Adaptive fuzzy sliding mode control with exponential reaching law and MPL method for the coupled-tank system

This study develops an adaptive fuzzy sliding mode control (ASMC) scheme incorporating an exponential reaching law (ERL) and a minimum parameter learning (MPL) strategy to achieve liquid-level regulation in a coupled-tank system. Such systems are widely used in industrial applications, including chemical and petrochemical processing, water treatment, power generation, and the manufacturing of construction materials, as well as in boilers, evaporators, reactors, and distillation columns. The ERL-based sliding mode controller is formulated to guarantee finite-time tracking of the desired liquid level while effectively suppressing chattering near the sliding surface. The MPL approach is embedded within the fuzzy system (FS), resulting in a single online adaptive parameter, which significantly reduces computational complexity and enhances real-time performance. The stability of the closed-loop system is rigorously established using Lyapunov theory. Simulation studies conducted in MATLAB/Simulink validate the effectiveness of the proposed controller, demonstrating a rise time of 6.1918 s, a settling time of 11.2553 s, zero overshoot, convergence of the steady-state error to zero, and a noticeable reduction in chattering.