## 7 An Experimental Validation: Optimization of Micro-Algae Biomass Productivity  
Figure 8 shows the lab-scale photobioreactor where the experiments are carried out to assess the performance of SSC. The PBR is equipped with several plunging probes for the online monitoring of the micro-algae concentration as well as the control of the temperature and pH of the medium. To optimize the homogeneity of the micro-algae culture, air-lift flows are achieved on both PBR sides. The PBR vessel is immersed in a water bath whose temperature is regulated by a chiller/heater and a pump that circulates the water to the chiller and back to the water bath. pH is regulated by injecting carbon dioxide. The incident light is generated by a horticultural light fixture with LED lights providing appropriate intensity for the micro-algae growth. Quantum sensors are used to measure the light intensity at the PBR surface, and a PI controller is designed to regulate the incident light intensity. To ensure a continuous mode operation, two peristaltic pumps control the inlet and outlet flows so as to achieve some required dilution rate. The control algorithm is implemented on a LabView platform for real-time computation, and Labjack cards are used for data acquisition. To validate the slope-seeking control (SSC) in a practical setting, the dilution rate and light intensity are used as manipulated inputs, while the measurable productivity is considered as the performance index. It is therefore a simpler situation than the one considered in the previous simulation experiments. Here, there is no need to measure or estimate the internal quota \(Q\), as it is not involved in the cost function. A sample experiment is described in what follows, which is conducted over 8.6 days, with a sampling period of \(T_{s}=0.1\) d = 2.4 h.  
After inoculation, the culture must first settle until biomass concentration reaches a steady-state corresponding to a constant dilution rate \(D(0)=\) 0.1 d\({}^{-1}\) and a constant average incident light \(I_{av}=500\) uE/(m\({}^{2}\cdot\)s). The inlet substrate concentration is \(S_{in}=0.1\) gN\(\cdot\)L\({}^{-1}\). Temperature and pH are kept constant, respectively, at 26 \({}^{\circ}\)C and 7.3. After the steady state has occurred (in this case for \(X(0)=0.88\) gX\(\cdot\)L\({}^{-1}\)), the slope seeking control is activated with a productivity setpoint of \(P=0.2\) gX/(L-d). The dilution rate and incident light are then manipulated by the controller so as to achieve the desired level of productivity. After 7.6 days, the setpoint is changed to \(P=0.1\) gX/(L-d) to challenge the tracking performance of the SSC. The time evolution of the several signals is shown in Figures 9 and 10. Figure 8: Lab-scale flat-panel photobioreactor. During the first phase, i.e., when the setpoint \(P=0.2\) gX/(L-d) is imposed, the system converges within 1 day to the desired productivity level, but the steady-state is only truly established after 3 days, as shown by the biomass concentration evolution in Figure 10. The steady-state values of biomass, dilution rate, and incident light are, respectively, approximately \(X=0.5\) gX/L, \(D=0.35\) d\({}^{-1}\) and \(I=380\) uE/(m\({}^{2}\)-s). When imposing the reference \(P=0.1\) gX/(L-d), the new steady-state is achieved faster, i.e., within 1 day, and the corresponding values are \(X=0.39\) gX/L, \(D=0.2\) d\({}^{-1}\) and \(I=150\) uE/(m\({}^{2}\)-s). This behavior can be explained by the fact that the RELS estimates need some time to converge when the first setpoint is imposed. The second setpoint can be achieved faster as the RELS estimation is probably close to the correct values and is able to track well the changes. We can only speculate about this observation as the values of the parameters are not known a priori. Figure 11 shows the evolution of the gradient components with respect to the dilution rate and light intensity.