Attitude control of a satellite using fuzzy controllers
Introduction
ROCSAT-1 was the first satellite of the Republic of China. It was launched on January 27, 1999, into a circular orbit with an altitude near 600 km. Its orbital inclination was 35°, its orbital period was 97 min, and its weight was 402 kg. The mission life of the satellite was at least 2 years, with a design life of 4 years. Reliability for the spacecraft was 0.9 at the end of its 4-year design life. Although its design life is over, ROCSAT-1 is still in motion in space.
A satellite must maintain a certain attitude while in orbit to allow precise pointing of an antenna toward the Earth, to allow the accurate orientation of observation instruments toward the object being observed, and to direct solar panels toward the Sun. In the short-term, the satellite receives interference from phenomena such as the Earth’s gravitation, airflow, magnetic fields, and the solar wind. These phenomena can disturb the satellite’s attitude at any time or place. This makes it necessary to control attitude to maintain the satellite’s stability. In the long-term, the satellite receives interference from phenomena such as the Sun and Moon’s gravitation, aerodynamic drag, plus other factors which will make the altitude of the satellite lower gradually.
The motion of the satellite can be influenced in its attitude by internal and external interferences. The factors that affect a low orbit satellite are the residual magnetic field, the disturbance torques caused by interacting with Earth’s magnetic fields, and gravity gradient torques affected by Earth’s gravitation. Recently many research studies have been done concerning about these factors.
Fuzzy theory was initiated in 1965 by Zadeh who had also worked in developing the concept of state, which forms the basis of modern control theory (Wang, 1997). As the control methods evolved, Zadeh thought that classical control theory put too much emphasis on precision to handle complex systems in a practical manner. Fuzzy theory generated many debates and there are still ongoing discussions regarding its excellent way of handling complicated nonlinear systems. Since the fuzzy logic controller successfully controlled the simple dynamic plant in the laboratory, it was applied to the controlling of commercial mercantile products in Japan (Akahoshi, 1991, Tersai et al., 1991).
Many applications of the fuzzy logic controller on attitude controlling of satellites have been proposed successfully. Three MISO fuzzy controllers are used for attitude stabilization of a small satellite in a low earth orbit, proving that the fuzzy controller solves the control constrain problem by choosing the best magneto-torque, polarity and switching instances. The fuzzy controller is also computationally less demanding than the adaptive MIMO LQR controller (Steyn, 1994). Fuzzy logic is incorporated in the robust LQG/LTR method and showed that the proposed method achieved precise attitude control (Nam & Zhang, 1997). Application of the fuzzy logic controller to attitude control of a satellite with bigger solar panels is proved that can have a low settling time, plus it can work in a very low force working environment (Zadeh & Wood, 1999). The Takagi–Sugeno type of fuzzy model and combined H∞ output feedback is used for attitude control of a flexible satellite to achieve precise attitude stabilization (Nam & Kim, 2001). An adaptive fuzzy mixed H2/H∞ attitude control is used for nonlinear spacecraft systems with unknown or uncertain inertia matrix and external disturbances (Chen, Wu, & Jan, 2000). The controller is tuned by means of reinforcement learning without using any model of the sensors or the satellite is proposed (Buijtenen, Schram, Babuška, & Verbruggen, 1998).
Since the applications of fuzzy logic attitude controllers on satellites in the cited references are mature, introducing an interference to disturb the attitude stabilization during the simulation demonstrates the performance of a fuzzy controller in restraining the disturbance. As previously stated two fuzzy controllers supersede the classical controllers to obtain faster convergent time and lower steady-state error. Two fuzzy controllers are consolidated to form one fuzzy controller and it is expected that this one will obtain the same effectiveness of control.
Section snippets
Mathematical model of spacecraft system
The attitude control system of satellite is shown in Fig. 1. The nonlinear equations in terms of components along the body fixed control axes are given by the attitude kinematics and the spacecraft dynamics and can be written as follows (Chen et al., 2000).
Design of fuzzy controller
The classical controllers include a PI controller for pitch axis control and a PID controller for roll/yaw axis control for attitude control of the satellite, which are shown in Fig. 2. The fuzzy controllers are used to supersede the PI controller and PID controller to improve the performance of the system. The proposed controllers output the control commands from the fuzzy logic controller via the inputs of angular error and differential angular error to control the speed-biased wheels. This
Simulation results and analysis
From the simulation results of the Flight Software (FSW) and the Dynamical Model designed by the National Space Program Office (NSPO), we observed a variation in errors of angle (degree) and angular velocity (degree/s, differentiation of angle), as well as control capability to reach steady-state when the satellite encountered the interference. The parameters are k1, k2, kp, kd, and ku, equal to 0.05, 0.04, 1, −1, and 0.6, respectively.
From the simulation results of FSW, we found that both the
Conclusion
A new approach using a fuzzy controller has been proposed for attitude control of the satellite. The simulation results indicate that the two fuzzy controllers are used to supersede two classical controllers for attitude stabilization of the satellite and to obtain a faster convergent time and lower steady-state error. The two fuzzy controllers are consolidated to form one fuzzy controller successfully, and the consolidated fuzzy controller also obtains the performance as expected. The proposed
Acknowledgment
This research was sponsored by National Space Program Office (NSPO), Taiwan, Republic of China under the Grant NSC91-NSPO(A)-PC-FD06-01.
References (12)
- et al.
An experiment in linguistic synthesis with a fuzzy logic controller
International Journal of Man-Machine Studies
(1975) SLR camera α-7xi using fuzzy logic in AF AE AZ
Fuzzy Engineering Toward Human Friendly System
(1991)- et al.
Adaptive fuzzy control of satellite attitude by reinforcement learning
IEEE Transactions on Fuzzy Systems
(1998) - et al.
Adaptive fuzzy matrix H2/H∞ attitude control of spacecraft
IEEE Transactions on Aerospace and Electronic Systems
(2000) - et al.
Fuzzy control based on H∞ output feedback for attitude stabilization of flexible satellite
IEEE International Conference on Fuzzy Systems
(2001) - et al.
Fuzzy multi-variable control for attitude stabilization of flexible spacecraft
IEEE International Conference on Intelligent Processing Systems
(1997)
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