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

## TL;DR

This paper develops a boundary control strategy for a parabolic system modeling Direct Contact Membrane Distillation, ensuring accurate temperature tracking and disturbance estimation, with proven exponential convergence and robustness to noise.

## Contribution

It introduces a novel control and observer design for a coupled parabolic system modeling DCMD, with rigorous analysis of solution properties and stability.

## Key findings

- Exponential decay of tracking error under the proposed control.
- Robustness of control strategy in the presence of flux noise.
- Existence, uniqueness, and regularity results for the DCMD model.

## Abstract

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

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Source: https://tomesphere.com/paper/1902.00964