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Evaluation of sensors for the control of a continuous ethanol fermentation

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Abstract

A method is presented for the evaluation of sensors used in the control of continuous fermentations. Simulations of open-loop response to input disturbance provided a starting point for the choice of sensor type. This was evaluated quantitatively through a sensitivity ratio. It was shown that in the case of ethanol fermentation, there existed three regions where different sensors could be used for the process control depending on the inlet sugar concentration. Sugar sensors were preferable above an inlet sugar concentration of 50 kg/m3, while ethanol sensors were preferable below 25 kg/m3. In the intermediate region, sugar and ethanol sensors demonstrated equally good performance. A controllability study of a continuous ethanol fermentation was also made. A single-stage continuous stirred-tank fermentor was simulated operating at a dilution rate of 0.1 1/h and inlet glucose concentration of 160 kg/m3. The outlet glucose concentration was controlled with a PI controller. Mean square error of the controller input signal during the first five hours after introducing input disturbance was taken as a measure of the controllability. This was studied in the relation to the two key sensor characteristics, sampling time and accuracy.

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Abbreviations

c p kg/m3 :

ethanol concentration

c ⋆ p kg/m3 :

fermentor ethanol concentration corresponding to c ⋆si and D⋆

c s kg/m3 :

substrate (glucose) concentration

c ⋆ s kg/m3 :

fermentor glucose concentration corresponding to c ⋆si and D⋆

c si kg/m3 :

inlet substrate (glucose) concentration

c ⋆ si kg/m3 :

inlet glucose concentration value used for sensitivity evaluation

c sm kg/m3 :

glucose concentration — measured value

c ss kg/m3 :

glucose concentration setpoint value

c x kg/m3 :

biomass concentration

D 1/h:

dilution rate

D ⋆ 1/h:

dilution rate value used for sensitivity evaluation

D i 1/h:

dilution rate at ith sampling interval

D 0 1/h:

dilution rate at steady state

K c m3/kgh:

controller gain

K p kg/m3 :

product inhibition constant

K s kg/m3 :

Monod constant

n 1, n 2 :

random numbers

r p kg/m3 h:

ethanol production rate

r s kg/m3 h:

substrate (glucose) consumption rate

r x kg/m3 h:

biomass growth rate

\(\vec \alpha \) :

vector of independent variables

y i :

ith dependent variable

Y ps :

ethanol yield

Y xs :

biomass yield

\(\vec x\) :

parameter vector

α j :

jth parameter

β ij :

sensitivity of yi with respect to αj

β p :

sensitivity of fermentor ethanol concentration

β s :

sensitivity of fermentor glucose concentration

γ :

sensitivity ratio

Δc ⋆ p kg/m3 :

ethanol concentration difference corresponding to a change of c ⋆si by 5%

Δc ⋆ s kg/m3 :

glucose concentration difference corresponding to a change of c ⋆si by 5%

Δc ⋆ si kg/m3 :

concentration difference added to c ⋆si

ε i kg/m3 :

error at ith sampling interval

μ 1/h:

specific growth rate

μ m 1/h:

maximum specific growth rate

σ s kg/m3 :

standard deviation of monitored glucose concentration

τ I h min kg/m3 :

integral time

τ s min:

sampling period

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Authors and Affiliations

  1. Department of Physics and Measurement Technology, Bioprocess Measurement Technology Group, Linköping Institute of Technology, S-581 83, Linköping, Sweden

    M. Polakovic & C. F. Mandenius

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  1. M. Polakovic
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  2. C. F. Mandenius
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The Swedish Ethanol Foundation and the National Board for Technical Development (NUTEK) are kindly acknowledged for the financial support of this project. The authors wish to thank Peter Warkentin for the linguistic advice.

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Polakovic, M., Mandenius, C.F. Evaluation of sensors for the control of a continuous ethanol fermentation. Bioprocess Eng. 10, 217–223 (1994). https://doi.org/10.1007/BF00369532

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