Sensorless Robust Observer-Based Immersion and Invariance Control With Input-to-State Practical Robustness for Disturbed Nonlinear Two-Tank Interacting Systems

This paper presents a novel sensorless robust control strategy for precise liquid level regulation in nonlinear two-tank interacting systems (NTTIS) subjected to multiple disturbances. We propose an observer-based Immersion and Invariance (I&I) control framework that simultaneously addresses three critical challenges in industrial fluid control: (1) elimination of the need for direct measurement of the first tank's liquid level, (2) robust performance against inflow, outflow, and sensor disturbances, and (3) preservation of nonlinear system dynamics without linearization. The developed I&I controller achieves practical stability and input-to-state stability (ISS)-type robustness on the operating domain, by immersing the NTTIS dynamics into a lower-dimensional target system with desirable stability properties, while a companion I&I observer provides accurate state estimation using only second-tank measurements. Comprehensive numerical simulations demonstrate the system's exceptional performance under various operational scenarios. Compared to industry-widely used PID control, the proposed method shows: (i) satisfactory setpoint tracking (ii) faster settling times, than the industrial PID, during large reference changes, and (iii) remarkable disturbance rejection capabilities - maintaining stability under combined heavy sensor degradation and outflow perturbations while still recovering faster than PID. The controller's model-aware nonlinear design inherently compensates for uncertainties without requiring additional disturbance observers or complex gain scheduling. These results establish the I&I framework as a superior solution for industrial fluid control applications where measurement limitations, nonlinear dynamics, and operational disturbances pose significant challenges. The proposed architecture offers practical advantages including reduced sensor requirements, improved reliability, and maintained performance across wide operating ranges - critical features for safety-critical systems in chemical processing, water treatment, and petroleum refining applications.