Khallouq Abdelmounaim, Karama Asma, Abyad Mohamed
Automation of Environment and Transfer Processes Laboratory/Faculty of Science Semlalia, Cadi Ayyad University, Marrakech, Morocco.
PeerJ Comput Sci. 2021 Apr 13;7:e458. doi: 10.7717/peerj-cs.458. eCollection 2021.
The design of an observer-based robust tracking controller is investigated and successfully applied to control an Activated Sludge Process (ASP) in this study. To this end, the Takagi-Sugeno (TS) fuzzy modeling is used to describe the dynamics of a nonlinear system with disturbance. Since the states of the system are not fully available, a fuzzy observer is designed. Based on the observed states and a reference state model, a reduced fuzzy controller for trajectory tracking purposes is then proposed. While the controller and the observer are developed, the design goal is to achieve the convergence and a guaranteed performance. By using Lyapunov and theories, sufficient conditions for synthesis of a fuzzy observer and a fuzzy controller for TS fuzzy systems are derived. Using some special manipulations, these conditions are reformulated in terms of linear matrix inequalities (LMIs) problem. Finally, the robust and effective tracking performance of the proposed controller is tested through simulations to control the dissolved oxygen and the substrate concentrations in an activated sludge process.
本研究对基于观测器的鲁棒跟踪控制器进行了设计，并成功应用于活性污泥法（ASP）的控制。为此，采用高木-关野（TS）模糊建模来描述存在干扰的非线性系统动态。由于系统状态并非完全可测，设计了一个模糊观测器。基于观测到的状态和参考状态模型，进而提出了一种用于轨迹跟踪的简化模糊控制器。在开发控制器和观测器时，设计目标是实现收敛并保证性能。通过使用李雅普诺夫理论，推导了TS模糊系统模糊观测器和模糊控制器综合的充分条件。通过一些特殊操作，将这些条件重新表述为线性矩阵不等式（LMI）问题。最后，通过仿真测试了所提出控制器在控制活性污泥法中溶解氧和底物浓度方面的鲁棒且有效的跟踪性能。
