## 3 Modeling and Analysis of Attitude Control of Missile
### Simulation and Analysis  
In this part, the simulation analysis combined with actuator dynamics and attitude control of the pitch channel is carried out. The parameters of the actuator refer to Table 1. Basic data of the missile can be seen in Table 2.  
In the simulation process, dynamic characteristics of the steering gear and vertical interfering wind factors are taken into account. The relevant parameters of ADRC control of the pitch channel are  
\[b_{\mathrm{o1}}=\ 158.2,\ \omega_{n1}=\ 6.96,\ k_{p1}=\ 40.4,\ k_{d1}=\ 15.3,\ \omega_{o1} =\ 110.\]  
As the contrast controller, the angular rate feedback coefficient, proportionality coefficients, integral coefficients and differential coefficients of PID are pre-calculated by the linear model at the characteristic points, and the global controller is obtained by fitting the linear controller parameters at all characteristic points by interpolation.  
According to the discussion in Section 2, for the non-linear actuator, the PID control effect is not satisfactory, which may have a great impact on attitude control. Therefore, this paper considers an actuator with a dead-zone voltage of 3 V and adopts ADRC control. The control parameters are still: \(b_{\mathrm{o}}\)= 188.5, \(\omega_{\mathrm{o}}\)= 312, \(\omega_{\mathrm{n}}\)= 56.5. That is, take the equivalent damping ratio is 1, the corresponding parameters are \(k_{p}=113\) and \(k_{d}=3192.25\).  
In order to illustrate the problem in this paper, without considering the structural strength and overload capacity of the missile, different vertical wind speeds (the wind speeds are set to be 15 m/s, 20 m/s, 25 m/s, 30 m/s and 35 m/s respectively, they are represented by wind-1, wind-2 wind-3, wind-4 and win-5, respectively, in the figures) are added in the model during the ascent phase when t = 4-8 s. The ADRC and PID controller responses of pitch control are presented, respectively. Simulation results are shown in Figures 18-23.  
Figures 18 and 19 show the pitch angle response curves under ADRC and PID control respectively. It can be known that under ADRC control, under a wide range of wind disturbances, the maximum fluctuation of pitch angle is only 0.8\({}^{\circ}\), and it reaches the command value after a recovery time of about 1.5 s. However, under PID control, the maximum fluctuation reaches up to 11.3\({}^{\circ}\), and the pitch angle changes dramatically, the control overshoot is large, and the recovery time is near 5 s.  
Figures 20-23 show the comparisons of actuator reflection angles and pitching moments under two control modes under different wind disturbances.  
Figures 20 and 21 show the output deflection angles of the actuator loop when the pitch attitude is controlled by ADRC and PID, respectively, under different wind strengths. Figures show that under the control of ADRC, the influence of the disturbance on the actuator is limited, the deflection range of the actuator is small, and the actions are steady. However, under the PID control, the deflection angle of  
Figure 19: Pitch angel responses under PID with different wind disturbances.  
Figure 20: Actual deflection angles under ADRC.  
the actuator is up to 6\({}^{\circ}\) due to the high wind, and the deflection angle is large. Correspondingly, as seen in Figures 22 and 23, the torque responses between the two control methods in the pitch channel are huge. Under the PID with high wind, the pitching torque varies up to 12 KN. In this case, the rocket is subjected to a large overload, and this is a significant challenge to the structural strength of the rocket. Under the control of ADRC, wind disturbance can be resisted and a good tracking effect is realized.  
Figure 21: Actual deflection angles under PID with different wind disturbances.  
Figure 22: Actual pitch movement under ADRC.