Page 142 - 《水产学报》2025年第8期

张铮，等 水产学报, 2025, 49(8): 089512

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溶解氧/(mg/L) DO 10 8 TOPTD: 84.56% 溶解氧/(mg/L) DO 10 8

SOPTD: −24.84%
FOPTD: 83.05%
6 FOPTDLD: 83.62% 6 SOPTDLD: 7.22%
测量数据 measure data 测量数据 measure data
4 4
0 2 000 4 000 6 000 8 000 10 00012 000 0 2 000 4 000 6 000 8 000 10 00012 000
时间/s 时间/s
time time
(a) 1.0 (b)
autocorrelation coefficient 0 −0.5

自相关系数 0.5 互相关系数 cross-correlation coefficient 0.5 0

−0.5
−20 −15 −10 −5
0
0
样本 5 10 15 20 −1.0 −20 −15 −10 −5 样本 5 10 15 20
samples samples
(c) (d)
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6
5

输出 output 4 3
2
1
0
−1
0 2 4 6 8
4
时间/(×10 s)
time
(e)
图 7 5 种传递函数与曝气实验获得的数据的拟合结果
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2
(a) 3 种模型和数据的拟合 R ，(b) 2 种模型和数据的拟合 R ，(c) 输出残差的自相关，(d) 输入与输出的互相关，(e) 模型的阶跃响应。
Fig. 7 Fitting results of the five transfer functions with the data obtained in aeration experiment
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2
(a) fitting R of 3 models and data, (b) fitting R of 2 models and data, (c) autocorrelation of residuals for output, (d) cross-correlation for input and out-
put, (e) step response of the model.

表 1 5 个候选模型的具体参数值
Tab. 1 Specific parameter values of the five candidate models
模型结构 参数值
model structure parameter value
FOPTD b 0 = 0.001,a 0 = 1,a 1 = 1.12e−04,T = 0
SOPTD b 0 = −2.134e−07,a 0 = 1,a 1 = 0.002,a 2 = 1.314e−14,T = 0
TOPTD b 0 = 3.316e−09,a 0 = 1,a 1 = 0.003,a 2 = 5.179e−06,a 3 = 4.978e−10,T = 180
FOPTDLD b 0 = −0.151,b 1 = 0.001,a 0 = 1,a 0 = 1,a 1 = 1.022e−04,T = 0
SOPTDLD b 0 = −2.134e−06,b 1 = −7.052e−09,a 0 = 1,a 1 = 0.004,a 2 = 1.021e−06,T = 0

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