Design and on-orbit test of RBF network friction compensation sliding mode control algorithm for Luojia1-01 satellite attitude

Aiming at the attitude maneuver mode of Luojia1-01 satellite attitude control system, this paper designs an RBF network friction compensation sliding mode control (SMC) algorithm. Firstly, the satellite attitude motion model is derived according to the needs of the imaging working mode. Secondly, a fast Terminal sliding mode control law is designed based on the tracking error motion model described by the error quaternion. Considering the suppression of disturbance, an extended state observer (ESO) is introduced to observe the total disturbance of the system. Then, the RBF network friction compensation system is used to approximate the switching term on line and further reduce the vibration, thereby reducing the switching gain in the sliding mode control law. The simulation results of RBF adaptive control algorithm and RBF network friction compensation sliding mode control algorithm are carried out to prove the perfect effect of the proposed algorithm. Finally, the on-orbit test and summary of Luojia1-01 satellite attitude control system are carried out. The results show that the attitude pointing accuracy is better than 0.02°, the attitude control stability is better than 0.005°/s, and the accuracy of control moment is 0.01mNm. This method satisfies the overall requirements of Luojia1-01 satellite’s working mode.


Introduction
On June 2, 2018, Luojia1-01 satellite developed by Wuhan University and Chang Guang Satellite Technology Co., Ltd. (Changchun, China) was successfully launched at the Jiuquan Satellite Launch Center [1]. Luojia1-01 satellite is the first scientific experimental satellite used in nighttime imaging in China. The satellite carries a large field of view high-sensitivity night-light remote sensing camera, as shown in Fig 1, which can provide special products such as China's and global GDP index, carbon emission index, and urban housing vacancy rate index. At the same time, it has a variety of working modes: push-broom mode, staring-imaging mode, digital transmission mode, inertial space imaging mode, navigation enhancement mode, navigation data down-linking mode. This requires Luojia1-01 satellite attitude control system to have fast maneuverability, high attitude pointing accuracy and attitude stability. Luojia1-01 satellite is a strongly coupled, strongly nonlinear dynamic system with parameter/model uncertainty, and it will be affected by time-varying unknown disturbances or even actuator installation deviations, faults, etc. during orbital operation. These have a significant impact on Figure 1. Luojia1-01 satellite In Reference [4], the author proposed a minimum sliding mode error feedback control strategy based on sliding mode control theory for the attitude control problem of small satellites. The real-time optimal estimation of the equivalent control error is fed back to the sliding mode. The controller makes it better to compensate for the effects of interference and uncertainty in the system, significantly improving the dynamic and steady-state performance of the system. In Reference [5], the author combined adaptive sliding mode control with active vibration control of flexible accessories to design a flexible spacecraft attitude controller to achieve high-precision attitude control while suppressing accessory vibration. In Reference [6], the author discussed the attitude tracking problem of rigid spacecraft in the presence of external disturbances, uses adaptive control algorithm to estimate the interference, and designs the sliding mode controller to ensure the system is asymptotically stable. In Reference [7], the author proposed an adaptive sliding mode control algorithm based on RBF network for the nonlinear problem in the attitude control system of flexible satellites. The neural network makes the uncertainty factors in the modeling process. It is estimated that the neural network parameters are adjusted online by the adaptive law, and the high-performance control of the satellite attitude is realized. In Reference [8], the author used neural network to realize online estimation of nonlinear part, uncertain part and unknown external disturbance of linear system, and realizes equivalent control based on neural network, which effectively eliminates chattering. In Reference [9], the author designed a sliding mode controller based on RBF neural network. The controller is completely realized by continuous RBF function, which cancels the switching term and eliminates chattering. In Reference [10], the author combined BP network learning algorithm with sliding mode control to form a new closed-loop control system, and used the online learning function of BP network to propose a new sliding mode-neural network controller to realize the induction. Adaptive sliding mode control of the motor.
At present, many RBF neural network control results for nonlinear systems have been published. This method is rarely applied in the engineering of attitude stabilization control of agile satellites, and there is no on-orbit experiment. Therefore, our team design an RBF network friction compensation sliding mode attitude control algorithm for the working modes of Luojia1-01 satellite attitude control system: attitude maneuver and staring-imaging working mode. A fast Terminal sliding mode control law is designed based on the tracking error motion model described by the error quaternion. An extended state observer is introduced to observe the total disturbance of the system, reduce the switching gain in the sliding mode control law, and weaken the system chattering. The RBF network friction compensation adaptive system is used to approximate the switching term on line and further reduce the vibration.

The kinematics modeling and control theory basis of Luojia1-01 satellite
The kinematics equation of the satellite described by the attitude quaternion q : In Equation (1), where q is the attitude quaternion, 0 q is the scalar of the attitude quaternion, and T q is the vector of the attitude quaternion transposition.  is the attitude angular velocity vector of the satellite relative to the inertial coordinate system;  q is the cross-multiplication operation of the vector q .
According to the momentum moment theorem, the attitude dynamics equation of a flexible satellite is given as In Equation (2) (4) The control torque of a single reaction wheel is: The control torque provided by the flywheel is: = u Aa (6) The relative motion equation (7) of Luojia1-01 satellite is obtained by equation (2)(4)(5).

Design of RBF network friction compensation sliding mode attitude controller
In ordinary sliding mode control, a linear sliding plane is usually selected, so that after the system reaches the sliding surface, the tracking error gradually converges to 0, and the progressive convergence speed can be achieved by adjusting the sliding surface parameters, but the effect is not good [11]. Therefore, Luojia1-01 Satellite attitude control system selects the fast terminal sliding mode control strategy. In this study, we choose Where p , q , g , h is positive odd number. Then the satellite attitude tracking error dynamics equation can be expressed as 1 00 The sliding mode control law can be designed as Where eq u is the equivalent control when 0 s = , and k u is the switching control. When At the same time, take: ; To prove that can be obtained from assumption 1 and assumption 2, where 1 The disturbance moments received by the orbiting spacecraft mainly include gravity gradient moments, solar radiation moments, aerodynamic moments, and geomagnetic moments. Although they have time-varying characteristics, they are bounded.

Formatting the title Second-order ESO design
The switching gain in the control law is affected by the parameter perturbation and unknown disturbance, so the control precision is reduced. The sliding mode controller is introduced into the extended observer (ESO), and the high gain error feedback makes the dynamic response of the observer much higher than the dynamic response of the system, which is equivalent to the fast-changing subsystem in the system, which can ensure that the observation error of fast convergence and high enough estimation precision, thus providing angular velocity signal available for feedback.  The expansion observer is designed to: In Equation (17), where ˆ1 x and ˆ2 x are the observer state, 1  and 2  are positive real numbers. Then the observer output ˆ2 x is close to x and ˆ1 x is close to 11  .
The ESO observationˆ1 x is compensated into the control law, and the control law is designed as follows:

RBF network friction compensation system
Sliding mode control combined with RBF neural network approximation is used in Luojia1-01 Satellite attitude control system. The RBF network friction compensation model is used to realize the adaptive approximation of the unknown part, which can effectively reduce the fuzzy gain. The friction compensation system of RBF network is derived by Lyapunov method, and the stability and convergence of the whole closed-loop system are guaranteed by the adjustment of adaptive weights. The RBF network friction compensation system introduced in this paper approximates the symbol function term, and its input plane is s , and the output symbol term estimated value The Lyapunov function can be used to derive the adaptive law of adaptive adjustment parameters, and the Lyapunov function can be established as

Numerical simulation of attitude control system
In order to verify the effectiveness of the control algorithm proposed in this paper, numerical simulation verification is carried out. Relevant parameters are shown in Table 1.  The maximum output of the flywheel control is 2mNm; the control output is -0mNm between -0.1mNm and 0.1mNm; the control delay is 0.5s; the whole star uses a control period of 0.5s. We make the simulation for the different mission modes of Luojia1-01 satellite. For the two imaging task modes of Luojia1-01 satellite, the RBF network friction compensation sliding mode attitude controller designed with the extended state observer is simulated and verified. The specific parameters of controller and expansion observer are shown as the following Table 2.

Theorical simulation of attitude maneuver mode
For the attitude maneuver mode, the initial attitude angle in the simulation is 0°. When the ground speed is maneuvered, the target values can be showed x-axis maneuver to 172.5°, z-axis maneuver to 52.5°, and y-axis constant speed 0.63°/s push-broom. The initial attitude angle of the satellite is set to [0 0 0]. The theoretical simulation and the deflection simulation are carried out. The RBF friction compensation sliding mode control algorithm is introduced into the simulation model, and the two sets of simulation results are compared. At the initial attitude angle and angular velocity, the simulation analysis of the attitude maneuver mode without the depolarization is performed without considering the measurement error of the measuring component and the influence of the mounting matrix error. ) that the system pointing accuracy is better than 0.1°, the attitude control stability is better than 0.001°/s, and the accuracy of control moment is 0.01mNm.

Pull-off simulation of attitude maneuvering mode based on RBF network friction compensation sliding mode control
In order to realistically simulate the actual on-orbit state of the satellite, the influence of the installation and measurement error of the measuring components such as the gyro and the star sensor on the system control accuracy and stability is further considered in the system simulation stage. The RBF network friction compensation term is introduced for the sliding mode controller to further approximate the switching gain. RBF friction compensation parameters are selected as shown in Table 2. Compared with the theoretical simulation, the control accuracy and stability after the pulling are reduced, but still can be meet the requirements of control accuracy and stability from Fig 3(a) The results show that the attitude pointing accuracy is better than 0.2°, the attitude control stability is better than 0.005°/s, and the accuracy of control moment is 0.01mNm. The sensors error is introduced into pull-off simulation, and the friction gain is weakened by the RBF network friction compensation system, so that the satellite attitude control system can still maintain a good effect in the maneuver process.

Pull-off simulation of attitude maneuvering mode based on RBF adaptive control
To further demonstrate the effectiveness of the RBF network friction compensation sliding mode controller. The RBF adaptive controller is applied to the attitude control system of the Luojia1-01 satellite with the same parameter model. The satellite attitude control stability parameters are visualized, and the simulation results are shown in

Luojia1-01 satellite attitude control system on-orbit test
The telemetry quaternion in the telemetry data is analyzed. First, the quaternion is converted into Euler angle, then the data is fitted, and then the standard deviation of the residual is obtained to get the attitude determination accuracy and attitude maneuverability of the system. In the closed-loop test, the satellite orbit is quadratic. Fig 5(a) shows the maximum maneuvering angular velocity of the satellite is 1°/s. Satellite control accuracy is an evaluation of the satellite attitude control system capability and can be extracted by the actual control deviation information of the satellite. During the test phase, multiple domestic telemetry data are recorded and analyzed, and the statistical results of the deviation quaternion in the telemetry data are obtained to verify whether it meets the satellite control system control accuracy requirements. The test results show that the control accuracy of the satellite control system meets the requirements of the index. The attitude pointing accuracy is better than 0.02°, and the attitude control stability is better than 0.002°/s. Control torque In the closed-loop test, the satellite orbit is quadratic. Fig 5(a) shows the maximum maneuvering angular velocity of the satellite is 1°/s. Satellite control accuracy is an evaluation of the satellite attitude control system capability and can be extracted by the actual control deviation information of the satellite. During the test phase, multiple domestic telemetry data are recorded and analyzed, and the statistical results of the deviation quaternion in the telemetry data are obtained to verify whether it meets the satellite control system control accuracy requirements. The test results show that the control accuracy of the satellite control system meets the requirements of the index. The attitude pointing accuracy is better than 0.2°, and the attitude control stability is better than 0.005°/s.

Conclusion
In this paper, we aim at the attitude maneuver mode of the Luojia1-01 satellite attitude control system, and design RBF network friction compensation sliding mode attitude control algorithm. The conclusions are as follows: (1) The fast terminal sliding mode control law is extended to the attitude control system of the Luojia1-01 satellite, which makes the strong nonlinear flexible satellite attitude control system achieve better control index.
(2) Through theoretical derivation, the extended state observer is introduced to observe the total disturbance of the system, and the switching gain in the control law is reduced. Combined with the RBF network friction compensation system, the system chattering is effectively weakened.
(3) The results of theoretical simulation and pull-off simulation are compared for attitude task modes of Luojia1-01 satellite, and the comparison experiment between RBF adaptive control algorithm and RBF network friction compensation sliding mode control algorithm is sufficient. The results show that the application of RBF friction compensation sliding mode control algorithm can reduce the switching gain in the sliding mode control law, and weaken the chattering of the system. The algorithm is applied to the in-orbit test, which verifies the effectiveness of the algorithm and improves the application efficiency of the satellite.
The on-orbit test results show that the attitude pointing accuracy is better than 0.2°, the attitude control stability is better than 0.005°/s, the accuracy of control moment is 0.01mNm, and the maximum