DE3831563A1 - Device for the desired value control and/or stabilisation of freely moving bodies having stored spin - Google Patents

Abstract

Published without abstract.

Description

The invention is concerned with the improvement of devices to follow up and stabilize freely around their rotational axes of moving bodies, in particular air and spacecraft rotating as a result of one of their Major axes, the so-called swirl axis or as a result of specially built swirl storage devices for this purpose have a non-zero angular momentum or "twist".

The dynamic movement of bodies that are stored To have a twist is known to be subject to the laws of Gyro theory. With free around their rotary axes movable bodies, such as. B. Aircraft and spacecraft a stored swirl causes a particularly strong one Coupling of the rotational movement around the swirl axis main orthogonal axes of the body Movement quantities such as torques, angular speeds and displacements.

Should such a free moving body with the help of a closed loop from an initial position given spatial directions and with respect to them Angular position must be stabilized, so the regulatory laws that are supposed to accomplish this, all the more so take into account more, the weaker the for Stabilizing torques available in relation to the stabilization Gyro couplings are. Are z. B. for the sake of Saving of discrete, roughly pulse-shaped energy saving Adjustments made, such as when using Reaction nozzles are often the case in spacecraft, so becomes more continuous instead of the precession movement Torque is an often undesirable nutation movement fanned.

Additional problems occur with setpoint control and Stabilization of such vehicles based on their spatial  Extent, their slenderness and / or their light, weight-saving design due to the presence weakly damped structural vibrations and danger of them Excitation through pulsed control interventions.

Flexible, freely movable body of the considered Kind, especially satellites moving in earth orbits generally consist of a swirl generating, rotating part, or one of its effects in Principle equivalent swirl storage device, such as. B. a reaction flywheel and a non-rotating one Part, such as a swirled platform or the satellite central body itself. This non-rotating part is supposed to with one of its body axes orthogonal to the swirl axis always be aligned as precisely as possible with the earth, because it mission-related, e.g. B. via transmitting and receiving devices, continuous communications between different Points of the earth. Now moves such a body in its orbit around the earth, must the swirled part carrying the payload pro Rotation once around an axis pointing perpendicular to the path plane turn, which is why such vehicles also as "dual spinner" be designated.

From the relationships described it is evident that at least three different types of periodic, practically undamped oscillation processes occur in such bodies, which must be mastered by the control system. These are the movements of the vehicle's own twist vector relative to the rail normal caused by orbit and earth orientation, the direction of which coincides with the orbital twist and also determines the average orientation of the vehicle axis directed towards the earth. This movement, whose oscillation period (1 / W ₀) is given by the orbital period, is therefore also called orbital movement. This is superimposed on the nutation movement, ie the movement of the body with respect to its own twist axis direction, the period (1 / W _N ) of which depends on the size of the stored twist and the transverse axis moments of inertia of the body. In addition, there are one or two groups of weakly damped vibrations, such as structural vibrations, the influence and frequency of which depends on the geometric, mass and elastic properties of the structural components used, or movements of liquids such as fuels carried in predominantly spherical and / or cylindrical containers, the waveforms of which depend on the tank geometry and liquid properties such as viscosity and surface tension. All of these vibrations are linked to one another via their interaction with the vehicle and the swirl coupling between the vehicle axles.

Should such a vehicle with its three, in general orthogonal axes with respect to each other Spatial directions stabilized, or during its orbit with one of these three axes of the earth, so is generally also the measurement of all deviations Vehicle axes from the desired spatial directions with the help suitable sensors are required, preferably earth and sun but also bright stars are used as reference objects will. To create a three-axis reference for the vehicle orientation are usually two reference objects necessary, with the vehicle orientation for each of the objects with respect to two, to each other and to the connecting line orthogonal directions can be measured. At Vehicles that are in orbit around the world can use the earth as a reference object continuously z. B. by means of infrared sensors or RF sensors always show the deviations of one vehicle axis directed towards earth in two to each other perpendicular directions, d. H. thus derived two measured values will. The required third reference direction can be from the sun as a reference object z. B. by means of sun sensors  with the exception of such positions of the Vehicle in its earth's orbit, in which sun, earth and satellite lie on a line, d. H. the two as Reference spatial directions coincide. In the Practice has therefore long been an endeavor swirling body to keep its direction in space exploited to stabilize satellites and spacecraft. In particular, it is possible depending on the size of the stored swirls over more or less long periods of time, with two-axis reference d. H. Earth alone as a reference object get along for the position measurement. The movement one by one The swirl vector of the vehicle axis lying in parallel becomes usually by accelerating or decelerating the Swirl storage device opposite the untwisted part of the Vehicle based on the measured by an infrared sensor East / west deviation of the vehicle axis pointing to earth accomplished within the railway level and should not here be considered in more detail.

For tracking or stabilizing both to the swirl axis orthogonal vehicle axles by means of just another one Deviations of the vehicle axis pointing to the center of the earth further measuring signal perpendicular to the path plane now consciously the gyro coupling between the transverse axes exploited. Related, known control devices usually exist next to the measuring element, e.g. B. one Infrared sensor from a suitable controller network and one Modulator, the pulse-shaped control signals for actuators, especially reaction nozzles generated, which are arranged are that they are not just moments related to one regulating vehicle axis but also torque components at the same time opposite sign to that Generate orthogonal vehicle transverse axis. As a controller or Modulators usually come with simple low pass filters or 1st order lead elements in connection with pseudo rate (PR) or pulse, wide pulse frequency (PWPF) modulators for Application. In addition, such control devices must be included be equipped with a nutation damping device  ensures that by successive, each at Triggered pulses not reached when a response threshold is reached Rocking of the nutation vibrations or limit cycle vibrations can occur. Said nutation damping devices are based on the so-called posicast principle, that means that undamped, periodic processes per se as stabilized in this case the nutation can be that a first discrete Control intervention after a fixed time, preferably in Range from ⅜ to half a period of the periodic Process with the same sign and energy content is repeated.

In spin-stabilized satellites, which are due to the Self rotation of the vehicle main body by a special high stored twist are usually additional from the regulation of the main axis directions of the untwisted part of the vehicle, especially for nutation damping serving control loops used with their own Sensors, e.g. B. accelerometers to control the in this case rotating with the rotating vehicle part Reaction nozzles are equipped. To align the vehicle axles with respect to the earth, in particular the direction of the swirl axis In this case, commands are usually used in the room sent from earth to the vehicle, its execution on board triggered by (position) sensor-controlled logic circuits becomes.

The known devices have a number in practice serious disadvantages. First one works Regulation of the type mentioned is far from optimal, which the Concerning expenditure on actuating energy. This fact lies is based on the fact that control interventions are then triggered if the measured filing from the target direction just reached an allowable threshold regardless on whether the control intervention with respect to the nutation movement at a favorable or just unfavorable, d. H. the nutation movement magnifying point of time. this leads to  not only to ensure stability compared to bilateral limit cycles, the threshold values for the Triggers intervention relatively large, d. H. at least equal to the maximum generated by an actuating pulse Diameter of the nutation cone must be chosen what the accuracy of the tracking of the axis to be controlled adversely affected, but it's also effectiveness the subsequent nutation damping is accordingly uncertain and the randomness of the trigger moment of the first Intervention dependent. This area of uncertainty will magnified by the inevitable fluctuations system-related parameters such as B. the actually delivered "effective" control impulse by approx. 20%, swirl fluctuations in the permissible operating range of usually ± 10%, Fluctuations in moments of inertia, measurement noise and the like. But above all, the well-known facilities not suitable, at the same time the stability of additional, weakly damped vibration processes such as structural vibrations and ensure fuel movements, especially if their frequencies do not differ sufficiently from the nutation vibrations distinguish or their coupling to the Vehicle is not weak enough, so that a mutual Influencing would be excluded. Because of the weak Self-damping of the said vibration processes is one Excitation possible even via subharmonic manipulation. In other cases, such as so-called spin-stabilized or spin-stabilized satellites because of the high swirl the nutation frequency in dangerous Proximity of the vibration range of the elastic deformations. Another disadvantage of the aforementioned known devices can be seen in the fact that the control accuracy regarding the second, only stabilized indirectly via the swirl coupling second transverse axis of the vehicle is often not the posed Meets requirements. Your deviation from the The desired angular position is determined almost exclusively by the size of the stored twist that is around this axis  acting external disturbance torque and by the size of the order first, directly controlled vehicle axle approved and off the stability reasons explained above are not arbitrary reducible control error.

The aim of the present invention is now to Devices for setpoint control and vibration stabilization one freely movable around its rotary axes, twisty, elastic body, in particular Aircraft and spacecraft with respect to two, transverse to the swirl axis lying body axes by means of one or more that Deviations of the first and / or second transverse axis from theirs Position sensors, controllers and one measuring target directions or several to both transverse axes positioning forces and / or To create torque generating actuators, which the avoid the disadvantages mentioned, d. H. better utilization ensure the stability of vibration processes elastic structures or moving liquids ensure and a greater control accuracy of the Allow angular movement around both transverse axes.

According to a first embodiment of the invention, this becomes achieved in that the control signal for setpoint control with respect to a first transverse axis, for stabilization with respect to a second transverse axis and for simultaneous vibration damping around both axes from a uniaxial measuring Position sensor can be obtained by means of a controller, the Transfer function has a three-order higher denominator than its counter. According to the invention is unnecessary thereby the effort for an additional nutation damping logic and in addition to saving on the energy in the known devices of this type inevitable nutation damping pulses stability all vibrations occurring in elastic vehicles ensured.  

According to a second, differently designed embodiment of the invention, not only is a saving in positioning energy and stability of structural-dynamic oscillation processes ensured, but also a considerable improvement in the control accuracy with respect to two vehicle axles orthogonal to the swirl axis, even when only a single-axis position sensor is used for the transverse axis control. This control device according to the invention is characterized in that a signal component ( Φ ₀) representative of the path movement and a signal component ( Φ _N ) representative of the nutation movement can be obtained from the measurement signal for the deviation of a first transverse axis via a first controller network, both of which in a nutation can be linked together such that the logical choice is determined by means of the first, the web motion representative signal component (Φ ₀) after passing through a spin regulator, a dead-zone, and a modulator network about the need to sign and duration of an adjustment operation, and with the aid of the second , the signal component representing the nutation movement ( Φ _N ) after signal processing in a differentiator, a nutation observer and an amplitude / phase converter, the point in time for the control intervention can be determined within a nutation period. In further, extremely advantageous refinements of the second inventive concept, additional measured values such as the instantaneous size of the stored swirl and one that is only available temporarily or continuously, eg. B. obtainable via sun sensors, the alignment error of the second transverse axis representing measurement signal both regulated to the swirl axis and mutually orthogonal transverse axes of a swirling body, in particular satellites in an energy-optimal manner and ensuring the stability of all described, weakly damped oscillation processes with the smallest possible error with respect to predetermined target directions.

The control devices according to the invention are intended below for a 3-axis stabilized satellite on geosynchronous Orbit based on the state of the art using Embodiments are explained in more detail. you are but equally for spin-stabilized satellites applicable. It shows:

Fig. 1a, the axis designations and desired orientation of a three-axis stabilized satellite in an equatorial orbit around the earth,

FIG. 1b is a typical and suitable for the present case arrangement of control components in a satellite of FIG. 1a,

Fig. 1c another reasonable arrangement of measuring elements in a satellite of the type mentioned,

Fig. 2 is a block diagram of a control circuit of conventional design,

Fig. 3 is an improved control device according to a first embodiment of the invention,

FIG. 4a is a block diagram of a second, different type of embodiment of the invention,

FIG. 4b is a simplification of the control device according to Fig. 4a for a better realization,

Fig. 4c is a geometric illustration of the phase conditions for an optimum control action per nutation,

Fig. 4d is a geometric illustration of the phase conditions for two optimum control interventions per nutation,

FIG. Enhanced, adaptable 5a the functional diagram to variable system parameters, control device according to the invention,

Fig. 5b shows the functional block diagram of a related by compensating for the observable interference. Their alignment accuracy improved control device.

Fig. 5c another extended embodiment of a device according to Fig. 5b,

FIG. 6a an apparatus for considerable improvement of the alignment accuracy of a second vehicle transverse axis at least temporarily available measurement values with respect to the second transverse axis,

Fig. 6b a further improved embodiment of the invention shown in Fig. 6a Störgrößenschätzung and compensation,

Fig. 6c, 6d, various advantageous embodiments of an apparatus according to the invention according to the principle of Fig. 6b,

Fig. 6e is a geometric illustration of the invention provisions for linking the modulator output signals and the impact of control interventions,

Fig. 7a-7c simulation results of a representation of the axle movements of vehicles of the type considered, the of the invention are equipped with control devices in accordance.

Table 1: A tabular compilation of the regulations for generating control interventions in an embodiment of the invention according to FIG. 5c.

Table 2: A tabular summary of the regulations according to the invention for generating control interventions in devices according to FIGS. 6a-6e.

Simplistic Fig. 1a shows the typical geometric configuration of a three-axis stabilized geosynchronous communications satellite (101) in orbit around the earth (102). The spacecraft ( 101 ) consists of a cube-shaped central body ( 103 ) in which large-area, flexible elastic solar generators ( 104 ) are rotatably mounted and which carries one or more antennas ( 105 ) oriented towards the earth ( 102 ), the radiation direction of which is controlled by the control system of the Spacecraft ( 101 ) to be maintained within predetermined, narrow limits. An axis system x (roll axis), y (pitch axis), z (yaw axis) is assigned to the spacecraft ( 101 ) in such a way that, when the control system functions ideally, the roll axis in the current flight direction, the yaw axis to the center of the earth and the pitch axis in the direction of the path normal shows. Reaction nozzles ( 106, 107 ) which are arranged on different sides and which are only shown schematically and as far as can be seen in this illustration are used to generate torques about this axis. In particular, the reaction nozzles ( 107 ) generating rolling moments are arranged by inclined installation at an angle ( α ) in such a way that when activated, in addition to rolling moments, they simultaneously generate yaw moment components of opposite sign to the rolling moment.

During normal operation of the spacecraft ( 101 ), disturbing torques to which the axis directions of the spacecraft ( 101 ) dissipate from their target position occur primarily due to solar pressure, residual magnetism of the spacecraft in interaction with the earth's magnetic field, and inhomogeneities of the earth's gravitational field ( 102 ) of the control system must be prevented.

FIG. 1b shows also greatly simplified perspective view of a typical arrangement of control engineering components as far as they are related to the present invention is important. These components are usually arranged on the central body ( 103 ) of the spacecraft and, in addition to the predominantly rolling moments ( 107 ) and yawing moment generating reaction nozzles ( 106 ), consist of a swirl storage device, e.g. B. an electro-motor-driven so-called swirl wheel ( 108 ), and position measuring sensors ( 109, 110, 111 ), which deviations of the vehicle axes from their desired direction compared to reference objects such as the earth by an infrared sensor ( 109 ) or the sun by sun sensors ( 110, 111 ) determine. If the z - (yaw) axis of such a spacecraft always remains aligned with the earth, an infrared sensor ( 109 ) with a suitable arrangement provides measurement signals for angular movements about the x - (roll) axis or y - (pitch) axis, of which only the roll angle measurement should be considered in the present case. Angular movements around the yaw axis pointing to the earth can be determined with the help of the sun sensors ( 110 ) pointing in the ± x -axis direction on those sections of an earth orbit in which the sun is in its field of view, which is ± in the sensor fields of view indicated in FIG. 1b 60 ° is the case during 2 × a third of the orbital period. On the other hand, if the sun is in the ± 30 ° wide sectors between the above-mentioned sun sensor facial areas, no yaw information is available in the example according to FIG. 1b. In these areas, however, the quality of a yaw measurement with sun sensors is already considerably restricted and is completely excluded in the area of the collinearity of sun, earth and satellite.

Fig. 1c shows another possible arrangement of measuring elements in a three-axis stabilized satellite in also highly simplified, schematic diagram and a different perspective. In this case, sun sensors ( 112, 113, 114 ) with viewing areas of ± 60 ° around their installation direction are arranged in such a way that they can deliver measured values at any position of the sun around the vehicle. As a result, the sector of unavailable yaw information can be significantly reduced compared to an arrangement according to FIG. 1b, without, however, fundamentally changing anything in the basic geometric restrictions discussed above in the area of the collinearity of the viewing directions to earth and sun.

Fig. 2 shows a basic circuit diagram of a control circuit of conventional design for setpoint control of a first transverse axis orthogonal to the swirl direction, in this case the roll axis and simultaneous stabilization around a second transverse axis, here the yaw axis of such a satellite by means of only one, the deviation ( ε _Φ ) of position sensor ( 202 ) measuring the first transverse axis. The deviation ( e _Φ ) of the first transverse axis direction ( Φ _i ) from its target orientation ( Φ _c ) is determined by a position sensor ( 202 ), the dynamic properties of which are simplified by a first-order delay element with a delay time constant ( T _s ) and a gain factor ( K _s ) are indicated. In general, the dynamics of the measurement process are fast enough, ie the time constant ( T _s ) representing them is small enough that they do not interfere with the control process and can therefore be neglected. In the case of FIG. 2, only a first-order filter ( 203 ) with a time constant ( T _F ) and a gain factor ( K _R K _M ) is provided as the controller network, the output signal of which is a pseudo-rate (PR) - modulator ( 204 ) is supplied, which consists of a summing element ( 205 ), a relay characteristic ( 206 ) and a feedback network ( 207 ) and has the task of converting the controller output signals fed to it into an on average equivalent sequence of correct control pulses for the actuating moments generating reaction nozzles. Instead of delay elements as controller networks in connection with PR modulators, in the known and functionally completely equivalent control devices, lead elements are also used together with pulse-width-pulse-frequency (PWPF) modulators. The modulator output pulses are fed to the reaction nozzles via a nutation damping device which, as already mentioned, repeats each primary actuating pulse emitted by the modulator after ⅜ to ½ the duration of the nutation period with the same sign, provided that no further, primary sense pulses have been emitted by the modulator in the meantime. Functionally, there is such a nutation damping device z. B. as indicated in Fig. 2 from logical OR gates ( 212 ) which in parallel branches each modulator pulse directly and on the other hand via time counters ( 210 ) for the delay time ( T _D ) and individual pulse generators ( 211 ) for generating the nutation damping pulses of predetermined pulse duration ( Δ t) are supplied and their output signals control the valves of the corresponding reaction nozzles ( 213 ) to generate the actuating torques ( T _cx ). The sign separation of the drive pulses generated by the modulator is shown schematically by appropriately polarized diodes ( 208, 209 ). The sum of the actuating torques generated in this way (± t _cx ) - formed in FIG. 2 by a summing element ( 214 ) - acts on the dynamic movement of the satellite about its two transverse axes, which is coupled via the swirl, with a connection in connection with FIG. 1b described oblique installation (angle α ) of the reaction nozzle control interventions ( T _cx ) not only affect the first transverse axis, the roll axis of the satellite, but also moment components of opposite signs (- k , | k | «1) about a second transverse axis, the yaw axis , which causes stabilization of the second transverse axis in a known manner using the swirl coupling. The following applies as a setting rule for the controller parameters of such a coupled roll / yaw control according to the known so-called WHECON principle:

⅜ T _N T _D ½ T _N (1b)

in which:

α - the oblique installation angle of the actuators, which mainly produce rolling moments,
w ₀ - the angular frequency of the period of the vehicle, z. B. 7.27 · 10 ^-5 (1 / sec) for geostationary satellites
T _F - the controller time constant ( Fig. 2)
T _D - the delay time of the nutation damping pulse compared to the primary pulse
T _N = 1 w _N - the nutation period,
H _γ - the stored twist,
I _x , I _x - mean the transverse axis moments of inertia of the vehicle.

It has already been stated elsewhere that a Control loop of the known type described above is able to track movement and at nominal values the system parameters to dampen nutation vibrations requires a great deal of energy for nutation damping, in the event of parameter deviations from their nominal values in its nutation damping behavior becomes largely ineffective and is not suitable, other vibration processes at the same time in the system, e.g. B. originating from structural elasticities and master fuel movements.

Fig. 3 of the invention shows an improved control device according to a first embodiment, the unnecessary by a special structure of the controller transfer function, the need for the installation of an additional Nutationsdämpfungseinrichtung, is characterized by high insensitivity to system-related parameter variations and minimal actuating energy requirement and moreover, the stability of additional weakly damped oscillation processes ensures. According to the detection, this is achieved by a controller network whose transfer function has a degree of the denominator polynomial that is 3 orders higher than its numerator polynomial. In the simplest case, z. B. When using a PR modulator, provide at least one controller of the following form:

When using a PWPF modulator and taking into account at least one of the equivalence conditions already mentioned Controller with the following structure of its transfer function:

In a generally valid, shorter product representation according to FIG. 3, the controller transfer function according to the feature of main claim 1 must have the form:

in which

K _R - the controller gain
w _Fi - the angular frequencies of the ( n + 3) controller poles ( i = 1... n +3)
w _vi - the angular frequencies of the controller zero (s) (i = 1... n) and

In practice, the minimal structures of the controller transfer functions deliver frequently according to equations 2a and 2b damping of the nutation vibration still too low. It recommends therefore the numerator and denominator terms are equal to at least to increase an order.

An increase in the order of the counter polynomials is known to bring also a deterioration in the signal / noise ratio in the control loop with itself. However, they are already non-linear single and double adaptive frequency domain filters have been developed which are characterized by particularly low Phase losses in the pass band and high steepness of waste to the restricted area and in connection with the control devices according to the invention present here in can be combined very advantageously, if this should be required.

Depending on the application, the pole and zero frequencies ( w _vi , w _vi ) can be real and then correspond to the reciprocal values of the controller time constants or conjugate complex in pairs, whereby such pairs can then be combined into transmission elements of the second order with damping coefficients less than 1. This controller structure also contains the special case of an integral controller if one of the pole frequencies is selected to be zero. Since integral controllers generally require special measures when setting their initial conditions, it is then expedient for the implementation of such networks to implement the integral component as a parallel connection. The transformation of the controller transfer functions (equation 2a-2c) by partial fraction decomposition to split off the integral component is familiar to any person skilled in the art. If, according to generally known rules or project-specific requirements, the dynamic conditions and stability conditions require a reserve higher than 1st order (equation 2b), ie additional zeros of the controller transfer function, the denominator must also be expanded by a corresponding number of terms according to the instructions of the invention.

In some cases, especially with spin-stabilized satellites, it can happen that, due to a relatively high nutation frequency, the dominant sensor time constant is no longer negligible but lies in the dynamic range of the controller bandwidth, which then practically equates to an additional pole of the controller transfer function. It is obvious that the position sensor is then to be regarded as a component of the controller transfer function and must also be taken into account when executing the regulation according to the invention. The same considerations apply to the inclusion of the modulator delay ( T _M ) when using PWPF modulators. For the selection of the parameters of the controller according to the invention, the generally applicable and known to the person skilled in the art setting rules for the amplitude and phase balance in the closed control loop must be observed, ie it must be for the transfer function (Y ₀ ( jw)) of the entire open loop including the dynamics of the controlled system

at the so-called crossover frequency ( w _{c 0} ) which is defined by the condition:

| Y ₀ ( jw _{c 0} ) | = 1 (2e)

the phase relationship apply:

arg Z (jw _{c 0} ) - α <arg N (jw _{c 0} ) (2f)

where arg Z , arg N the phase angle of the numerator - (Z) or denominator terms (N) and α mean the inclined mounting angle of the actuator.

For the practically undamped nutation vibration from it with real pole and zero frequencies useful approximation for the controller transfer function Derive simplified condition:

because the steepness of the amplitude / phase curve means that the crossover frequency (w _{c 0} ) and nutation frequency (w _N ) practically coincide. In any case, with a controller structure according to the invention, the demands for follow-up control and stabilization of elastic, swirling bodies can be met in an energy-optimal manner by, depending on the position of the natural frequencies of the body to be controlled, the corresponding undamped or very weakly damped oscillation processes in one of the third Known stability ranges are shifted, in which with circular gain

| Y ₀ ( jw) | 1 (2h)

Stability through phase advance

-180 ° <arg Y₀ (jw) <+ 180 ° (2i)

or by phase delay

-540 ° <arg Y ₀ ( jw) <-180 ° (2k)

is ensured or by reducing the amount condition

| Y ₀ ( jw ) | <1 (2l)

can be fulfilled.  

Device of the type described above in connection with Fig. 3, not only represent a simplification in the implementation by eliminating previously necessary nutation damping devices, but also a significant improvement over the prior art, in particular with regard to point energy consumption and mastery of all vibration problems mentioned. However, they are still subject to considerable restrictions in practical use when it comes to meeting particularly high demands on the alignment accuracy of the body axes lying transversely to the swirl axis, in particular when the control interventions are carried out in a discrete, certain minimum pulse increment that cannot be undercut, such as assumed in the considered examples. It has already been mentioned that when using only one position sensor measuring the deviation of a first transverse axis from its desired direction, the alignment accuracy about a second transverse axis stabilized using the swirl coupling from the tracking error around the first and, given the swirl, above all from the size of the disturbing moments depends on the second transverse axis. In satellites of this type, the typical alignment accuracy around said second transverse axis is 4 to 10 times worse than around the first, directly controlled vehicle axis. The alignment error about the first transverse axis is determined by the effective dead zone provided there and, in order to avoid inadmissible limit cycle vibrations, must always be selected somewhat larger than the diameter of the nutation cone which, under the most unfavorable conditions, by a discrete control intervention, e.g. B. a minimal pulse of the reaction nozzles can occur. This error is also transformed into the second transverse axis as an inevitable inaccuracy via the axis coupling with a certain gain factor.

The present invention has the further task provided devices for improving the alignment accuracy around both transverse axes while already maintaining the described advantages of the invention to create 1st type.  First, a completely different approach is used to solve the task. Below become the advantageous, already described special Regulator structures included in this invention of the 2nd kind. As part of further developments of this further inventive concept will ultimately be under the best possible use more available on board such spacecraft anyway Information, measured values and intervention options, d. H. Alignment accuracy without additional control components around both transverse axes step by step until they are fulfilled highest demands improved.

FIG. 4a shows the basic block diagram showing a control device of said second kind, which according to the invention characterized in that a first transverse axis from its desired direction by a first controller network (401), a representative from the measurement signal for the deviation (e _Φ) for the path movement Signal component ( Φ ₀) and a signal component ( Φ _N ) representative of the nutation movement can be obtained via a second controller network ( 402 ), both of which can be linked together in a nutation controller ( 410 ) in such a way that by means of the first signal component ( Φ ₀) after passing through a swirl controller ( 404 ), a dead zone element ( 405 ) and a modulator network ( 406 ), the logical decision about the need for an intervention, the sign and duration ( Δ t _cx ) of which can be determined and with the help of the second one representing the nutation movement Signal component ( Φ _N ) after signal conditioning in a differentiator ( 407 ) A nutation observer ( 408 ) and an amplitude / phase converter ( 409 ) determine the point in time for the intervention within a nutation period.

Low-pass filters of the 1st to 4th order are used to separate the path movement component ( Φ ₀) in the first controller network ( 401 ). The signal components ( Φ _N ) representative of nutation and higher-frequency movement processes are obtained from the measurement signal via the second controller network ( 402 ) with a high-pass character. It is obvious that for the intended separation of the signal components, the corner frequencies of both networks must lie between the vehicle's orbit frequency and its nutation frequency, and in particular can be chosen to be the same.

As shown in Fig. 4b, it is therefore usually sufficient in practice to implement only the aforementioned first controller network ( 401 ) and the signal component formed above for the path movement of the vehicle in a summing point ( 403 ) from the measurement signal ( ε _Φ ) to form the Subtract nutation vibration signal ( Φ _N ). In separate realization of the controller networks (401, 402), the second network controller (402) may optionally may be undesirable for the suppression, the nutation superimposed higher-frequency signal components are formed as a bandpass. The signal ( Φ ₀) obtained in the first controller network ( 401 ) for the path movement component about the first transverse axis, the roll axis of the vehicle under consideration, is approximately proportional to the angular momentum or swirl component ( H _z ^* ) in the direction of the second vehicle transverse axis, here the yaw axis, with the twist ( H _y ) stored in the vehicle as a proportionality factor.

In the simplest case, the swirl controller ( 404 ) in FIGS . 4a, 4b consists of a dimension-related gain factor. To improve the stability and movement dynamics, however, additional retaining elements, preferably first or second order, or complete or reduced, e.g. B. the estimation of only one swirl component serving, according to known rules of observer theory formed estimation algorithms for one ( H _z ) or both transverse axis components of the vehicle swirl ( H _z , H _x ), or such observers equivalent electrical networks are used. A particularly advantageous combination of the 1st controller network ( 401 ) and swirl controller ( 404 ) is obtained if the features of the controller structure according to the invention of the first type already described are fulfilled for the overall transfer function, ie a 3rd order low-pass filter as the 1st controller network ( 401 ) in conjunction with constants or PD elements as swirl controller ( 404 ). According to a further embodiment of the inventive concept, integral components in the transfer function of the swirl controller ( 404 ) are also suitable. These then form a measure for estimates of constant disturbance torque components, the compensation of which contributes to an increase in accuracy. Disturbance estimation and compensation will be discussed in more detail later.

The equations for a complete observer of the Swirl components are:

in which

w₀ - the frequency of the path movement,
_x , _x  - Estimates for the swirl components (H _e.g. ,H _x ) in the direction of the vehicle's transverse axes (e.g.-, xAxis) transformed into a with the vehicle's center of gravity path co-ordinate system carried along
k₂₀,k₂₁ - gain factors
H _y  - stored vehicle twist
Φ₀ - for the component of the path movement around the first vehicle transverse axis (roll axis) representative measurement signal component
T _cz ,T _cx  - Torques
T _Dz ,T _Dx  - Interference torques mean.

For the stationary, d. H. steady The control and disturbance torque terms can be in the state of the control loop be ignored as they become later on average just pick up. Her influence will be discussed later will.  

With the implementation of such a regulation can be how Equation 3a shows estimates for the swirl components both towards the second ( _e.g. ) as well as the first Transverse vehicle axis ( _x) determine. Since the swirl component in Direction of the second transverse axis (H _e.g. ) with a good approximation the output signal of the first controller network via the proportionality factor (H _y ) can be won a simplified observer in particular to serve one Measure for the first transverse axis component (H _x ) to win. A such simplified observer is by a simple one Transfer function with a counter term first and one Second order denominator term can be represented. On its use should be in a further embodiment to be described later of the invention. At the moment is just an estimate for the swirl component ( _e.g. ) in the direction of the second vehicle transverse axis relevant.

A realization of the observer equation 3a as a calculation algorithm in a programmable, digital on-board electronics does not cause any difficulties for the expert. An implementation in equivalent, analog networks is in practice because of the extremely slow movements and the inevitable Amplifier drift problematic.

The dead zone ( 405 ) in the swirl control branch of the control device according to the invention is acted upon by the output signal of the swirl controller and only delivers an output signal when predetermined threshold values (z. B. ± d) are exceeded. At this point, the advantage of the control device of the second type according to the invention is already noticeable insofar as the response thresholds of the dead zone element can be chosen to be significantly smaller than in conventional systems due to the lack of superimposed nutation vibrations, which significantly improves the alignment accuracy of the first transverse vehicle axis and consequently also the corresponding error portion transformed into the second transverse axis is reduced. In the present case, the triggering of an actuation intervention is not made dependent on the storage currently measured by the sensor, but rather on whether the deviation of the swirl vector from its desired direction exceeds a predetermined dimension.

The modulator ( 406 ), which, when using discontinuously operating actuators, such as reaction nozzles, has the task of converting the storage signal into an equivalent sequence of control pulses, can be designed as a PWPF or PR modulator ( FIG. 2) in the manner already described . Since, in the present case, as will be explained later, the phase position of the pulses generated by the modulator is not as important, it is also possible to use circuits such as pulse width modulators which are easier to implement. Since such modulators (e.g. 204 in FIG. 2) already contain a response threshold ( h _E in FIG. 2), it is not only expedient, but in order to comply with the accuracy requirements, the threshold values of the dead zone element ( 405 ) and the To link the modulator ( 406 ). A simple embodiment of such a modulator, which is very useful for the present invention, sees e.g. B. before that when a first response threshold (± d ₁) the repetition frequency of predetermined, physically realizable minimum pulses is increased proportionally to the input signal and when a second response threshold is exceeded (± d ₂, | d ₂ | <| d ₁ |) at constant permissible maximum frequency of the repetition rate, the pulse duration is increased in proportion to the input signal, in each case in such a way that on average the generated pulse / time areas increase linearly with the input signal.

The signal ( Φ _N ), which is formed from the measurement signal via a second controller network ( FIG. 4a) or via a first controller network in connection with a summing element ( 403 ), is representative of the differentiation element ( 407 ) in the arrangement according to the invention Transfer function

supplied, whereby a measure of the angular velocity ( w _x ) about the measured vehicle axis (roll axis) is formed from the angular movement ( Φ _N ). The downstream nutation observer ( 408 ) is used from the component of the nutation movement around the first transverse axis ( w _x ), which is based on measurement and differentiation, to form estimated values for the complete nutation dynamics via a model of the physical process, ie the vibration component ( w _z ) not measured directly. to supplement the second vehicle transverse axis. Instead of a second order nutation observer, simplified observers (for w _z ) or equivalent networks can again be used in a known manner. In embodiment of the first and second network controller according to Fig. 4b particular additional filter for removing unwanted higher frequency signal components to the observer (408) and / or the differentiating element can be (407) combines with a corresponding total transmission behavior. The equations for said full nutation observer are:

in which

_x , _e.g.  - Estimated angular velocities (w _x ,w _e.g. ) around the vehiclex- respectively.e.g.-Axis,
I. _x ,I. _e.g.  - moments of inertia of the vehicle around the corresponding axes
 T _cx ,T _cx  - Torques around the respective Vehicle axles
k₁,k₂ - gain factors
H _y  - the swirl stored in the vehicle
w₀ - the orbit frequency

and points above the respective variable derivatives of time mean. The realization of such observers through corresponding algorithms in a digital on-board computer or their conversion into equivalent transfer functions and analog circuits are familiar to any person skilled in the art. With the very small numerical value of the orbit frequency multiplied terms in equations 3c are per se negligible and only given for the sake of completeness. The freely selectable gain coefficients (k₁,k₂) are to be chosen so that the observer in shorter, z. B. the half the duration of a nutation period. At this point it is expressly pointed out that the formation of the angular velocity components (w _x , w _e.g. ) for the nutation movement from a measurement signal for the Deviation (ε _Φ) a first transverse axis from its target direction via first and second controller networks (401, 402) to Fig. 4a or alternatively by an appropriate arrangement toFig. 4b via a first controller network (401) and difference formation in a summing point (403) with downstream Differentiator (407) then superfluous if via additional sensors such. B. Speed gyroscope - possibly in connection with high-pass filters for elimination of the path movement share (w₀) - a measurement signal for the said movement size (w _x ) the nutation vibration directly is available. Are also measurement signals for the Angular velocities (w _x ,w _e.g. ) around both vehicle transverse axles before, then these measured values are expediently direct used, with which the nutation observer then also is replaced. In the past the use has been such gyroscopes mainly for long-term missions  Reliability reasons for normal operation control too then prohibited when such devices carry out others operational phases, e.g. acquisition maneuvers, were available on board spacecraft anyway. Technological progress in the field of laser and fiber optic gyroscope, which, in contrast to the corresponding classic, electromechanical components hardly anymore no longer contain any mechanically moving parts, however, allow for a significant increase in the future Reliability and also cheaper gyroscopes expect what their use in the devices according to the invention not only for short but also for long periods enables. The present invention is not so the use of only a single measuring element per vehicle axle in connection with the described electrical Circuits, networks or algorithms to form the required signal components limited but can in general even in a simpler way with the help suitable additional measured values can be realized. This applies mutatis mutandis even if in the further description of the invention not always for such opportunities Reference is made. In one Amplitude / phase converter (409) are according toFig. 4a and 4b from the estimated components ( _x , _e.g. ), Sizes (A _N ,β _N ) formed that the nutation amplitude (A _N ) or the Phase angleδ the angular velocity of the nutation vibration (β _N ) correspond. This can easily be done through a Cartesian / Polar Coordinate transformation done according to the regulation:

A _N = (3d)

In vehicles whose transverse axis moments of inertia ( I _x , I _z ) differ only slightly, which is practically always the case with spin-stabilized vehicles and often with three-axis stabilized vehicles, in particular communications satellites, these relationships represent sufficiently good approximations. If the transverse axis moments of inertia are different, it is it is advantageous according to the invention to determine the nutation amplitude ( A _N ) according to a formula which takes these conditions into account and has the form:

A more precise relationship for the phase angle is in this case:

and means that in this definition the nutation phase goes through zero if the nutation movement about the second transverse axis goes through zero and at the same time reaches its maximum (+ A _N ) about the orthogonal first transverse axis. According to the feature of claim 2, the signals ( Δ t _cx ; A _N , β _N ) formed step-by-step in the functional elements described above are linked together at the output of the modulator ( 406 ) or the amplitude / phase converter ( 409 ) . The linkage takes place in such a way that the modulator decides on the necessity, sign and duration of an actuation intervention and the output signals of the amplitude / phase converter ( 409 ) decide on the time of the actuation intervention ( Δ T _cx ) within a nutation period. According to the invention, two cases are to be distinguished, depending on whether the pulse repetition frequency of the modulator prescribes one or two manipulations per nutation period.

In the former case, an intervention should be made as prescribed by the modulator according to duration and sign in the following range of the nutation angle ( β _N , ₀ β _N 360 °):

γ ₀ + Δγ - Δβ β _N (t) γ ₀ + Δγ + Δβ (3g)

provided:

that is, if the instantaneous value (equation 3d, 3f) of the nutation amplitude ( A _N ) determined continuously is more than half but less than one and a half _times the nutation half-cone generated by a minimum pulse ( Δ P _x ), where:

or approximately:

and fixed values ( γ ₀, Δβ ) , preferably:

Δβ 0.1 rad

γ ₀ = π - α for positive manipulation (3m)
γ ₀ = 2 π - α for negative manipulation

If, on the other hand, the nutation amplitude ( A _N , equation 3d, 3f) is greater or smaller than the specified limits, then the control intervention should take place in the following range of the nutation angle ( β _N (t) ; 0 β _N 2 π ) :

γ ₀ + Δβ β _N (t) γ ₀ + Δβ (3n)

It means:

γ = γ ₀ + Δγ - the optimal phase angle for manipulation within a nutation vibration
T _cx - the moment level of the intervention
Δ t _cx - the duration of the control intervention commanded by the modulator
α - the oblique mounting angle of the actuator

The other quantities ( Δ P _x , γ ₀, Δγ ) are defined by the equations 3i, 3m, 3l that describe them. In the case of two manipulations per nutation period, the first manipulation is to be carried out according to the invention if:

γ ₀- Δγ ₁- Δβ β _{N 1} (t) γ ₀- Δγ ₁ + Δβ (3o)

provided:

A _N 2 Δ P _x (3p)

in which:

and the 2nd intervention if

γ ₀- Δβ β _{N 2} (t) γ ₀ + Δβ (3r)

However, this requires that the nutation amplitude ( A _N ) and phase ( β _N ) are determined in a shorter time than half the nutation period (equation 1c). If e.g. B. due to high nutation frequency and / or slow data processing in the on-board electronics, this cannot be guaranteed, then the requirement for the second pulse according to equation 3r must be replaced by equation 3s according to the regulation of the present invention

β _{N 2} (t) = 2 ( π - Δγ ₁) (3s)

is against

A _N <2 Δ P _x (3t)

then you have to bet

Δγ ₂ = 0 (3u)

and conditions 3o and 3r go together about.

The conditions formulated in inequalities 3g, 3o, 3r for the generation of discrete control interventions to ensure highly precise follow-up control and energy-optimal nutation damping are to be explained in more detail with the help of FIGS. 4c and 4d:

Fig. 4c 3g of movement shows the engaged condition by means of a two-dimensional representation of the spin vector in the plane of rotation of a vehicle of the type considered, the normalized swirl component in the direction of the mutually orthogonal transverse vehicle axis (H _z / | H _y |, H _x / | H _y |). one thinks plotted along the coordinate axes. The associated Euler angles ( Φ, Ψ ), which are proportional to the swirl components , are given in brackets. The circles shown represent, in a schematic form, nutation movements, which describes the tip of the vehicle swirl vector ( H _y ), which goes essentially perpendicular to the plane of the drawing. The center of the respective circle ( 411, 412 ) marks the tip of the overall swirl vector in the plane of the path coordinate system. The starting point ( β _N = 0) of the nutation movement with an amplitude ( A _N , equation 3d, 3e, 3f) that corresponds to the circle radius ( 411 ) and the assumed sense of rotation are given. If the z component of the total swirl vector now reaches the permissible limit of the dead zone (- d) used as the intervention criterion, an actuation intervention ( Δ T _cx ) is triggered which moves the total swirl vector by a distance ( Δ P _x , equation 3i ) moves to a new position ( O ₂). If, as assumed in the present case, the moment level of the control intervention is high and the pulse duration is very short compared to the nutation period, then the swirl vector of the vehicle ( H _y ) performs a nutation movement after the control intervention around the new position of the overall swirl vector as the center, whose initial conditions correspond to the position of the vehicle swirl vector before the intervention. A torque increment ( Δ T _cx ) around the vehicle x axis essentially corresponds to a swirl increment ( Δ H _x ) along the same axis combined with a small component of opposite sign (- Δ H _z ) around the vehicle z axis because of that Inclined installation of the reaction nozzles already described in the example considered. The minimum length of the swirl displacement vector is determined by the size of the minimum, realizable pulse increment.

From Fig. 4c shows clearly that the optimum time is given for a control intervention, when the phase angle of the nutation is straight in the direction of Drallinkrementes generated by the control intervention. This phase angle with a tolerance range (2 Δβ ) is described mathematically by the condition according to equation 3g. The associated point is designated in Fig. 4c with P ₁. Depending on the size of the minimum pulse ( Δ T _cx ), the size of the stored swirl ( H _y ) and the current nutation amplitude ( A _N ), the time of the control intervention (3g) must be varied (3i, 3k) if it is to be ensured that the remaining nutation amplitude also assumes its smallest possible value after each actuation intervention to correct the twist direction. If the initial conditions are within the scope of inequality 3h, this requirement can be met with a single actuating pulse. Outside of this range, the regulation then to be applied (equation 3n) ensures the best possible, energy-optimal nutation degradation, but without minimally possible residual nutation being achievable with a single control intervention.

If the disturbing torques acting on a vehicle of the type under consideration or the deviations of the vehicle axles from their nominal position are so large that two actuating interventions per nutation period are required by the modulator output signal, then the actuating regulations according to equations 3o to 3u are to be applied according to the invention. The corresponding relationships are shown in Fig. 4d. An energy-optimal displacement of the swirl vector, ie based on Fig. 4d of the center ( O ₃) of a nutation circle ( 412 ) is achieved according to the posicast principle already mentioned, if two equally large manipulations are made at intervals of a nutation half-cycle, without, however, at the same time a breakdown of an initial nutation is achieved. If the initial amplitude of the nutation is smaller than the displacement of the swirl vector caused by two actuating pulses (equation 3p), the best possible nutation damping according to the regulation (3o) according to the invention is achieved without increasing the energy expenditure required for swirl correction when the first control intervention takes place at a phase angle that the intersection ( P _z ) of the initial nutation circle ( 412 ) ( A _{N 1} ) with a second imaginary nutation circle ( 413 ) ( A _{N 2} ) takes place, the center point ( O ₄) of which is shifted according to size and direction of the twist increment is, as indicated in Fig. 4d. The second actuating intervention (equation 3r) then shifts the orbital twist vector at the right time to the point at which the direction of action of the actuating intervention crosses the nutation movement, so that the nutation movement ( A _{N 2} ) initiated for the swirl displacement is eliminated, and the residual nutation ( A _{N 3} ) is minimal becomes.

From the description of the functional elements ( 401 to 410 ) of the invention according to FIGS . 4a and 4b, in particular the equations 3a to 3u representing their functional features, it can be seen that knowledge of some system-related parameters is necessary to carry out the regulations according to the invention. However, the numerical values of some of these system parameters are either conscious or due to changing operational conditions, such as. B. temperature fluctuations, aging, life and the like, subject to temporal fluctuations that affect the quality of the control devices according to the invention, aimed at optimal behavior. According to a further embodiment of the invention, it is therefore proposed to determine the instantaneous values of the system parameters which are subject to strong changes and to take them into account when carrying out the teachings according to the invention for technical action.

In Fig. 5a the functional diagram of a correspondingly extended control means is shown. It has already been mentioned that the swirl storage devices are used to stabilize such vehicles about their pitch ( y -) axis ( FIG. 1) orthogonal to the track plane. Within the nominal working range, a change in the swirl amount of z. B. ± 10% connected. Since the mass properties of such swirl storage components are known very precisely, the magnitude of the angular momentum can easily be determined with the aid of a rotational speed measurement of the swirl wheel or only the back emf of its drive motor on board the vehicle and its exact value can be taken into account without difficulty when carrying out the regulations according to the invention. As you can easily see, the swirl magnitude ( H _y ) goes into the equation for determining the nutation frequency ( W _N , equation 1c), the nutation amplitude ( A _N , equation 3f), the nutation observer (Equation 3c), the phase angle of the intervention ( Δγ , Equation 3k, 3l, 3q), the standardized twist increment (3i) and in the rule laws (equation 3g, 3n, 3o, 3r, 3s) and in their application criteria (3h, 3p).

In a corresponding manner, taking into account the best possible knowledge of the control intervention actually generated, e.g. B. emitted nozzle pulses ( Δ T _cx , Δ T _cz ) to comply with the optimality conditions and for a rapid settling of the functional elements ( 408, 409, 410 ) or the algorithms and / or networks representing them. The efficiency of reaction nozzles, ie their effectively delivered pulse increments, depend to a large extent on the pulse duration ( Δ t _cx ), their control signals and, especially with short control times (e.g. 10 m / sec), drop to below 50%. However, this area of work is of particular interest in practice for reasons of accuracy, because this size determines, among other things, the residual nutation. The functional dependence of the effective pulse increment on the duty cycle can, for. B. determined before use of such components by test bench measurements, stored on board and called for the duration of the respective control interventions required by the modulator ( 406 ) and taken into account accordingly in the algorithms (equations 3c and ff.). This procedure is referred to as "controlled adaptation" and is shown in Fig. Schematically indicated by the additional introduction or return of the swirl sizes (H _y) and pulse increments (Δ T _cx, Δ T _cz) 5a. Of course, the above-mentioned parameters can of course also be determined completely or partially by additional observers and estimation algorithms provided on board or on the ground. In accordance with the rule in practice that it should not be estimated what can be measured with simple means, it is advisable for further improvement to determine only those quantities which cannot be measured directly or only with considerable additional effort are accessible on measuring equipment. This can e.g. B. apply to unforeseen or occurring over the lifetime changes in the functional relationship between efficiency and pulse duration of reaction engines due to changes in delivery pressure, mixing ratio of the fuel components and aging processes. In this case, z. B. from the difference between theoretical and estimated nutation amplitude in an expanded nutation observer also identify the effective pulse increment and take it into account in the data processing and / or control algorithms. The torque components about the second transverse axis, which are simultaneously mentioned with interventions about a first vehicle axis, can also be reversed by simultaneously actuating separate actuators acting on the second axis with the same signal ( Δ t _cx ) instead of by inclined installation of the actuators around the first axis Sign can be realized. The possible effects of such a procedure will be discussed later.

Another extension of the present invention, which is particularly important for improving the alignment accuracy and is based on observer and estimation methods, is shown in FIGS. 5b, 5c and consists in the determination of the interference torques acting on the vehicle and their compensation.

As indicated schematically in FIG. 5b, it is proposed to add a disturbance variable observer to the previously described swirl controller ( 404 ) and to add the estimated values obtained to the subsequent dead zone-modulator combination. The disturbances that occur during the normal operating phase of such spacecraft are thought to be broken down by means of a Fourier analysis into constant parts and integer multiples of the orbital frequency ( w ₀), the amplitudes of the higher harmonics (2 w ₀ etc.) being more or less strong depending on the geometric shape of the vehicle are pronounced. To expand the swirl controller ( 404 ) to a swirl and disturbance variable controller ( 504, 505 ), use is made of the observer form of the swirl controller (equation 3a), the complete model equations of which contain _{disturbance torque terms} ( T _Dx , T _Dz about the vehicle _{transverse axes} . To be replaced in this representation e.g. the _{disturbance torque} about the first transverse axis ( T _Dx ) through its optimal estimate ( T _Dx ), which can be obtained as part of an extended swirl and interference observer algorithm (equation 4a) and switches the variables determined in this way using suitable amplification factors ( K _Hz , K _{Dx 0} , K _{Dx 1} , K _{Dx 2} ) in the manner of a state _controller ( 505 , equation 4b) on the input of the subsequent functional element ( 506 ) of the control device according to the invention acting on the first transverse axis ( x axis), so the desired swirl control and disturbance variable compensation is achieved, assuming that the disturbance torque profile about the first transverse axis ( x axis) due to its constantan part and a first harmonic is written with sufficient accuracy, these are the observer and controller equations:

where the terms of Equation 3a apply and additionally

_{Dx 0} - Estimated value of the constant disturbance torque component (T _{Dx 0}) to theX-Axis
_{Dx 1}, _{Dx 2} - Sine and cosine components one on the first Transverse axis (XAxis) acting, with rotational frequency (w₀) periodic disturbance torque component
k₃₁,k₄₁,k₅₁ - gain factors
K _{H 2},K _{Dx 0},K _{Dx 1},K _{Dx 2} - Activation values of the state controller
η x - the output signal of the state controller (input signal of the dead zone / modulator link506) and
[. . .] ^T  - mean transposed vectors / matrices.

In the present case, it is sufficient to apply only one component (e.g. T _{Dx 1} ) of the harmonic _{disturbance torque} component in the compensation part of the state _controller ( 505 ), since the phase position is set automatically by the disturbance variable observer. In the event that the second or higher harmonic of the interference moments have not insignificant amplitudes, observer and controller can of course be expanded accordingly in a known manner, namely by 2 orders per additional periodic component.

The principle of a particularly advantageous embodiment disturbance compensation is inFig. 5c shown. Then in the state controller (505) instead of the respective time(t) determined estimates of the disturbance variables (T _{Dx 0} (t),T _{Dx 1} (t)) the disturbance observer (504) Prediction values of these sizes (T _{Dx 0} (t-1/w₀),T _{Dx 1} (t-1/w₀)) activated, which a disturbance variable memory (511) whose values at the corresponding time the previous period (1 /w₀) determined and recorded were. The by the disturbance observer (504) in this Estimates determined in the case do not represent the Absolute values but the deviation from the switched on Prediction values and these form a new prediction value for the same point in time the following period. In this way occurs e.g. B. with geosynchronous satellites in the steady state State of the control loops only the daily change of the disturbance torque profile as the disturbance variable to be corrected. The Orbital twist component ( _e.g. (t)) against it, as inFig. 5b shown directly and without intermediate storage for swirl control used. In this block diagram is also from the made use of the fact mentioned that for a harmonic Interference torque component is usually only an activation value ( _{Dz 1}) enough.

The accuracy improvement of the follow-up control of a vehicle of the type mentioned in theFig. 5b, 5c brings yet another advantage with it. It turns out that  that in an observer according to equation 4a or one reduced form of the same obtained estimate for the Total swirl component ( _x) in the direction of the first vehicle transverse axis also a significant improvement in accuracy experiences. As in the discussion of 42272 00070 552 001000280000000200012000285914216100040 0002003831563 00004 42153dynamic processes in Connection with theFig. 4c and 4d, this is Swirl component proportional to the alignment error around the second vehicle transverse axis and can therefore with a suitable Link in the nutation controller (510) advantageous for regulation can be used around this axis. InFig. 5c one of the functional unit (505) corresponding state controller (512), which also connects the second Fourier component the harmonic disturbance from the disturbance variable observer (504) via a corresponding gain factor (K _{Dx 2}) can contain and via a second dead zone / modulator combination (513) on the nutation controller (510) acts. For the combination of the additional output signals of the second (e.g.-) modulator (513) in the nutation controller (510) for generation optimal interventions around the vehicle's transverse axles the intervention conditions already described apply (Equations 3g and ff.), If only in the definition equations (3m) for those with the respective job interventions associated swirl displacement directions (q₀) the corresponding Numerical values can be used. These values (γ₀) are in for all possible initial filing and manipulations Table 1 compiled. Finally, it should be mentioned that the design of the swirl and disturbance variable observer Equation 4a in complete or simplified form as described in connection with Equation 3a can be. A possibly appropriate conversion into corresponding transfer functions and their implementation through equivalent algorithms or networks Expert no difficulties.

In the following FIGS. 6a to 6d, further refinements of the invention are shown, which serve the purpose, as far as possible without additional equipment expenditure, that is to say using measuring and actuating components that are present anyway, the alignment accuracy about the second transverse axis, the z - or yaw axis of the vehicles under consideration Kind of increasing further. In connection with the typical component arrangement according to FIGS . 1b and 1c, it has already been stated that by means of sun sensors, which are also required for acquisition and orbit correction maneuvers, bearing reference signals for the second transverse axis over wide angular ranges - in the case of geosynchronous satellites, e.g. B. are available for 8-10 hours twice a day.

In Fig. 6a thereof (yaw) information (deviation _ε ψ), use is made in an additional controller branch of a second inlet guide vane (602) and a modulator (604) with a dead zone (603) consists of a third regulator power value (601) and a nutation controller ( 610 ) additionally provides information about the need, sign and duration of intervention about a second transverse vehicle axis. For the control of a first transverse axis, this basic circuit diagram is again based on a simpler configuration of the device according to the invention, for example according to FIG. 5a. For the design of the additional functional elements of the controller branch for a second transverse axis, in particular controller network ( 601 ), swirl controller ( 602 ), dead zone and modulator ( 603 ), the same considerations apply as for the description of the swirl control loop for the first transverse axis. However, the path control component ( Ψ ₀) that can be obtained from the storage signal for the second transverse axis from its desired direction via the preferably low-pass behavior of the third controller network ( 601 ) is then proportional to the component of the vehicle twist ( H _x ) in the direction of the first ( x -) - vehicle axis. The second swirl controller ( 602 ) has proportional, PD or PID behavior and is optionally designed together with the third controller network ( 601 ) according to the features of claim 1. If the x component of the vehicle swirl ( H _x ) exceeds the response thresholds of a dead zone element ( 603 ) which is implemented separately or together with the modulator, a modulator of possible embodiments already described decides on the need, sign and duration of intervention about a second vehicle transverse axis.

At this point, the present invention has a very essential, characteristic feature. So far, it has always been assumed that a signal that can be obtained from the deviation of a first vehicle transverse axis ( x axis) from its desired direction is also used to carry out control interventions around said transverse axis according to the intervention criteria already explained in detail. It would be obvious in itself to proceed in the same way for the control interventions with regard to the second vehicle transverse axis ( z -axis) and to use control networks ( 601, 602 ), dead zone elements ( 603 ) and an assigned modulator ( 604 ) to also make necessary control interventions ( Δ T _cz ) to trigger this axis. It turns out, however, that such a procedure does not lead to energy-optimized movements. With reference to FIG. 4c and the associated description, it can be seen that an actuating pulse derived from the placement of a first transverse axis ( x axis) and generating actuating moments about this first transverse axis predominantly produces a displacement of the swirl vector in space, which results in a placement of the second Corresponds to the transverse axis from its target direction. According to the invention, it is more expedient to just interchange the assignment of the control interventions about the respective axes with respect to the information obtained from the measurement signals. However, according to the previous teaching of the invention, the control interventions around both transverse axes are still to be carried out correlated with the current state of the nutation movements.

According to this further embodiment of the invention, the signal component ( Φ ₀) that can be obtained from the measurement signal for the deviation ( ε _Φ ) of a first transverse axis ( x axis) via a first controller network ( 401 ) for a first component of the path movement and the additional signal the measurement signal for the deviation ( ε _ψ ) of a second transverse axis ( z -) via a third controller network ( 601 ) for a second component of the web motion signal component ( Ψ ₀) which can be obtained via a second controller network ( 402, Fig. 4a) or an equivalent difference formation ( 403 ) obtainable from the measurement signal ( ε _Φ ) of a first controller network ( 401 ) representative of the nutation movement signal component ( Φ _N ) in a nutation controller ( 610 ) are linked so that by means of the first, a first component of the path movement Representative signal component ( Φ ₀) after passing through a first swirl controller ( 404 ), a dead zone element ( 405 ) and a second modulator network ( 604 ) the decision Identification of the need, sign and duration of an intervention about a second vehicle transverse axis ( z axis), by means of a third signal component ( Ψ ₀) representing a second component of the path movement after passing through a second swirl controller ( 603 ), a second dead zone element ( 603 ) and a decision of a first modulator network ( 605 ) about the necessity, sign and duration of an intervention about a first vehicle transverse axis ( x axis) and with the help of a second signal component ( Φ _N ) representing the nutation movement after signal conditioning in a differentiator ( 407 ), a nutation observer ( 408 ) and an amplitude / phase converter ( 409 ) the point in time for the respective control interventions can be determined within a nutation period. The generally mathematically formulated conditions in the inequalities 3g to 3u for the point in time or phase angle ( β _N ) of the control interventions within a nutation period and the areas of use relating to the respective nutation amplitude ( A _N ) z. B. Equation 3h, 3p remain valid if you use the size used there. Δ P _x consistently replaced by a new quantity Δ P , which is defined as follows:

Δ P = √ (5a)

in which:

Δ P _x , Δ P _z - normalized swirl increments
T _cx , T _cz - actuating torque levels around the vehicle's transverse axes ( x, z)
Δ t _cx , Δ t _cz - mean the duration of the control intervention prescribed by the respective ( x -, z -) modulator for the corresponding transverse axis.

Furthermore, for optimum swirl control and simultaneous nutation damping for manipulations around the first ( x -) and / or second ( z -) transverse axis, the corresponding correct angle of action ( γ ₀) of the swirl increment ( Δ P) generated must be used in the engagement conditions. A distinction must be made between three cases, depending on whether an intervention is required after the modulation output signals have been instructed
- only around the first vehicle transverse axis ( x axis)
- only around the second vehicle transverse axis ( z -axis) or
- around both vehicle axles ( x = roll, z = yaw axis)
should take place within a nutation period. The numerical values for the said reference angle ( γ ₀) are compiled in Table 2 as a function of the permitted deviations, that is to say the threshold values of the dead zone elements ( 405, 603 ) connected downstream of the first ( 404 ) or second swirl controller ( 602 ) for all cases that occur.

To illustrate those given in Table 2 Numerical values for the triggering conditions of the control interventions  (Equation 3g and ff.) Serves the diagram afterFig. 6e). According to the invention, the prerequisite is first assumed that the remaining nutation cone after performed intervention should be as small as possible. With reference to the explanations for theFig. 4c, 4d is the stationary value of the residual nutation by the size of the physically realizable, minimal adjustment increments or of the associated increment of the swirl shift (Δ P _Min ) determines its value when generating a minimum pulse (Δ P _xmin ,Δ P _min ) around each transverse axis within a Nutation period is determined by equation 4a. Writes the rule law within a nutation period an intervention around both transverse axes, so these are Expediently triggered at the same time, which is the same size Increments for both axes of a swirl shift direction below 45 ° in the diagram ofFig. 6c corresponds. In contrast, there is only an intervention about a vehicle transverse axis required, its value can be the same in terms of amount Shift of the swirl vector by a factor larger be selected as the predetermined minimum value, which z. B. at Using reaction nozzles is a desired improvement the fuel efficiency. With reference to Fig. 6e the swirl shift occurs during interventions only one transverse axis parallel to the coordinate axes (Δ H _x / |H _y |,Δ H _e.g. / |H _y |) which accordingly corresponds to at least threshold valuesd _Φ| = |d _c| =Δ P _Min / 2 requires and the average alignment accuracy of the vehicle's transverse axles. Medium misalignment of the vehicle swirl vector (-Δ H _e.g. ,Δ H _x ), according to the Storage of the vehicle axles (e _Φ ,ε _Ψ ) of their target orientations pose inFig. 6c, due to deviations from the Coordinate jump (0) and should theoretically by Twist increments or manipulations undone that return the swirl vector to the origin (0), which is not enough for a given size of the minimum impulses any, any deviations around both vehicle transverse axes corresponding starting positions is possible in one step.  According to the invention, the storage field (6c) is therefore in eight Sectors classified from which the return to the best possible environment of origin (±d Φ, ±d _ψ) he follows through interventions

± Δ T _cz from sectors I, II
± Δ T _cx from sectors III, IV
± Δ T _cx and Δ T _cz from sectors V, VI, VII, VIII

corresponding to the directions of action ( γ ₀) of the swirl changes caused by control interventions ( Δ P _x , Δ P _z ). So z. B. a positive offset of the first transverse axis or x axis ( e _Φ ∼ Φ ₀∼- Δ H _z <+ α _ϕ ) in sector I (point P _I ) an actuating pulse (+ Δ T _cz ∼ + Δ H _z ) , which shifts the swirl vector parallel to the abscissa axis ( Fig. 6e, P _I → P _I *), but can only reach the zero point if the offset around the second transverse axis ( z axis) is just zero at the same time; ie the placement of the second transverse axis remains unchanged, if one disregards the change in the nutation vibration associated with the displacement. By observing the phase conditions in the nutation movement sequence at the time of the control intervention (equations 3g and ff.) And the duration determined by the modulator, optimal nutation damping and minimal residual nutation are ensured at the same time as the twist vector shift.

In a considered second case, z. B. the Storage of both transverse axes from their target direction the permissible Barriers (e _Φ∼Φ₀∼-Δ H _e.g. <+d _Φ), (ε _c1∼Ψ₀∼ +Δ H _x <d _ψ) what a point (P _v ) in the intervention sector V (Fig. 6e) corresponds to, at the same time a positive control intervention around the second transverse axis (Δ T _cz ∼ +Δ H _e.g. ) and a negative intervention around the first (x-)Axis (-Δ T _cx ∼-Δ H _x ) triggered with the same amount a shift of the swirl vector at 45 ° in the direction of Effect zero. Simultaneous nutation breakdown will again by complying with the phase condition for the  Nutation movement at the time of the intervention (β _N (t)) ensured For the complete assignment of the intervention by sign (±Δ T _cz , ±Δ T _cx ) and for the associated, in the intervention conditions (equations 3g and ff.) Swirl displacement directions (γ₀) depending on the Storage of the transverse vehicle axes (sectors I to VIII) referred to Table 1.

InFig. 6a is a double changeover switch (607) indicated, the Has changeover contacts in both channels and with it Help to switch the control loops in the event of loss of Position reference made about the second vehicle transverse axis must become. Are the actuators around the first transverse axis as assumed in the previous exemplary embodiments (e.g. through inclined installation around the angleα) arranged so that they at the same time an opposite moment component Generate sign around the second transverse axis, so in the the simplest case is a switchover of the axis assignment, e.g. B. their modulators in one of the given exemplary embodiments (e.g.Fig. 4a, 5a, 5b) corresponding configuration and simultaneous shutdown of the additional swirl control channel (H _x ) toFig. 6a). The location of the second transverse axis then becomes dependent on the influence of external disturbances drift away from their size and sign, as a result of their relatively precise alignment at the time of switching to limited periods of unavailable position reference in general, however, lower alignment errors than in the Build previously considered comparative cases. Are the Actuators for the first vehicle transverse axis are not so arranged that they also simultaneously with each intervention Moment components of opposite signs around the Generate second transverse axis, so according to another Embodiment of the invention in this case stability and Alignment around both transverse axes in the same way be ensured that with every adjustment to the first transverse axis at the same time by corresponding Control of the actuators for the second transverse axis  Momentary increment of opposite sign around this Vehicle axis is generated. This case is inFig. 6a schematically drawn and corresponds to position 2 of the Double switch (607). From a physical point of view this with the same torque increments, an effective one Tilt angle of the actuators around the first axis of 45 ° and all related to previous corresponding Quotations made in examples keep their considerations Validity. InFig. 6b is the functional diagram of one another embodiment of the present invention, that the essential characteristics of the control devices after theFig. 5c and 6a and thus their advantages with each other connects. In a swirl and Disturbance Observer (504) z. B. according to the algorithm from equation 4a estimates of the components of the vehicle swirl ( _e.g., _x ) and the constant portion ( _{Dx 0}) as well as periodic Interference parts formed, of which here again the For the sake of simplicity, only the components of the first harmonic ( _{Dx 1}, _{Dx 2}) are shown. The swirl component in the direction the second vehicle transverse axis ( _e.g. ) is referenced however towards theFig. 6a made statements about a suitable gain factor (K _Hz ) in the sense of a state regulation (608) and a dead zone (603) for generating control interventions around a second transverse axis (e.g.Axis) by means of a Modulators (604) used. Instead of one in swirl and Observer (504) formed estimate for this Swirl component (H _e.g. ) can also be proportional to this Output size (Φ₀) of the first controller network (401) directly can be used, which is particularly advantageous if the observer equations 4a as equivalent transfer functions will be realized. This possibility is in the the present case for generating the second swirl component (H* _x ) from the filing signal (Ψ₀) via a third controller network (601) and a proportionality factor (1 /H _y ) applied. As long as position reference with respect to the second (e.g.-) transverse axis is available, the size thus formed becomes Generation of control interventions for a first (x-) Vehicle transverse axis  via a status controller and disturbance variable compensator (609) and a dead zone / modulator combination (506) used as they are equivalent, on a direct Provides measurement based values. However, the position reference goes temporarily lost for the second transverse axis, so the Estimates ( _x ) from the observer (504) resorted to what inFig. 6b with a switch (608. Position 2) is indicated. The device afterFig. 6b is in the already described manner with disturbance variable memories (511, 612) whose values (* _{Dx 0},* _{Dx 1},* _{Dx 2}) in State controllers (608, 609) for disturbance compensation with are processed. In theFig. 6b and 5c were at the two components of the harmonic interference component ( _{Dx 1}, _{Dx 2}), which are sine or Cosine components of the first harmonic of a Fourier decomposition represent because of their phase shift against each other also in the mutually orthogonal vehicle axes activated.

Fig. 6c shows an advantageous further embodiment of the present invention. It is based on the knowledge that with at least temporary availability of measured values for the deviation of a second transverse axis from its target direction also an identification and compensation of the external interference acting on this axis must be possible, at least what their constant ( _{Dz 0}) their slowly changing periodic shares ( _{Dz 1}, _{Dz 2}) concerns. To theirs Determination is used in the present exemplary embodiment extended swirl and disturbance variable observer (606) the as Input signals both representative of the path movement, via a first controller network (401) and a third controller network (601) obtainable, processed measured variables (Φ₀,Ψ₀) are fed. For this purpose, the swirl and Algorithm serving the disturbance size estimation or the algorithm equivalent representation by transfer functions and / or Networks according to equation 4a corresponding to three orders be expanded. This procedure is every specialist  familiar and leads to equations 4a and 4b corresponding state representation on a system of eight Equations with the state vector:

X = [ _x , _e.g. , _{Dx 0}, _{Dx 1}, _{Dx 2}, _{Dz 0}, _{Dz 1}, _{Dz 2}] ^t       (6a)

As well as an innovation term of the form:

and the rule law corresponding to equation 4b

In the control law (equation 6c) and the associated oneFig. 6c in turn, only one component of the harmonic interference component ( _{Dx 1}, _{Dz 1}) is used because at Presence of a first harmonic these parts complete. Is the observer interpreted so that he in much less time than half an orbital period settles, and is particularly from the storage of disturbances (511, 613), Shares can also be used higher harmonics can be detected and compensated for. For the storage of disturbance variables, it is sufficient during implementation a certain number per circulation period, e.g. B. twenty or to record thirty values with their timing that representative mean values over assigned time intervals represent and between those for the connection to be validly numerically interpolated in each case can. InFig. 6c again indicates that loss the position reference around a second transverse axis (e.g.-Axis) what at usual measuring elements indicated by a logical signal  the estimates of those acting on the second transverse axis Interference torques via a switch (615) can be switched off must, because these quantities are then not observable. For the Controller activation values (* _{Dz 0},* _{Dz 1}) at the output of the disturbance variable memory (613) are the last according to the invention valid estimate based disturbances for the following Period kept constant until sensor-based, valid estimates are available or based on the previous function course according to the applicable sine / cosine law added. It is also recommended that Dwell time of a satellite in the previously known one Earth shadow phase, where the solar pressure moments disappear, by appropriately preprogrammed state changes in the disturbance estimate.

InFig. 6d is a last embodiment of FIG present invention demonstrated that differ from the previous (Fig. 6c) only by splitting the swirl and disturbance variable observer (606) in one observer (613, 504) differs per vehicle transverse axis. For each of these The form of the matrix equation (4a) applies. These Embodiment is particularly recommended for implementation in digital on-board computers because of the complexity versus a full observer for both axes (606) toFig. 6c lower due to the low order and is only repeated for the second vehicle axle Calling an identical program with others numerical values and input / output variables required is. There is a further simplification, as already mentioned when in each vehicle transverse axis instead of an estimate the swirl components ( _x , _e.g. ) the respective, the Path component representing the path movement (Φ₀,Ψ₀) or its swirl equivalent (* _x ,* _e.g. ) used directly and only the second share is estimated. Also in this Case is a switch in the direction of a first Swirl component pointing vehicle transverse axis (H _x ) in case of loss the position reference around the second transverse axis, as well as a shutdown  of the disturbance variable estimates over the indicated Counter (611, 615) required.

The gradual improvement is a three-axis stabilized satellite of the type considered in application of various embodiments of devices for setpoint control and stabilization in accordance with the dynamic behavior of apparent transverse axis movements of the present invention shown in FIGS. 7a to 7c. For a typical spacecraft according to FIG. 1a and a component arrangement according to FIG. 1c, the control algorithms described were implemented and their functionality checked while maintaining the characteristic system parameters and disturbance torque profiles. The movement of the vehicle axes ( X, Z) arranged transversely to the stored swirl ( H _y ) and orthogonally to one another over a full orbit was recorded in the usual representation in a Cartesian coordinate system as a function of one another, as already explained to explain the dynamic processes in FIGS . was used 4c and 4d. The Euler angles ( Φ , Ψ ) ) represent angular deviations of the vehicle roll or yaw axis from their target values, ie the ideal orientations of a bank coordinate system carried along according to FIG. 1a. The curves are again more clearly than the movements of the tip of the vehicle swirl vector in FIG Circulation level interpretable.

The simulation result according to FIG. 7a relates to a control device of the first type according to FIG. 3, which is designed according to the features of patent claim 1. For the person skilled in the art, the improvement with regard to energy-optimized control interventions can be seen from the fact that control interventions take place only when the measured offset of the first transverse axis ( x axis) reaches the response thresholds (± h _E , FIG. 3) built into the modulator from its desired direction , which in the present case was set to values of ± 0.6 °, but due to the system-induced noise superimposed on the storage signals, this usually triggers control interventions even with alignment errors of ± 0.5 °. In conventional control systems of this type, control interventions also occur within the dead zone area, which are triggered by the nutation damping logic described ( FIG. 2) and would be recognizable by abrupt changes in the nutation movement within said dead zone area.

The dynamic behavior generated by a device according to FIG. 4a is shown in FIG . The mode of operation of the device of the second type according to the invention is clearly recognizable from the fact that the mean alignment accuracy with respect to a first vehicle transverse axis ( x axis), which according to the statements made is at the center of the respective nutation circles, is ± 0.3 °, ie twice as good is as in the case of Fig. 7a. The improvement in the accuracy of the follow-up control around the first transverse axis, as can clearly be seen, results in a significant improvement in the alignment accuracy around the second transverse axis, which is carried via the swirl coupling, the yaw or z axis. This effect is achieved with the control device according to the invention without the slightest additional expenditure of actuating energy.

FIG. 7c shows the simulation result of a further embodiment of the invention of the second type corresponding to FIG. 6d. It was assumed that no position reference with respect to the second vehicle transverse axis is available for a satellite in geostationary orbit for a period of 4 hours and that the interference torques during this period are kept constant in the manner described above at the last valid estimates. As can be seen from FIG. 7c, the alignment accuracy that can be achieved with respect to the second transverse axis ( Ψ ) is extremely high and, despite the loss of information for the second transverse axis ( z axis ), can be compared with that of the first transverse axis ( Φ ) over the period of time mentioned.

With the present invention, a number of those skilled in the art Novel options for setpoint control and stabilization of freely moving bodies with stored swirl given in the different embodiments the fulfillment of the respective requirements without additional equipment costs in an energy-optimized manner enable.

The detailed description of the physical relationships on which the inventive idea is based and their configuration in the various embodiments also enable the person skilled in the art to make appropriate adaptations, possibly also modifications, to the data processing algorithms and rule laws for the respective application. For example, the nutation measuring and control branch explained in various stages of expansion with the functional elements ( 402 ), ( 403 ), ( 407 ) to ( 410 ) in FIGS. 4a, 5a and ( 508 ) to ( 510 ) in FIGS. 5a to 5c or ( 610 ) in FIGS. 6a to 6d basically based on the formation of an angular velocity signal ( w _x , w _z ) for the nutation movement of the spacecraft, which, when such a variable is derived from a position measurement signal ( E _Φ ), realizes a differentiating element ( 407 ) or at least one high-pass element with differentiating properties in the frequency range of the nutation vibration. In view of the already mentioned deterioration in the signal-to-noise ratio due to such a measure, this procedure is only recommended if the high-frequency interference (sensor noise) superimposed on the (storage) measurement signals is still in a reasonable relationship to the useful signal amplitude. Although additional measures already mentioned, in particular nonlinear filters with low phase loss, can also improve the signal-to-noise ratios again, in such a case a simple redesign of this signal path leads to the same, if not better, results with less effort. If the said signal processing and control branch of angular velocity signals ( w _x , w _z ) is translated into position angle signals ( Φ _N , Ψ _N ), which is possible without difficulty by appropriately adapting the nutation observer and amplitude / phase converter, the differentiator is omitted ( 407 ) completely and correspondingly also its disadvantageous effect on the noise. The matrix equation (3c) for the complete nutation observer ( 408, 508 depending on the embodiment) then takes the form (3c *):

With:

Φ _N - the positional part of the measurement signal representative of the nutation movement as input variable and
- The estimated values for the roll angle component ( Φ _N ) and yaw angle component ( Ψ _N ) of the nutation vibration as output variables.

The optimal switch-off factors of this observer ( k * ₁, k * ₂) then receive in a known manner correspondingly adapted physical dimension and numerical values than in equation 3c. The calculation rules for the amount ( A * _N ) and phase angle ( β * _N ) according to equations 3e and 3f on which the downstream amplitude / phase converter is based are then analogously (3e *, 3f *):

The phase conditions for the generation of actuating pulses (equations 3g and following and tables 1 and 2) remain unaffected by the modification. In an analogous manner, as shown above in the calculation rules for nutation observers and amplitude / phase converters, it is also possible for the person skilled in the art, with knowledge of the teachings according to the invention, to apply the logical conditions for triggering interventional interventions on the basis of intervention criteria which are defined differently but are equivalent in their effect formulate. This can be done, for example, with the aid of the vectors of the nutation movements indicated in FIGS. 4c and 6e ( A _{N 1} , A _{N 2} in FIG. 4c) and the swirl displacement vectors in FIG. 4c, and in FIG. 6e) or their vector components in a suitable, such as the coordinate system chosen there.

Finally, it should be pointed out possibilities for significantly expanding the areas of application of the control devices according to the invention. So far, the areas of use of spacecraft of the type under consideration have been tied to a narrow environment of the specified mission, which is coupled by the required illumination areas of the transmitting and receiving devices and the corresponding arrangement of the antennas with respect to the vehicle axes. In most cases, the required coverage areas are in the northern hemisphere and their supply for communications between continents such as. B. Europe and the USA is ensured by appropriate, from the satellite as seen northeast and northwest antenna reflectors. Spacecraft of the same payload configuration can, if necessary, be located in the southern hemisphere, for example, under the same geographical latitude and length difference. B. in Africa and South America, if it is possible to operate such satellites in an angular position rotated by 180 ° around the center of the earth, ie "upside down". Control systems for vehicles with stored swirl of the type described are only stable under such operating conditions if the stored swirl, relative to the satellite coordinate system, is "reversed" and the sign of the intervention about the second transverse vehicle axis carried and / or directly controlled via the swirl coupling is reversed. This is possible in all of the described embodiments of the present invention without difficulty if the actuators generating actuating torques about a respective first transverse vehicle axis are deliberately not arranged in such a way that they, e.g. B. by inclined installation, with each actuation simultaneously also supply torque components of opposite sign about a respective second vehicle transverse axis, but instead to generate the torque increments about this second axis, the actuators provided for this purpose are used and are also operated with the correct sign according to the sign of the stored swirl. This possibility has already been explained in connection with the exemplary embodiment according to FIG. 6a. With knowledge of the teachings for technical action according to the present invention, the person skilled in the art has no difficulty in making the appropriate assignment of the necessary control interventions for the various embodiments. As a simple rule of thumb, the moment coupling factor ( 215, Fig. 2, 3) in a path coordinate system according to Fig. 1a must have the same sign as the y component of the vehicle swirl vector ( H _y ) and the angular velocity vector ( w ₀) of the orbit frequency.

Table 1 (for Fig. 5c)

Table 2 (for FIGS. 6a-6e)

Claims (21)

1.Device for regulating setpoint values and / or stabilizing freely, twisty, elastic bodies about their rotary axes, in particular aircraft and space vehicles with respect to two body axes lying transversely to the twist axis by means of the deviation of a first transverse axis from position sensors, controllers, modulators and one measuring their desired direction or several actuators and / or moments generating actuating forces about both transverse axes, characterized in that the actuating signals for setpoint control with respect to a first transverse axis ( x axis), for stabilization with respect to a second transverse axis ( y axis) and for simultaneous vibration damping about both transverse axes from one uniaxially measuring position sensor ( 202 ) can be obtained by means of a controller ( 301 ), the transfer function of which has a denominator degree 3 orders higher than its numerator. 2.Device for regulating the setpoint and / or stabilization, swirling bodies freely movable about their rotary axes, in particular aircraft and space vehicles with respect to two body axes lying transversely to the swirl axis by means of the deviation of a first transverse axis from position sensors, controllers, modulators and one or more measuring their desired direction Actuators and / or moments generating actuators about both transverse axes, characterized in that from a measurement signal for the deviation ( ε _Φ ) of a first transverse axis via first controller networks ( 401 ), a signal component ( Φ ₀) representative of a first component of the path movement and via second controller networks ( 402 ) a signal component ( Φ _N ) representative of the nutation movement can be obtained, both of which can be linked together in nutation controllers ( 410 ) in such a way that the first signal component ( Φ ₀) representing the first component of the path movement after passing through first swirl controllers ( 404 ), first r dead zone elements ( 405 ) and first modulator networks ( 406 ) the logical decision about the necessity, sign and duration of intervention can be determined and with the help of the second signal component ( Φ _N ) representing the nutation movement after signal conditioning in differentiators ( 407 ), nutation observers ( 408 ) and amplitude / phase converters ( 409 ) the point in time for the actuation about actuators generating actuating moments about both transverse axes can be determined within a nutation period (1 / w _N ). 3.Device for regulating the setpoint and / or stabilizing bodies which are free to swirl about their rotary axes, in particular aircraft and space vehicles with respect to two body axes lying transversely to the swirl axis, by means of one or more position sensors which measure the deviations of the two transverse axes from their desired direction at least temporarily Controllers, modulators and actuators and / or moments generating actuators about both transverse axes, characterized in that a signal that can be obtained from a measurement signal for the deviation ( ε _Φ ) of a first transverse axis ( x axis) via first controller networks ( 401 ) for a first component of the path movement Signal component ( Φ ₀) and a signal component ( Ψ ₀) that can be obtained from a measurement signal for deviation ( ε _ψ ) of a second transverse axis ( z axis) via third controller networks ( 601 ) for a second component of the path movement with one signal via second controller networks ( 402 ) obtainable, representative for the nutation movement Sig nalanteil (Φ _N) are connectable in Nutationsreglern (610) that by means of the first, a first component of the web motion representative signal component (Φ ₀) after passing through the first inlet guide vane (404), dead zone (405) and second modulator networks (604) a decision on the necessity, sign and duration of an intervention about a second vehicle axis ( z axis), by means of a third signal component ( Ψ ₀) representing a second component of the path movement after passing through two swirl controllers ( 603 ), second dead zone elements ( 604 ) and first modulator networks ( 605 ) a decision on the necessity, sign and duration of intervention about a first vehicle axis ( x axis) and with the help of a second signal component ( Φ _N ) representing the nutation movement after signal conditioning in differentiators ( 407 ), nutation observers ( 408 ) and amplitude / Phase shifters ( 409 ), the times for control interventions by a first and / or two te transverse axis can be determined within a nutation period. 4. The device according to claim 1, characterized in that when using a pseudo rate modulator ( 204 ) for controlling the actuators, a controller network can be used, the numerator polynomial of at least first and the denominator polynomial of at least fourth order. 5. The device according to claim 1, characterized in that when using a pulse width pulse frequency modulator for controlling the actuators ( 213 ), a controller network can be used, the transfer function of at least second order in the numerator and at least fifth order in the denominator is. 6. The device according to one or more of claims 1, 4 and 5, characterized in that the signals which can be obtained from a controller ( 301 ) via a modulator ( 204 ) simultaneously for actuating actuators which generate actuating torques about a first vehicle transverse axis ( x axis) and actuators generating opposing sign actuating torques can be used about a second vehicle transverse axis ( z axis). 7. The device according to claim 2 or 3, characterized in that as the first controller networks ( 401 ) for obtaining a representative of a first component of the web movement signal portion ( Φ ₀) low-pass filter and as a second controller networks ( 402 ) to form a representative of the nutation movement signal part ( Φ _N ) filters with a high-pass character can be used. 8. The device according to one or more of claims 2 or 3, characterized in that second, for the nutation movement representative signal components ( Φ _N ) from the output signals ( ε _Φ ) first measuring elements by subtracting the representative of a first component of the path movement, over the first Regulator networks ( 401 ) formed signal components ( Φ ₀) in summing elements ( 403 ) can be obtained. 9. The device according to one or more of claims 2, 3, 7 and 8, characterized in that modulators ( 406, 604, 605 ) can be used to generate control pulses for discretely operating actuators, the repetition frequency of which (constant) (minimum) pulses after exceeding a first response threshold (± d ₁) and its pulse width ( Δ t _cx , Δ t _cz ) at a constant (maximum) repetition frequency after exceeding a second response threshold (± d ₂, | d | <| d ₂ |) so proportional to the modulator Input signal is variable that the generated pulse / time areas increase and decrease linearly with the input signal. 10. The device according to one or more of claims 2, 3, and 7 to 9, characterized in that as the first and / or second swirl regulator (404, 602) simple amplification factors, lead elements first or second order, PID controller and / or the estimate components of the vehicle swirl ( _x , _e.g. ) and or constant or periodic disturbance torque components (e.g. _{Dx 0}, _{Dx 1}, _{Dx 2}) observer algorithms serving the vehicle or equivalent transfer functions or networks can be used. 11. The device according to one or more of claims 2, 3, and 8-10, characterized in that algorithms for forming flat Cartesian / polar coordinate transformations or such equivalent circuits can be used as amplitude / phase converter ( 409 ). 12. The apparatus according to claim 11, characterized in that nutation amplitude (A _N ) and Phase angle of the nutation (b _N ) after relationships can be determined: in which: _x , _e.g.  - Output signals from a nutation observer (408)
W _n  - the nutation frequency and
I. _x, I_e.g. - mean transverse axis moments of inertia. 13. The device according to one or more of claims 2, 3 and 8-12, characterized in that the time for the generation of a control intervention within a nutation period can be determined by the condition: γ ₀ + Δγ - Δβ β _N (t) γ ₀ + Δγ + Δβ (3g) if: otherwise: γ ₀- Δβ β _N (t) γ ₀ + Δβ (3n) where A _N , β _N - nutation amplitude and phase,
Δ P - swirl increment of an intervention, standardized to the vehicle twist
Δβ - tolerance range of a control pressure angle
γ 0 - the direction of action of a twist increment generated by an actuating intervention in the path plane in relation to the nutation start angle ( β _N ) and or approximately: 14. The device according to one or more of claims 2, 3 and 8-12, characterized in that the times for the generation of two optimal control interventions ( β _{N 1} , β _{N 2} ) can be determined within a nutation period by the conditions q ₀- Δγ ₁ - Δβ β _{N 1} (t) γ ₀- Δγ ₁ + Δβ (3o) for the first control intervention: A _N 2 Δ P (3p) and: γ ₀- Δβ β _{N 2} (t) γ ₀ + Δβ (3r) for the second intervention
in which
A _N , β _N - nutation amplitude and phase angle
Δβ - a predetermined tolerance of the time of intervention
γ ₀ - the direction of action of a twist increment in path coordinates generated by an intervention or: Δγ ₁ = 0 if A _N <2 Δ P (3u, 3t) 15. The device according to one or more of claims 2, 3 and 8-14, characterized in that in the nutation observer ( 408 ), amplitude / phase converter ( 409 ) and / or nutation controller ( 410 ) embodying algorithms or these corresponding networks system-related, variable, recoverable additional measured values and / or functional correlations stored parameters such as spin (H _Y) and / or effectively produced positioning increments (Δ T _cx, Δ T _cz) are insertable. 16. The device according to one or more of claims 2, 3 and 8-15, characterized in that in swirl and disturbance variable observers ( 504, 606, 613 ) formed estimates of constant and / or periodic disturbance torque components downstream dead zone / modulator combinations ( 506, 604 ) can be fed via gain factors either directly or via disturbance variable memories ( 511, 612, 613 ), the values of which correspond to the disturbance variables estimated at the same path point of the previous orbital period of the vehicle at the time of activation. 17. The apparatus according to claim 16, characterized in that from the storage of a second vehicle transverse axis via third controller networks ( 601 ) and swirl and disturbance observer ( 613 ) obtainable estimates of disturbance torque components acting on this vehicle axis with temporary loss of position reference with respect to this second vehicle axis can be switched off and values of the disturbance variables based on a last, valid estimate can be supplied either directly and / or to modulators ( 604 ) connected downstream from disturbance variable buffers ( 613 ) for disturbance variable compensation. 18. The device according to one or more of claims 3, 8-17, characterized in that which directly via first and / or third controller networks  from measurements of the deviations of a first (e _Φ) and / or second (ε _ψ) Vehicle axis from its target direction extractable components of the vehicle swirl temporary loss of position reference with respect to a Transverse vehicle axis (x-,yAxis) by estimated values ( _x , _e.g. ) these quantities are replaceable, which result from a measurement the other transverse axis deviation can be obtained. 19. The device according to one or more of the preceding claims, characterized in that the signs of actuating moments about a second vehicle transverse axis ( z -axis) generating actuators are reversible depending on the sign of the swirl stored in the vehicle. 20. The apparatus of claim 2 or 3 with additional, the angular velocity around at least one transverse axis sensors, z. B. speed gyros, characterized in that 2nd, for the nutation movement ( w _N ) representative signal components ( w _x or w _x , w _z ) can be obtained from the measurement signals of the additional sensors either directly or in conjunction with high-pass filters and / or nutation observers. 21. The device according to one or more of claims 2, 3, 9 to 11, 13 to 19, characterized in that the times for control interventions about a first and / or second transverse axis within a nutation period with the aid of a second signal portion representing the nutation movement ( Φ _N ) after signal processing in complete or reduced nutation observers ( 408 ) and amplitude / phase converters ( 409 ) or their function, equivalent electrical networks or computing algorithms can be determined.