Tube MPC for a two-tank system based on Eigensystem Realization Algorithm

Abstract

This paper presents the design of a linear, data-driven, tube-based robust model predictive control (MPC) for level control in a coupled nonlinear two-tank system. Two state-space models are identified from step responses using the eigensystem realization algorithm (ERA): one from a high-fidelity nonlinear process simulator and the other using data from the physical plant. The obtained models have states that lack physical meaning, necessitating a state observer to estimate the states from the level sensor measurements. The paper shows that a proportional-integral Kalman filter provides more robust state estimates than a standard Kalman filter and is thus used for controller implementation. The proposed ERA-based tube MPC demonstrated robust performance and constraint satisfaction compared to a conventional MPC in both simulation and experimental settings. However, it violated constraints under certain disturbances within the predefined bounds because of modeling mismatches caused by applying a linear control strategy to a nonlinear system. Addressing these violations by incorporating parametric uncertainty in the disturbance bounds and using more aggressive tuning mitigates the issue but increases conservatism and control effort. These findings offer insights into the tuning of Tube MPC for desired trade-offs in industrial applications.