# On-Line Tendency Control of Dissolved Oxygen Concentration during Aerobic Fed-Batch Fermentations
## 2 Materials and Methods
### DO Control Model
#### 2.3.2 DO Control Algorithm  
During the initial growth phase, as the oxygen demand increased due to the gradual increase in biomass concentration, the DO rapidly decreased. The following parameters were assumed: DO tendency variation is b, the DO set point is DOset, the DO measured value is DOmeasured, and the dead zone width of the actuator is Wdead-zone, also known as dead band, the region of insensitivity of a actuator. If b \(<\) 0 and DOset \(-\) DOmeasured \(>\) Wdead-zone, the DO concentration was monitored with a DO probe and maintained at a set point by increasing the airflow rate and, subsequently, the stirrer speed. The DO control and fermentation data recording interval for DO-Stat ('traditional' or improved) was set to 1 min. Once the substrate was depleted, the DO level began to rise; if b \(>\) 0 and DOset \(-\) DOmeasured \(<\) \(-\)Wdead-zone, substrate was fed to the fermentor via a peristaltic pump controlled using a DO-Stat ('traditional' or improved) method. The DO level decreased once again as recoverable cell metabolism, and biosynthesis of the fermentation product increased after the substrate was supplied. Figure 1 illustrates the algorithm used as part of the DO tendency control strategy [21].  
Figure 1: The algorithm used for dissolved oxygen (DO) tendency control.  
As the fermentation process continued, the characteristics of the biochemical dynamics changed significantly over time; moving window (MW) technology was used to track the variation tendency of the DO. It was necessary to add the newest data and discard the old data as the DO level changed; in fact, the selection of the window length was one of the most challenging aspects of DO control. Sufficient information could be included to determine the actual trend in the change of DO levels by setting an appropriate window size; a suitable window length ensured that the sampling data reflected the process dynamics. If the window size was too large, the automated control of DO lagged. If window size is too small, the DO variation trend was disturbed by noise in the data caused by the fermentation process. Subsequently, the data window was updated by inserting the current data point and dropping the oldest value, which enabled the DO control algorithm to adapt to variations in the fermentation process [22; 23; 24]. For different fermentation processes, the window size was set to different values, which were determined by trial-and-error.  
Because of stochastic disturbances occurring during the fermentation process, the DO values obtained for each time point were unreliable because they were outside the desired range. In addition, this caused the controller to have high activity, which may damage the control equipment. At the same time, the DO level fluctuated dramatically around the set point. This challenge could be overcome by utilizing the measurement of DO within a moving window over time; the stirrer speed was intermittently adjusted in accordance with the DO variation tendency that was determined based on the current data window, rather than every data point [25].  
Figure 2 shows the control structure used for DO during _Corynebacterium glutamicum_ fermentation. The window size was set to 5 min, with five data points. The DO was maintained at or above 10% of air-saturation; its low limit was set to 9%.  
Figure 2: DO control structure for _Corynebacterium glutamicum_ fermentation.  
The control structure used for DO during _Pichia pastoris_ fermentation is shown in Figure 3. As it utilizes a longer DO control cycle, the window size was set to 30 min, with 30 data points. The DO was maintained at or above 10%.