Figure 1 : Transition from a high circular geostationary orbit to a low circular orbit for AOTV
The purpose of this study consists in analysing guidance and control methods for space vehicles during the atmospheric phases of change of orbit. The analysis will be based on the definition of a moderate Lift/Drag ratio vehicle carrying out AOTV (aero-assisted orbit transfer vehicle) type missions. An orbit change from a high circular geostationary orbit to a low circular orbit having an altitude of 400 km and an inclination of 28.5 deg will be analysed.
The main objective of entry into the atmosphere during AOTV manoeuvre is to dissipate the substantial initial orbital energy. This energy loss is effected by reducing the speed of the spacecraft through the action of aerodynamic forces that will act on it during the atmospheric phase. In an orbital-change type mission, the global objective is to reach a low circular recovery orbit characterised by a given orbital energy. The atmospheric phase must therefore be adjusted so that the vehicle is in an energy state that corresponds to the final desired orbit.
Through the use of flexible guidance and control methods, this objective is reached by commanding to the spacecraft the attitude it must adopt when it meets the atmosphere, so as to control the aerodynamic forces that will reduce its energy.
The transition from a high circular geostationary orbit to a low circular orbit for vehicles of the AOTV type is divided into several phases:
Figure 1 : Transition from a high circular geostationary orbit to a low circular orbit for AOTV
An algorithm of Near Optimal Guidance (NOG) has been studied, based on
considerations of NLP (Non Linear Programming) and of cost
function. This tool, which enables reference trajectories to be
created. This law of NOG will be considered as a self-adaptable
guidance technique, such as following guidance techniques :
The main objective of the guidance laws is to fulfil the mission in terms of the apogee by controlling the aerodynamic forces acting in the orbital plane: this mission will be quantified by the impulse DV1 to be applied to the spacecraft at atmosphere exit. The mission is successful when DV1 = 0.
Disturbances occurring during flight, relating to uncertainties of modeling and to ambient conditions, such as winds, atmospheric density variations, and uncertainties on vehicle data, together with uncertainty on the state-vector of the spacecraft will impair success of the mission insofar as the guidance laws will no longer satisfy DV1 =0.
Figure 2 : The vertical guidance logic is based on the control of the aerodynamic forces in the orbital plane.
It is therefore imperative to define an interval [ -DV1 acc ; DV1 acc ] acceptable in terms of the mission, such that the value of DV1 acc may be considered as being close to zero, knowing that the orders of magnitude for DVd (de-orbiting pulse) and DV11 (circularisation pulse) are 1500 and 100 m/s in the case of an orbit change from a high geostationary-type orbit towards a low circular orbit.
DV1 acc = 20 m/s is a criterion of mission-success compatible with the value of DVd, and represents only 1/5 of the value of the circularisation pulse DV11.
The second objective of the guidance laws is to make the final orbit coincide with the initial one, that is to say that the inclination of the orbit and the longitude of the ascending node of the final orbit are identical with those of the initial orbit. This double condition may be reduced to a single condition, that of making zero the value of the wedge angle h that represents the angle between the initial and final orbital planes. Lateral guidance must be capable of ensuring this by controlling the forces acting in a direction perpendicular to the orbital plane.
For h = 0.1 deg, the positional error at the end of the atmospheric phase is of the order of 11 km. This value is to be compared with the uncertainties of knowing the position, which on board navigation can only furnish at best with a 5 km margin.
Thus, for h less than 0.1 deg, the position error is of the same order of magnitude as the uncertainties on knowledge of the position, and, in this case, the final orbit will be considered identical with the initial orbit. The maximum heating rate HRmax along the trajectory does not involve closed-loop control by the algorithm during the atmospheric phase. It thus enables the heating induced by the guidance to be taken into account, but not used in the feedback loop.
The two criteria DV1 and h that permit evaluation of the guidance laws are linked with the trajectory of the mass-centre of the spacecraft. The evolution of the mass-centre depends on the aerodynamic attitude which is determined by the desired angle of attack a, sideslip angle b, and bank angle s. The angle of attack is kept constant for AFE, and determines the lift/drag ratio. The sideslip angle is kept at 0 so as not to create any lateral forces. The lift and drag aerodynamic forces are thus contained in the symmetry plane of the spacecraft.
The bank angle is derived from the guidance laws, it positions the space-craft's vertical axis with reference to the earth's vertical axis, and ensures the mission during the atmospheric phase : DV1 = 0 and h = 0.
The objective of control laws is to ensure that the attitude of the
spacecraft agrees with the attitude dictated by the guidance laws: a =
a0, b = b0 and s = sguidance. A trade-off analysis will be performed
between the different adaptive control techniques :
Control of the spacecraft attitude is obtained by the application of torques with respect to the axes of the spacecraft frame. These torques are supplied by the thrusters, whose mode of operation is of the ON or OFF type. A modulator transforms the continuous torque coming from control into a pulse train for each thruster. The fuel consumption linked to the activity of the thrusters is estimated and will be considered as a criterion allowing qualification of the control laws for a given guidance law.
As a main output of the study, a simulation software has been developed so as to assess the performances of various guidance and control laws.