## 5 Experimental Results
Figure 12: Comparison of the theoretical and experimental control signal for a total gain of \(\hat{K}_{p}\approx 0.64\) and an integral time of \(T_{i}=1\) for an operating temperature of 20 \({}^{\circ}\)C.  
In addition to forcing the system's response in the stimulated emission region, Equation (29) provides a theoretical solution for generating a constant output that is centered on \(y_{sp}\). The term \(u_{0}\) is calculated so that the number that accompanies the exponential in Equation (29) is zero, leaving \(u_{0}\) as:  
\[u_{0}=\frac{T_{i}}{\eta K_{p}}\left(y_{sp}+\eta\,I_{th}\right) \tag{31}\]  
Figure 15 shows the system response under the previous conditions for \(u_{0}\). There, we observed that the mean value of the output power was centered at \(y_{sp}\) with damped oscillations. A performance test was conducted to simulate how the laser driver works in a space environment of high vacuum at \(\sim\)9 \(\times 10^{-7}\) Torr (see Figure 16). To achieve this, the laser was operated in a thermal vacuum chamber of NANO-MASTER (NDT-4000). During its operation, the temperature of the chamber was reduced for one hour from 35 \({}^{\circ}\)C to \(-25\)\({}^{\circ}\)C, which produced a reduction in the temperature on the laser from 30 \({}^{\circ}\)C to \(-10\)\({}^{\circ}\)C (measured directly on the mount of the laser using a SHT31 temperature sensor) at a rate of \(\sim\)0.9 \({}^{\circ}\)C/min. During the second hour, the temperature in the chamber was increased from \(-25\)\({}^{\circ}\)C to 35 \({}^{\circ}\)C to complete the thermal cycle. The driver's performance is shown in Figure 17. We observed that the maximum and mean variation in the stabilized optical power were 1.3% and 0.4%, respectively. Figure 11:0 Theoretical and experimental control signals on the stimulated emission zone for \(\hat{K}_{p}\approx 0.64\), \(T_{i}=1\) and \(u_{0}=T_{i}(I_{th}/K_{p}-y_{sp})\). Figure 11:1 Theoretical and experimental responses of the system output on the stimulated emission zone for \(\hat{K}_{p}\approx 0.64\) and \(T_{i}=1\). Finally, the system was forced to operate during a fast change of temperature of \(\sim\)9 \({}^{\circ}\)C/min as shown in Figure 18b. Figure 11:2 Image of the laser inside the thermal vacuum chamber (NDT-4000, Nanomaster) during the performance test. Figure 11:3 The laser was evaluated under space conditions. The reached pressure was 9 \(\times\) 10\({}^{-7}\) Torr with the operating temperature varying at a rate of \(\sim\)0.9 \({}^{\circ}\)C/min. Performance testing was realized by using a thermal vacuum chamber (NDT-4000 from Nanomaster) to emulate the low-Earth orbit conditions. Subplot (**a**) shows the temporal evolution of the output optical power (blue line) and the temperature (orange line) measured by a SHT31 temperature sensor attached close to the laser. Subplot (**b**) shows a close-up of the region where the temperature and optical power are dropping from \(\sim\)21 \({}^{\circ}\)C to \(\sim\)17 \({}^{\circ}\)C and \(\sim\)3 mW \(\pm\)2%, respectively. Figure 11:4 Experimental response of the system for the constant theoretical output condition with system parameters defined by \(\hat{K}_{p}\approx\) 0.64, \(T_{i}=1\) and \(u_{0}=T_{i}\big{(}y_{sp}+\eta I_{th}\big{)}/\left(\eta K_{p}\right)\). The instabilities of the system around \(y_{sp}\), or the system error, were dependent on the thermal change rates and \(\eta K_{p}\) value (see Figure 18a). However, the system error began to converge to zero when the thermal change rate became constant or fell to zero. Thus, the designed APC can be used to stabilize the optical output power for a broad temperature range if the control parameters are valid on the temperature range too.