Energy Management Simulation

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Energy Management Simulation Powered By Docstoc
					A New Energy Management
       Strategy for
   IPACS of Spacecrafts
                                   W. ZHANG[1]
    Beijing Univ. of Aerospace and Astronautics, Beijing, P.R.China, 100083
                                        and
                                    J.ZHANG[2]
           Beijing Institute of Technology, Beijing, P.R.China, 100081

   [1] Graduate Student, School of Astronautics, Beijing Univ. of Aerospace and
                             Astronautics, 100083.
 [2] Associate Professor, School of Mechatronics Engineering, Beijing Institute of
                              Technology, 100081

                       Email:     zhangjingrui@bit.edu.cn
IPACS: Integrated Power and Attitude Control System
Energy System for Normal Satellites

                                  electricity
 During Sunlight




                   Solar Arrays                       Fly Wheels             Attitude
                                                                             Control
                                        electricity
                          electricity
                                                      Devices Installed on
                                                           Satellite
                    Batteries
 Earth’s Shadow




                                                      Devices Installed on
                                                           Satellite

                     Batteries
                                                       Fly Wheels              Attitude
                                                                               Control
            Several disadvantage of chemical batteries:


  low energy desity,large mass(except Li-ion battery)
  limited charge-discharge cycles(Li-ion battery <10000 times, other
chemical batteries about 25000-30000 times)
  little depth of discharge, normally 20~40%;



                     Lead to the position of IPACS
 IPACS can accomplish the energy storage and the attitude control
 simultaneously by using Flywheels / Variable speed control moment gyros
 IPACS has advantages in energy storage than chemical batteries
The work before ---- without the limitation of power,
In fact           the power provided by the solar arrays is limited,
                  the power of flywheel’s motor is also limited.

Energy stored = the energy consumed, i.e. it requires to arrive the energy balance.
Ref.[8] proposed a simple energy management strategy.
       assumed that the power provided by solar arrays was constant.
              just out of the shadow
the solar array --------------------lower temperature, the provided power is larger.
the rotation speed of flywheels/rotors--------lower,
                                              store the energy with a higher
speed.
With the temperature rising
the power (by the solar arrays) reduced step-by-step and tended to a constant.

        constant power assumption           lose a part of energy


   So it is necessary to further discuss the energy management
A spacecraft equipped with 4 flywheels (3 orthogonal +1 skew)

• A Lyapunov-typed controller of IPACS is designed.

• A control law to accomplish simultaneously the attitude control / energy storage.

• A new strategy of energy management is proposed with considering limitations

A simulation example illustrates the validity of the designed IPACS.
    Dynamics of Spacecraft

                     Iω  ω Iω  3ω 0 C  IC  U  D
                                     2




      I 11   I 12     I 13        1         0       3   2           d1       u1 
                                                                                         
I   I 21
             I 22     I 23 , ω   2 , ω    3
                                                      0       1 , D  d 2  U  u 2 
                                                                             
     I                I 33        3          2   1      0         d 3         u 3 
                                                                                           
   ,  31                                                               
              I 32


    ,
     c1   sin  2 cos 3                                   0           c3      c2 
C  c 2   cos 1 sin  2 sin  3  sin  1 cos 2 , C    c3
                                                                         0       c1 
                                                                                          
    c 3   sin  1 sin  2 sin  3  cos 1 cos 2 
                                                            c 2
                                                                             c1      0  
 I 11 
           ( I 3  I 2 ) 2 3   u1    ( I 3  I 2 ) c 2 c 3   d 1 
 I      ( I  I )    u   3 2  ( I  I )c c   d 
     
 2 2       1 3 1 3   2              0      1    3    1 3      2
 I 3 3 
          ( I 2  I 1 )1 2  u 3 
                                         ( I 2  I 1 )c1c 2   d 3 
                                                                    

The kinematics of the spacecraft

              cos 3        sin  3        sin 1 sin  2           
1  
                     1            2                   0        
               cos 2        cos 2            cos 2
                                                                 
 2             sin  31  cos 3 2  cos1 0                 
 3   sin  2 cos 3
                             sin  2 sin  3              sin 1    
                    1                    2  3           0 
            cos 2               cos 2                   cos 2 
The Controller Design Approach
Theorem: If the following control laws are used
           k11
   u1                         
                  ( I 3  I1 ) 03  30( I 3  I 2 )c2 c3  d1
                                        2

          1  12
                1 cos 3                 sin  2 cos 3
                           2 sin  3  3
                 cos 2                      cos 2
         k 2( 2   0 )                                              0
         1 (   )2        3 0 ( I 1  I 3 )c1c3  d 2  c0 
                                   2
                                                                               [-c 0  c 4 ] ,
                                                                   ( 2   0 )
                 2     0

         if  2   0   ,
        
   u2  
         k 2( 2   0 )                                         sgn  2   0 )
                                                                        (
                           3 0 ( I 1  I 3 )c1c3  d 2  c 0  0
                                2
                                                                                    [-c0  c 4 ] ,
        1 ( 2   0 )
                         2
                                                                         
         if    ≤ ,
                2     0



         k 3 3
   u3            3 0 ( I 2  I 1 )c 2 c1  d 3   3
                      2

        1   32
 With
               1 sin  3                 3 sin  2 sin  3
        c0                2 cos 3 
                cos 2                         cos 2
                 sin 1 sin  2                3 sin 1
        c 4  1                  2 cos1 
                    cos 2                     cos 2

the system is Lyapunov stable, where k1 , k2 , k3, ε are the constant parameters.
                  ,




  Proof: Omitted
Control Law of the Flywheels
        Tcx  u1   2 h z   3 h y 
                                         
   Tc  Tcy   u 2   3 h x   1 h z 
         
        Tcz  u 3   1 h y   2 h x 
                                       
   where hx , h y , hz is the angular momentum produced by the flywheels
                       on the three axes of the spacecraft respectively


                 
   Tc  Cw JΩCr Ω

        Ω  Ω1 Ω2          Ω3 Ω 4 
                                        T
        
        Ω  C r (C r C r ) 1 Tc  S 1 q
              T        T
                                                                       (9)



        S 1  E n  Cr (C r C r ) 1 C r
                     T        T
                                           with an identity matrix En (here n=4)



In fact, S1 is the project matrix of Ν (C r ) , so S 1q lies in the null space of matrix C r , i.e.

 S 1 q does not produce the torque.
To design an IPACS, the flywheels should
provide the control torque and store the energy simultaneously

      1 T
   E  Ω JΩ
      2

                         
   P(t )  (JΩ) T Ω  h T Ω                                             (12)
One can choose the vector q so that the power equation is satisfied.
Substituting Eq.(9) into Eq.(12) yields

                                                    T 1
  h S1q  Pf (t )  P(t )  h C (Cr C ) Tc
    T                                 T   T
                                          r         r




                              1
  q  S1h(h S1h) Pf (t )
                    T


                                       T 1
  Pc (t )  h C (C r C ) Tc
                    T     T
                          r            r
Energy Management
In the works before it was assumed that the solar arrays
provided a constant power during the sunlight period
just enters into the sunlight period----the plane of the array is cold
                      the efficiency of power conversion is rising;
along with the rising of arrays’ temperature---- the efficiency is decreasing;
About 6 minutes after leaving the eclipse area---- drops until P0.

If the power provided by the solar arrays is assumed as the constant,
it may lose the energy more than 5%

Assuming that the power is presented as follows during the sunlight period:

 Ps (t )  P0 (1  1.6(t   1) exp( t  ))
Ps(t) is the power provided to the flywheels by the solar arrays;
t is the running time of the spacecraft on the obit;
 and  are two constants.
The stored power should be restrained since the angular velocity of the
flywheels is limited (e.g. by the intensity of the material) and the angular
acceleration of the flywheels is restricted by the input power
Assume that P (t )  P when the spacecraft just enters the sunlight area, and after a while P (t )  P
                s     m ax                                                                        s   m ax



one can use the energy management strategy as follows:

             
             
              Pm ax ,                               if max(  i )   r , Pm ax  Ps (t )
                                                              i
     P(t )   Ps (t ) ,                              if max(  i )   r , Ps (t )  Pm ax
             
                                                             i

                         m ax  max(  i )
              Pc (t )                      [ Ps (t )  Pc (t )], if  r  max(  i )   m ax
                                   i

                            m ax   r                                     i




     Here, Pmax is the allowed maximum input power of the flywheels;
     Pc(t) is practical resumed power required by attitude control;
     P(t) is the practical stored power by the flywheels
     r is a designed rotating speed which should be close to max
             and leave a certain range for the attitude control
                               Simulation Results

Consider the parameters and the initial condition of the spacecraft as

       1054.94    0       0 
     I 0
               3015.73    0  kg  m 2
                               
                                               0 =0.0011 rad/s
        0
                  0    3041.75
                               
                                               =1.1,
     1 (0)  0.7
      (0)  1.5  deg                      =0.38,
      2   
      3 (0)  1.5 
                                           P0=1000 W,

     1 (0)  0.1                           Pmax=2500 W
      (0)  0.1 deg / s
      2   
     3 (0)  0.1
              
the flywheels have the configuration of 3 orthogonal + 1 skew,
with the parameter r = 45000 rpm , max = 50000 rpm, and


      0.0438    0      0      0                              1 0 0   3 / 3
       0     0.0438    0      0                                           
   J                             kg  m 2             C w  0 1 0   3 / 3
       0        0   0.0438    0 
                                                             0 0 1   3 / 3
       0        0      0   0.0438                                         


The environment torque considered as disturb can be presented:

     w1   0.2  0.1sin 0 t  0.05 sin 20 t 
     w   0.4  0.2 sin  t  0.05 sin 2 t  10-3
     2                   0               0 

     w3   0.1  0.1sin 0 t  0.05 sin 20 t 
                                             
       The simulation results of IPACS for a spacecraft during four orbital periods are
       shown in Fig.1-Fig.6, which is carried out based on Eqs.(3)(4)(12)(17)

                                                                                                           -3
                                                                                                       x 10
         0.09                                                                                     2
                          2
         0.08
                                                                                              1.5
                                                                                     1, 2, 3        /
1,2,3 0.07                                                                        rad/s        1
/rad
         0.06
                           3                                                                                   1
                                                                                                                           3
                                                                                              0.5
         0.05

         0.04                                                                                     0
                                                                                                                                           2
         0.03
                               1                                                            -0.5
         0.02
                                                                                                  -1
         0.01

           0                                                                                 -1.5

        -0.01                                                                                     -2
                0   100   200       300   400 t/s
                                                500   600   700   800   900   1000                     0      100    200        300   400 500
                                                                                                                                        t/s     600   700   800   900   1000



                    Fig.1 History of attitude angles                                         Fig.2 History of attitude angular velocities
                                                                                                                4
                                                                                                             x 10
         0.35                                                                                           6

                                                                                                1,2,3,
             0.3              u2                                                                         4
u1,u2,u3 /                                                                                      4 / r/min
N                                                                                                                                       3
         0.25                                                                                           2                      2
                                                                                                                    1
             0.2                                                                                        0
                       u1
         0.15                  u3
                                                                                                       -2
                                                                                                                                         4
             0.1                                                                                       -4

         0.05                                                                                          -6

              0
                                                                                                       -8

         -0.05
                   0    100        200   300   400         500   600   700   800   900   1000         -10
                                                     t/s                                                    0            0.5    t/s 1        1.5   2      2.5
                                                                                                                                                          4
                                                                                                                                                       x 10
               Fig.3 Attitude control torques                                                           Fig.4 Angular momentums of 4 flywheels
      2500                                      2600

                                                                                                           3000
                                                2400


                                                2200



      2000                                      2000


                                                1800
                                                                                                           2800
                                                                                                                              3000
                                                1600


                                                                                                                              2800
      1500
                                                1400
                                                                                                           2600
                                                1200                                               Ps /W                      2600
                                                1000
                                                       0   100   200   300   400   500   600


                                                                                                           2400               2400
      1000                                                                                                                    2200

P/W                                                                                                        2200               2000
       500                                                                                                                    1800

                                                                                                           2000               1600

         0                                                                                                                    1400
                                                                                                           1800               1200

       -500                                                                                                                   1000
                                                                                                           1600                      0   50   100     150   200   250   300   350   400   450    500



      -1000                                                                                                1400

      -1500                                                                                                1200


      -2000                                                                                                1000
                                                                                                                  0   500   1000          1500              2000         2500             3000         3500
              0        0.5        1       1.5                    2                         2.5                                                      t/s
                                t/s                                                            4
                                                                                   x 10

                  Fig.5 Storage power of the flywheels                                                                  Fig.6 Power provided by solar arrays
                                                                                                                        in one orbital period
                     Conclusion
   A Lyapunov-typed controller has been designed for a
    spacecraft with 4 flywheels (3 orthogonal +1 skew)
    This controller keeps in strong nonlinear property of the
    system (not to use the assumption of small angles)
   Presented a control law of the flywheels to accomplish the
    attitude control and energy storage simultaneously
   Aiming at the limitations existed in the power conversion
    characteristic of solar arrays and the input power of motor,
    Proposed a new energy management strategy
               Reduce the size and mass of solar arrays
                    Economize the cost of spacecraft
Thanks

				
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