## 4 Discussion  
In general, the investigated control techniques perform similarly when considering the whole process duration. The type of controller that should be selected, therefore, depends on the existing knowledge of the process and the control type. The adaptive PI controller with fuzzy-based parameter adaptation demonstrates advantages over the gain scheduling PI and model-free adaptive algorithms when compensating the SGR deviations that could be caused by various process disturbances or equipment malfunctions. The gain scheduling PI approach requires deep process knowledge and analytical skills to develop the adaptation model. This control type performs best when no disturbances or malfunctions are present in the system. The MFA controller tends to perform best during the second phase of the process. At phase II, the recombinant protein is produced, thus the SGR is lower.  
The study also revealed that the fuzzy-based control system was stable within the investigated ranges. Considering practical implementation, the developed adaptive control system requires off-gas  
Figure 8: Transient processes of the SGR in the simulated process. Setpoint change: PI controller with fuzzy-based adaptation (– solid line), PI controller with gain scheduling (– dashed line), model-free adaptive (MFA) (–– dash-dot line).  
Figure 9: Transient processes of the specific growth rate during a simulation run. Disturbance rejection when using: PI controller with fuzzy-based adaptation (– solid line), PI controller with gain scheduling (– dashed line), MFA (- - dash-dot line).  
analyzers/flow meters and continuous-flow peristaltic pumps, so that the control system's sampling interval stays within defined ranges. This can occur due to the time constants of the measuring devices or gas transport delays. Based on the simulation result, it can be concluded that, in regard to control performance, the described control algorithms are applicable for SGR control in fed-batch biotechnological processes if a substrate feeding rate manipulation and limitation approach are used. Considering the time needed to design and tune the controller, the fuzzy-based PI controller is suitable for practical applications when expert knowledge is attainable in form of a qualitative understanding of the relationships between various important process variables. Such knowledge is usually available from the process operators. The developed controller also performed better when handling disturbances and setpoint-tracking in the first phase of the process. Principally, the proposed approach could be applied in other aerobic cultivation processes with significant oxygen uptake rates. Nevertheless, the fuzzy model needs to be adapted, especially taking into account different OUR ranges and implemented feed-rate controllers. Hence, the fuzzy-based control algorithm is an attractive alternative approach to control the SGR in fed-batch recombinant protein production processes.  
In future work, the authors plan to perform further investigations and to split the fuzzy-based adaptation system into two smaller separate fuzzy models for each phase, respectively. This should more accurately approximate the process dynamics and consequently improve the control performance at the second phase.  
Conceptualization, M.B., J.R. and V.G.; methodology, M.B., J.R. and V.G.; software, M.B. and V.G.; writing--original draft preparation, M.B.; writing--review and editing, V.G.; supervision, V.G.; project administration, V.G.; funding acquisition, M.B. and V.G. All authors have read and agreed to the published version of the manuscript. 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.  
The authors declare no conflict of interests.