Abstract:
A deformation compensation system for use with a large phased-array antenna system to electronically compensate for surface deformations occurring on the phased-array antenna which would otherwise compromise antenna performance. In one embodiment, a plurality of strain gauges are disposed on or integrally formed in structure forming the phased-array antenna. The strain gauges are placed at those locations on the antenna structure, where, through prior structural modeling and testing, it has been determined that high strains associated with the expected deformation of the phased-array antenna are expected to occur to a significant degree. The strain gauges output signals to a data acquisition system which uses a strain-to-displacement algorithm to produce displacements corresponding to the estimated, deformed shape of the phased-array antenna. These displacements are input to a beam steering controller which is used to generate phase shift or time delay commands used for electronically compensating, in real time, for the overall estimated, deformed shape of the phased-array antenna. The invention eliminates the need for heavy and large structural supports or trusses which have traditionally been required to maintain surface planarity of a large, phased-array antenna, and further enables the use of even larger phased-array antennas in space-based applications. The invention enables surface deformation to be compensated for in a non-intrusive manner which does not significantly increase the overall complexity of the phased-array antenna system.

Description:
TECHNICAL FIELD 
     This invention relates to large phased-array antennas, and more particularly to a structural deformation compensation system for compensating for surface deformations in a large, space-based, phased-array antenna. 
     BACKGROUND OF THE INVENTION 
     Current spacecraft often employ large, phased-array antennas to perform reconnaissance missions, collect radar images, track ground-based and air-based targets and provide high bandwidth communications. These large, phased-array antennas are made up of a large plurality of independent antenna elements. The surfaces forming the phased-array antenna must be maintained very flat or the distortion in the antenna surface must be known to within a very small fraction of the wavelength corresponding to the operational frequency of the antenna (e.g., one-thirtieth of the wavelength for space-based radar at 10 GHz=1 mm flatness tolerance) in order for the antenna to perform correctly. In particular, for space-based radar (SBR) applications, a very high degree of surface planarity must be maintained to enable the effective use of ground clutter suppression algorithms. A high degree of surface planarity is also critical for space-based optics applications and ground moving target tracking applications. 
     Present day large, phased-array antennas achieve this required flatness by using high stiffness structural designs (i.e., trusses) that add significant weight and volume to the antenna when it is stowed in a launch vehicle. As will be appreciated, as the antenna area increases, the stowed volume of the array limits the antenna size due to the restrictions imposed by the launch vehicle fairing within which the stowed antenna must fit. 
     Other systems for measuring the flatness of planar structures have relied on metrology devices that measure the distance from a common source to pre-determined points on the structure, typically through laser reflection from a surface mounted target. For large, deployable, space-based phased-array antenna systems, there is a need for a measurement system that does not interfere with the operation of the antenna, and which provides feedback, in real time, and which further does not add significantly to the complexity of the antenna system or to the spacecraft with which it is associated. 
     Accordingly, it is a principal object of the present invention to provide a system for compensating for deformation occurring in a large, phased-array antenna which eliminates the need for large and heavy structural members, such as trusses, to maintain the planarity of the antenna when the antenna is subjected to external factors which would otherwise cause a deformation of its surface. 
     It is another object of the present invention to provide an apparatus and method for electronically compensating, in real time, for the deformation experienced by a large, phased-array antenna through non-intrusive means which permit the deformation to be monitored and suitable corrections generated to provide needed phase shifting or time delay of the signals transmitted by or received by the phased-array antenna. 
     It is still another object of the present invention to provide a system for detecting and compensating for the deformation occurring in a large, phased-array antenna, in real time, without significantly complicating the construction of the antenna and without impeding the ability of the antenna to be deployed in space-based applications. 
     SUMMARY OF THE INVENTION 
     The above and other objects are provided by a structural deformation compensation system and method for use with a large, phased-array antenna. The system and method of the present invention are particularly well adapted for use with large, spaced-based, phased-array antennas, but could just as readily be implemented with ground-based or aircraft based phased-array antennas. 
     The present invention employs a number of deformation sensing devices which are either placed on or formed within structure supporting the antenna elements of the phased-array antenna at predetermined locations on the antenna where significant stresses or strains are expected to occur. In one preferred embodiment the deformation sensing devices are comprised of strain gauges. At least one such strain gauge is disposed on, or formed within, the composite structure supporting the phased-array antenna at each of those locations where strains are expected to occur as a result of the external forces experienced by the antenna which can cause deformation of the antenna. In some applications, a pair of strain gauges are preferably located at each such location. If a pair of strain gauges is used, then one of each pair may be orientated in the X direction and the other may be orientated in the Y direction. Each strain gauge provides output signals indicative of the stresses experienced by the phased-array antenna at that approximate location where it is located. 
     The output signal from each strain gauge is then input to a data acquisition system which makes use of a transformation algorithm for transforming the detected surface strains into signals representing the displacements of the antenna at various locations thereof. Electronic signals corresponding to these displacements are then output to a beam steering controller which generates phase or time delay commands needed to provide the necessary degree of phase shifting or time delay of the signals transmitted or received by the antenna elements making up the phased-array antenna to correct for the estimated overall deformation of the phased-array antenna. In this manner, the antenna can be electronically “steered” to compensate, in real time, for the deformations occurring over the entire area of the phased-array antenna as a result of various factors, such as changes in temperature, experienced by the antenna. Advantageously, the compensation of surface deformation is accomplished “non-intrusively” and without interfering with normal antenna operation. 
     In one preferred embodiment, the deformation sensing devices are comprised of fiber-optic strain gauges which output signals to a fiber-optic strain demodulator. The fiber-optic strain demodulator, in turn, provides corresponding signals to the data acquisition system. In this embodiment true-time-delay (TTD) units are used for receiving the output signals from the beam steering controller to electronically compensate for the surface deformations of the antenna. The beam steering controller may also receive attitude information concerning the antenna if the antenna is a space-based antenna system. A beam pointing command generated is also used to supply beam pointing commands to the beam steering controller. 
     The method of the present invention makes use of suitable surface modeling equations developed during laboratory testing and on-orbit measurements made for space-based, large, phased-array antennas in order to collect a sufficient number of modes to represent displacements likely to occur as a result of predicted load conditions which the antenna will likely experience. From this testing a suitable “strain-to-displacement” algorithm is developed. The information obtained from ground-based testing and on-orbit measurements is also used to optimize the number and location of the strain gauges used on the antenna. This information is then used to place deformation sensing devices at those locations on the antenna where significant degrees of strain are likely (i.e., predicted) to occur. The strain-to-displacement algorithm is used by the data acquisition system to generate displacement signals corresponding to the strains occurring at those approximate areas of the antenna where the deformation sensing devices are located. 
     The apparatus and method of the present invention thus provides a means for compensating for surface deformations occurring over the entire area of a large, phased-array antenna system, in real time, and further in a manner which allows smaller, lighter and less costly antenna support structures to be used. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The various advantages of the present invention will become apparent to one skilled in the art by reading the following specification and subjoined claims and by referencing the following drawings in which: 
     FIG. 1 is a simplified flow chart of the steps performed to produce the strain-to-displacement transformation matrix and the optimal locations for the strain gauges used by the present invention, in addition to the steps of using the predicted displacements to compensate for the detected deformation of a large, phased-array antenna; 
     FIG. 2 is a simplified block diagram of the system of the present invention; 
     FIG. 3 is a highly simplified perspective view of a portion of a phased-array antenna illustrating one preferred arrangement of a pair of deformation sensing devices embedded therein; 
     FIG. 4 is an illustration of a binary string, representing a solution variable, and a crossover print for determining the optimal placement of the strain gauges to represent specific deformed shapes; 
     FIG. 5 is a simplified perspective view of a panel, representing a phased-array antenna, illustrating a measured surface deformation, represented by solid lines, together with the predicted deformation, indicated by dashed lines, as predicted by the deformation sensing devices of the present invention; 
     FIG. 6 is a view of the measured shape of a panel, representing an antenna, as indicated by solid lines, together with the predicted shape of the panel, indicated by dashed lines; 
     FIG. 7 is a view of a panel, representing an antenna, illustrating the measured shape thereof in solid lines, together with the predicted shape of the panel indicated by dashed lines; 
     FIG. 8 is a view of a panel, representing an antenna, with the actual measured shape thereof indicated by solid lines, together with the predicted shape of the panel indicated by dashed lines; 
     FIG. 9 is a perspective view of a panel illustrating the preferred locations of various pairs of deformation sensing devices thereon, where the short vertical lines represent locations for deformation sensing devices placed along an X axis, and the long vertical lines represent locations where a deformation sensing device is placed along a Y axis; 
     FIGS. 10-12 illustrate the high degree of correspondence between the measured surface of a panel, indicated by solid lines, and the predicted surface shape indicated by dashed lines, when the relatively large plurality of pairs of strain gauges indicated in FIG. 9 are employed; 
     FIG. 13 illustrates the placement of fewer strain gauges on the panel; 
     FIGS. 14-16 indicate the increased variation between the measured shape of the panel and the predicted shape as a result of the fewer number of strain gauges being employed, as shown in FIG. 13; and 
     FIG. 17 is a graph the results of an antenna deflection simulation test illustrating the relationship between RMS surface distortion and clutter cancellation improvement ratio for a space-based radar application. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring to FIG. 1, there is shown a flowchart  10  illustrating the general steps performed in developing a strain-to-displacement transformation matrix for predicting the displacements normal to a surface of a large, phased-array antenna. Initially, step  12  involves performing ground-based tests of suitable structures and collecting a sufficient number of modes to represent displacements associated with predicted load conditions on the structure. Step  14  indicates that strain gauge and accelerometer measurements are also preferably collected from on-orbit antennas. More specifically, these steps involve using modal testing to collect accelerometer frequency response functions (AFRF) and strain frequency response functions (SFRF). Displacement and strain modes (eigenvectors) are then generated from this data. The strain modes are used to develop a least squares transformation from strain measurements to modal coordinates. As indicated at step  16 , the displacement modes are then used to transform modal coordinates to displacements. 
     Analytically, using finite element techniques, strain modes can be developed by using displacement eigenvectors to generate strains from typical strain recovery transformations (SRT). Experimentally, strain gauges and accelerometers need to be attached to the antenna structure and then outputs recorded simultaneously during dynamic testing. This information is also used to determine the optimal number and location of deformation sensing devices (i.e., strain gauges) that will be needed on a phased-array antenna of particular dimensions in order to accurately determine the overall surface deformation of the antenna when the antenna is in use. 
     At step  18 , the information determined at step  16  is used to predict the actual surface deformation at various points on a large, phased-array antenna during use of the antenna. The information obtained at step  18  is then used by a deformation compensation system, as indicated at step  20 , to compensate for the detected surface deformations of the antenna. It will be appreciated, then, that steps  12 - 16  comprise those steps which will be needed to not only determine the needed strain-to-displacement transformation matrix for the particular shape of phased-array antenna that will be employed, but also to determine the optimal locations of the deformation sensing devices on the antenna so as to be able to accurately predict the deformation that will be experienced by the antenna during use. 
     Referring now to FIG. 2, there is shown a system  22  in accordance with a preferred embodiment of the present invention for detecting and compensating for surface deformations in a large, phased-array antenna system. The phased-array antenna is represented in simplified form by a planar antenna panel  24  having a plurality of independent antenna elements  24   a  and a plurality of pairs of deformation sensing devices  26 , represented in simplified form by squares, disposed about its overall area. It will be appreciated that antenna elements  24   a  have been shown apart from the panel  24  only to simplify the drawing figure, but in practice will be disposed on or within the panel  24 , as will be explained more fully in the following paragraphs. 
     Deformation sensing devices  26 , in one preferred embodiment, comprise strain gauges, and more preferably Bragg grating fiber-optic strain gauges. However, any suitable device capable of sensing the strain occurring in its immediate area could be used. The strain gauges  26  detect the strain of that portion of the panel  24  at the approximate area where they are located. As shown in FIG. 3, in one preferred embodiment, one of each pair of the strain gauges  26  is disposed on the panel  24  along an X axis while the second one of the pair is disposed perpendicularly thereto along a Y axis. The X axis strain gauge senses the x-axis component of the strain occurring at its location and the Y-axis strain gauge senses the Y-axis component of the strain occurring at its location, both of which are used to predict the deformation of the surface of the antenna panel in the Z direction normal to the antenna  24  surface. Both strain gauges  26  may be disposed within a composite structure forming the panel  24  while the antenna elements  24   a  are integrated into large suitable supporting structure, such as possibly being clipped onto large, grid stiffened panels. Alternatively, one of the strain gauges  26  may be disposed on the outer surface of the panel  24  while the other is embedded within the panel. 
     It will be appreciated that in some structures only a singe deformation sensing device may be needed at various determined locations on the panel  24 , depending on the expected deformed shape of the panel. Also, various shapes of panels  24  may require pairs of devices  26  to be disposed at predetermined locations with the devices  26  being orientated non-perpendicular to each other. 
     The pairs of strain gauges  26  are further disposed at those locations (determined at step  16  of FIG. 1) where previous laboratory and/or space-based testing and analysis has determined that stresses are likely to occur as a result of the antenna panel  24  experiencing external forces that cause it to deform in shape. It will be appreciated that those locations may not necessarily be at the same areas where displacement is expected to occur. For example, a long, cantilevered antenna panel may be expected to experience significant stresses at the end thereof where it is secured to supporting structure, but the majority of surface displacement of the antenna will be known to occur for such an antenna at specific other areas located substantially away from those points where the majority of stresses in the panel will occur. It will be appreciated immediately, then, that while the pairs of strain gauges  26  are illustrated on the antenna panel  24  as being evenly spaced apart along the X and Y directions, that in practice the strain gauges  26  may not be so evenly spaced apart from one another. It is anticipated that, depending upon the precise dimensions of the phased-array antenna, a greater plurality of strain gauges  26  may need to be concentrated at particular areas of the antenna, while a lesser plurality may be required near other areas, such as near the outermost edges of the antenna panel  24 . 
     The output of each one of the strain gauges  26  is input to a fiber-optic strain demodulator  28  which provides electronic signals to a data acquisition system  30 . The transformation algorithm is produced from a modal displacement transformation and a modal strain transformation, both of which are determined through steps  12 - 16  in FIG.  1 . The data acquisition system  30  incorporates the strain-to-displacement algorithm needed to predict displacements of the antenna panel  24  over the entire area of the antenna panel. The transformation algorithm is represented by the following formula: 
     
       
         {d}=[φ d ][[φ s ] T [φ s ] −1]][φ   s ] T {ε} 
       
     
     where 
     φ d =displacement mode shapes of the structural system (i.e., the phased-array antenna  24 ) 
     φ s =the strain mode matrix of the structural system; and 
     {ε}=the actual strain measurements from the strain gauges 
     With reference to FIG. 4, a genetic algorithm is used to determine optimum sensor placement along with the optimum number of sensors for a phased-array antenna of given dimensions. Genetic algorithms are well suited to the sensor placement problem since they, in general, involve manipulation of binary strings. The optimal placement of sensors is a chosen subset of a larger set of potential locations so as to minimize an objective or cost function. The solution defines whether a sensor is placed at a potential location or not (i.e., “1” or “0”). The solution can therefore be viewed as a binary string. An initial set of candidate optimal solutions are generated randomly as binary strings. They are then evaluated via a cost function. A subset of high performance candidates are chosen and randomly recombined in pairs. The new candidates are evaluated and the process repeats itself until some user defined conditions are reached. A random subset of candidate solutions are changed randomly so as to introduce a “mutation”. This helps to avoid falling into a local optimization. 
     The cost function for the sensor placement problem can be generated a number of different ways. One way involves calculating the square root of the sum of differences between a set of representative (measured or calculated) displacements and strain mode transformation predicted displacements. This is then weighted by the number of strain gauges  26  raised to a power. The greater the power used, the fewer strain gauges  26  needed to minimize the cost function. However, the approximation to known displacements will be less accurate. The number of desired sensors can be fixed and the function will optimize their placement. The cost function can be represented by the following formula:          (         ∑     i   =   1       N   d              (       x   p     -     x   k       )     2         )            (     N   s     )     P                            
     where 
     N d =number of displacement locations; 
     N s =number of active strain gauges  26 ; 
     x p =transformation estimated deformation; 
     x k =expected deformation; and 
     P=Arbitrary power 
     With continued reference to FIG. 2, the output from the data acquisition system  30  represents the predicted displacements of the antenna panel  24  (in the Z direction) over the entire area of the antenna panel. These outputs are input to a beam steering controller  32 , which also receives inputs from a beam pointing command generator  34 . If the antenna panel  24  is a space-based antenna, then the beam steering controller  32  also receives attitude information from a satellite/array attitude data generator  36 . It will be appreciated that the beam steering controller  32  is well known in the art and therefore no further description will be provided for this component. 
     The beam steering controller  32  operates to generate a plurality of phase shift or time delay commands for electronically “steering” each of the independent antenna elements  24   a  which form the phased-array antenna  24 . These commands electronically compensate for the predicted surface deformation. occurring over the entire area of the antenna  24 . If the compensation commands are time delay commands, then true-time-delay (TTD) elements  38  can be used in connection with each antenna element  24   a  of the antenna panel  24 . Importantly, the compensation commands, whether phase or time based, are applied to the antenna elements  24   a  in real time. Thus, essentially instantaneous corrections can be applied by the system  22  to compensate for the changing overall shape of the antenna panel  24 . Since the surface deformation of the antenna panel  24  is compensated for electronically, the system  22  also forms a non-intrusive means which does not require significant additional structure to be used with the antenna panel  24 . The system  22  therefore does not add significantly to the size, weight or overall complexity of the antenna panel  24 . 
     Referring now to FIGS. 5-8, the results of tests conducted on a 36″×36″ (0.914 m by 0.914 m) planar panel  40  are shown. In this test, strain readings from a plurality of the strain gauges  26  were collected while the panel  40  was subjected to external forces causing mechanical deflection of the panel  40 . Direct measurements of the deformed panel  40  were taken using linear displacement measurement devices in contact with the panel  40  surface. The solid lines represent the measured surface of the panel  40  while the dashed lines represent the “estimated” or “predicted” curvature of the panel  40  surface compiled from information collected from the strain gauges  26 . The very close overall similarity of the measured shape of the panel  40  and the estimated shape of the panel by using the strain gauges  26  and the data acquisition system  30  can be readily seen. 
     Referring to FIG. 9, the genetic algorithm described previously herein has been used to optimize the number and position of the strain gauges  26  for maximum implementation economy and effectiveness. The long vertical lines  42  in FIG. 9 represent those approximate locations on the 36″×36″ panel 40 where strain gauges  26  should be disposed parallel to the Y axis. The short vertical lines  44  represent those approximate locations where a strain gauge  26  should be located parallel to the X axis. It will be noted that two strain gauges  26  are provided relatively closely adjacent to one another such that a plurality of pairs of strain gauges  26  are arranged at critical locations around the panel  40  where significant strains are expected to occur. FIGS. 10-12 illustrate the high correspondence of the predicted shape of the panel  40  relative to the measured shape when the panel  40  is deformed by external forces, with the strain gauges  26  placed as indicated in FIG.  9 . 
     It will be appreciated, however, that the overall shape of the phased-array antenna will have a strong influence on the precise number and locations of the strain gauges  26  that will be required for use therewith. If the accuracy requirements are relaxed, then a lesser plurality of pairs of strain gauges  26  will likely be needed for any given size and shape of antenna  24 . FIG. 13 illustrates the use of fewer strain gauges  26  on the planar panel  40 , while FIGS. 14-16 illustrate the slightly increased difference between the measured shape of the panel (in solid lines) and the predicted shape (in dashed lines) resulting from the use of fewer strain gauges  26 . 
     Referring now to FIG. 17, a graph  50  is shown which illustrates the results of an antenna deflection simulation of two vibration modes (i.e., labeled modes “7” and “8”) to determine the relationship between root means square (RMS) surface distortion and the clutter cancellation improvement ratio for a large, phased-array antenna used in a space-based application. The clutter improvement ratio (“CIR”) is summarized in the graph  50 . The graph  50  plots 10 times the log to the base of 10 CIR, expressed in decibels, versus the RMS value of the maximum deflection. Results are shown for two and three phase centers. In the two phase center cases, the phased-array antenna  24  is divided into two sections with the payload body of a spacecraft associated with the antenna panel  24  in the middle of the antenna panel. A 25 dB CIR, denoted by line  52 , is considered to be a threshold value for minimum allowable cancellation. This is about 10 dB above the minimum threshold for receiver noise effects. For three phase centers, the threshold is passed when the RMS peak deflection is between eight to ten percent of the radar signal wavelength. The two phase center results are a much more stringent three to four percent. Space borne antennas will use radio frequencies in the 10 Hz range, so that the signal wavelength is about 30 mm. The peak allowable deflection is thus about 2.5 mm (about 0.1 inches). Since the phased-array antenna panel  24  dimensions are assumed to be about five meters by eight meters, the maximum deflection of 2.5 mm is at a distance of four meters from the payload body center line. 
     The deformation detection and compensation system  22  is particularly well adapted for use with satellite systems that employ large, phased-array antennas mounted on lightweight support structures, and more specifically for space-based surveillance, optics and ground target tracking applications. However, the system  22  is just as readily useable with applications involving ground-based large, phased-array antennas or even aircraft-borne phased-array antennas. 
     A principal advantage of the present invention is the ability to reduce the mass and volume of the overall antenna system due to the lesser stability requirements for the structure supporting the antenna. This allows even larger phased-array antennas to be packaged with existing launch vehicles when the antenna system is to be used in a space-based application, thus enabling new missions previously considered impossible or economically unlivable. The elimination of the need for ultra-stable, high tolerance support structures for supporting large, phased-array antennas also permits a significant reduction in the mass of a phased-array antenna by a factor of up to about 40%, or possibly even greater. Presently, large phased-array antenna systems using the conventional structural approach have a mass density on the order of about 12 kg/m 2 . It is anticipated that a large, phased-array antenna can be constructed having a mass density of about 7 kg/m 2 . Presently, the largest phased-array antenna launchable using conventional approaches is approximately 130 m 2 . However, a phased-array antenna system incorporating the deformation compensation system described herein permits structural mass and volume minimization to a degree which allows up to, or possibly greater than, 450 m 2  deployable, phased-array antennas to be launched into space. It is also anticipated that the implementation of the deformation detection and compensation system  22  of the present invention will result in significant reductions (up to or greater than about 50%) in antenna calibration costs during the integration and test processes associated with phased-array antenna systems. 
     Those skilled in the art can now appreciate from the foregoing description that the broad teachings of the present invention can be implemented in a variety of forms. Therefore, while this invention has been described in connection with particular examples thereof, the true scope of the invention should not be so limited since other modifications will become apparent to the skilled practitioner upon a study of the drawings, specification and following claims.