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摘要: 城市污水处理过程非均匀采样使数据呈现不连续性及稀疏性, 难以实现稳定控制. 为了解决该问题, 文中提出了一种非均匀采样预测控制方法. 首先, 建立了一种城市污水处理过程增广式动态线性化模型, 实现了非均匀采样城市污水处理关键过程变量的准确预测. 其次, 设计了基于控制增益优化策略的预测控制器, 实现了非均匀采样城市污水处理关键过程变量的稳定控制. 最后, 分析了非均匀采样预测控制方法的稳定性. 将所提控制方法应用于城市污水处理过程基准仿真平台, 实验结果显示该方法能够实现城市污水处理过程的稳定控制.Abstract: The non-uniform sampling phenomenon in municipal wastewater treatment processes (WWTPs) leads to discontinuous and sparse data, posing challenges for stable control of WWTPs. To address this problem, a non-uniform sampling predictive control (NUSPC) method is proposed. First, an augmented compact form dynamic linearization model (ACFLM) for WWTP is established. Then, the key process variables of non-uniform sampling WWTP can be accurately predicted. Second, a predictive controller based on the control optimization strategy is designed to obtain the optimal control law. Then, the key process variables of non-uniform sampling WWTP can be stably controlled. Ultimately, the theoretical stability of the proposed NUSPC is rigorously analyzed. The proposed NUSPC method is applied to a benchmark simulation model for WWTPs. Experimental results demonstrate that this method can achieve stable control of WWTPs.
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Key words:
- Data-driven /
- non-uniform sampled-data /
- predictive control /
- dynamic linearization
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图 1 城市污水处理过程非均匀采样预测控制器结构
(图中$ \hat{\phi}(t) $为$ \phi(t) $的估计值, $ \eta\in(0,\; 1] $为一阶因子, $ \mu $是惩罚因子, $ \boldsymbol{\Psi}_{N_u}(t) $为控制增益矩阵, $ {\bf{e}}(t) $为系统控制误差向量, $ \tilde{\boldsymbol{\Psi}}_{N_u}(t) $为增广式控制增益矩阵, $ {\bf{r}} $为系统的跟踪设定向量, $ \lambda_t>0 $为惩罚因子)
Fig. 1 Schematic diagram of non-uniform sampling predictive controller for WWTP
(In the figure, $ \hat{\phi}(t) $ is the estimated value of $ \phi(t) $, $ \eta\in(0,\; 1] $ is the first-order factor, $ \mu $ is the penalty factor, $ \boldsymbol{\Psi}_{N_u}(t) $ is the control gain matrix, $ {\bf{e}}(t) $ is the system control error vector, $ \tilde{\boldsymbol{\Psi}}_{N_u}(t) $ is an augmented control gain matrix, $ {\bf{r}} $ is the tracking set vector of the system, $ \lambda_t>0 $ is the penalty factor)
图 8 氧传递系数和内回流量变化曲线(雨天天气)
Fig. 8 Results of ${{K_L}{a_5}} $ and $ {Q_a}$ (Rain weather)
图 11 氧传递系数和内回流量变化曲线(暴雨天气)
Fig. 11 Results of $ {{K_L}{a_5}}$ and ${Q_a} $ (Rainstorm weather)
表 1 控制器性能指标
Table 1 Control performance of controllers
天气 性能指标 溶解氧 硝态氮 NUSPC MPC NUSPC MPC 晴天 IAE 1.20$\times10^{-2}$ 0.17 2.30$\times10^{-2}$ 0.16 ISE 3.38$\times10^{-4}$ 8.47$\times10^{-2}$ 1.01$\times10^{-3}$ 0.11 ${\rm{Dev^{max}}}$ 7.30$\times10^{-2}$ 1.30 9.01$\times10^{-2}$ 2.92 雨天 IAE 1.20$\times10^{-2}$ 0.19 2.42$\times10^{-2}$ 0.16 ISE 3.47$\times10^{-4}$ 0.11 1.08$\times10^{-3}$ 7.64$\times10^{-2}$ ${\rm{Dev^{max}}}$ 7.20$\times10^{-2}$ 2.00 9.03$\times10^{-2}$ 1.46 暴雨天 IAE 1.25$\times10^{-2}$ 0.20 2.60$\times10^{-2}$ 0.20 ISE 3.26$\times10^{-4}$ 0.17 1.22$\times10^{-3}$ 0.23 ${\rm{Dev^{max}}}$ 7.27$\times10^{-2}$ 2.67 8.59$\times10^{-2}$ 3.47 
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