Identification of system parameters

The time used for parameter identification was the first two days of the fed-batch fermentation. The initial conditions were given by Equation A.4 in Appendix A. The model equations of the single-feed rate hybridoma cell culture

Batch Fermentation

Fig. 3.1. Schematic diagram of the methodology proposed.

Fig. 3.1. Schematic diagram of the methodology proposed.

were also given in Appendix A. Ten samples measured in equal time length were used as actual state variables. A sampling time of 0.2 day was used. The deliberate inlet single-feed flow rate employed for the two-day identification period was as follows:

F = 0.005 - (-1)" x 0.0025 , n = 0,1, •••, 10 (3.7)

where, n is the number of samples.

The upper and lower bounds on the variables to be estimated was set to be ±50 percent of the actual values. The initial population size was 50 for the GA at each sampling point. The GA was run for 50 generations for each measured input-output data pair, and the best population found by the GA at each sample was stored. In order to find a system model which is as close as possible to the actual model instead of suboptimal results, the whole best populations were stored, and were used as an initial population of the GA which was to be run for another 200 generations. The GA took a total of 700 generations to estimate the parameters. The on-line identification procedure is illustrated in Figure 3.2.

Fig. 3.2. On-line parameter identification procedure using genetic algorithms.

The estimation of parameters is shown in Figure 3.3 and Figure 3.4. The percentage of error is shown in Table 3.1. The time spent for running 50 generations of the GA at each sample was about 30 minutes on a Pentium II Celeron 300MHz computer using MATLAB GAOT software. The time required for the last 200 generations was about 2 hours which is negligible when compared to the long fermentation period (10 days).

From Figure 3.3 and Figure 3.4, one can see that most parameters converge to stable values after 500 generations. Table 3.1 shows that some of the final estimated parameters have very large percentage errors. In the following sections, via simulation, it is shown that these large percentage errors have little effect on the final level of MAb.

Table 3.1. Parameter values obtained by on-line identification.

Parameters

Actual values

Estimated values

Percentage of error (%)

Mmax

1.09

1.0848

0.47

Yxv/glc

1.09

1.1525

5.7

mglc

0.17

0.2122

24.8

Kglc

1.0

0.6394

36.1

ao

2.57

2.5599

0.4

P

0.35

0.3532

0.9

kdamm

0.06

0.0304

49.3

Ylac/glc

1.8

1.7998

0.01

kdmax

0.69

0.5418

21.5

Yxv/gln

3.8

3.8062

0.16

k kmglc

19.0

11.5548

39.2

Kgln

0.3

0.3411

13.7

0.02

0.0176

11.8

kdlac

0.01

0.0106

6.1

kdgln

0.02

0.0210

5.0

Yamm/gln

0.85

0.8539

0.5

m nr

2UU 5UU

Generations

2UU 5UU

Generations

2UU 5UU

Generations

2UU 5UU

Generations

2UU 5UU

Generations

2UU 5UU

Generations

Fig. 3.3. Identification of system parameters.

ri

jl

r

U

I

200 500

Generations

200 500

Generations

200 500

Generations

200 500

Generations

lvdgln

Yamm/gln

Fig. 3.4. Identification of system parameters (continued).

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