## 7 Conclusions  
The purpose of this study was to extend the time of earth observation and data communication by carrying out satellite maneuver and antenna motion concurrently. Due to the size of the satellite the effect of the antenna motion was significant and did affect the attitude of the system such as time variability of the moment of inertia of the whole system and reaction torque. Therefore, in order to take the effect of the antenna motion into consideration, we combined a satellite control system and an antenna drive system into one control system by governing equations and constructing the Minimum-time optimal control problem. To solve Minimum-time optimal control method. We converted the optimal control problem into a NLP by discretizing the control input (a series of pulses) to minimize the final time of the total maneuver that includes the antenna adjustment. On the other hand, it is considered that satellites have modeling error in real space and nonlinear equation. Therefore we designed robust controller by using SDRE control method. In proposed method, we calculated the reference attitude by the application of optimal control input torque to the ideal model. The reference attitude was time-variant so that we designed nonlinear servo controller by expanding SDRE control method. In addition, to reduce the settling time we designed proposed method which switch the SDW matrix. However, SDRE servo controller increased settling time when the measuring error of RW wheel speed occured and RW wheel speed closed to the limit value of it. Thus, we designed a cooperative control method to reduce the steady error caused by RW reaching performance limit. We design the cooperative control method so that the antenna motor generates torque for satellite attitude maneuver when RW reaches the limit of RW wheel speed.  
We conducted two numerical simulations to verify the effectiveness of the proposed method. Using the results of the Simulation I, this study confirmed that the proposed method could reduce the settling time when compared with LQR, SDRE, SDRE servo controller by transforming the SDW matrix from a servo controller to a regulator, when the reference trajectory is fixed and the error is constant. In addition, from Simulation II, we confirmed that the proposed method could reduced the settling time comparatively with other controllers by antenna motor generating torque for satellite attitude maneuver when RW reaches the limit of RW wheel speed.  
Although this paper assumes that a small rigid satellite of 400 kg was mounted with a 50 kg DRC antenna, it is considered that the antenna mass ratio may be different from this paper for example in the case of LEO to LEO link. Therefore it is necessary to verify how the effectiveness of the proposed method varies depending on the antenna mass ratio by performing numerical simulations with various antenna mass ratios in the future work.  
[PERSON] and [PERSON] conceived and designed the proposed method and verification simulations; [PERSON] performed the numerical simulations; [PERSON] wrote the paper.  
This work was supported by education and research fund from Keio University.  
The authors declare no conflict of interest.