## 4 Experiments and Evaluation
### Adaptive Scheduling: Performance Analysis
#### 4.5.1 The Effect of Fitness Function Weights on the Performance  
In this part, we evaluate the effect of normalized fitness function weights, \(\alpha\) (for speed) and \(\beta\) (for power), on the performance of the system. How to optimally respond to a predicted maintenance need (i.e., an abnormal condition) depends on the user preferences, which is depicted as a balance between the operational speed and the power drained. However, since the chromosomes are formed from the fingerprint (nominal operation) of the system, each selection ensures a safe operation. Based on the fitness function in Equation (2), to get a fitness as large as possible, the algorithm tends to select an individual with a closer speed value to the requested one as well as a lower allowed power interval to save the motor from the abnormal conditions (details are in Section 3.4.1). Therefore, different combinations of \(\alpha\) and \(\beta\) can largely affect the performance of the system. The comparison results of different \(\alpha\) and \(\beta\) are shown in Figure 9. The black sinusoidal signal with a period of \(T=50\) s indicates the torque disturbance introduced on the system. Our intention is to simulate a periodic friction that can happen on the angular motion of the motor, for example, a glitch on a part of the gear. The cyan color shows the requested speed, power or efficiency in different graphs. The other colored curves are the actual behavior of our PM-based adaptive control mechanism running with different parameter values.  
The speed behaviours in Figure 9a show that most of the speed curves inversely follow the disturbance torque curve, which indicates that the algorithm controls the motor speed to compensate the changes on the torque. A smaller \(\alpha\) means more importance is given to reduce the power consumption; hence, the speed values are selected to be lower when the applied load torque increases. In addition, smaller \(\alpha\) also means the algorithm gives less importance to match the requested speed when there is a disturbance applied and when it is withdrawn. This can be verified for the case of \(\alpha=0.25\) and \(\beta=0.75\), where the system is not able to restore the requested behavior when the disturbance drops (see in Figure 9a). For the maximum \(\alpha\), the system always satisfies the initially requested speed; however, this time it leads to an excessive power consumption as shown in Figure 9b.  
As for the power consumption, results in Figure 9b indicate that our algorithm responds towards neutralizing the power increase caused by the abnormal torque. Bigger values of \(\beta\) favors for a safe operation as the power is kept very low during the abnormal conditions. However, we also want to maintain the operation so we are not pursuing a minimum power (i.e., a minimum speed) but a proximity to the requested operation. On the other hand, smaller values of \(\beta\) causes the power to dangerously increase and fluctuate a lot to keep the speed as requested. As the balance between preserving speed or power is very sensitive, we use the efficiency algorithm in Equation (7). The calculated efficiency values are shown in Figure 9c. From the graphs, we deduce that the pairs of \(\alpha=0.55,\beta=0.45\) and \(\alpha=0.6,\beta=0.4\) have the highest efficiencies. The selection of the final values is subject to the user preferences. In our case, a safer option would be to pick the pair of \(\alpha=0.55,\beta=0.45\) as it kept the power consumption below the expected one during the abnormal condition, whereas the pair of \(\alpha=0.6,\beta=0.4\) may lead to a better preservation of the operational speed. With that, we ensure that the fitness function is well formulated and provides the user with the option of optimizing for the operational needs.