CET Volume 86


 
 

 

                                                                    DOI: 10.3303/CET2186165 
 

 
 

 
 

 
 
 
 
 
 
 
 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 

 
 
 
 

Paper Received: 4 September 2020; Revised: 12 March 2021; Accepted: 28 April 2021 
Please cite this article as: Butkus M., Simutis R., Galvanauskas V., 2021, Unified Structure of Adaptive System for Control of Basic Process 
Variables in Biotechnological Cultivation Processes: Ph Control System Case Study, Chemical Engineering Transactions, 86, 985-990  
DOI:10.3303/CET2186165 

 CHEMICAL ENGINEERING TRANSACTIONS 
VOL. 86, 2021 

A publication of 

The Italian Association 
of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors: Sauro Pierucci, Jiří Jaromír Klemeš
Copyright © 2021, AIDIC Servizi S.r.l. 
ISBN 978-88-95608-84-6; ISSN 2283-9216

Unified Structure of Adaptive System for Control of Basic 
Process Variables in Biotechnological Cultivation Processes: 

pH Control System Case Study 

Mantas Butkus, Rimvydas Simutis, Vytautas Galvanauskas* 

Department of Automation, Kaunas University of Technology, Kaunas LT-51367, Lithuania 
vytautas.galvanauskas@ktu.lt 

A unified scheme for control of the important bioprocess variables is proposed in this case study. The scheme 
includes feedback PI controller, controller adaptation algorithm based on statistical characteristic of the 
controlled variable, and feedforward compensator. In this case study, an adaptive pH control system is 
investigated. The adaptation algorithm analyses statistical characteristic of the controlled variable in on-line 
mode and performs adaptation of the controller’s parameter when dynamics of the control channel has 
changed. The feedforward compensator employs oxygen uptake rate estimates to compensate system’s load 
disturbances related to the time-varying biomass growth rate and biomass concentration in the bioreactor. 
Simulation runs of the pH control system have demonstrated that the proposed unified control scheme can 
increase performance of the control system. 

1. Introduction

The modern food, chemical and pharmaceutical industry walk hand in hand with biotechnology. Production of 
various recombinant proteins makes a big part among pharmaceutical ingredients. These processes can be 
described as nonlinear and nonstationary, making modeling and control a complicated control engineering 
task (Galvanauskas et al., 2019). In the biotechnology industry this is even more challenging due to strict 
safety regulations and operational constraints (Boudreau et al., 2007, Dochain, 2008, Schuler et al., 2012). 
Therefore, often application of complex and time-consuming mathematical models for off-line optimization, 
indirect state estimation and optimal online control is required. On the other hand, control systems should use 
mathematical models as simple as possible to avoid high computer resource usage and numerical problems.  
High quality control of pH is difficult because of many reasons: very strong nonlinearity of biochemical 
processes, titration curves and pH measurement itself, high sensitivity of the microorganisms even to small 
temporary deviations of pH level in the cultivation media, and drift of the pH sensors (Carr-Brion, 1991, 
McMillan et al., 2005). The academic community has proposed various PID controller parameter tuning 
approaches for high-quality pH control. Nevertheless, most of them suffer from the drawbacks already 
described (Henson et al.,1994, Ylöstalo et al., 2001, Nsengiyumva et al., 2018), such as complex controller 
design, huge time investments for development, expensive hardware, or many tuning parameters. On the 
other hand, well-functioning pH control systems can be used to monitor biological reaction rates (Siano, 1995). 
Therefore, it is of primary importance to elaborate simple, robust, and easy to implement methods for precise 
pH control. In this paper, the performance of a simple and innovative pH adaptive control system, which does 
not require additional hardware and software as compared to the ordinary control systems implemented in 
commercial controllers is investigated. 

2. Mathematical model for pH control simulation

In this study, a mathematical model (Galvanauskas, 2009) was used to simulate the biotechnological process. 
The process PI&D is presented in Figure 1. This study focuses on the adaptive pH control loop marked as 
QC4. 

985



Figure 1: Basic control system loops for a typical microbial cultivation process (Galvanauskas et al., 2019). 

The main control variable in the analysed system is the pH level of the medium. pH can be described as the 
concentration of free hydrogen-ions as = − log  (1) 
where  is the concentration of hydrogen-ions in the cultivation medium. Concentration of hydrogen-ions in 
a fed-batch cultivation process can be modelled considering influence of bacterial growth, addition of acid and 
alkali solutions during pH control and dilution effects: 

= ( + ) + ( − ) − (2) 
where  is the concentration of hydrogen-ions in the alkali solution. This concentration can differ from the 
one calculated theoretically and is subject to model-based identification. x – biomass concentration in the 
cultivation medium, g/l; μ – biomass specific growth rate, 1/h; FpH – flow of the alkali solution for pH control, l/h; 
Fs – flow of the feeding solution, l/h; V – cultivation medium volume, l; α1, α2 – model parameters to be 
identified from experimental data. 
The initial value (0) is equal to 10−7 mol/l, and this level corresponds to pH 7. The biomass growth in the 
fed-batch process can be modelled by means of the differential equation: 

= − +  (3) 
Oxygen uptake rate (OUR) is modelled as follows: 

= +   (4) 
where  β1 ,β2 are model parameters that need to be identified from experimental data. 
Additionally, for the simulation purposes, the model for evaluation of feeding solution flow is described as: 

986



= (5) 
where S0 – substrate concentration in the feed, g/l; Yxs – biomass/substrate yield coefficient, g/g.  
In this study, = , since the real specific growth rate is not measured directly, and the process is 
controlled under substrate limitation conditions. Values of the model parameters are given in Table 1. 

Table 1: Values of the model (1)-(5) parameters. 

Parameter  Value Parameter Value 
Model parameter  0.422·10

-7 mol/g Initial biomass concentration 2 g/l 
Model parameter  0.011·10

-7 mol/g Initial hydrogen-ions concentration 10-7 mol/l 
Model parameter β1 0.8646 g/g Initial medium volume 5 l 
Model parameter β2 0.0180 g/gh Substrate concentration in feed S0 450 g/l 
Biomass/substrate yield coefficient Yxs 0.52 g/g pH setpoint 7 

As the real measurements of pH and OUR are corrupted by noise, the measurements in this simulation study 
were simulated by adding white Gaussian noise: 

_ ( ) = ( ) + ·  (6) 
where _  is the measured value of pH or OUR;  is standard deviation estimated from real measurements 
( = 0.1 % in the analysed case),   is a number from Gaussian random numbers sequence with zero 
mean and unit variance;  denotes an index of discrete measurement point. Time discretization step of the 
adaptation and the control algorithms is set to ∆ = 0.18 . 
In the simulation experiments, time profile of the biomass specific growth rate variation, presented in Figure 2, 
is chosen to simulate close to realistic operating conditions in fed-batch cultivation process.  In this study, the 
specific growth rate  was maintained constant at 0.5 1/h. To simulate a system malfunction (feeding pump 
failure or negative influence of the antifoam agent addition), it was reduced to 0.1 1/h for 0.2 h every 2 hours 
starting from the 1st hour of the cultivation process. 

Figure 2: Specific growth rate  trajectory during a simulation run. 

3. Adaptation of PI controller parameters based on feedback signal statistical analysis

Previous studies of pH control systems in bioreactors have shown that due to changes in the process 
dynamics, it would be appropriate to adapt the parameters of the PI controller, especially the integral time 
constant Ti, that was proven to be the main tuning parameter that depends on the process load. The optimal 
value of the control parameter Kr depends only on the culture broth volume, that does not change significantly 
during the process (Galvanauskas 2009). The adaptation of the controller parameter Ti  is based on statistical 
analysis of the feedback signal of the system. In the controller adaptation algorithm, the average value of the 
error of the feedback signal  is calculated on-line from a moving window: 

( ) =  1 ( ) (7) 
_ ( ) = − ( ) (8) 

where n is the moving window length that is subject to model-based optimisation.  is the feedback signal 
value and  is the setpoint value. 
Additionally, the average absolute deviation is calculated from the feedback signal: 

, 
1

/h

987



 _ ( ) = 1 | ( ) − ( )| (9) 
The above statistical parameters are applied for on-line tuning of the controller integration constant Ti using 
the following rule:  _ ( ) >    _ ( ) > ( ) = ( − 1) 1 − _ ( )    ( ) =  ( − 1) (10) 
where ,  and  are tuning parameters and are subject to model-based optimization. Controller gain 
Kr was not changed and held constant during the controlled process. Block-diagram of the adaptive pH control 
system is presented in Figure 3. 

Figure 3: Block-diagram of the adaptive pH control system 

To account for the variation of the bioprocess state, the adaptive PI controller is additionally supported by a 
feedforward compensator block (Di Capaci et al., 2017), which produces control action based on the OUR 
online estimation. Basic changes in the bioprocess state can be reflected by OUR, that also correlates well 
with the dynamic of the system. This signal can be used as a basis for the feedforward compensation block in 
the proposed hybrid adaptive control. Currently, the industrial bioreactors are equipped with affordable and 
reliable off-gas composition (O2, CO2) and aeration gas flow rate measurement devices. This allows on-line 
estimation of the OUR signal. The feedforward compensator can be described as follows: =  (11) 
where  is a tuning parameter that can be calculated from other model parameters and manually tuned. 
The feedforward part defines the main part of the control signal, and the PI output signal is used for more 
precise tracking of the set pH value. The feedforward part of the control algorithm alone cannot assure 
sufficiently precise pH setpoint tracking under real conditions due to occurring unpredictable metabolic shifts 
within the culture. The feedforward part is also inefficient because it cannot compensate large transients 
caused by the disturbances, even when used with a standard PI algorithm. There are various possible 
technological or specific growth control-related reasons why pH set-point can change or be manipulated, and 
system malfunctions could be one of them. It should be considered that manipulating the pH set-point during 
the controlled process distorts the data in moving window and, therefore, the statistical parameter estimates 
as well. Since these values are used for the controller parameter adaptation, the adaptive control system 
based on feedback signal statistical parameters is preferable to control the pH at constant set-point only. 
A suitable width of moving window and the value of the coefficient  in the tuning rule (10) was determined 
from early simulation experiments by evaluating the IAE criterium with different parameter values. Different 
widths of the moving window n were tested. Optimal values of the tuning parameters are given in Table 2. 

988



Table 2: Values of the control system tuning parameters 

Parameter Value 
Controller gain Kr 6.6 h/l 
Width of moving window  2.7 s 

 
 

 
 

0.0205 
0.8174 l/g 
0.0001 
0.0015 

4. Results and discussion

The simulation results show that the investigated pH control system with the properly selected values of the 
tuning parameters provides reliable adaptation of controller integration parameter Ti and stable performance. 
Simulation results, including trajectories of OUR (Figure 4a), alkali solution addition rate (Figure 4c), and 
adaptation of the controller tuning parameter Ti (Figure 4b) are shown in Figure 4. For comparison, 
performance of the standard PI control system with constant parameters (tuned to minimize the IAE criterion) 
is presented in Figure 4d. 
The adaptive control system tended to perform better at disturbance rejection, where the adaptive controller 
reduced the IAE criterion almost 2.5 times (Table 3).  

Table 3: Comparison of the adaptive and standard control system performance 

Control type 
IAE 

Standard PI Adaptive PI 
Disturbance rejection 0.00408 0.001662 
Setpoint tracking and disturbance rejection 0.01261 0.009852 

Analysis of the simulation results (Figures 5a and 5b) shows that in the late phases of the cultivation process 
the adaptive controller decreases the overshoot by approx. 80 % in the adaptive system. Such a reduction in 
pH fluctuations is very important for cultivation process monitoring algorithms, where the rate of carbon 
dioxide production rate, CPR, is used to monitor the state of the process and the fluctuations in pH can cause 
drastic changes in CPR estimates. These disturbances can occur due to temporary substrate feeding 
disruption, faults of the bioreactor aeration or mixing systems or sudden metabolic shifts. The presented 
results prove efficiency of the pH adaptive control system and potential of implementation in industrial 
controllers. 

Figure 4: Adaptive control system output: (a) time profile of OUR, (b) adaptation of Ti controller parameter, (c) 
feeding solution rate (control variable), (d) comparison of the adaptive (–) and standard (–) PI controller 
performance 

O
U

R
, 

g
/h

T
i, 

h

F
p
H

, 
l/
h

p
H

989



Figure 5: Transient processes of pH during a simulation run - disturbance rejection when using adaptive (–) 
and standard (–) PI controller 

5. Conclusions

The developed simple adaptive PI control system has been investigated for controlling pH in a fed-batch 
fermentation process. The control system remained stable and showed improvements of the pH control 
accuracy in comparison with the standard PI control system with fixed controller parameters. 
The adaptive control system based on the statistical analysis of the feedback signal can be easily 
implemented in many commercial controllers. It can be applied for controlling pH at steady set-point in 
standard fed-batch fermentation processes under ordinary conditions. The application of the proposed 
adaptive control system with feedforward compensator can be extended to control of other basic process 
variables of biotechnological cultivation processes. 

Acknowledgments 

This research was funded by the European Regional Development Fund according to the supported activity 
“Research Projects Implemented by World-class Researcher Groups” under Measure No. 01.2.2-LMT-K-718. 

References 

Boudreau M.A., McMillan G.K., 2006, New directions in bioprocess modelling and control: maximizing process 
analytical technology benefits. ISA, Durham, USA. 

Carr-Brion K.G., 1991, Measurement and Control in Bioprocessing. Elsevier Science Publishers, London. 
Di Capaci B.R., Claudio C., 2017, Performance improvements of cascade and feed-forward control schemes1 

for industrial processes. Chemical Engineering Transactions, 57, 985-990.   
Dochain D., 2008, Bioprocess control. John Wiley&Sons, London. 
Galvanauskas V., 2009, Adaptive pH control system for fed-batch biochemical processes. Information 

Technology and Control, 38(3), 225-231. 
Galvanauskas V., Simutis R., & Vaitkus V., 2019, Adaptive control of biomass specific growth rate in fed-batch 

biotechnological processes. A comparative study. Processes, 7(11), 810. 
Henson M.A., Seborg D.E., 1994, Adaptive Nonlinear Control of a pH Neutralization Process. IEEE 

Transactions on Control Systems Technology, 2(3), 169-182. 
Ylöstalo T., Hyötyniemi H., Jutila P., Ylen J.-P., Rangaiah G.P., 2001, Comparison of Practical Adaptive 

Algorithms in pH Control. Commentary. European Journal of Control, 7(5), 463-475. 
Nsengiyumva W., Chen X., 2018, Design and implementation of a novel self-adaptive fuzzy logic controller for 

a pH neutralization process.,3rd International Conference on Electrical, Automation and Mechanical 
Engineering (EAME 2018). Atlantis Press, 127, 97-102.  

McMillan  G.K., Cameron R.A., 2005, Advanced pH Measurement and Control. ISA. 
Schuler M.M., Marison I.W., 2012: Real-time monitoring and control of microbial bioprocesses with focus on 

the specific growth rate: current state and perspectives. Applied Microbiology and Biotechnology, 94, 
1469–1482. 

Siano S.A, 1995, On the Use of the pH Control Reagent Addition Rate for Fermentation Monitoring. 
Biotechnology and Bioengineering, 47(6), 651-665. 

p
H

p
H

990