# Modeling and Control of an Articulated Multibody Aircraft
## 5 Discussion
### Yaw Attitude Control  
Figure 7 shows the lateral-directional control input plots for yaw angle control. YC 1 uses ailerons exclusively and zero abdominal yaw deflection, abdominal yaw deflection exclusively and zero aileron deflection for YC 2, and both aileron and abdominal yaw deflection for YC 3. The transient response for the lateral-directional dynamic response in terms of sideslip angle \(\beta\), roll angle \(\phi\) and roll rate \(p\) are presented in Figure 6a-c. Please note that prior to implementation of a controller, the aircraft was laterally unstable (Equation (73), which is not unusual for tailless aircraft [141; 143]. Similar behavior can be observed based on the effect of yaw control effector choice on the transient of these states. The exclusive use of the aileron (YC 1) produces the most stable response in \(\beta\), \(\phi\) and \(p\), while using the abdominal yaw alone for control (YC 2) caused the aircraft to be more unstable as a result of dynamic effects of the oscillatory movement of the abdomen as seen in Figure 7b. Simultaneously using both ailerons and abdominal yaw (YC 3), on the other hand, reduced the instability experienced with the exclusive use of abdominal yaw in YC 2. The main remark regarding the state evolution of roll angle (Figure 6b) and roll rate (Figure 6c) is the presence of a strong coupling between lateral and directional dynamics, caused by aileron and abdominal yaw deflection. A yaw controller generates a sideslip to induce a turn and a significant problem associated with turning of a rudderless aircraft is adverse yaw resulting from the differential lift and drag on the left and right wing. The sideslip angle \(\beta\) is a key performance indicator for aircraft turn coordination, i.e., with zero sideslip angle \(\beta=0\). The time history for sideslip angle \(\beta\) in Figure 6a shows that the exclusive use of ailerons (YC 1) and exclusive use of abdominal yaw (YC 2) resulted in negative sideslip. However, simultaneously using ailerons and abdominal yaw achieved better turn coordination over time. Regarding the time histories of the yaw rate \(r\) (Figure 6d), for the three yaw controllers, an increase in yaw angle resulted in an increase in yaw rate as expected. From the simulation results presented in Figures 6 and 7 and Table 8, it can be observed that YC 3 has a better response in terms of settling time of 2.29 s compared to that of YC 1 and YC 2 with settling times of 3.33 s and 6.25 s, respectively. In terms of overshoot, YC 2 has the least overshoot 0.89%, compared to YC 1 and YC 3 with overshoots of 5.80% and 2.95%, respectively. YC 2 gives the highest steady-state error of 2%, with the steady-state errors of YC 1 and YC 3 being 0% and 0.04%, respectively. In addition, the corresponding control efforts for aileron deflection \(\delta_{a}\) and abdominal yaw angle fall within the set limits with maximum absolute deflections being 0.056\({}^{\circ}\) and, 0.013\({}^{\circ}\) respectively. The states also fall within the simulation constraints set for \(\beta\), \(p\) and \(r\), with maximum absolute values of 22.24\({}^{\circ}\), 6.53\({}^{\circ}\)/s and 26.56\({}^{\circ}\)/s, respectively. Of all the controllers, only YC 3 meets the controller performance requirements. For insects, the lack of a dedicated yaw-controlling surface similar to the aerodynamic rudder of many aircraft causes inherent instability on the lateral axis; however, \"ruddering\" movements of the abdomen have been observed [144]. The results attest to the potential use of a yaw-like abdominal airframe-based control mechanism that can be beneficial for the reduction of sideslip during turns (see Figure 6a) as sideslip is a critical control state of the entire aircraft. The results obtained for yaw control are consistent with the observation in the analysis by [PERSON] in [36] that used internal moving mass for turn trim and trajectory control.