Patent Abstract:
A momentum management system for attitude control of a spacecraft includes a housing to be fixed to the spacecraft and a momentum wheel rotor in the housing for storing angular momentum. A gimbal assembly mounts the rotor in the housing. The rotor is driven by a drive with its output coupled to the rotor. A torque generation imparts torque to the rotor about axes orthogonal to the drive axis. The gimbal assembly includes a gimbal ring coupling the drive output to the rotor. The gimbal ring in turn includes flexure joints connecting the gimbal ring to the drive and the rotor. The flexure joints are configured to permit the rotor to tilt about two flexure axes orthogonal to the drive axis to incline the rotor axis through a range of angles from about 0 degrees to about 7 degrees with respect to the drive axis under the control of said torque generation device. The preferred flexure joint is formed from two resilient, crossing webs. The webs have ring ends connected to the body of the gimbal ring and mounting ends connected to either the drive or the rotor. The system includes a launch restraint system to limit movement of the rotor along the drive axis, including a stop mounted on the drive output and a cage mounted on the rotor, surrounding the stop. Under high acceleration, the cage engages the stop to support the rotor, relieving excess stress on the flexures of the gimbal suspension. The launch restraint system also includes deflection stops adjacent opposite sides of each web of each flexure for limiting deflection of the webs.

Full Description:
CROSS REFERENCE TO RELATED APPLICATION 
   This application is a continuation-in-part of international application PCT/CA99/00678, filed Jul. 23, 1999. 

   FIELD OF THE INVENTION 
   The present invention relates to spacecraft attitude control systems and methods. In particular, the present invention relates to a system and method for momentum management in spacecraft attitude control. 
   BACKGROUND OF THE INVENTION 
   Spacecraft attitude control systems, such as those used to control the attitudes of satellites, are based on the direct control of angular momentum. The goal of such systems is to point a satellite, or portions of a satellite, at the earth, other celestial bodies, or another spacecraft. Attitude control may be achieved by maintaining a non-zero angular momentum state by including spinning bodies within the spacecraft. Such spacecraft are generally called body stabilized or three axis spacecraft. The present invention is intended for such three axis spacecraft, whether in geosynchronous or low earth orbit missions. 
   High accuracy three axis attitude control is currently based on control of stored angular momentum. For high accuracy, it is possible to use three or more reaction wheels, so that the total angular momentum magnitude and direction can be controlled, within the spacecraft body, by varying the speeds of each of the wheels. The wheels are usually mounted in an orthogonal triad. To provide redundancy, an additional wheel must be supplied for each axis, a costly and heavy approach. Control versatility can also he obtained with four wheels mounted in a skewed configuration so that any three wheels can be used for control in the event of the failure of any one wheel. A major drawback of the multi-wheel configurations is the number of wheels, with attendant redundancy, and the associated duplicated electronic boxes which are needed. 
   An alternative momentum management system uses a double gimballed momentum wheel in which a single momentum wheel is mounted within a two axis gimbal fixed to the spacecraft. Actuation of the gimbals to re-orient the momentum wheel provides control of the angular momentum within the spacecraft body as required for control while limiting the total number of rotors to just a prime and redundant system. A conventional double gimballed wheel consists of a momentum wheel mounted on a platform which can articulate. A trio of stepper motor driven linear jack screws is used to provide the tilt capability. The three actuators are needed to provide some redundancy in each wheel since jack screws can wear and eventually fail. A total angular deviation of about 6 degrees is adequate for this configuration. In principal, the double gimballed wheel has all the advantages of three reaction wheels with a momentum control capability in all directions while using but a single wheel. However, it suffers from two major disadvantages. The first is a result of the actuators which operate in discrete steps. This limits the pointing accuracy and requires careful nutation control. The second disadvantage is the complex mechanical configuration. It has numerous points of possible failure. These extra mechanisms add mass and cost and unreliability which are not desirable for small, low cost satellites. 
   It is noteworthy that all of the current momentum management approaches, provide momentum control only and cannot be used to measure body rotation rates. 
   It is, therefore, desirable to provide a novel system and method for momentum management in spacecraft attitude control that obviates or mitigates the disadvantages of the prior art. 
   SUMMARY OF THE INVENTION 
   According to one aspect of the present invention there is provided, in a momentum management system for attitude control of a spacecraft, the system having: 
   a housing to be fixed to the spacecraft; 
   a momentum wheel rotor in the housing and rotatable about a rotor axis for storing angular momentum; 
   a gimbal assembly mounting the rotor in the housing; 
   a drive having an output rotatable about a drive axis, the output being coupled to the rotor for rotating the rotor; and 
   a torque generation device for imparting torque to the rotor about axes orthogonal to the drive axis, the improvement wherein: 
   the gimbal assembly comprises a gimbal ring coupling the drive output to the rotor; and 
   the gimbal ring includes respective flexure joints connecting the gimbal ring to the drive and the rotor, the flexure joints being configured to permit the rotor to tilt about two flexure axes orthogonal to the drive axis, to incline the rotor axis through a range of angles from about 0 degrees to about 7 degrees with respect to the drive axis under the control of said torque generation device. 
   Thus, the gimbal suspension for the rotor is a spinning gimbal. Spinning gimbals have been used in the past with tuned rotor gyros (TRG) as rate sensors. Examples are found in U.S. Pat. Nos. 4,528,864 and 4,825,713. The requirements for these devices conflict with those of momentum actuators. A TRG operates about a null (zero tilt angle) with respect to the case of the device. Torque coils are used to null the tilt angle, with the required input to the coils serving as the measure of the rotation rates being monitored. This contrasts with the present momentum management system, where torque is applied to the rotor to cause a rotation out of the null position and thus cause an alteration of the spacecraft attitude. 
   The preferred flexure joint is formed from two resilient, crossing webs. The webs have ring ends connected to the body of the gimbal ring and mounting ends connected to either the drive and the rotor. 
   The system may include a launch restraint system to limit movement of the rotor along the drive axis, including a stop mounted on the drive output and a cage mounted on the rotor, surrounding the stop. Under high acceleration, the cage engages the stop to support the rotor, relieving excess stress on the flexures of the gimbal suspension. The launch restraint system may also include deflection stops adjacent opposite sides of each web of each flexure for limiting deflection of the webs. 
   According to another aspect of the present invention there is provided a momentum management system for attitude control of a spacecraft, the system having: 
   a housing; 
   a rotor drive having an output rotatable about a drive axis, the drive axis being fixed with respect to the housing; 
   a gimbal assembly connected to the drive output; 
   a momentum wheel rotor rotatable about a rotor axis for storing angular momentum, the rotor being mounted on the gimbal to be rotated about the drive axis by the rotor drive and for tilting movement about transverse axes orthogonal to the drive axis; 
   a torque generation device for tilting the rotor about the transverse axes; and 
   a sensor for measuring the rotation of the rotor about the rotor axis, the sensor comprising:
         a part spherical surface on the momentum wheel rotor;   a pattern formed on the part spherical surface; and   a sensor mounted at a fixed position relative to the housing and positioned adjacent the part spherical surface for detecting the passage of the pattern past the sensor with rotation of the rotor.       

   TRGs use magnetic sensors to measure tilt error, but these devices can only operate over an extremely small tilt angle, amounting to fractions of a degree. They are null sensors and become rapidly nonlinear as the tilt angle deviates from zero. The momentum wheel rotor must be capable of a much larger tilt range, and the sensor must be able to operate reliably over a wide tilt range. The part spherical rotor surface ensures that the spacing between the sensor and the rotor pattern remains essentially constant regardless of the tilt angle. 
   To detect the tilt angle, the pattern may have leading and trailing edges with a spacing circumferentially of the rotor that varies with position along the rotor axis. It may, for example be triangular. The sensor may then detect the leading and trailing edges of the pattern. The timing between the edges as detected by the sensor may be used to determine the tilt angle of the rotor. 
   The sensor may be an optical sensor responding to changes in reflected light from an optical emitter. It may alternatively be a magnetic sensor responding to changes in the magnetic field as the pattern moves past the sensor. 
   According to another aspect of the present invention there is provided a momentum management system for attitude control of a spacecraft, the system having: 
   a drive having a rotatable output about a drive axis; 
   a gimbal assembly connected to the drive output; 
   a momentum wheel rotor rotatable about a rotor axis for storing angular momentum, the rotor being mounted on the gimbal to be rotated by the drive and for rotation about transverse axes orthogonal to the drive axis; 
   a torque generation device for imparting torque to the rotor about the transverse axes, the torque generation device comprising:
         an inner permanent magnet annulus mounted on the rotor, concentric with the rotor axis and with poles spaced apart by a pole spacing dimension along the rotor axis;   an outer permanent magnet annulus mounted on the rotor, concentric with the rotor axis and spaced radially from the inner permanent magnet annulus, with poles spaced apart by the pole spacing dimension along the rotor axis;   a torque coil annulus between the inner and outer permanent magnet annuli and concentric with the drive axis, the torque coil annulus having a core with a dimension axially of the drive axis that is greater than the pole spacing dimension.       

   By spacing the upper and lower parts of the torque coil at a distance greater than the pole spacing of the permanent magnets, the variation in the torque scale factor is reduced significantly to be nearly constant over the operational tilt range of the rotor. This makes calibration of the device as a rate sensor much simpler. 
   According to a further aspect of the present invention there is provided a momentum management system for attitude control of a spacecraft, the system having: 
   a drive having a rotatable output about a drive axis; 
   a gimbal assembly connected to the drive output; 
   a momentum wheel rotor rotatable about a rotor axis for storing angular momentum, the rotor being mounted on the gimbal to be rotated by the drive and for rotation about transverse axes orthogonal to the drive axis; 
   a torque generation device for imparting torque to the rotor about the transverse axes, the torque generation device comprising:
         inner and outer permanent magnet annuli mounted on the rotor, concentric with the rotor axis and spaced apart radially with respect to the rotor axis;   a torque coil annulus between the inner and outer permanent magnet annuli and concentric with the drive axis; and   a ferromagnetic cage mounted on the rotor and surrounding the inner and outer permanent magnet annuli and the torque coil annulus.       

   The ferromagnetic cage is used minimize disturbance torques introduced by external magnetic fields. Unlike with TRGs, this function cannot be provided by the housing of the device because the large rotor tilt angles relative to the housing during operation would induce significant magnetic hysteresis. This will compromise the rate sensing precision that can be obtained. 
   Because the magnetic properties of permanent magnets are temperature dependent, thermal sensors may be used within the ferromagnetic cage for measuring the temperature of the magnets. This can be used as an input to the calibration of the system. The preferred sensors are miniature non-contact infra-red (IR) sensors, for example microbolometers mounted on the support for the torque coils inside the magnetic cage. The cage preferably has its inner surface coated with a high emissivity material, for example flat black paint, so that the IR signal from the sensor is not dependent on rotor tilt, but only on the temperature of the magnets. This avoids any need to thermally control the whole device. 
   According to another aspect of the present invention there is provided, in a method of manufacturing a gimbal assembly comprising:
     (i) providing a substantially cylindrical inner ring;   (ii) providing a substantially cylindrical outer ring larger than the inner ring;   (iii) mounting the inner ring coaxially within the outer ring;   (iv) forming openings through opposite lateral sides of said inner and outer rings by wire electric discharge machining with substantially planar flexures extending across the openings and inclined to the axes of the rings;   (v) separating the inner and outer rings;   (vi) re-orienting the inner and outer rings to re-align the openings with the flexures perpendicular to one another; and   (vii) welding said inner and outer rings together to form a gimbal ring, the improvement comprising:
 
after separating the rings and before re-orienting the rings, removing re-cast material from the flexures.
   

   Where the gimbal is machined using travelling wire electrical discharge machining (EDM) techniques, the flexures are left with an uneven surface and a re-cast layer that is susceptible to fatigue crack initiation. With small deflections and low stresses, as with a TRG, this is not a significant problem. However, with the momentum management system, the tilt angles and stresses are relatively large and the surface treatment to remove the re-cast layer significantly improves the fatigue life of the flexures. 
   The re-cast removal process may include treating the flexures with an abrasive slurry. They may also be chemically etched to provide a smooth surface finish. Other surface modification techniques may be applied, for example micro-peening, to further extend the fatigue life of the flexures. 
   According to yet another aspect of the present invention there is provided a method of tuning a gimbal ring for use in a gimbal assembly, the ring comprising a substantially cylindrical gimbal ring with a centre of mass, a ring axis through the centre of mass, slots in the ring separating diametrically opposed mounting sections of the ring from the remainder of the ring, and resilient flexures coupling respective ones of the mounting sections to the remainder of the ring, the flexures having flexure axes passing through the centre of mass, the method comprising removing material from axially opposite ends of the ring so as to maintain the centre of mass of the ring at the intersection of the ring axis and the flexure axes. 
   Trimming the gimbal ring provides for a large range of tuned speeds without changing any other design features of the device. 
   According to another aspect of the present invention there is provided a momentum management system for attitude control of a spacecraft, the system having: 
   a rotor drive having an output rotatable about a drive axis at a variable drive output speed; 
   a gimbal assembly connected to the drive output; 
   a momentum wheel rotor rotatable about a rotor axis for storing angular momentum, the rotor being mounted on the gimbal to be rotated about the drive axis by the rotor drive and for tilting movement about transverse axes orthogonal to the drive axis; 
   a torque generation device for tilting the rotor about the transverse axes; 
   a sensor for measuring the speed of the rotor rotation about the rotor axis and generating a sensor output representative of said speed; and 
   drive control means responsive to the sensor output for varying the drive output speed so as to maintain the speed of the rotor rotation substantially constant. 
   The kinematics of the gimbal assembly cause the rotor angular velocity to oscillate slightly at a frequency of twice the spin rate when the drive is driven at a constant angular velocity. This oscillation produces large loads on the gimbal flexures and also reduces the rate sensing accuracy. Therefore, the speed control for the drive uses the rotor speed and mot the drive speed as its input speed. The rotor is then driven at a constant speed, with the drive speed oscillating to compensate. The moment of inertia of the very small compared to that of the rotor so that the drive oscillation has a negligible effect on gimbal flexure loading and does not significantly affect the rate sensing measurements. 
   According to a further aspect of the present invention there is provided a combined momentum management and rate sensor apparatus for spacecraft attitude control, comprising: 
   a rotor drive having an output rotatable about a drive axis at a variable drive output speed; 
   a gimbal assembly connected to the drive output; 
   a momentum wheel rotor rotatable about a rotor axis for storing angular momentum, the rotor being mounted on the gimbal to be rotated about the drive axis by the rotor drive and for tilting rotation about transverse axes orthogonal to the drive axis; 
   a torque generation device for rotating the momentum wheel rotor about the transverse axes to vary the spacecraft attitude; 
   a sensor for measuring the rotor rotation about the transverse axes, and for generating a sensor output representative of the measured rotation; 
   a processor for receiving the sensor output and calculating from the sensor output spacecraft rotation rates about said transverse axes; and 
   an attitude control for controlling operation of the torque generation device in accordance with the rotation rates calculated by the processor. 
   The device thus acts as both a momentum control actuator and as a rate sensing gyro. This is a considerable simplification of systems that use separate elements for these different functions. In the preferred combined device, the sensor measures both the rotor speed and tilt. Because the device provides both functions, rate measurements are required when operating at a non-tuned speed, the rotor is at a non-zero tilt angle and the tilt angle is varying with time. To improve precision under these conditions, the control system includes notch filters for filtering frequencies from the sensor output equal to the rotor speed of rotation and twice the rotor speed of rotation. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Presently preferred embodiments of the present invention will now be described by way of example only, with reference to the attached drawings in which: 
       FIG. 1  is an isometric view, partially cut-away of a momentum management system according to the present invention; 
       FIG. 2  is a cross section of the system of  FIG. 1 ; 
       FIG. 3  is an isometric view of a gimbal; 
       FIGS. 4   a  and  4   b  are schematic views of a cross flexure pivot, showing the flexure pivot with no relative rotation and with relative rotation, respectively; 
       FIGS. 5   a  and  5   b  show isometric views of outer and inner gimbal rings, respectively; 
       FIGS. 6   a  and  6   b  are cross sectional views of a launch restraint stop and cage, showing the rotor in undeflected and deflected positions, respectively; 
       FIG. 7  shows a cross section of a launch restraint for a flexure pivot; 
       FIG. 8  is a cross section of one embodiment of torque coils and axial rotor magnets; 
       FIG. 9  is a cross section of another embodiment of torque coils and radial rotor magnets; 
       FIG. 10  is a block diagram of a momentum management control system; 
       FIG. 11  is a block diagram of a motor speed control circuit of the control system of  FIG. 10 ; 
       FIG. 12  is block diagram of a spacecraft attitude control system; 
       FIG. 13  is an isometric view, partially broken away illustrating an adjustable mounting of the gimbal on the drive shaft; and 
       FIG. 14  is a cross section showing an alternative embodiment of the torque actuator. 
   

   DETAILED DESCRIPTION 
   Embodiments of a momentum management system  10  according to the present invention will now be described with reference to the accompanying drawings. Momentum management system  10  is a form of double gimballed momentum wheel based on a spinning gimbal assembly  12 , as opposed to the conventional non-spinning gimbal. A spinning gimbal provides the capability to control the angular momentum about three axes, and to provide two axes of angular velocity measurement at the same time. 
   Referring particularly to  FIGS. 1 and 2 , system  10  includes a rotor  14  mounted in a housing  16  of non-ferromagnetic material and suspended by a gimbal assembly  12 . Gimbal assembly  12  includes a cylindrical gimbal ring  18 . Four flexure joints  20  are arranged orthogonally around the ring. The ring is connected through the flexure joints to the rotor  14  and to a drive shaft  22  which is the drive output of a drive  25  including a motor  74  mounted in the housing. The gimbal assembly  12  behaves somewhat like a universal joint, allowing the drive shaft and rotor to rotate about non-aligned axes. Four sensors  24  are mounted on the housing around the rotor to measure the tilt angles of rotor  14  and the rotor speed. An annular torque generator  27  surrounds the rotor and serves to control the rotor tilt angles. 
   The momentum management system  10  may be treated as a system of three rigid bodies coupled by flexure joints. The three bodies are: drive  25 , including the motor  74  and its drive shaft  22 ; gimbal ring  18 ; and rotor  14 . The drive shaft  22  is coupled to the gimbal ring  18  by two diametrically opposed flexures  20   a . The gimbal ring  18  is in turn coupled to rotor  14  by two other diametrically opposed flexures  20   b . A full non-linear three body analysis, as described in detail below, can be simplified considerably by assuming that the tilt angles are small, in which case linear equations result and the problem reduces to an equivalent two body problem in which motor  74  is controlled to a constant speed. The linear analysis provides insight but is not completely accurate as the tilt angles increase beyond more than a few degrees. A fill non-liner analysis of the three body problem cannot be solved explicitly but can be simulated. In this case it is found that if the motor speed control system is derived from error signals obtained from rotor  14  rather than from motor  74 , and with a wide bandwidth, then the three body system approaches the two body linear system in performance. These results allow for calibration of system  10  as a rate sensor as well as an actuator. 
   The torque generator  27  includes radially spaced inner and outer permanent magnet rings or annuli  30  mounted in a downwardly open channel  31  in the rotor  14 , as shown in  FIGS. 1 and 2 . The torque generator  27  also includes four torque coils  28  arranged in two pairs spaced uniformly around the drive shaft  22 . The coils  28  are mounted on the housing by a torque coil stand  29 , as shown in  FIG. 2 , and are located between the two permanent magnet rings  30  in rotor  14 . Coils  28  are made using a very fine copper wire (e.g., 32 gauge) wound around a form with a large number of turns (e.g., 400 turns). When a voltage is applied to coils  28 , the resulting current in coils  28  interacts with the magnetic flux B in the gap between rotor magnets  30 , imparting an axial force on rotor  14 . A pair of coils  28 , opposite each other, and with the current running in opposite directions, is used to impart a moment on rotor  14  without imparting a net force. The torque required to move rotor  14  or hold it fixed is related to the angular rates of the spacecraft. Hence, the measured current in coils  28  can be used in computing the rate measurements about two orthogonal axes. 
   A cross section of coils  28  and rotor magnets  30  is given in  FIG. 9 , showing the magnetic configuration and the direction of the magnetic flux in the gap where coils  28  are located. The configuration shown in  FIG. 8  uses permanent magnets that are axially magnetized. In this case, the rotor material used is non-ferromagnetic allowing the flux to be concentrated in the gap between the magnets. Also with this configuration, the outer magnet width can be sized so that the magnetic flux external to the rotor can be made very small, Another possible magnetic configuration is one that uses permanent magnet rings that are radially magnetized. This configuration is shown in  FIG. 9 . In this case, rotor  14  is made from a ferromagnetic material I 0 to provide a flux path between the magnets. 
   In the permanent magnet design of  FIG. 8 , the axial length of the magnets relative to the torque coil geometry determines performance. If one plots the magnetic strength along the axial direction in the middle of the gap in between magnets  30 , the flux will have sharp peaks at the ends of magnets  30 . However, over the tilt range of rotor  14 , it is highly desirable to maintain a constant torque scale factor (i.e., N−m/Amp) from the torque coils  28  to improve the calibration. This can be accomplished by selecting the length of magnets  30  appropriately. If the magnets are too short, the torque scale factor is reduced as the tilt angle is increased. Similarly if the magnets too long, the torque scale factor increases as the tilt angle is increased. A similar situation exists with the radial magnets shown in  FIG. 9 , however in this case, the axial spacing between the upper and lower magnets is the determinant parameter. The radial magnets can have an advantage over the axial magnets as they tend to flatten out and widen the magnetic flux peaks which helps to further reduce the variation of the torque scale factor over the range of tilt angles. The desired scale factor reduction can be achieved by making torque coil with a core with a dimension axially of the drive axis that is greater than the axial pole spacing dimension, that is the distance between the poles of the permanent magnet rings. With this relationship, the scale factor remains nearly constant over the full operational tilt range. 
   The rotor  14  has an outer, part spherical surface  32  as shown most particularly in  FIG. 2 . A pattern of relieved triangular areas  33  is etched into this surface as shown in  FIG. 1 . This etched pattern  33  is used with the tilt sensors  24  to establish the tilt angles of rotor  14 . The tilt sensors  24  inductive pick-offs  34  that use a small sensing coil located very near the part spherical surface  32 , as shown in  FIG. 1 . The pattern  33  on rotor  14  introduces a changing gap size between tilt sensor  24  and the ferromagnetic rotor surface as rotor  14  rotates past one of tilt sensors  24 . This changing gap introduces a signal in the tilt sensor coil  34  that can be used to measure the rotor tilt. The principle is that as a single triangular etched pattern  32  rotates past the sensors  24 , the leading edge of the pattern  32  causes a current spike in sensing coil  34  and the trailing edge of pattern  32  causes a negative current spike. Since pattern  32  is triangular, the time between the leading edge pulse and the trailing edge pulse is related to the rotor tilt for a given rotor speed. When tilt sensor  24  is near the top part of pattern  32 , the pulses are further apart, and when sensor  24  is near the bottom part of pattern  32 , the pulses are closer together. To remove any dependence on the rotor spin rate, the ratio T 1 /T 2  is defined where T 1  is the time between the leading edge pulse and the trailing edge pulse and T 2  is the time between the leading edge pulses of two consecutive patterns. Then the tilt angle is proportional only to the ratio T 1 /T 2  (assuming the spin rate remains constant over the measurement interval). Tilt sensors  24  are arranged in pairs of diametrically opposed sensors as shown in  FIG. 1 , with one pair used to measure the tilt about an axis defined by the two sensors and the other pair is used to measure the tilt about another axis orthogonal to the first. 
   With the permanent magnet design shown in  FIG. 9 , the rotor material is non-ferromagnetic (e.g., stainless steel), to actuate the inductive pick-offs, a ferromagnetic ring  36  is press fit onto the stainless steel body of the rotor and the pattern  33  is etched into the ferromagnetic ring. Other embodiments may use other types of senor and pattern, for example a visible pattern and an optical pick-off. 
   The top surface of rotor  14  is polished to a mirror finish to allow for fine calibration of system  10 . 
   The configuration of the gimbal assembly  12  is illustrated most particularly in  FIGS. 3 ,  4  and  5 . The gimbal attaches the rotor  14  to the drive shaft  22 . It incorporates the flexure joints  20  that permit the rotor  14  to tilt about two axes x and z orthogonal to the axis y of shaft  22 . Two of the flexure joints, diametrically opposed and designated  20   a  in the drawings, are used to couple the gimbal ring  18  to the rotor, while the other two diametrically opposed flexure joints, designated  20   b , are used to couple the gimbal ring  18  to the drive shaft  22 . The gimbal assembly includes four pairs of axial slots  37  in the ring, with the slots of each pair extending from the top end of the gimbal to a respective circular aperture  38  through the gimbal ring. The slots separate four spaced mounting sections  39  and  40  of the ring from the remainder of the ring. Mounting sections  39  are diametrically opposed, as are mounting sections  40 . The resilient flexures  20  couple the mounting sections  39  and  40  to the remainder of the ring. Each flexure has two independent, substantially planar webs  42   a  and  42   b  extending across a respective one of the circular openings to join the gimbal ring to the associated mounting section. The webs cross, in this embodiment at right angles, with one web inside the other. The points  44  at which the webs cross are on two orthogonal flexure axes which pass through the centre of mass of the gimbal. 
   At the top of the gimbal is a drive shaft mounting flange  45 . This has a generally circular centre  46  and two diametrically opposed spokes  47  that are secured to the gimbal ring mounting sections  40 . The drive shaft mounting flange is fixed to the drive shaft to rotate the gimbal with the shaft. The other two mounting sections  39  connected to a rotor mounting flange  48  around the gimbal ring by radial spokes  49 . 
   The cross configuration of the webs  42   a  and  42   b  allows the rotor mounting flange, and the rotor to which it is attached, to rotate relative to drive shaft mounting flange and the drive shaft while keeping the centre of rotation very close to the intersection of the flexure axes. 
   The material used for webs  42  should have a resistance to fatigue sufficiently high that under the stresses encountered during normal operation the flexures  20  will have an essentially infinite life. In a presently preferred embodiment, the material used for gimbal  18  and webs  42  is AerMet 100 which has a yield stress of nearly 300 ksi and a fatigue limit of over 100 ksi. 
   Gimbal ring  18  also has a set of balance screws  50  as shown in  FIG. 3  that can be adjusted during calibration to ensure that the mass centre of gimbal ring  18  is located at the intersection of the flexure axes. 
   When spinning rotor  14  is oriented so that there is an angle between drive shaft  22  and the rotor spin axis, gimbal ring  18  tends to flutter with a frequency of twice the spin frequency. The tuned speed of system  10  is that which causes the inertial forces resulting from the gimbal ring flutter to counter the torsional spring forces arising from deformed flexures  20  so that, to a first order approximation rotor  14  behaves very nearly like a free rotor in space. This is a feature that permits system  10  to be used as a precise rate sensor. 
   Gimbal  18  is designed so that the tuned speed of the system  10  can be adjusted by simply changing the height of gimbal ring  18  without altering any of the interfaces between gimbal assembly  12  and rotor  14  or drive shaft  22 .  FIG. 3  shows the full height gimbal ring  18  which corresponds to the lowest possible tuned speed. A reduced height gimbal ring corresponds to a higher tuned speed. This easily adjustable tuned speed permits the system  10  to be easily adapted for a variety of speed ranges, making it applicable to a broad class of spacecraft. The reduction in gimbal ring height can be easily implemented for each individual system  10  produced, thereby tailoring the tuned speed to specific customer requirements. 
   The spokes  47  of the drive shaft mounting flange  45  and the spokes  49  of the rotor mounting flange  48  are designed to deform under launch loads in reduce the deflection of flexures  20  in response to the deflection of rotor  14  relative to drive shaft  22 . The magnitude of the rotor deflection under load should be sufficient to engage a launch restraint system described in the following. 
   The gimbal is fabricated from two concentric cylinders  52 ,  54  that are shown in  FIGS. 5   a  and  5   b , respectively. Initially, the inner and outer cylinders are machined separately. They are then assembled concentrically. The apertures  38  are then machined into the cylinders, leaving webs  42  in place. At this point, the outer webs  42   a  and inner webs  42   b  are aligned. The cylinders are machined using, for example, a wire Electric Discharge Machining (EDM) process. Outer cylinder  54  is then rotated 180 degrees. This procedure creates the cross-flexure configuration of the flexures  20 . Inner and outer cylinders  52  and  54  are welded together at the top to form gimbal ring  18 . The two cylinders are then welded at the bottom as well. A sink EDM process can then used to remove the material required to form slots  37  to separate the mounting sections  39  and  40  shown in  FIGS. 5   a  and  5   b  by the dashed lines on gimbal inner and outer cylinders  52  and  54 . The drive shaft and rotor mounting flanges are then secured in place. 
   The system  10  incorporates a launch restraint system  61  to limit the deflection of rotor  14  during launch to ensure that flexures  20  in gimbal assembly  12  are not over-stressed. Referring to  FIGS. 6   a  and  6   b , a stop in the form of ball  64  is mounted on the drive shaft  22 . A cage in the form of part spherical cup  66  is mounted on the hub  68  of rotor  14 . Under normal operational conditions, the rotor  14  is suspended by the flexures  20  so that the cup  66  in the rotor hub  68  does not contact the ball  64 . The centre of rotation of rotor  14  is located at the centre of caging ball  64 , so that as rotor  14  tilts the gap  70  between the ball  64  and the cup  66  is maintained. Therefore, during normal operational conditions, the ball  64  does not come into contact with rotor  14  and hence does not affect the operation of system  10 . However, when loads are applied to rotor  14  during launch and also during handling, rotor  14  may be deflected until the cup  66  engages the ball  64  as shown in  FIG. 6   b . The ball  64  therefore limits the maximum deflection of rotor  14  and thus limits the maximum stress in gimbal flexure webs  42 . Although  FIG. 6   b  shows a rotor deflection in the vertical direction, the ball  64  can limit deflection of rotor  14  in any arbitrary direction. 
   To limit the angular deflection of rotor  14 , stops  71  are incorporated into rotor hub  68 , such that as rotor  14  is tilted to the maximum allowable angle, the hub  68  contacts drive shaft  22 . To limit the angular deflection and the maximum stress in webs  42  due to the tilt of rotor  14 . The size of gap  70  is selected so that webs  42  cannot be overstressed even when rotor  14  is tilted to the maximum angle. 
   As shown in  FIG. 7 , the launch restraint system includes deflection stops  72  in the circular apertures  38  to ensure that webs  42  in gimbal flexures  20  will not be overstressed. Deflection stops  72  are machined out of the parent gimbal ring material during the wire EDM operation described above. A small gap  73 , in the range of 0.1524–01778 mm, is formed between web  42  and deflection stop  72 . such that under normal operating conditions of 1 G, flexure  42  does not touch deflection stop  72 . However, under high loads, such as launch and handling loads, the lateral deflection of flexure  42  is restrained at the midpoint, allowing it to carry more load. The buckling behaviour of flexure  42  in this case is forced into a second mode that effectively increases the buckling load by a factor of  4 . Hence, it is possible to design webs  42  that will not be over stressed in the worst loading conditions. 
   Referring to  FIG. 2 , a spin motor  74  is positioned at the end of drive shaft  22  to drive the shaft at the required speed. The drive shaft is supported in the housing by bearings  75  and is connected to the gimbal assembly  12  at the top end by the mounting flange  45  on the gimbal. The bearings  75  are housed in a separate thermal sleeve  76  made from the same material as the bearings and drive shaft  22 , thus reducing thermally induced stresses on the bearings. The thermal sleeve  76  also permits removal of the complete rotor assembly, including the drive shaft, bearings, gimbal and rotor, from the housing  16  without disassembly. The drive shaft  22 , bearings  76  and the thermal sleeve  76  are a single subassembly that can be assembled and tested separately before installing into system  10 . 
   The spin motor  74  is a brushless DC electric motor that is integrated into a lower compartment  80  in a base  82  of housing  16 , as shown in  FIG. 2 . Permanent magnets are mounted on the shaft and the stator is integrated into the housing  16 . 
   Housing  16  includes a case  84 , a bottom cover  86 , and a top cover  88 . Top and bottom covers  86 ,  88  have O-ring seals and connectors that are hermetically scaled so that the complete system  10  can be evacuated and placed into a vacuum. This reduces windage effects on rotor  14  and creates a thermal environment more similar to that in space to allow for more precise calibration on the ground. 
   Housing  16  is also designed to separate an electronics package  89  and spin motor  74 , which are located in the lower compartment  80 , from gimbal assembly  12  located in the upper compartment  87 . This permits thermal isolation and active control of the rotor temperature while the lower compartment  80 , where the primary power/heat dissipating devices are located, does not require active thermal control and can have a good thermal interface to the spacecraft. 
   A theoretical analysis of system  10  will now be provided, with reference to the preceding structural description. For present purposes it can be assumed that housing  16  and motor shaft  22  are fixed in inertial space. The three elements are motor drive shaft  22 , gimbal ring  18  and rotor  14 . Motor  74  is driven at a constant speed ω s . Gimbal ring  18  is connected to shaft  22  by a pair of torsion flexures  42   a  aligned along the x-axis. Rotor  14  is connected to gimbal  18  by another pair of torsion springs  42   b  aligned along the y-axis. The x and y axes are spinning around the spin axis (z-axis) and gimbal  18  can rotate about the x-axis while rotor  14  can In turn rotate about the gimbal&#39;s y-axis. In the following, the spinning coordinates are retained until the results are transformed to non-spinning coordinates appropriate for the angle sensors, torque generators (torquers) and the rebalance control loop. 
   Let φ be the angle of rotation of gimbal ring  18  about the x-axis and let θ be the angle of rotation of rotor  14  with respect to gimbal  18 , about the y-axis. The two body dynamic equations may be derived using a vectorial or a Lagrangian dynamic formulation assuming that motor  74  speed is a constant. It will be assumed that the moment of inertia of gimbal  18  about the z or spin axis is I gs  and that gimbal  18  is symmetric with transverse inertia I gt ,. Similarly the spin axis inertia of the rotor  14  is I rs  and the symmetric transverse inertia is I rt . The dynamic equations that result are: 
                 (       I   rt     +     I   gt       )     ⁢       ω   .     rx     ⁢     C   θ       -       I   rt     ⁡     (         ω   rx     ⁢     ω   gy     ⁢     S   θ       +       ω   rx     ⁢     ω   gt         )       +       I   rs     ⁢     ω   rz     ⁢     ω   gy     ⁢     C   θ       +       (       I   rs     +     I   gt       )     ⁢       ω   .     rz     ⁢     S   θ       +       (         I   gt     ⁢     ω   gz       +     I   ⁢           ⁢     ω   rz     ⁢     C   r       -     I   ⁢           ⁢     ω   rx     ⁢     S   θ         )     ⁢     (       ω   ry     -       ω   s     ⁢     S   θ         )       -       (       I   gz     -     I   gx       )     ⁢     ω   gy     ⁢     ω   gz       +       k   x     ⁢   ϕ       =   0             and                   I   rt     ⁢     ω   ry       +       I   rt     ⁢     ω   rx     ⁢       ω   .     gz       +       k   x     ⁢   θ       =   0         
where:
     I rs  rotor inertia about the spin axis   I rt  rotor inertia about the transverse axis   I gs  gimbal inertia about the spin axis   I gt  gimbal inertia about the transverse axis   k x  x-axis flexure spring constant   k y  y-axis flexure spring constant   φ angle of rotation of the gimbal about the x-axis   θ angle of rotation of the gimbal about the y-axis   C θ  cosθ   S θ . sinθ   C φ  cos φ   S φ  sin φ   ω s  motor spin speed   ω gx  gimbal angular velocity about the x-axis   ω gy  gimbal angular velocity about the y-axis   ω gz  gimbal angular velocity about the z-ax, s   ω rx  rotor angular velocity about the x-ax&#39;s   ω ry  rotor angular velocity about the y-axis   ω rz  rotor angular velocity about the z-axts
 
Using small angle approximations, these reduce to
   
                 (       I   rt     +     I   gt       )     ⁢     ω   rx       +       (       I   gt     +     I   rs     -     I   rt       )     ⁢     ω   s     ⁢     ω   ry       +       [       k   x     -     2   ⁢     (       I   gt     -       I   gs     2       )     ⁢     ω   s   2         ]     ⁢   ϕ       =   0         
and
   I   rt ω ry −( I   rs   −I   rt ){dot over (ω)} s ω x   +k   y θ=0 
Define
 
           J   =     (       I   gt     -       I   gs     2       )           
and the nutation frequency
 
             ω   n     =         (       I   rs     +     I   gt       )       (       I   rt     +       I   gt     2       )       ⁢     ω   s             
and introduce the Laplace transform with the auxiliary variables:
 
           α   =         k   x     +     k   y     -     2   ⁢   J   ⁢           ⁢     ω   s   2             2   ⁢     I   r1       +     I   gt                     β   =         k   x     -     k   y     -     2   ⁢   J   ⁢           ⁢     ω   s   2             2   ⁢     I   rt       +     I   gt                     γ   =       I   gt         2   ⁢     I   rt       +     I   gt               
the characteristic equation may be found in the form:
 
                 (       S   2     +     ω   s   2       )     2     +           ω   n   2     -     2   ⁢     ω   n     ⁢     ω   s       +     2   ⁢     (     α   -     γ   ⁢           ⁢   β       )           1   -     γ   2         ⁢     (       S   2     -     ω   s   2       )       +         2   ⁢   α   ⁢           ⁢       ω   s     ⁡     (       ω   n     -     2   ⁢     ω   s         )         +     α   2     -     β   2         1   -     γ   2           =   0         
There are two solutions for (S 2 +ω s   2 )
 
   
     
       
         
           
             ( 
             
               
                 s 
                 2 
               
               + 
               
                 ω 
                 s 
                 2 
               
             
             ) 
           
           = 
           
             
               
                 
                   
                     ω 
                     n 
                   
                   ⁡ 
                   
                     ( 
                     
                       
                         ω 
                         n 
                       
                       - 
                       
                         2 
                         ⁢ 
                         
                           ω 
                           s 
                         
                       
                     
                     ) 
                   
                 
                 + 
                 
                   2 
                   ⁢ 
                   
                     ( 
                     
                       α 
                       - 
                       γβ 
                     
                     ) 
                   
                 
               
               
                 2 
                 ⁢ 
                 
                   ( 
                   
                     1 
                     - 
                     
                       γ 
                       2 
                     
                   
                   ) 
                 
               
             
             ⁢ 
             
               
 
             
             ± 
             
               
                 1 
                 2 
               
               ⁢ 
               
                 
                   
                     
                       
                         
                           
                             [ 
                             
                               
                                 
                                   
                                     ω 
                                     n 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         ω 
                                         n 
                                       
                                       - 
                                       
                                         2 
                                         ⁢ 
                                         
                                           ω 
                                           s 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       α 
                                       - 
                                       γβ 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 2 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       γ 
                                       2 
                                     
                                   
                                   ) 
                                 
                               
                             
                             ] 
                           
                           2 
                         
                         - 
                       
                     
                   
                   
                     
                       
                         4 
                         ⁡ 
                         
                           [ 
                           
                             
                               
                                 2 
                                 ⁢ 
                                 
                                   
                                     αω 
                                     s 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         ω 
                                         n 
                                       
                                       - 
                                       
                                         2 
                                         ⁢ 
                                         
                                           ω 
                                           s 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                               
                               + 
                               
                                 α 
                                 2 
                               
                               - 
                               
                                 β 
                                 2 
                               
                             
                             
                               1 
                               - 
                               
                                 γ 
                                 2 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
             
           
         
       
     
   
   There are also two more solutions when the square root is taken. Thus there are four roots in all. The classic condition for tuning a timed rotor gyro is the condition that α=0. that is: 
               k   x     +     k   y       =     2   ⁢   J   ⁢           ⁢     ω   s   2             
and if k x =k y =k say, then the classic tuned condition is
 
   
     
       
         
           k 
           = 
           
             J 
             ⁢ 
             
                 
             
             ⁢ 
             
               
                 ω 
                 s 
                 2 
               
               . 
             
           
         
       
     
   
   The resulting roots may be transformed to non-spinning coordinates by adding ω s , and it will then be found that the first of the roots is a resonance at twice the spin frequency and the second root is the nutation frequency. The third root is an additional resonance which presumably represents a beat frequency between the gimbal oscillations and the rotor nutation. The last of the roots is at a very low frequency and will appear as a drift rate or slow precession as the result of an off-null rotor, precessing in a coning motion. This last root, which in the two body linear model can be precisely defined, provides a determination of the effect of spin speed and rotor tilt angle on control torque requirements. Consequently, since the roots may be calculated and calibrated accurately, the effect of a rotor tilt angle and non-fined speed can be precisely calculated and subtracted from the torquer measurements so that angular velocities may be measured under any rotor condition. 
   A higher degree of tuning can be obtained directly from the characteristic equation if the last term is set to zero. The resulting low frequency root will then be identically zero and no drift will be experienced. This more precise tuning condition is:
 
2αω s (ω n −2ω s )+α 2 −β 2 =0
 
which may be approximated for small values of J to give:
 
   
     
       
         
           k 
           ≈ 
           
             J 
             ⁢ 
             
                 
             
             ⁢ 
             
               
                 ω 
                 s 
                 2 
               
               ⁡ 
               
                 [ 
                 
                   1 
                   + 
                   
                     
                       J 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ω 
                         s 
                       
                     
                     
                       
                         ( 
                         
                           
                             2 
                             ⁢ 
                             
                               I 
                               rt 
                             
                           
                           + 
                           
                             I 
                             gt 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             ω 
                             n 
                           
                           - 
                           
                             2 
                             ⁢ 
                             
                               ω 
                               s 
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 ] 
               
             
           
         
       
     
   
   This maybe considered as a condition on the flexure stiffness k. or on the spin speed ω s . For system  10 , this precise tuned condition identifies the nominal spin speed. A more complete analysis can also be done by a three body analysis which includes the inertial properties of motor  74  and drive shaft  22 , however, such analysis is beyond the scope of this disclosure. 
   A control system  90  is intended to provide high efficiency drive for motor  74 ; provide precise rotor speed control; process pulses for tilt sensors  24 ; provide drive of rotor torque coils  28 ; measure the torque current to the highest possible precision; monitor the system temperature; provide a microcomputer for general processing; provide a serial interface to the spacecraft attitude control system, or flight computer, to accept momentum commands (speed and 2-axis tilt), and possible software uploads; and support calibration of system  10  for temperature and non-linear effects. 
   A limitation with inertial measurement systems is often the electronics rather than the mechanical components. Control system  90  uses digital control to achieve the level of performance required, and includes electronics  89 . Electronics  89  are built into the lower compartment  80  of housing  16  to control torque coils  28 . Referring to  FIG. 10 , electronics  89  include a microcomputer  91  provided with appropriate software applications, A/D and D/A converters  92 ,  93 , respectively, a phase locked loop  94 , amplifiers  95 , and power supplies (not shown). While there are actually four torque coils  28 , two drivers  97  have been found sufficient if pairs are connected in parallel or series. Four drivers  97  can be used if it is desired to provide soft failure redundancy. Electronics  89  further include a speed control  98 . and a motor drive  99 . 
   A block diagram of motor speed control circuit  98  is shown in  FIG. 11 . The required speed range for rotor  14  is typically 1300–1600 revolutions per minute (rpm). The speed is measured using a tachometer (not shown) with K z  pulses per revolution. The reference frequency for the phase locked loop  94  is derived using a 4N counter  104 . This gives non-linear control, but computer  91  can calculate the required N and the hardware is simpler that using an accumulating rate multiplier or DDS to synthesize the reference. The phase locked loop  94  uses a phase/frequency detector  106  to automatically acquire lock after a step speed change. The rotor  14  speed can be given, in revolutions per second (rps), by: 
           Speed   =       F   ref       NK   z             
Where,
 
   F ref  is the crystal oscillator frequency 
   N is the divider value 
   K z  is the tachometer pulses per revolution 
   Therefore, selecting K z  is a compromise between noise and speed resolution, both of which can affect spacecraft jitter. A large K z  reduces noise by increasing the frequency of the pulses at the phase detector. This shifts the frequency of the noise components at the output of the phase detector outside the bandwidth of the phase looked loop  94  where it can be attenuated by filtering. It also reduces the required gain after the phase detector which can reduce noise, However, a large K z  decreases the speed resolution which increases jitter when the speed control 98 switches speeds. Assuming a 10 MHz reference, K z =8, and 500:1 spacecraft to rotor momentum ratio, the spacecraft jitter caused by finite speed resolution can vary from 0.0004 to 0.005 0 /sec. Depending on the rotor speed. 
   Motor  74  consumes a significant portion of the power budget and a high efficiency motor drive  99  is required. The motor speed range is typically in the range of 1500±200 rpm to 5200±800 rpm. A suitable motor drive  99  should be ˜90% efficient, and provide regenerative breaking when a negative torque is commanded. 
   Control system  90  also compensates for temperature dependent effects. The main source of temperature dependence is likely permanent magnets  30 , particularly if ceramic magnets are used, which have a 0.6% PC temperature coefficient. A thermistor sensor  110  can provide temperature readings, and is unaffected by nuclear radiation, Microcomputer  91  processes the temperature readings to provide suitable calibration to system  10 . 
   For earth pointing missions, the spacecraft pitch dynamics decouples from the roll-yaw dynamics which allows a pitch controller to be designed separately from a roll-yaw controller (note: the roll and yaw dynamics remain coupled due to the momentum bias). System  10  provides control torques about all three axes, and hence can be used for an attitude control system  150 , as shown in  FIG. 12 . However, since it also provides rate measurements about the roll and yaw axes, this provides for significantly simplified and improved control system for the roll-yaw dynamics of the spacecraft. In particular, since the roll and yaw attitude errors are coupled due to the momentum bias, then system  10  is controllable by only using a roll measurement, which can be obtained using an earth sensor, and the roll and yaw rate measurements. Therefore, to achieve fine pointing control in all three axes with system  10 , only a two-axis earth sensor is required that provides a pitch and roll angle measurement, where the pitch angle is used for the pitch control loop. This eliminates the need for a separate sensor (e.g., a sun sensor or a star camera) to directly measure yaw which simplifies the design of attitude  20  system  150  and significantly reduces the cost. Also, the performance of attitude control system  150  is not affected by going in and out of eclipse as it would be if a sun sensor is used to determine yaw as is the ease for most earth pointing spacecraft. 
   A classical PD control system can be used for the pitch axis control where the control law is expressed as:
 
 M   y   =−K   p α y   −K   d{dot over (α)} 
 
where K p  and K d  are the proportional and derivative gains respectively, α y  and {dot over (α)} y  are the pitch angle and pitch rate, and M y  is the control torque about the spacecraft pitch axis. The pitch angle α y  can be obtained from an earth sensor and the pitch rate {dot over (α)} y  is estimated using a finite difference scheme:
 
               α   .     y     =         α   y     -     α   y   pre         Δ   ⁢           ⁢   t             
where α y   pre  is the pitch angle at the previous sampling time and Δt is the controller time step.
 
   For the roll-yaw control, a direct output feedback control structure can be used as follows 
             {           M   x               M   z           }     =       [   F   ]     ⁢           ⁢     {           α   x               ω   x               ω   z           }             
where M x  and M z , are the control torques about the spacecraft roll and yaw axes, [F] is the feedback gain matrix; α x  is the roll angle measurement, and ω x  and ω y : are the measured inertial rates of the spacecraft about roll and yaw axes respectively. This arrangement, as shown in  FIG. 12 , uses earth sensor measurements and measurements from system  10  directly and does not require an attitude determination algorithm to process the measurement data which further simplifies the ACS design. Since the roll and yaw axes are dynamically coupled, this control structure can provide fine pointing control in both the roll and yaw axes and there is no need to explicitly estimate the yaw angle (although this is also possible).
 
   To establish appropriate values for the feedback gain matrix [F], a WHECON control structure  151  can be used with an added yaw rate feedback loop  152 . The classical WHECON control algorithm makes use of the coupling between the roll and yaw dynamics of the system to express the control law as follows:
 
 M   x   =−K (α x +τ{dot over (α)} x )cos φ
 
 M   z   =K (α x +τ{dot over (α)} x )sin φ
 
where K is the proportional gain, τ is the damping gain, and φ is the constant offset angle (selected based on the spacecraft inertial properties), and α x  and {dot over (α)} x  are the roll angle and the roll rate. To improve the control performance particularly in yaw, an additional yaw rate feedback loop is designed using rate measurement about the yaw axis ω z , and also rate measurement about the roll axis ω x  is used in place of roll rate {dot over (α)} x  as provided by system  10 . The roll-yaw control law therefore becomes as follows:
 
 M   x   =−K (α x +τω x )cos φ
 
 M   z   =K (α x +τω x )sin φ− K   r ω z 
 
where K r  is the rate feedback gain ω x  and ω z  are the components of the spacecraft rates about the roll and yaw axes measured by system  10 . The control law can be put into matrix form and the feedback gain matrix [F] then becomes:
 
   
     
       
         
           
             [ 
             F 
             ] 
           
           = 
           
             [ 
             
               
                 
                   
                     
                       - 
                       K 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     cos 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     ϕ 
                   
                 
                 
                   
                     
                       - 
                       K 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     τ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     cos 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     ϕ 
                   
                 
                 
                   0 
                 
               
               
                 
                   
                     K 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     ϕ 
                   
                 
                 
                   
                     K 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     τ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     ϕ 
                   
                 
                 
                   
                     - 
                     
                       K 
                       r 
                     
                   
                 
               
             
             ] 
           
         
       
     
   
   This structure for the roll-yaw control law only has four parameters to be specified to establish the gain matrix (K, τ, φ, and K r ), each of which has some practical interpretation for an orbiting, bias momentum spacecraft. Therefore, this makes it much easier to select an optimal set of gains that provide the best performance of attitude control system  150 . 
   Another approach to establishing the gains is to specify the eigenvalues and eigenvectors for the closed loop roll-yaw dynamics. However, due to the coupling between the roll and yaw axes, it is difficult to relate the eigenvalues and the eigenvectors to the physical behaviour of system  10 . Hence, it essentially becomes a trial and error process to some extent to select the appropriate parameters. Therefore, since one has to select S parameters for the closed-loop eigenvalues and 6 parameters for the eigenvectors to design the controller, it becomes a very difficult task to select the optimum set of parameters which will give the best performance for the system. The WHECON  151  with yaw rate feedback is therefore a superior controller structure that can provide very fine pointing performance in both roll and yaw axes. 
   The feedback control loop  152  for attitude control system  150  must provide both control of the tilt angle of rotor  14  as well as minimize the addition of drift errors for purposes of measuring rates. A successful feedback control loop  152  depends on the careful control of the feedback loop phase characteristics. The basic difficulties are inherent in any tuned rotor gyroscope rebalance loop and those skilled in the art of tuned rotor gyroscope rebalance loop design will be familiar with the requirements. 
   The basic purpose of feedback loop  152  is to provide precession control of rotor  14 . A simple proportional-plus-integral controller is applied on each of the two tilt axes to ensure asymptotic tracking of the tilt demand even when the system is dc-tuned. In addition, to account for the cross-axis control requirements for precession control, a −90 degree phase shift is introduced. The justification for this can be seen most easily by examining the complex variable formulation of the rotor dynamics. However, this simple and straightforward precession control system will excite the nutation dynamics of rotor  14 . Thus, nutation damping must be included. One method for handling the nutation dynamics. as represented in the complex variable formulation of rotor  14  dynamics, is to employ low pass fillers that provides a full 180 degrees of phase shift at the nutation frequency. This ensures that as frequencies pass through the nutation resonance, the response locus with the added 180 degrees resonant phase lag and infinite gain will be restricted entirely to the right half plane. in a Nyquist analysis. It is necessary that the overall gain of this low pass phase lag loop be small enough so that the first unity gain cross over point occurs well before a 180 degree lag, that is, well below the nutation frequency. Consequently, this nutation damping approach assumes that the overall precession control bandwidth requirement is well below the nutation frequency. 
   Two other requirements are placed on the feedback control loop  152 . Firstly, signals, which are inevitably generated by tilt sensor  24  at the spin speed of rotor  14 , must be reduced to negligible amplitude using a notch filter. In addition, the gimbal motions, introduce an oscillation at twice the spin frequency in the rotation of the rotor  14 , and this will be sensed by tilt sensors  24 . These twice spin frequency signals must also be reduced to negligible amplitude using a notch filter. However, it is not possible to reduce the amplitude of these signals precisely to zero and any portion that is fed back to the rotor controller will interact with the actual twice spin frequency dynamics. The phasing of the twice spin speed feedback signal can introduce an effective drift rate in the sensed external rates applied to the system  10 . Thus, careful phase adjustment of the twice spin frequency notch filters is required to limit this drift effect. Care is needed in ensuring that the phase shifts for these notch filters and the nutation control lag filters continue to sum to roughly 180 degrees, at the nutation frequency. 
   An adjustable mounting of the gimbal ring on the drive shaft is illustrated in  FIG. 13 . As shown, the drive shaft mounting flange  45  is fixed to a flange  112  on the drive shaft  22 . Three adjustment screws  114  are screwed into bores through the drive shaft mounting flange. These screws engage the drive shaft flange  112 . These screws are used to adjust the alignment angle of the drive shaft mounting flange  45  on the shaft flange  112 . Because the flexures  20  are positioned below the drive shaft mounting flange  45 , this angle is converted to a translational positioning of the pivot axes relative to the drive shaft. This arrangement allows the correction of small transverse misalignments that could cause large static imbalances due to the large rotor mass. 
     FIG. 14  illustrates an embodiment of the invention designed to minimize disturbance torques introduced by external magnetic fields. In this embodiment the rotor  14  carries a ferromagnetic cage  120 . The permanent magnets  30  are mounted inside the cage, on opposite sides. The torque coils  28  are mounted in the centre of the cage, between the permanent magnets. The ferromagnetic cage is used minimize the disturbance torques. Unlike with TRGs, this function cannot be provided by the housing of the device because the large rotor tilt angles relative to the housing during operation would induce significant magnetic hysteresis. This would compromise the rate sensing precision that can be obtained. 
   Because the magnetic properties of permanent magnets are temperature dependent, thermal sensors  122  are mounted on the torque coil stand  29  within the ferromagnetic cage. The sensors measure the temperature of the magnets. The sensor outputs are used as inputs to the calibration of the system. The sensors are miniature non-contact infra-red (IR) sensors, for example microbolometers, mounted on the support for the torque coils inside the magnetic cage. The cage has its inner surface coated with a high emissivity material, for example flat black paint, so that the signal from the sensor is not dependent on rotor tilt, but only on the temperature of the magnets. This avoids any need to thermally control the whole device. 
   Some of the advantages and innovations of system  10 , and attitude control system  150  can be summarized as follows. Use of a spinning mechanical suspension system for rotor  14  allows for momentum steering about two axes. Such an approach, where mechanical gimbal ring  18  with flexure pivots  20  is used to support spinning rotor  14  has never before been used for a torque actuator. There are other approaches that use a magnetic suspension system that permit two axis momentum steering, and mechanical systems that tilt a spinning wheel. The use of gimbal  18  with flexure pivots  20  for suspending rotor  14  has a number of advantages. It can be designed to have infinite life with no wear-out modes and hence has much higher reliability than the magnetic suspension systems. It allows for a very simple. compact and cost effective implementation approach using torque coils  28  and permanent magnets  30  in rotor  14  to effect the momentum steering. And, it permits system  10  to be used as a precise rate sensor. 
   The gimbal design permits setting the tuned speed of system  10  to a particular value for each customer in a simple and cost-effective way that does require a design modification. This is required because a spacecraft momentum actuator must be able to perform over a relatively large speed range where the particular speed is a mission specific (i.e., customer specific) requirement. Hence each customer will have different tuned speed requirements. The tuned speed of gimbal  18  can be set by simply reducing the gimbal ring height from a baseline value which is designed for the lowest permissible tuned speed. This does not alter any other design feature in system  10 , since ring  18  is free to flutter and the material removed is off the free ends of the ring  18  ensuring that the gimbal&#39;s interface to shaft  22  and rotor  14  remain unaltered. This process can easily be accommodated for each customer as trimming the gimbal ring height requires only a few extra machining operations prior to final welding of gimbal ring  18 . 
   To operate over a relatively large tilt angle range, a tilt sensor is required that can  30  accommodate this range and yet maintain high precision through-out the range. Tilt sensor  24  which uses a relieved triangular pattern  32  on the ferromagnetic rotor surface and inductive pick-off  34  achieves this requirement and is very cost-effective to implement. Inductive pick-offs used in tuned rotor gyros and other concepts using optical techniques would not function over this required tilt range  610  deg. 
   The ability of system  10  to measure rates when the device is not operating at a tuned speed and when it is at non-zero angles was previously unachievable. This ability permits system  10  to be used as an actuator at the same lime as it is sensing rates. The conventional theory on tuned rotor gyros only addresses operating at zero angles while at the tuned speed. Therefore, the control approach and the rate sensing algorithms at untuned speeds provide key advantages. 
   Achieving a nearly constant torque scale factor over the entire tilt range 610 deg. Is an innovative feature permits significant improvement of the calibration of the system  10  over the full tilt range. By selecting the proper length of the axially magnetized permanent magnet rings  30  in rotor  14 , the resultant rotor torque applied to rotor  14  from the current in torque coils  28  remains nearly constant with tilt angle. Equivalently, if radially magnetized rings are used, then the proper axial spacing of the rings is determinant. 
   Measuring rotor speed from tilt sensors  24  for the motor speed control gives improved precision of the rate sensing, since it reduces the nonlinear precession torques that are imparted to rotor  14  when it is at a non-zero tilt angle. Inductive tilt sensors  24  are also well suited to providing the signals required for rotor spin speed measurements. The traditional approach is to use the drive shaft speed using, for example, hall sensors that are integral to spin motor  74 . However, such a high bandwidth control system could cause relatively large precession torques in system  10  when rotor  14  is at large tilt angles (e.g., a few degrees). 
   The integrated launch restraint system  61  ensures that flexures  20  cannot be overstressed under launch and handling loads without introducing other mechanisms that introduce new failure modes into system  10 . Launch restraint system  61  is completely passive and does not engage unless a large load is applied to rotor  14 . 
   The mirrored surface of the top of rotor  14  permits easy calibration. An auto-collimating telescope can be mounted to a one axis tilt table on which system  10  is also mounted to precisely align rotor  14  at specific angles relative to drive shaft  22 . This set-up can be used to statically balance rotor  14  while it is not spinning, and it can also be used to calibrate tilt sensors  24  when rotor  14  is spinning. 
   High accuracy 3-axis pointing is possible using system  10  and only one additional 2-axis earth sensor(i.e. a yaw sensor is not required) is required to provide a highly accurate and lightweight attitude control system  150 . The accuracy of this attitude control system  150  is driven by the earth sensor accuracy and the rate sensing accuracy of system  10 , and is not dependent on an environmental disturbance torque requirement. Other approaches using a single bias momentum wheel have an accuracy that is dependent on the magnitudes of the wheel momentum and the environmental torques. Attitude control system  150 , based on system  10 , in a simple 3-axis attitude control system  150  consisting of only two primary components which significantly reduces the mass, power, and cost of attitude control system  150 . 
   For earth pointing missions, the control law uses the measured roll angle from the earth sensor and the rate measurements from system  10  about the roll and yaw axes directly without the need for an attitude determination algorithm. 
   The form of the control law using the WHECON controller  151  with an additional yaw rate feedback loop  152  provides a form for the controller gain matrix that uses only four independent quantities. Since these four quantities have a practical significance, then it is possible to more easily select the set of parameters that give the best control system performance. 
   It will be apparent to those skilled in the art that the foregoing is by way of example only. Modifications, variations and alterations may be made to the described embodiments without departing from the scope of the invention which is defined solely in the claims.

Technology Classification (CPC): 1