# A Novel Disturbance Rejection Control of Roll Channel for Small Air-to-Surface Missiles
## 4 Numerical Simulation
### Effectiveness of the Control Method against Multiple Disturbances  
Experiment 1: Deviation based on steerage  
The rudder torque deflection was set as \(-10\%\), and the experimental verification was carried out in the three-axis direction and in combination to test the robustness and stability of the controller.  
As can be observed from Figures 2 and 3, when steerage deviation is applied, the attitude tracking error of the roll channel is almost 0, and the control precision of the controller is relatively high, with rapid response and no overshoot. The disturbance is accurately estimated by the extended attitude observer, which successfully compensates the influence of the rudder effect deviation in the model, and verifies the feasibility of the controller.  
Figure 3: Change curve of roll angle rate under the combination of two steerage deviations.  
Figure 2: Change curve of roll angle rate under steerage deviation.  
As shown in Figures 4 and 5, when a single or integrated steerage deviation is applied, the roll angle deflection of the roll channel can quickly become stable, which successfully illustrates the effectiveness of the extended attitude observer for rudder deflection disturbance estimation.  
Experiment 2: Based on centroid deviation  
Considering the variation range of the missile's three-axis centroid deviation, the centroid deviation is 1% and 2% respectively for comparative experiments. The experimental results are shown in Figures 6 and 7. The controller in this paper can suppress the disturbance of centroid deviation quickly and realize the stable control of diagonal rate.  
Figure 4: Roll angle response curve under steerage deviation.  
Figure 5: Roll angle response curve under the combination of two steerage deviation.  
Experiment 3: Based on the steering gear stuck  
The effectiveness of the ADRC controller proposed in this paper is studied under the condition that the single actuator is stuck and fails. The experimental results are shown in Figures 8 and 9. It can be observed from the figure that, in the case of steering gear stuck, although there are some fluctuations in the middle, the overall stable control of roll angle can be achieved.  
Figure 6: Change curve of roll angle rate under centroid deviation.  
Figure 7: Roll angle response curve under centroid deviation.  
Experiment 4: Based on wind disturbance  
In this section, comparative experiments are carried out when the gust wind is 5 m/s, 10 m/s and 20 m/s, respectively, and the gust wind action height is 2650-2850 m. The experimental results are shown in Figures 10 and 11. It can be observed from the figure that the larger the tangential wind speed is, the greater the amplitude change of the system at the early stage is. At 10 s, the system is near stable, meeting the performance indicators of fast response and effective response to trimming wind disturbance.  
Figure 8: Change curve of roll angle rate in case of steering gear stuck.  
Figure 9: Roll angle response curve under steering gear stuck.  
Experiment 5: Based on drifts error  
In this section, the control effect of the system with drift error deviation in the range of \(0.01^{\circ}/\)s and \(0.1^{\circ}/\)s is verified by experiments. As can be observed from Figures 12 and 13 below, the system rapidly changes to a stable state after the controller starts acting. It is further verified that the active disturbance rejection controller in this paper can effectively suppress the zero-drift disturbance of the model.  
Figure 11: Roll angle response curve under wind disturbance.  
Figure 10: Change curve of roll angle rate under wind disturbance.