinear systems. \begin{table}
\begin{tabular}{l l c c} \hline \hline
**Main Author and Reference** & **Methodology** & **Mathematical** & **PID** \\  & **Tank Model** & **Methodology** \\ \hline \multirow{2}{*}{[PERSON] [5]} & Self-tuning fuzzy PID for dynamic model of & \multirow{2}{*}{X} & \multirow{2}{*}{X} \\  & Coupled Tank System (CTS) & & \\ \multirow{2}{*}{[PERSON]. [6]} & Meta-heuristic PID tuning for two-tank system & \multirow{2}{*}{X} & \multirow{2}{*}{X} \\ [PERSON] [7] & Modified ACO for PID tuning in CTS & & \\ \multirow{2}{*}{[PERSON], [PERSON] [8]} & GWO and battle royale optimization (BRO) for & & \\  & decentralized PI in Quadruple-Tank Process (QTP) & & \\ \multirow{2}{*}{[PERSON]. [9]} & Hybrid Artificial Bee Colony (ABC) for nonlinear & \multirow{2}{*}{X} & \multirow{2}{*}{X} \\  & PID in CSTR & & \\ \multirow{2}{*}{[PERSON] [10]} & CSA-tuned Nonlinear Proportional Plus Integral & \multirow{2}{*}{X} & \multirow{2}{*}{X} \\  & Plus Derivative (NFPID) for surge tank control & & \\ \multirow{2}{*}{[PERSON] [11]} & Genetic Algorithm (GA)-tuned FOPID for & & \\ \multirow{2}{*}{[PERSON] [11]} & nonlinear conical tank & & \\ \multirow{2}{*}{[PERSON]. [12]} & Particle Swarm Optimization (PSO)-tuned Neural & \multirow{2}{*}{X} & \multirow{2}{*}{X} \\  & Network (NN) Robustness, Setpoint tracking, & & \\ \multirow{2}{*}{[PERSON] C. [12]} & Disturbance Rejection, Aggressiveness (RTDA) for & & \\ \multirow{2}{*}{} & nonlinear conical tank & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of intelligent self-tuning fuzzy PID controller research. Table 2 and Figure 1 present a comprehensive overview of significant research advancements in intelligent self-tuning PID controllers applied to various nonlinear tank systems.