Recursive Bilinear Subspace Modeling and Model-free Adaptive Control of Wastewater Treatment
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摘要: 污水处理过程中, 生化反应硝态氮浓度和溶解氧浓度是决定出水水质好坏的两个最关键变量, 难以采用常规基于模型的方法进行有效控制. 本文基于数据驱动建模与控制技术, 提出一种污水处理过程递推双线性子空间辨识(Recursive bilinear subspace identification, RBLSI)建模和无模型自适应控制方法. 首先, 针对污水处理过程的非线性时变动态特性, 采用最小二乘递推双线性子空间辨识方法建立污水处理生化反应过程具有参数自适应能力的递推双线性模型; 其次, 基于建立的数据驱动模型, 采用基于多参数灵敏度分析(Multi-parameter sensitivity analysis, MPSA)和遗传粒子群优化(Genetic algorithm-particle swarm optimization, GA-PSO)算法的无模型自适应控制(Model-free adaptive control, MFAC)方法对硝态氮和溶解氧浓度进行直接数据驱动控制; 最后, 数据实验及其比较分析表明了所提方法的有效性和优越性.
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关键词:
- 污水处理 /
- 递推双线性子空间辨识 /
- 无模型自适应控制 /
- 多参数灵敏度分析
Abstract: Conventional model-based approaches are unable to control the nitrate nitrogen concentration and dissolved oxygen concentration of biochemistry reaction effectively, which are the two most critical variables that determine the quality of effluent in wastewater treatment process. In this paper, a recursive bilinear subspace identification (RBLSI) modeling and model-free adaptive control method for wastewater treatment based on data-driven modeling and control technology was proposed. Firstly, according to the nonlinear time-varying dynamic characteristics of wastewater treatment process, a recursive bilinear model with parameter adaptability for biochemical reaction process of wastewater treatment was established by using the least square recursive bilinear subspace identification method. Secondly, the model-free adaptive control (MFAC) method based on the multi-parameter sensitivity analysis (MPSA) and genetic algorithm−particle swarm optimization (GA-PSO) algorithm was used to directly control the nitrate concentration and dissolved oxygen concentration in a data-driven mode based on the established data-driven model. Finally, data experiments and comparative analysis show the effectiveness and superiority of the proposed method. -
图 2 不同算法
$S_{\rm{NO},2}$ 和$D_{\rm{O},5}$ 的模型预测效果Fig. 2 Model prediction effects of
$S_{\rm{NO},2 }$ and$D_{\rm{O},5}$ with different algorithms
图 3 不同算法
$S_{\rm{NO},2}$ 和$D_{\rm{O},5}$ 的预测误差PDF曲线Fig. 3 Error PDF shapes of
$S_{\rm{NO},2 }$ and$D_{\rm{O},5}$ prediction with different algorithms
图 5 控制器参数累计频率分布曲线
Fig. 5 Cumulative frequency distribution curve of controller parameters
图 6 CFDL-MFAC控制器灵敏参数优化收敛过程
Fig. 6 The optimization convergence process of sensitive parameter based on CFDL-MFAC controller
表 1 不同算法的RMSE比较
Table 1 Comparison of RMSE based on different algorithms
算法 RMSE $(S_{\rm{NO},2 })$ RMSE $(D_{\rm{O},5})$ RBLSI 0.0165 0.0046 RLSI 0.0211 0.0085 
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表 2 CFDL-MFAC控制器参数灵敏度分析结果
Table 2 Sensitivity analysis results of CFDL-MFAC controller parameters
序号 参数 含义 DS 不灵敏参数固定值 1 $\lambda$ 输入权重因子 0.9981 0.5 2 $\mu $ PJM权重因子 0.9985 0.6 3 $\eta $ PJM步长因子 0.9996 0.5 4 $\rho $ 输入步长因子 0.9378 1.0 5 $\alpha $ PJM重置限定参数 0.998 1.5 6 $b_1 $ PJM重置限定参数 0.9991 0.55 7 $b_2 $ PJM重置限定参数 0.9995 0.8 8 $\phi _{11}(0)$ PJM初值 0.5551 − 9 $\phi _{12}(0)$ PJM初值 −0.6339 − 10 $\phi _{21}(0)$ PJM初值 0.7289 − 11 $\phi _{22}(0)$ PJM初值 0.5779 −
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表 3 GA-PSO算法参数
Table 3 GA-PSO algorithm parameters
前期 GA 参数 后期 PSO 参数 种群规模 $M=40$ 种群规模 $M=40$ 指定遗传代数 60 最大迭代次数 240 基因重组概率 0.7 加速系数 ${c_1} = 4,\;{c_2} = 2$ 变异概率 0.25 最大惯性
权重系数$W_{\max } =0.9$ 子代选择系数 T = 1,
${\alpha _T} = 0.5$最小惯性
权重系数$W_{\min } =0.1$
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表 4 不同算法控制性能对比
Table 4 Comparison of control performance based on different algorithms
算法 RBL-MPC CFDL-MFAC 控制量平均求解时间 (s) 0.0987 0.00003528 方波扰动 RMSE $S_{\rm{NO},2} $ 0.0865 0.0297 $D_{\mathrm{O},5} $ 0.0158 0.0107 正弦扰动 RMSE $S_{\mathrm{NO},2} $ 0.0859 0.0249 $D_{\mathrm{O},5} $ 0.0099 0.0089
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