Model Predictive Control Paradigms for Direct Contact Membrane Desalination Modeled by Differential Algebraic Equations

Direct Contact Membrane Distillation (DCMD) is an emerging sustainable desalination technology that can utilize solar energy to desalinate seawater. The low water production rate associated with this technology prevents it from becoming commercially feasible. To overcome this challenge, advanced control strategies may be utilized. An optimization-based control scheme termed Model Predictive Control (MPC) provides a natural framework to optimally operate DCMD processes due to its unique control advantages. Among these advantages are the flexibility provided in formulating the objective function, the capability to directly handle process constraints, and the ability to work with various classes of nonlinear systems. Motivated by the above considerations, this paper proposes two MPC schemes that can maximize the water production rate of DCMD systems. The first MPC scheme is formulated to track an optimal set-point while taking input and stability constraints into account. The second MPC scheme termed Economic Model Predictive Control (EMPC) is formulated to maximize the distilled water flux while meeting input, stability and other process operational constraints. To illustrate the effectiveness of the two proposed control paradigms, the total water production under both control designs is compared. Simulation results show that the DCMD process produces more distilled water when it is operated by EMPC than when it is operated by MPC.