The wastewater treatment process (WWTP) is characterized by unknown nonlinearity and external disturbances, which complicates the tracking control of dissolved oxygen concentration (DOC) within operational constraints. To address this issue, a data-driven tube-based robust predictive control (DTRPC) strategy is proposed to achieve stable tracking control of DOC and satisfy the system constraints. First, a tube-based robust predictive control (TRPC) strategy is designed to deal with system constraints and external disturbances. Specifically, a nominal controller is designed to ensure that the nominal output accurately tracks the set-point under tightened constraints, while an auxiliary feedback controller is designed to suppress disturbances and restore the nominal performance of the disturbed WWTP. Second, two fuzzy neural network identifiers are employed to provide accurate predictive outputs for the control process, overcoming the challenges of modeling the WWTP with strong nonlinearity and unknown dynamics. Third, the generalized multiplier method is utilized to solve the constrained optimization problem to obtain the nominal control law, and the gradient descent algorithm is used to obtain the auxiliary control law. The implementation of this composite controller ensures the satisfaction of the system constraints and the effective suppression of disturbances. Finally, the feasibility and stability of the proposed DTRPC strategy are guaranteed through rigorous theoretical analysis, and its effectiveness is demonstrated through the simulations on the benchmark simulation model No.1.

中文翻译：

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针对受限废水处理过程的数据驱动的基于管的鲁棒预测控制


废水处理过程（WWTP）具有未知的非线性和外部干扰的特点，这使得在运行限制内溶解氧浓度（DOC）的跟踪控制变得复杂。为了解决这个问题，提出了一种数据驱动的基于管的鲁棒预测控制（DTRPC）策略来实现DOC的稳定跟踪控制并满足系统约束。首先，设计了基于管的鲁棒预测控制（TRPC）策略来处理系统约束和外部干扰。具体来说，标称控制器旨在确保标称输出在严格约束下准确跟踪设定点，而辅助反馈控制器旨在抑制干扰并恢复受干扰污水处理厂的标称性能。其次，采用两个模糊神经网络标识符为控制过程提供准确的预测输出，克服了对具有强非线性和未知动态的污水处理厂进行建模的挑战。第三，利用广义乘子法求解约束优化问题得到标称控制律，利用梯度下降算法得到辅助控制律。该复合控制器的实现保证了系统约束的满足和扰动的有效抑制。最后，通过严格的理论分析保证了所提出的DTRPC策略的可行性和稳定性，并通过基准仿真模型No.1的仿真验证了其有效性。