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This paper considers the performance output tracking for a boundarycontrolled Direct Contact Membrane Distillation (DCMD) system. First, themathematical properties of a recently developed mathematical model of the DCMDsystem are discussed. This model consists of parabolic equations coupled at theboundary. Then, the existence and uniqueness of the solutions are analyzed,using the theory of operators. Some regularity results of the solution are alsoestablished. A particular case showing the diagonal property of the principaloperator is studied. Then, based on one-side feedback law the control problem,which consists of tracking both the feed and permeate outlet temperatures ofthe membrane distillation system is formulated. A servomechanism and an outputfeedback controller are proposed to solve the control problem. In addition, anextended state observer aimed at estimating both the system state anddisturbance, based on the temperature measurements of the inlet is proposed.Thus, by some regularity for the reference signal and when the disturbancevanishes, we prove the exponential decay of the output tracking error.Moreover, we show the performance of the control strategy in presence of theflux noise.

Analysis and Output Tracking Design for the Direct Contact Membrane Distillation Parabolic System