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V. A. Obukhov et al.
the inclination 0°. SSC moves in an orbit coinciding with that of SDO. SSC is 40 m
behind SDO, 5 m in vertical deflection, and 5 m away from the orbit plane. The SDO
mass is 2000 kg, and SSC initial mass is 1500 kg. The ion beam injector thrust is
50 mN, and the propulsion system comprises two EPTs with 35 mN thrust each.
As an algorithm for controlling the SSC lateral motion, we consider the algorithm of angular deflections of EPS thrust vector direction taking into account the
magnitudes and derivatives of the angles between the transversal and the axes of the
SSC-associated coordinate system being orthogonal to the SSC longitudinal axis [5]
with the parameters k 0 = 0.3, k 1 = 300 s. The value of control angle is limited by
α i ≤ α max = 5
◦ .
The control options with and without taking into account the control algorithm
for the thrust vector longitudinal component are considered. As an algorithm for
controlling the thrust vector longitudinal component, we considered a proportionalderivative controller with parameters k 0D = 0.0001, k 1D = 0.1 s; the average relative
range took the values: 45, 30, and 20 m. We took into account the restriction of the total
momentum relative to the SSC longitudinal axis to ±10 Nm s. When calculating the
momentums produced by EPS relative to the center of the SSC mass, the deflections
of the EPT position from the origin of the SSC-associated coordinate system were
assumed to be 1 m. The amplitudes and phase shifts for the oscillatory component of
the force of IB impact on SDO for the axes OX S , OY S , and OZ S were, respectively:
0.1, 90°; 0.3, 0°; 0.1, –90°. The oscillation periods were equal along all axes and
amounted to 10 min, 1 h, and 3 h. The maximum effective radius was 1.5 m.
10.5.2 Dynamics of Changes in the Relative Range
Projection onto the Transversal
The dependence of the relative range projection onto the transversal most vividly
characterizes the process of the SDO removal from the GEO region. Figure 10.2
shows the simulation results for different parameters of the control algorithms and
different parameters of the simulation model of the IB momentum transfer to SDO.
It is obvious from the graphs in Fig. 10.2 that show the changes in the relative
range projection onto the transversal that the control of only lateral deviations for
the rotation period of 1 h or less is enough to transfer SDO to the disposal orbit.
In this case, the thrust vector longitudinal component is the maximum possible and
the increment in the SDO orbit altitude during 3 days is large enough—of about
90 km. At the same time, with a rotation period of 3 h, the SDO removal becomes
impossible, the SDO acceleration has low value for a long time, and SSC overtakes
SDO.
The use of control for the thrust vector longitudinal component together with the
control for the lateral deviations with an average relative distance of 45 m makes it
possible to maintain a predetermined distance between objects. This is achieved by
reducing the EPS thrust vector longitudinal component through the EPT pivoting.
V. A. Obukhov et al.
the inclination 0°. SSC moves in an orbit coinciding with that of SDO. SSC is 40 m
behind SDO, 5 m in vertical deflection, and 5 m away from the orbit plane. The SDO
mass is 2000 kg, and SSC initial mass is 1500 kg. The ion beam injector thrust is
50 mN, and the propulsion system comprises two EPTs with 35 mN thrust each.
As an algorithm for controlling the SSC lateral motion, we consider the algorithm of angular deflections of EPS thrust vector direction taking into account the
magnitudes and derivatives of the angles between the transversal and the axes of the
SSC-associated coordinate system being orthogonal to the SSC longitudinal axis [5]
with the parameters k 0 = 0.3, k 1 = 300 s. The value of control angle is limited by
α i ≤ α max = 5
◦ .
The control options with and without taking into account the control algorithm
for the thrust vector longitudinal component are considered. As an algorithm for
controlling the thrust vector longitudinal component, we considered a proportionalderivative controller with parameters k 0D = 0.0001, k 1D = 0.1 s; the average relative
range took the values: 45, 30, and 20 m. We took into account the restriction of the total
momentum relative to the SSC longitudinal axis to ±10 Nm s. When calculating the
momentums produced by EPS relative to the center of the SSC mass, the deflections
of the EPT position from the origin of the SSC-associated coordinate system were
assumed to be 1 m. The amplitudes and phase shifts for the oscillatory component of
the force of IB impact on SDO for the axes OX S , OY S , and OZ S were, respectively:
0.1, 90°; 0.3, 0°; 0.1, –90°. The oscillation periods were equal along all axes and
amounted to 10 min, 1 h, and 3 h. The maximum effective radius was 1.5 m.
10.5.2 Dynamics of Changes in the Relative Range
Projection onto the Transversal
The dependence of the relative range projection onto the transversal most vividly
characterizes the process of the SDO removal from the GEO region. Figure 10.2
shows the simulation results for different parameters of the control algorithms and
different parameters of the simulation model of the IB momentum transfer to SDO.
It is obvious from the graphs in Fig. 10.2 that show the changes in the relative
range projection onto the transversal that the control of only lateral deviations for
the rotation period of 1 h or less is enough to transfer SDO to the disposal orbit.
In this case, the thrust vector longitudinal component is the maximum possible and
the increment in the SDO orbit altitude during 3 days is large enough—of about
90 km. At the same time, with a rotation period of 3 h, the SDO removal becomes
impossible, the SDO acceleration has low value for a long time, and SSC overtakes
SDO.
The use of control for the thrust vector longitudinal component together with the
control for the lateral deviations with an average relative distance of 45 m makes it
possible to maintain a predetermined distance between objects. This is achieved by
reducing the EPS thrust vector longitudinal component through the EPT pivoting.