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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 11 ( 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 31 cos 3 2 cos1 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 k11 u1 ( I 3 I1 ) 03 30( 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 cos1 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 JΩCr 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 20 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 20 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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posted: | 1/31/2011 |

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