MODELLING A SATELLITE CONTROL SYSTEM SIMULATOR

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1 National nstitute for Space Research NPE Space Mechanics and Control Division DMC São José dos Campos, SP, Brasil MODELLNG A SATELLTE CONTROL SYSTEM SMULATOR Luiz C Gadelha Souza rd nternational Workshop and Advanced School - Spaceflight Dynamics and Control October 8-, University of Beira nterior - Covilhã, Portugal.

2 ntroduction Placing a satellite in orbit is a risky and expensive process. Space Projects must guarantee that satellite and/or its equipments work properly. Attitude Control System ACS should use new control techniques to improve reliability and performance. Experimental validation of new equipment and/or control techniques through simulators prototypes is one way to increase confidence and performance of the system.

3 Types of Simulators Basically, there are two types of simulators: The Planar one, with translational motion in one or two directions The spherical one, with rotation around one, two or three axes. The simulators consist of a platform supported on a plane or a spherical air bearing. The platform can accommodate various satellites components: like sensors, actuators, computers and its respective interface and electronic.

4 Example of Simulators Planar Simulador - Stanford University robotic arm 4

5 Example of Simulators Spherical Simulator - Georgia nstitute of Technology GT 5

6 DMC Lab ativities Brazilian Data Collection Satellite Prototype for experimental verification of its various sub systems 6

7 DMC Lab ativities 7

8 DMC Lab ativities Attitude Maneuvers Software for the China Brasil Earth Remote Sensing Satellite CBERS 8

9 DMC - Simulators DMC is responsible for constructing two simulators to test and implementing satellite ACS. A D simulator with rotation around the vertical axis with gyro as sensor and reaction wheel as actuator. 9

10 DMC - Simulators A D simulator with rotation around three axes, over which is possible to put satellite ACS components like sensors, actuators, computers, batteries and etc.

11 DMC Simulators

12 Objetives This talk presents the development of a D Satellite Attitude Control System Simulator Software Model. This simulator model allows to investigate fundamental aspects of the satellite dynamics and attitude control system.

13 Objetives From the Simulator Model One designs the simulator ACS based on a PD controller with gain obtained by the pole allocation method After that, using recursive least squares method the platform inertia parameters are estimated, considering data from the Simulator model.

14 Objetives Once the recursive least squares method has been checked. One uses it to estimate the D simulator inertia moment having experimental data from gyro and reaction wheel. 4

15 D Platform Equations of Motion The platform angular velocity is given by W pi qj rk w W The total angular moment is the sum of the base and reaction wheels angular moment r cg mg H B r W r dm R RW i R W ρ w i i ρ dm i w w Deriving the previously expression the equation of motion of the platform is given by r cg dh mg h dt r W h h W i r i i hi 5

16 D Platform Equations of Motion The reaction wheels equations of motion are T T T [ w p ] [ w q ] [ w r ] w W The kinematic equations considering Euler angles φ, θ, ψ in the sequence -- are w mg r cg w φ θ ψ p tan θ q cos φ r sin φ sec θ [ q sin φ r cos φ ] [ qsin φ r cos φ ] 6

17 7 [ ] [ ] cos sin cos sin cos cos sin tan sin cos sin sin cos cos cos sin cos cos T T T r q r q r q p mgr mgr p w q w p q pr qr pq mgr mgr p w r w r p qr pq pr mgr mgr q w r w q r pq pr qr w w w r q p y x xy yz xz yy xx z x xz xy yz xx zz z y yz xz xy zz xx zz yz xz yz yy xy xz xy xx φ φ θ φ φ φ φ θ θ θ φ θ θ φ θ φ θ φ ψ θ φ Putting together the previous equations of motion in matrix form yields D Platform Equations of Motion D Platform Equations of Motion

18 8 Control Law Design Control Law Design T T T r q p r q p zz yy xx ψ θ φ ψ θ φ CX Y Bu AX X u X The control gains are obtained applying the pole allocation method To design the control law, one needs the linear system. therefore, assuming small angles the equations of motion for designing purpose are

19 Simulation Results TABLE Typical Platform data used in the simulations Platform Platform Reaction wheel External torque xx. xy..5 Mgr x. yy. xz -..5 Mgr y.5 zz. yz..5 Mgr z.755 9

20 Simulation Results Using pole allocation method, one has defined three sets of poles p,,, in order to analyze the dynamic behavior of the system. p p p {.5 i.5 i. i. i. i. i} {. i. i.5. i.5. i.5. i.5. i} { } The first set of poles p is closer to the imaginary axis than the second set p and the third set p has only real part

21 Simulation Results 5 Simulacao nao linear p x t polos polos polos 5 velocidadedeg/s 5 5 Figures show the angular velocity p, q and r of the platform for the three set of poles p, p and p. velocidadedeg/s t s Simulacao nao linear q x t polos polos polos t s 8 7 Simulacao nao linear r x t polos polos polos 6 5 velocidadedeg/s t s

22 Simulation Results 5 Simulacao nao linear phi x t polos polos polos 5 angulodeg Figures show the angles φ, θ, ψ of the platform for the three set of poles p, p and p. angulodeg t s Simulacao nao linear theta x t polos polos polos t s Simulacao nao linear psi x t polos polos polos - angulodeg t s

23 Simulation Results 4 Simulacao nao linear w x t polos polos polos velocidaderpm - Figures show the reaction wheel rotation ω, ω, ω for the three set of poles p, p and p. velocidaderpm t s Simulacao nao linear w x t polos polos polos t s Simulacao nao linear w x t polos polos polos - -4 velocidaderpm t s

24 Simulation Results Simulacao nao linear T x t polos polos polos - torquen.m Figures show the torques T,, applied by reaction wheel for the three set of poles p, p and p. torquen.m t s Simulacao nao linear T x t polos polos polos t s 5 Simulacao nao linear T x t polos polos polos torquen.m t s 4

25 Comments : Dynamics and Control The first set of poles red line have the undesirable low damping rate associated with great oscillation. The third set of poles blue line although it shows short time for damping the overshoots reach great values. The second set of poles green line, reduce the angular velocities and angles in short time, with small overshoot and the reaction wheels rotation are in acceptable levels. n the sequel the D platform model with the control law designed with the second set of poles are used to generated data to estimate the platform inertia parameters. 5

26 6 Parameters Estimation Parameters Estimation [ ]{ } { } Y X G [ ] G G G G { } Y Y Y Y n the estimation process the vector X has the inertia parameters and the location of the platform gravity center. The matrix G and vector Y contain angles, angular velocities, sensor measures and reaction wheels inertia which are known.

27 7 Parameters Estimation Parameters Estimation [ ] [ ][ ] { } [ ][ ] { } Y G P X G G P T T [ ] [ ][ ] [ ] [ ][ ][ ] [ ] [ ] [ ][ ] [ ] { } { } [ ] { } [ ]{ } T T X G Y L X X P G L P G P G G P L The recursive form of the least square method needs to satisfy the following equations :

28 8 Parameters Estimation Parameters Estimation [ ] T sin sin sin sin rq p p r p q r r p q pq r r q q p rq p rp q r pr rq pq q rq q p r p p G cos coscos cos cos cos θ θ φ θ θ φ θ φ θ φ { } wp w q w w p wr w wq wr w Y yz xz xy zz yy xx z y x mgr mgr mgr X,,,,,,,, The matrices G, Y and X are given by

29 Parameters Estimation The parameters are estimated with measures that have been done in time interval of 5s for simulation of s. The results are shown in the next Figures 9

30 Parameters Estimation 5 x 8 Mimimos quadrados recursivo 4 xx yy zz inercia kg.m t s Platform principal inertia moments estimation

31 Parameters Estimation 5 x 8 Mimimos quadrados recursivo 4 xy yz xz inercia kg.m t s Platform cross inertia moments estimation

32 Parameters Estimation 5 x 8 Mimimos quadrados recursivo 4 mgrx mgry mgrz Força x braço N.m t s External torque estimation

33 Comments : Parameters Estimation From the previous result, one observes that the recursive least square method is reliable. Therefore, it will be used to estimate the D simulator inertia parameter from experimental data.

34 nertia estimation - D Platform The previous recursive procedure is applied considering the simplification of the D equation of motion for rotation around the vertical axis which is given by r zz w J [ r ]{ } { Jw } zz [ G ]{ X } { Y} mg W r cg z x y w y z x Z X Y Where the experimental data come from gyros and reaction wheel. 4

35 nertia estimation - D Platform The equipments used to perform the experiments are : The air baring platform diameters : 65mm Sunspace reaction wheel Angular rotation : -/ 4 rpm Maximum torque : 5mNm Maximum angular moment :.65Nms nertia moment :.5E- gm.m Voltage : Vdc Sunspace Fiber Optics Gyroscope Field of measure : -/ 8º/s Freeware Radio-Modem ; MHz Rate : bps with RS- protocol Battery : Vdc National nstruments PC.6GHz nterface : RS-/RS-485 5

36 Experiment Procedure One stars with both angular velocities of the platform and reaction wheel equal to zero. Then one sends a commander to the reaction wheel so that it increases its angular velocity up to a certain value. That action makes the platform to move with opposite angular velocity. After that, one sends a commander to decrease the reaction wheel angular velocity up to zero. Again the platform will react with angular motion in opposite direction. During that process the platform is monitored by the gyroscope and the reaction wheel angular velocity is also measured. t is important to say that the platform friction has been neglected. 6

37 Experiment Procedure The reaction wheel angular velocity 7

38 Experiment Procedure The platform angular velocity 8

39 nertia moment estimation zz.495 gm.m 9

40 Summary This talk presents a mathematical model of a platform that simulates a satellite ACS in -D with three reaction wheels as actuators and three gyros as sensors. A control law based on a PD controller using poles allocation method is designed and its performance is evaluated. That model is used to generated data to estimate the inertia parameters of the platform, using the least square recursive method. The simulations has shown that the recursive method is reliable for the simulator objectives. The D platform inertia moment is estimated using real data using the recursive method. 4

41 National nstitute for Space Research NPE Space Mechanics and Control Division DMC São José dos Campos, SP, Brasil MODELLNG A SATELLTE CONTROL SYSTEM SMULATOR Luiz C Gadelha Souza Thank you! rd nternational Workshop and Advanced School - Spaceflight Dynamics and Control October 8-, University of Beira nterior - Covilhã, Portugal. 4

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