Probabilistic Bi-Level Assessment and Adaptive Control Mechanism for Two-Tank Interacting System

Liquid level control is a fundamental aspect employed across various industries, where the precise regulation of liquid levels and flow rates is of utmost importance. The Proportional-integral-derivative (PID)controller is widely employed but in practice, the operation of a PID may not always align with the desired outcome due to various factors such as system dynamic behavior, model uncertainties, time-varying parameters, and disturbances. To effectively address these challenges, the article proposes model reference adaptive control (MRAC) based on the Massachusetts Institute of technology (MIT) law feedback PID technique for a two-tank interacting system. The detailed comparative analysis is carried out in MATLAB/Simulink with open loop, PID, and MRAC in respect of time domain specifications. The proposed approach stability is verified using the Lyapunov approach. The robustness of the control mechanism is validated through probabilistic assessment by introducing a bi-level uncertainty framework such as gain mistuning and dynamic system behavior. In the first level, the gain mistuning is accomplished in three aspects i.e., fine-tuned, increased, and decrease gain. In the second level, it is considered that system behavior is dynamic in nature. Based on the findings, the MRAC-PID exhibits superior performance against uncertainties as compared to PID and MRAC with enhanced tracking rapidity, accuracy, and robustness.