# Comparative Real-Time Study of Three Enhanced Control Strategies Applied to Dynamic Process Systems
## 1 Introduction  
In industrial processes, precise control of liquid levels and flow between multiple tanks is essential across various sectors, including power generation, biochemical and petrochemical industries, and water distribution systems. Accurate regulation of liquids stored, transferred, or mixed within tanks is crucial for ensuring operational efficiency, safety, and reliability. Among the most widely used systems for such applications are coupled tanks, consisting of interconnected vertical tanks that share orifices. These setups typically employ electrical pumps and motorized valves as actuators, while pressure sensors and flowmeters provide real-time monitoring of liquid levels and flow rates. However, managing coupled tank systems comes with unique challenges, primarily due to their nonlinear characteristics. These arise from the dynamic behaviour of pumps, valves, and fluctuations in system parameters. When it comes to industrial process control, attaining accurate as well as steady regulation is critical, particularly for systems exhibiting complex and dynamic tendencies. Because of their simplicity and efficiency, the traditional control methods, which include proportional-integral-derivative (PID) controllers, have been widely adopted. PID control is well-suited for single-input, single-output systems and provides satisfactory performance in environments with minimal disturbances and well-understood dynamics. In a liquid level system, PID controllers are often used to maintainthe desired level by adjusting the input flow based on the error between the setpoint and the actual level. However, the effectiveness of PID controllers diminishes when applied to nonlinear systems or systems subject to significant external disturbances [1]. In such cases, the controller may struggle to maintain stable and precise control, leading to oscillations, overshoots, or slow response times. However, these controllers often fail to meet requirements in cases where there is significant nonlinearity, time delays, and external disturbance processes involved [2]. One of the main problems in real-time control is ensuring that the controller can respond fast enough to dynamic changes in the process [3; 4; 5; 6; 7; 8]. The speed must be supported by not only processing power but also a way of predicting and compensating for time delays and disturbances applied to the system undergoing control [9]. In some such cases, more advanced control methodologies are required to satisfy demanding performance specifications, especially under real-time conditions. To address the limitations of traditional PID control, more advanced control techniques, such as the cascade nonlinear feedforward proportional integral retarded (CNPIR) controller, have been developed [10]. The CNPIR controller builds upon the foundational principles of PID control by incorporating a cascade control architecture, where an inner loop manages fast system dynamics while the outer loop regulates slower dynamics. This structure enables more effective disturbance rejection and improved control over nonlinear processes like liquid level systems [11]. Additionally, the feedforward component in CNPIR control anticipates disturbances before they affect the system, further enhancing stability and performance [12; 13]. Cascade control structures have always been preferred in automation methods based on their capability to decouple various process objectives and handle multiloop systems. The retarded (time-delay) element incorporated into this control scheme allows the system to handle time delays common in industrial processes, such as those caused by sensor lags or actuator delays [14; 15; 16]. Despite these advantages, the CNPIR controller still has limitations when dealing with highly nonlinear or unpredictable dynamics, as well as when external disturbances are severe [17; 18; 19; 20].