# Comparative Real-Time Study of Three Enhanced Control Strategies Applied to Dynamic Process Systems
## 1 Introduction
While the controller improves upon PID control in terms of stability and disturbance rejection, it can still struggle with maintaining optimal performance under varying operational conditions [21]. To address these challenges, advanced control methods are needed to provide more robust performance and finer control accuracy under varying operational conditions [22]. For example, a fractional order (FO) control introduces the concept of fractional calculus into the control strategy, which allows for the tuning of non-integer order derivatives and integrals [23]. This flexibility gives FO controllers the ability to handle more complex dynamics and long-term system behaviours, making them particularly well-suited for systems with memory or history effects. In the context of liquid level control, FO controllers provide smoother transitions and more precise control over nonlinearities compared to traditional integer-order controllers like PID [24]. The ability of FO controllers to model and control dynamic processes with more accuracy allows them to outperform conventional control methods in systems with significant time delays and nonlinearities [25; 26]. In addition to the above controller, the adaptive control technique has emerged as a powerful technique for managing systems with unknown or time-varying parameters. Adaptive PID controllers adjust their control parameters in real-time based on the observed behaviour of the system, which allows them to maintain effective control even when the system undergoes significant changes [27; 28; 29]. For liquid level systems, where flow rates, valve characteristics, and other system parameters can change over time, adaptive PID control ensures that the controller can dynamically respond to these variations [30]. By continuously updating its parameters, adaptive PID control offers improved robustness and flexibility over standard PID and CNPIR controllers, particularly in environments where system dynamics are uncertain or subject to frequent changes [31]. Another important controller technique in the literature is the SMC control method. sliding mode control (SMC) is widely recognized for its robustness in handling systems with uncertainties and external disturbances [32]. The SMC approach works by driving the system's state trajectory onto a predefined sliding surface and keeping it there, ensuring that the system behaves in a desired manner regardless of disturbances [33]. However, a significant drawback of classical SMC is the phenomenon known as \"chattering\", which refers to the high-frequency oscillations that occur near the sliding surface due to the discontinuous control action [34]. These oscillations can lead to undesirable effects, such as increased wear and tear on actuators or degraded control performance. To address this issue, modifications to SMC, such as higher-order sliding modes or incorporating fractional-order elements, have been introduced [35; 36]. Within the scope of this study, APIDSMC combines the benefits of both adaptive PID control and sliding mode control [37]. This hybrid approach allows for real-time adaptation of the control parameters, ensuring that the system can handle time-varying dynamics and disturbances, while the sliding mode component guarantees robustness against uncertainties [38]. The adaptive nature of the controller allows it to continuously adjust to changing conditions, providing more consistent performance in complex systems like liquid level control. Furthermore, by integrating adaptive control with sliding mode techniques, APIDSMC offers the potential for reduced chattering compared to traditional SMC methods [39; 40]. The proposed FO-APIDSMC controller combines the strengths of fractional order calculus, adaptive PID, and sliding mode control into a unified framework. This novel control approach is specifically designed to address the challenges of nonlinear, time-delayed, and dynamically uncertain systems such as liquid level control in industrial processes.