Special Issue Article

A semi-physical simulation platform of attitude determination and control system for satellite

Advances in Mechanical Engineering 2016, Vol. 8(5) 1–11 Ó The Author(s) 2016 DOI: 10.1177/1687814016646975 aime.sagepub.com

Yuanjin Yu1,2 and Zhaohua Yang3

Abstract A semi-physical simulation platform for attitude determination and control system is proposed to verify the attitude estimator and controller on ground. A simulation target, a host PC, many attitude sensors, and actuators compose the simulation platform. The simulation target is composed of a central processing unit board with VxWorks operating system and many input/output boards connected via Compact Peripheral Component Interconnect bus. The executable programs in target are automatically generated from the simulation models in Simulink based on Real-Time Workshop of MATLAB. A three-axes gyroscope, a three-axes magnetometer, a sun sensor, a star tracer, three flywheels, and a Global Positioning System receiver are connected to the simulation target, which formulates the attitude control cycle of a satellite. The simulation models of the attitude determination and control system are described in detail. Finally, the semi-physical simulation platform is used to demonstrate the availability and rationality of the control scheme of a micro-satellite. Comparing the results between the numerical simulation in Simulink and the semi-physical simulation, the semi-physical simulation platform is available and the control scheme successfully achieves three-axes stabilization. Keywords Attitude determination and control system, semi-physical simulation, Real-Time Workshop, satellite

Date received: 10 November 2015; accepted: 6 April 2016 Academic Editor: Jianyong Yao

Introduction Attitude determination and control system (ADCS) is the core subsystem of satellite mission. To guarantee the availability and reliability of the attitude stabilization, the attitude control algorithm should be validated on ground. ADCS simulation is a way of ground-based validation. The method of ADCS simulation includes numerical simulation, semi-physical simulation, and physical simulation. The numerical simulation utilizes the mathematical models to simulate the attitude control cycle. Aleksandrov et al.1 used computer algebra method to simulate the attitude control system of a satellite. In Lin et al.,2 the simulations of the ADCS in MATLAB and Simulink are developed, which include physical models, estimators, and controllers. This

numerical simulation is used to verify the attitude control of the acquisition mode and attitude stabilization mode. Physical simulation builds a simulator of the satellite on ground. Kwan et al.3 designed a physical ground testing platform for spacecraft attitude 1

School of Astronautics, Beihang University, Beijing, China Guangdong Key Laboratory of Popular High Performance Computers, Shenzhen University, Shenzhen, China 3 School of Instrumentation Science and Opto-Electronics Engineering, Beihang University, Beijing, China 2

Corresponding author: Zhaohua Yang, School of Instrumentation Science and Opto-Electronics Engineering, Beihang University, No.37, XueYuan Road, Haidian District, Beijing 100191, China. Email: [email protected]

Creative Commons CC-BY: This article is distributed under the terms of the Creative Commons Attribution 3.0 License (http://www.creativecommons.org/licenses/by/3.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/ open-access-at-sage).

2 dynamics and control based on the small size air bearing. This platform can simulate the behavior of small or nano satellites. The motion about the yaw axis had been realized and validated, but the realizations of motions about the pitch and roll axes are still a challenge. Xu et al.4 designed a 5-degree-of-freedom (DOF) air floating platform for the simulator of the small satellite. Most of the physical simulations rely on threeaxes air-bearing table for dynamic simulator.5–7 However, the physical simulation system is expensive and complex. The semi-physical simulation for ADCS is a kind of control cycle experiment under the simulated dynamic and environment. In semi-physical simulation, the dynamic of partial control system and control target is simulated by the numerical models8 and the partial or all devices of ADCS are included. The numerical models are usually executed in a simulation target. In Kumar et al.,9 a xPC target is used to execute the exe file of the simulation model. The target PC connects the controller hardware according to the data acquisition cards. The correctness and rationality of designed scheme of attitude control system can be validated by the semi-physical simulation experiments.10 Moreover, the semi-physical simulation plays significant role on development of attitude control system for satellite.11 The performances of the simulation targets are crucial to the semi-physic simulation missions. Wang et al.11 utilized two PC targets to improve the operational capability. The two targets are connected by Ethernet, thus the synchronization problem and realtime data interface of the two targets are important but not considered in Wang et al.11 Real-Time Workshop (RTW) is an open development tool proposed by MATLAB. RTW can be used for real-time simulation and fast modeling of product. In Simulink, large and complex systems can be built and simulated within a graphical user interface, whereas the RTW can automatically generate executable programs from Simulink models.12 The simulation system dSPACE and xPC are developed for real-time simulation using RTW. Many researchers establish the semi-physical simulation platform based on xPC simulators13,14 and dSPACE simulators.15–17 VxWorks is a real-time embedded operating system. Based on RTW and VxWorks, a real-time semi-physical simulation platform is developed in section ‘‘ADCS semi-physical simulation system design.’’ The simulation platform consists of a host PC and a real-time simulation target. The simulation target composed of central processing unit (CPU) board with VxWorks operating system and input/output (I/O) board connected via Compact Peripheral Component Interconnect (CPCI) bus. To guarantee the high real-time performance, the simulation platform adopts VxWorks operating system and high-frequency multi-core processor. Then a kind of

Advances in Mechanical Engineering semi-physical simulation for ADCS is described in detail. The devices placed in control cycle include three orthogonal fixed reaction flywheels, three-axes magnetometer, three-axes gyroscope, sun sensor, star tracer, and Global Positioning System (GPS) receiver. The Simulink models of satellite dynamics are developed in detail. The aim of the semi-physical simulation is to demonstrate the availability of the semi-physical platform and the performance of attitude control scheme. A simulation experiment for a sun synchronous micro-satellite is constructed in section ‘‘Simulation result.’’ Finally, the conclusion is drawn out in section ‘‘Conclusion.’’

ADCS semi-physical simulation system design Simulation environment design Simulation platform. A simulation manager computer and a real-time simulation target connected with Ethernet compose the simulation platform. The simulation manager computer can be a high-performance PC, named host PC, which is mainly used to develop the dynamics, the attitude estimation algorithm, and attitude control algorithm of ADCS using the MATLAB/ Simulink. The host PC generates the executable programs automatically and manages the simulation process. The generated executable programs will be downloaded to the simulation target through Ethernet. The real-time performance and expansibility are the primary performances of the simulation target. Figure 1 shows the diagram of the simulation target. The target consists of a CPU board and many I/O boards connected via CPCI bus. The CPU board adopts highfrequency multi-core processor to improve the operational capability. VxWorks operating system adopts real-time multi-task and fast interrupt response, which improves the execution speed of the programs. VxWorks is utilized as the operational system of the CPU board. Because CPCI bus has the merits of high bandwidth, high reliability, and can be hot swap, the CPCI is used in the simulation target to improve the data processing capability. Furthermore, the boards with standard CPCI interface are easily added to the simulation target, which improves the expansibility of the simulation target. The simulation target with AD,

Figure 1. Diagram of simulation target.

Yu and Yang DA, DI, DO, SIO, and CAN interfaces can meet the requirements of most simulation missions. ADCS simulation structure. Generally speaking, the simulation system can be divided into hardware and software parts. The hardware of ADCS semi-physical simulation system is composed of a host PC, a realtime simulation target, three orthogonal fixed reaction flywheels, three-axes magnetometer, three-axes gyroscope, sun sensor, star tracer, GPS receiver, GPS simulator, starlight simulator, and sunlight simulator. The structure diagram is shown in Figure 2. The host PC connects with the simulation target via Ethernet. The flywheels connect with the simulation target via CAN bus, and the other devices connect with the simulation target via serial port. Because the communication delay of serial port is larger than that of CAN, the real-time performance is limited by the communication delay of serial port. Improvement of the baud rate and interrupt triggered receiver are applied to reduce the delay.

Simulation model design The Simulink models are the simulated parts of the ADCS designed in MATLAB/Simulink. The models consist of satellite dynamics model, attitude actuator model, attitude controller model, attitude determination model, and external interface model. Figure 3 shows the diagram of the Simulink models for ADCS.

Figure 2. Structure of semi-physical simulation for ADCS.

3 The satellite dynamic model simulates the attitude dynamics of satellite, whose input is the control moment generated by attitude actuator and the outputs are the attitude and angular velocity of satellite. The attitude controller model simulates the function of digital controller, whose inputs are the measured attitude and expected attitude and the outputs are the instruction of control torque for actuator and work mode of satellite. The attitude determination model simulates attitude estimate algorithm, whose inputs are the data acquired from attitude sensors and GPS receiver and the outputs are the estimated attitude and velocity to the controller. The external interface model is significant for semi-physical simulation, which realizes the communication between Simulink model and the actual devices. Satellite dynamics model. Satellite dynamic model includes attitude dynamics model, attitude kinematic model, space environment disturbance moment model, and solar sail vibration mode equation model. The angular momentum for satellite with flexible solar sail and flywheel is H = Iv + hw + C h_

ð1Þ

where H 2 R3 is the total angular momentum of the satellite. I 2 R3 3 3 is the inertia tensor matrix. v 2 R3 is the angular velocity of the satellite body frame with respect to the inertia frame. hw is the angular

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Figure 3. Structure of Simulink models for ADCS.

Figure 4. Simulink model of attitude dynamics.

momentum of the flywheels. C is the coupling matrix between solar sail and satellite. h 2 R3 is a three-order mode vector of the solar sail vibration. The vibration mode equation of the solar sail is given as follows18 h € + 2j  L  h_ + L2  h + C T  v_ = 0

ð2Þ

where j is the mode damping ratio matrix of the solar sail vibration. L is the mode frequency matrix of the solar sail vibration. The attitude dynamic equation of satellite with flexible solar sail becomes _ + C€ h =  h_ w + Tc + Td I v_ + v 3 (Iv + hw + C h) ð3Þ

where  h_ w is the flywheel control moment. Tc is the control torque of the non momentum exchange actuators (such as thruster and magnetic torque bar). Td is the disturbance torque, which includes disturbances of external space environment and internal devices. Figure 4 shows the Simulink model of attitude dynamics. Attitude kinematics equation is given as follows11 1 qob  A(vbob ) 2 vbob = vbib  Tob (qob )voio q_ ob =

ð4Þ

where qob is the attitude quaternion of body frame with respect to orbit frame.  is the quaternion multiplication. vbob is the angular velocity of body frame with

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Figure 5. Simulink model of attitude kinematics.

respect to orbit frame. A(vbob ) = ½ 0 (vbob )T T . vbib is the angular velocity of body frame with respect to inertia frame. Tob (qob ) is the direction cosine matrix of attitude qob . voio = ½ 0 v0 0 T . v0 is the orbit angular velocity. Figure 5 indicates the Simulink model of attitude kinematics. Attitude controller model. Thruster and three orthogonal fixed reaction flywheels are adopted as the actuator of control cycle. The requirement of attitude controller mainly includes two points. One is the algorithm for work mode determination. The other is control scheme. Figure 6 shows the Simulink model of attitude controller. Attitude determination model. Attitude sensors adopted by attitude determination system include gyroscope, magnetometer, sun sensor, and star tracer. There are many

estimate schemes based on these sensors. In order to design and verify the attitude estimate scheme for convenience, attitude determination model is designed based on modular construction. Figure 7 shows the Simulink model of attitude determination. Each kind of attitude estimate algorithms is a module with specified input and output interfaces. The attitude determination system would recognize the work mode and call the corresponding module. External interface model. External interface model is used to realize communication between simulation target and external devices. In this work, two types of I/O interface are used. The serial port is used to communicate with gyroscope, sun sensor, star tracer, magnetometer, GPS receiver, GPS simulator, and starlight simulator. The CAN is used to communicate with reaction flywheel. Figure 8 shows the Simulink model of serial port.

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Figure 6. Simulink model of attitude controller.

Figure 7. Simulink model of attitude determination.

The pack module transforms the input data into byte array based on data type. The framing mode forms data frames by adding head and tail byte to byte array. The send module sends data frames according to specified port in setting baud rate. The receive module receives data frames from specified port in setting baud rate. The decode module removes the specified head and tail bytes after identifying. The

unpack module transforms the byte array into data in specified data type. Figure 9 shows the Simulink model of CAN. The model includes CAN setup module, CAN send module, CAN receive module, and unpack module. The functions of send module, receive module and unpack model are similar to that of serial port model. The CAN setup module is used to specify the frame type

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Figure 8. Simulink model of serial port.

Figure 9. Simulink model of CAN.

(standard frame or extended frame), baud rate, and ID filter.

Simulation result An experiment of ADCS semi-physical simulation for a sun synchronous micro-satellite is constructed based on the platform described in section ‘‘ADCS semi-physical simulation system design.’’ The aim of the microsatellite control system is to control the attitude of body frame with respect to orbit frame. The satellite is first in rate damping mode after starting. The gyroscope powers on and measures the angular velocity, and then the controller will reduce the angular velocity magnitude less than 0:28 =s through thruster. The mode switching flowchart of the micro-satellite is indicated in Figure 10. The performance parameters of the actuators and the sensors used in the simulation platform are given. The drift of the gyroscope is 0:258 =h. The measurement errors of the sun sensor, star tracer, magnetometer, and GPS receiver are 0:058 , 399, 100 nT, and 5 m, respectively. The maximum speed and the maximum torque of the reaction flywheel are 6000 r/min and 50 mN, respectively.

Simulation parameter           





Simulation time: 650 s; Simulation step time: 0.02 s; Frequency of control: 2 Hz; Frequency of attitude refresh: 10 Hz; Orbit velocity: 0.0011 rad/s; Minimum on-time for a thruster: 50 ms; Force of a thruster: 50 mN; Initial value of mode: ½ 0:002 0:002 0:002 ; Initial value of attitude: ½ 0:05 0:03 0:05 rad; Initial value of velocity: ½ 0:03 0:03 0:03 rad=s; Satellite inertial matrix: 2 3 5:5 0:0614 0:0218 4 0:0614 6:14 0:0218 5kg m2 ; 0:0218 0:0218 2:18 Frequency matrix of solar 2 3sail vibration mode: 3:8055 0 0 4 0 5:2995 0 5; 0 0 4:8173 2 3 0:08 0 0 Damping matrix: 4 0 0:08 0 5; 0 0 0:08

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Figure 10. Flowchart of mode switching.

Figure 11. Attitude (numerical simulation).

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Figure 12. Velocity (numerical simulation).

Figure 13. Attitude (semi-physical simulation).

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0:8443 Couple matrix: 4 0 0:0311

0 0:1222 0

3 0 0 5. 0:8233

Simulation figure To validate the availability of the semi-physical system proposed in section ‘‘ADCS semi-physical simulation

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Figure 14. Velocity (semi-physical simulation).

system design,’’ the Simulink models of attitude control cycle for micro-satellite are all established and simulated in Simulink, named numerical simulation. The results of the numerical simulation are compared with that of semi-physical simulation. Figures 11 and 12 show the curve of three-axes attitude and angular velocity of body frame with respect to inertia frame (results of numerical simulation). Figures 13 and 14 show the results of semi-physical simulation, which are almost the same as the results of numerical simulation. It is distinct that the time that satellite stays in solar capture mode of semi-physical simulation is longer than that of the numerical simulation and attitude control precision of semi-physical simulation is lower than that of the numerical simulation. The cause is that the errors of the actual devices are different from the noise models simulated in Simulink. Thus, the semiphysical simulation system is available and the availability and rationality of attitude control scheme for satellite can be demonstrated through the designed ADCS semiphysical simulation system.

Conclusion A semi-physical simulation platform used for the ADCS is described. Based on the simulation platform, a type of ADCS simulation system is designed and realized. Except the thruster, the instruments for the ADCS are linked with the simulation target to simulate the attitude control cycle. The Simulink models of the satellite dynamics are described in detail and formulated. The formulated models are generated to executable programs of attitude control cycle automatically.

On this condition, a simulation example for sunsynchronization micro-satellite is constructed. The results of the semi-physical simulation are similar to the numerical simulation except time consumptions in many flying modes. It can be drawn out that the semiphysical simulation platform is available. Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported, in part, by the National Natural Science Foundation of China (grant nos 61374211, 61473022, and 61503015) and the China Postdoctoral Science Foundation (grant no. 2015M580961).

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