## 3 Methodology
### Genetic Algorithm
The response produced by the Full State Feedback controller shows that all three tuning methods are heavily compromised by the noise in the system, this is due to the architecture of the controller as opposed to a specific tuning method. Figure 11: Full State Feedback response for Manually tuned, PSO and GA. The response for each tuning method for Pitch displacement is very similar with no obvious best method. When compared to roll displacement, both PSO and manually tuned responses possess similar behavior. However, the controller tuned by GA has a larger overshoot although it does become stable faster than other tuning methods. When analyzing yaw rate, the response is in terms of angular velocity, making it hard to compare with the pitch and roll displacement due to the change in unit. To better understand

Figure 12: Full State Compensator response for Manually tuned, PSO and GA.

Figure 13: Linear Quadratic Gaussian response for Manually tuned, PSO and GA.

the displacement of the vehicle in its yaw direction the integration of yaw velocity, yaw displacement offers a better insight. Clearly, the controller tuned by GA generates the smallest amount of displacement in the yaw direction only being displaced by 1.7 degrees. The second-best tuning method by process of manual tuning being displaced by a total 26 degrees and the worst preforming controller was tuned by PSO reaching a maximum displacement of 68 degrees. The response for each of the Full State Compensator tuning methods has better noise attenuation than the Full State Feedback controller due to its state observer (Luenberger observer) to predict the output of the states instead of measuring the noisy outputs directly. However, it is still apparent that there is still some noise in the system such as PSO in Yaw Rate resulting in a particularly poor response. This type of disturbance must be better attenuated if an acceptable controller is to be achieved. When analyzing pitch displacement both controllers tuned by GA and PSO appear to settle faster than other tuning methods. However, when %OS is considered, the response tuned by PSO overshoots its target by over double the controller tuned by GA. Both the controller tuned by GA-Hybrid and by manual tuning appear to have a similar response both overshooting their target the most out of any tuning method, whilst also taking the longest time to settle. When analyzing roll displacement, the controller tuned by GA performs the best in both settling time and %OS. The second-best response is the controller tuned by PSO, the %OS is less than that of both manually tuned and GA-Hybrid. The controller tuned by PSO has a settling time similar to GA-Hybrid and the manually tuned controller but not as fast as GA tuned controller. Both manually tuned and GA-Hybrid controller have a similar response in terms of %OS, but GA-Hybrid outperforms manually tuned in terms of settling time. When analyzing yaw rate, the GA controller falls quickly initially, but flattens slightly at around 50 degrees per second and settles slowly to zero in 1.5 seconds. When this response is analyzed in terms of displacement, the reduction of gradient decent in velocity causes a greater displacement as the controller tuned with GA reaches its highest displacement of 35 degrees. The manually tuned controller shows the best settling time which results in the least maximum displacement. Figure 14: Comparison of the best tuning methods for each controller type. ### Linear Quadratic Gaussian

The responses shown in Figure 13 show the Linear Quadratic Gaussian tuned manually, by PSO, GA and a GA-Hybrid method. When analyzing pitch displacement, the controller tuned by GA stands out as the best in terms of percentage overshoot and on settling time. The controller tuned by PSO also produced an impressive response with slight overshoot, but a faster settling time than manually tuned and GA Hybrid. Manually tuned and GA-Hybrid both fall slowly until zero but overshoot slightly, taking a long time to correct the overshoot back to equilibrium.