A nonlinear adaptive resilient observer for fouling detection and localization in direct contact membrane distillation systems

Because freshwater source exhaustion is a growing issue, the use of seawater desalination technologies is constantly increasing. More attention is drawn to Direct Contact Membrane Distillation (DCMD), thanks to its high rejection factor and low energy consumption, which makes it a promising sustainable solution for water desalination. Nevertheless, the DCMD system is prone to membrane fouling which alters its produced water’s properties, deteriorates the membrane performance, and induces huge operation and maintenance costs if not detected in early stages. Considering the above, the present paper proposes a new approach based on an adaptive resilient observer, not only to detect fouling in DCMD systems but also to localize it with high accuracy to further reduce the maintenance costs. The paper starts by recalling the DCMD model in presence of fouling that was developed using the thermal-electrical analogy and the lumped capacitance method. Then, under Lipschitz conditions of the nonlinear terms, the design of the nonlinear adaptive resilient observer is presented to estimate simultaneously the system’s states and the fouling thermal resistance. The proposed observer’s convergence proof is given using the Lyapunov method, from which a set of linear matrix inequalities (LMI) is derived in order to obtain the observer’s gain. To demonstrate the effectiveness of the proposed method compared to the classical adaptive observer-based method, the states and parameter estimation are compared through numerical simulations under both observer designs. Simulation results reveal that the nonlinear adaptive resilient observer outperforms the adaptive observer.