An automatic load monitoring system with remote sensing.

TECHNICAL FIELD

0001This invention relates to load monitoring devices and relates more particularly to automatic load monitoring systems having remote sensing.

BACKGROUND OF THE INVENTION

0002Systems for monitoring force loads are well known and are used with a variety of products to determine struc­tural conditions in mechanical components. These systems are characterized by a plurality of parameter sensors, such as strain gauges, which are positioned locally with the mechanical elements and provide signals to a remote processor. The measured data is correlated by the processor in accordance with a pre-established relation­ship. The processor output signals are indicative of the stress or loading conditions of the elements.

0003In many applications the direct instrumentation of mechanical elements is possible. For example, strain gauges and sensors can easily be positioned locally on an airplane's wings and aerilons, with signals from the sen­sors conventionally routed to a remote cockpit processor. However, for some elements, such as rotating turbine blades in a jet engine, direct instrumentation is impossible or impractical. Another such example is a rotating heli­copter blade. Direct instrumentation of the blade with locally positioned sensors can only be accomplished by employing a sophisticated slip ring apparatus which is prone to wear and must therefore be maintained on a fre­quent basis. As a result, remote blade mounted instrumen­tation is configured with a helicopter only for purposes of initial testing and calibration.

0004Techniques for indirectly measuring structural parameters of loaded mechanical elements have also been explored. With these techniques, sensors are remotely positioned from the loaded components of interest. For example, in an airplane, a plurality of sensors can be positioned on the aircraft body. The signal received at these sensors comprises a component due to the loading of the airplane body, as well as a component indicative of the loads on the aircraft wings. Using pre-determined relationships, a processor could ideally isolate the strain information from the element of interest and corre­late that data to the loading of the element. To date, no system has demonstrated a consistent capability of extracting desired loading information using signals from remotely positioned sensors.

0005Determining the signal component output loads on helicopter elements are additionally more difficult, since the loads imposed upon the various rotating elements are periodic. Systems which have attempted to remotely deter­mine structural parameters in the rotating elements of a helicopter, such as blade strains or moments, have been unsuccessful because the mathematical computations re­quired have been deemed too complex and that the requisite data is insufficiently measurable. It would be desirable to have a system which remotely senses loads on structural elements of a mechanical system and would establish corre­lation between measured parameters and desired values using matrix methods for correlative regression and infor­mation processing in real-time, with a minimal sensor signal input generating a fixed data stream. The present invention is drawn towards such a system.

SUMMARY OF THE INVENTION

0006An object of the present invention is to provide for a system that determines the magnitude of an element parameter from signals sensed remote from that element, and/or to provide an electrical circuit which provides, in response to a received periodic signal, a signal locked thereto with phase synchronization, and/or to provide a helicopter recording system that determines, from signals measured on the helicopter fuselage, values of parameters for the rotating helicopter blades, and/or to provide improvements to such apparatus generally.

0007In a preferred embodiment, a method of generating, from signals measured in a first element in­dicative of a first element parameter, associated signals indicative of a corresponding determinative parameter in a cooperative second element; the method includes the steps of measuring signals indicative of the first element parameter, measuring signals in the second element, in­cluding those signals indicative of corresponding determi­native parameters, computing from the first signal set an independent signal subset thereof, and generating from said independent first signal subset and the second signal set, signals correlating the measured signal sets.

0008In a further preferred embodiment, an electronic phase synchronization circuit includes means for receiving a periodic timing signal and a con­troller. The controller receives the periodic timing signal and provides, for a select numbers of time during the timing signal, control signal to a first circuit that generates first and second periodic signals. The first circuit control signals selectively enable the first cir­cuit to output one of the first or second periodic signals. The controller also provides control signals to a second circuit that receives the selected and periodic signal. The second cicuit control signals enable the second circuit to process the periodic first circuit signal present thereto, thereby synthesizing the phase of the first and second periodic signals with the timing signal.

0009In another preferred embodiment, a system for determining the value of parameter in a first element includes a measuring device for measuring signals in a second element that cooperates with the first element.

BRIEF DESCRIPTION OF THE DRAWINGS

0010<ul id="ul0001" list-style="none"><li>Fig. 1 is a simplified schematic diagram illus­trating a portion of an automatic load and monitoring and recording system (HALMARS) provided according to the present invention adapted for use with a helicopter.</li><li>Fig. 2 is a detailed description of a portion of analysis circuitry used with the controller of Fig 1.</li><li>Fig. 3 illustrates a portion of the coefficient programming module of the controller of Fig. 1.</li><li>Fig. 4 is a schematic illustration of a component synthesis circuit portion of the controller of Fig. 1.</li><li>Fig. 5 is a schematic illustration of an analog summary circuit of the controller of Fig. 1.</li><li>Fig. 6 is a detailed schematic illustration of a portion of a component synthesizer circuit of the con­troller of Fig. 1.</li><li>Fig. 7 is a simplified schematic illustration of a period locked loop with phase assertion circuit of the controller of Fig. 1.</li><li>Fig. 8 is a simplified schematic illustration of a prior art phase lock loop circuit.</li><li>Fig. 9 diagrammatically illustrates the closure phase error in the synthesized tachometer signals gener­ated by the controller of Fig. 1 when a helicopter rotor is overspeed.</li><li>Fig. 10 illustrates measured flatwise blade bending moments on a helicopter blade as compared to blade bending moments computed by the system of Fig. 1.</li></ul>

DESCRIPTION OF THE PREFERRED EMBODIMENT

0011Referring now to Fig. 1 there is illustrated a portion of a system 10 which is used with a Helicopter Automatic Load and Monitoring Recording System (HALMARS) provided according to the present invention. For the ro­tating mechanical systems of the helicopter it is most often not physically possible or desirable to locally ob­tain parameter data, for example by positioning stress-strain gauges on a rotating helicoper blade to determine edgewise blade bending moments. The system of Fig. 1 determines a desired parameter (i.e. load) by means of indirect measurements taken remote from the rotating components. The process of determining physical parame­ters of a dynamic element from only a few localized opera­ tional measurements has been named a "holometric" process, from the Greek "holos" (the whole) and "metricus" (to measure).

0012As an example, helicopter 11 shown in phantom has rotating blades 12, 13, 14 and 16 are characterized by rotor blade bending strains or loads resulting from corre­sponding rotor blade bending moments. These moments are determined from strains measured on fuselage 18. Controller 20 receives a plurality of analog input data signals, such as the eight data lines indicated schemati­cally at 22, that extend from a corresponding plurality of "monitor" transducers (indicated schematically at 28 are) located on the fuselage or the "fixed" system of the helicopter. It is advantageous for the transducers or sensors in the fixed system to be strain gauges or similar instruments. These transducers are placed preferably along load paths or stations in the airframe (fuselage). The process of determining the number of required monitor transducers and their placement is described hereinafter.

0013During flight, the helicopter rotor blades experience strains or bending moments at various stations or positions which vary with the flight condition. Such flight conditions would include, for example, a high g-load in the pullout from a dive, lower than gravity g-load in a pushover maneuver, hover, or high speed flight. In each flight condition or maneuver, the motions of the rotor blades differ from the motions in other flight conditions or maneuvers both in magnitude and phasing in a highly sig­nificant manner.

0014Each of the transducer signals can be decomposed by conventional Fourier analysis to generate a series of real and imaginary time independent signal components. As detailed hereinafter, it has been determined that only the zeroth and Nth harmonic or Nth Fourier signal component (N/rev.) in a helicopter with N rotor blades (for N greater than 2) is needed to fully describe the loads on the helicopter rotating system (i.e. the helicopter blades). Those skilled in the art will note that the zeroth harmonic may sometimes be ignored for blade vibratory loads only. Therefore, for each flight condi­tion or maneuver a relationship can be determined between the strains measured by the monitors (sensors) and the corresponding strain or bending moment in the rotor. Although it has been determined that use of only the (steady) zeroth and Nth harmonic produces quite satis­factory results using the present holometric process with monitors in the fuselage for strains and bending moments on a helicopter rotor, the process can be made more pre­cise using other harmonics which are integer multiples of N, the number of blades.

0015The linear relationship of the monitor signals of the fixed or fuselage system to those signals of strain in the rotating system can be found using the well estab­lished Moore-Penrose Generalized Inverse if, and only if, the monitor signal over flight conditions matrix of which the Moore-Penrose Generalized Inverse is to be taken is conditioned in terms of the informational reliability of the measured sensor signals. The process of determining this informational matrix conditioning described here­inafter is critical to the practicality of the invention.

0016The matrix relating the Fourier coefficients strains or bending moments at various rotor monitor stations to the Fourier coefficients of the monitor signals of the fixed system (fuselage) consists of constants and covers all flight conditions (helicopter maneuvers). This marks a first point of departure of the present invention over the prior art. It has been incorrectly assumed by those skilled in the art that the above relational matrix is comprised of time varying coefficients, and is therefore very complex, requiring microprocessors to simulate the time dependent coefficients for various load conditions.

0017In Equation 1 the columns of matrix R are the R complex Fourier coefficients of a parameter of interest in the rotating system; e.g., flatwise rotor blade bending moment at a given station. Each of the C rows represent a flight condition in the sampling. The columns of matrix K are the zeroth, Nth harmonic (and other harmonics if desired) complex Fourier coefficients of L monitor trans­ducers in the fixed system. For H harmonics and the steady component, there are LxH columns in the matrix K [R] = [K] [C] + [E] C x R C x (L x H) (L x H)x R CxR      (1) C is the relational matrix and E a matrix of errors or residuals, allowing for the number of rows, C, to be greater than the number of columns, LxH, in matrix K so that Equation 1 does not violate the mathematical princi­ple that there is no solution to more equations than un­knowns.

0018Equation 1 establishes that the matrices form a linear system that can mathematically be considered to reside in a linear vector space. As detailed hereinafter, both the K and C matrices comprise corresponding reduced matrices K_O and C_O which mathematically span the vector space and which consist of J informationally independent columns of K and J rows of C, respectively. In other words, K_O and C_O are subsets of K and C, such that there exists linear combinations of K_O,C_O which can generate all the elements of R with minimum Euclidian norm of error. Therefore, only the reduced matrices K_O, C_O, are needed to establish a correlation between R and K. It is important to note that it is only the indentification of the consis­tent informational content of matrix K_O that allows for a consistent analytical solution. The method and apparatus of the present invention which obtains the reduced matrices K_O and C_O marks an important, second point of de­parture of the present invention over the prior art.

0019To find the reduced matrix K_O, the matrix K is generalized to be a NxM order matrix. The first column of K is independent by definition. Subsequent columns are compared with the independent column(s) in accordance with an algorithm detailed hereinafter to establish which ele­ments are independent and ultimately comprise the reduced matrix K_O. After the reduced matrix K_O has been deter­mined, the reduced matrix C_O can be computed using conven­tional mathematical techniques by the use of measured load data on the rotating helicopter system which comprise the matrix R.

0020The present method and apparatus for obtaining K_O simply determines whether the vector defined by the subse­quent column K is independent of the subspace defined by the matrix of columns previously determined to be indepen­dent. As an example, let K be an NxM matrix with the first J columns independent. The independence of the J+1 column is to be determined. K_n,j+1 indicates the sub-matrix of F having only columns 1 through j+1. The independence of vector k_{N, j+1} comprising the elements of the the J+1 column of K is determined as follows:<maths id="math0001" num=""><img file="EP0339833A2_D0001.tif" /></maths> where K^T_{N, j+1} corresponds to the transpose of K _{N, j+1}, with k_J+1 corresponds to the j+l row of K and k^t_j+1 is its transpose.

0021Furthermore, define k⁰ ₍j₊₁₎ to be:<maths id="math0002" num=""><img file="EP0339833A2_D0002.tif" /></maths> where "e" is the error value indicative of the indepen­dence of the column vector K_{N, j+1}. Define the function e^te to be: e^Te = e^tK_N^T_,JK_N,J C -C^T K^T_N,J k_j+1 - k^T_j+1K_N,Je + k^T_j+1k_j+1      (4) The function e^te corresponds to the sum of the squares of the error of equation (1). The rate of change of the function e^te with respect to the transpose of the function C^T at a maximum or minimum is as follows:<maths id="math0003" num=""><img file="EP0339833A2_D0003.tif" /></maths> this allows us to solve for c: C = (K^T_N,JK_N,J)⁻¹K^T_N,Jk_j+1      (6) This value of c is then inserted back into equation 2, yielding: k_j+1 = K_N,J(K^T_N,JK_N,J)⁻¹K^T_N,Jk_j+1      (7) The value of K⁰_j+1 which results allows for the following identity:<maths id="math0004" num=""><img file="EP0339833A2_D0004.tif" /></maths> The function e^te can then be rewritten as:<maths id="math0005" num=""><img file="EP0339833A2_D0005.tif" /></maths>

0022Equation 11 corresponds to the dot product of K⁰_j+1 and e. These vectors are orthogonal, since their dot product is 0. Therefore, k^o_j+1 is orthogonal to e. Conse­quently, equation 10 corresponds to the Pythagorean Theorem, where e^te and K⁰_j+1K⁰_j+1 can be thought to correspond to the orthogonal sides of a right triangle having K^t_j+1K_j+1 as the hypotenuse with angle opposed to the e^te side. Sin² ²x corresponds to:<maths id="math0006" num=""><img file="EP0339833A2_D0006.tif" /></maths>

0023Physically, k⁰_j+1 is in the vector space of K_N,J while e is orthogonal to that vector space. If the value of sine²α exceeds a pre-selected value, typically 2x10^-d where d is the number of significant figures of the measured signal, then that column can be considered to be independent of the vector space K_N,J and is retained in the reduced matrix K₀.

0024For two dimensions, the above analysis can be simplified. The matrix K_N,J corresponds to an arrow vector A postioned in a plane. A second vector B corresponds to the j+1 column of K and is arbitrarily po­sitioned in the plane with respect to A; K⁰_j+1 correspond to the projection of B onto A while e corresponds to that portion of B which is orthogonal to A.

0025The process described hereinabove is repeated sequentially on an element by element basis for each of the columns of K. If a column is determined to lack sufficient independence, i.e. if the magnitude of sine² α is less than the independence criterion, then that column is not included in K_O.

0026Once the reduced matrix K₀ is determined, the corresponding elements of R are measured by local instru­mentation. For the rotating helicopter blades of Fig. 1, blade bending loads (moments) are established from local blade bending measurements for each flight conditions. Having determined R, C₀ can be determined using the relationship: [C_O] = ([T_O]^T[T_O])⁻¹[T_O]^T[B]      (13) The columns of C missing from C₀ are made to equal 0. The remaining elements of C are then linear combinations of the elements of C₀.

0027After the matrix C has been determined in a cali­bration process, the controller 20 is configured to analyze signals from the transducers according to: R = K C      (14)

0028Referring again to Fig. 1, the transducer signals pre-entered on line 22 comprise the data input to the con­troller. The present controller accepts a plurality of analog Data Input signals being independent measurands transduced from the fixed system of the helicopter by strain gauges, accelerometers or other mechanical sensing devices. In the present embodiment, such inputs are employed. However, there is no fundamental limit on the number of such inputs that may be employed. The trans­ducer signal levels are preferably + or - 10 volt levels with known voltage-to-measure and scale constants. Additionally, the controller receives a once per blade revolution (tachometer) signal on lines 31 that comprises a single "1/Rev" temporal reference signal, being a pulse train at the (radian) frequency, p, of the main rotor. This signal is derived from a "once per turn" or "blooper" sensor that physically monitors each complete rotation of the rotor. The tachometer signal is conditioned by signal conditioning logic circuitry 32 which provides a con­ditioned 1/Rev logic signal on line 33. This signal (5) is level compatable with the controller's logic signal levels and exhibits rapid rise and fall times. This signal also exhibits a sharp rising edge once per rotor revolution.

0029The Conditioned 1/Rev signal is the input to a "period-locked loop with phase assertion" (PLLPA) circuit, 34. This circuit provides three output signals. A 2048/Rev PLLPA output signal presented on lines 35 com­prises a signal pulse train a 2048 times the frequency of the rotor. This pulse train determines the frequencies of synthesized sine and cosine waveforms. A Phase = Zero PLLA output signal (line 36) is a pulse train of 1/Rev frequency, with a rising edge time locked to the rising edge of 2048/Rev, 7, that immediately follows the rising edge of Conditioned 1/Rev, 5. This signal determines the phasing of the synthesized waveforms. A Lock Output logic signal (line 37), is asserted "high" whenever 2048/Rev signal and the Phase = Zero signal are synchronized to the conditioned 1/Rev signal. This condition denotes "normal" operation of the controller and correct signal processing. Whenever the rotor speed departs from the normal flight envelope (as in starting and stopping) the signal on line 37 is asserted "low" to indicate that proper processing has ceased.

0030Both the 2048 and Phase = Zero signals are input to a multiple sine/cosine synthesizer circuit 38. This circuit generates the required sine and cosine digital word streams. These are rapidly sequenced onto Sine/Cosine Data Buses, 39, at each of 2048 equally time spaced intervals during the rotor's rotation. This bus also presents certain operative timing signals required by other circuitry detailed hereinafter to access the input data signals. A second bus, Order (n) Select Bus 40, is used to indicate which Sine or Cosine function is present on 10 at any given time. Signals presented on the order bus are also routed to other processing circuits.

0031As detailed hereinafter the Order (n) Select Bus, 40, has N signal lines. Each of these is asserted (solely) in turn, indicating the harmonic order (1 to N) of the data present on bus 10. One cosine sample followed by one sine sample is present on data bus 39 for each such assertion. Alternative and more compact codings are possible for more extensive implementations.

0032The transducer signals are received by a Fourier Coefficient detector 41 that allows the system to decom­pose the input signal and selectively output one or more of the real and imaginary Fourier coefficient signal com­ponent pairs. Preferably each of the analog input signals is applied to a separate Fourier coefficient detector circuit. Each of the detector circuits is interconnected to the digital data buses.

0033Each Fourier coefficient detector circuit, computes two analog coefficient signals provided on lines 42, 43. These are voltages proportional to the real and imaginary Fourier coefficients (respectively) for a single harmonic order of rotor rotation, (the rth). Each detec­tor is separately programmable as to which order it will detect. This is accomplished by jumper connection to one of the N signals in the Order (n) Signal Bus, 40.

0034For the preferred embodiment, all Fourier coefficient detector circuits are programmed for the 4th harmonic of rotor rotation (r=4) in the examination of a four bladed helicopter. Those skilled in the art will note that each detector circuit is completely independent of the others.

0035Corresponding sets of analog coefficient signals are transmitted on lines 42, 43 to a Coefficient Programming Module, 44, one set from each detector circuit. By way of illustration and not of limitation, each detector circuit transmits these signals and their negatives.

0036As previously discussed, the Holometric relation­ships between measurands of the rotating and non-rotating systems are related by the complex matrix equation of equation 1.

0037Note that this relationship defines a multiplicity of rotating system response. The embodiment of Figure 1 is restricted to the measurement of a single response variable. Only a single column of the R matrix or vector is sought.

0038In this circumstance, consequently only a single corresponding column of the C matrix is needed as the strain or movement is also a vector.

0039To express this restricted computation in terms of the variables illustrated in the figure of page 1 the equation notation can be modified. Note that rather than utilizing complex notation, the dimensions of both vectors and the matrix are doubled and employ corresponding real valued coefficients. This results in:<img file="EP0339833A2_D0007.tif" />

0040Here the pairs of a and b vector elements are the real and imaginary detector circuit output signals pre­sented on lines 42 and 43 respectively. The N pairs of A and B vector elements are the real and imaginary Fourier coefficient signals output by the Coefficient Programming Module on lines 46 and 47 and required by the N component synthesizer 48.

0041The C, D, E, and F matrix terms are the (K matrix) Holometric coefficients derived by the calibration methodology detailed above. Note that a total of 4MN of these are required, and that they are each real valued constants.

0042The matrix multiplication is implemented by weighted analog summations implemented with operational amplifiers. This real-time process continuously updates the N pairs of coefficient signals in response to instantaneous variations in the M pairs of detected co­efficients.

0043In the current embodiment, the K matrix coeffi­cients are programmed by 4MN precision resistors mounted to an interchangeable programming printed circuit board.

0044This represents a minimum production cost embodiment. In alternative implementations, this coefficient pro­gramming module can be replaced by a like number of four-quadrant multiplying digital to analog converters (DACs). This permits programming the Holometric coeff­icients from an internal microprocessor or external com­puter. Such a configuration maintains the instantaneous computation of the required Fourier coefficients. It simplifies changing the device's program and supports rapid changes in a target measurand. It further supports adaptive "learning" of the Holometric coefficients in an "artificial intelligence" sense.

0045Each of the N pairs of analog Fourier coefficient signals, (lines 46, 47) is applied to one of N identical component synthesizers, 48. Each of these receives signals from the digital data buses, 39, 40. Each component syn­thesizer performs a pair of digital/analog multiplications and sums the two resulting analog product signals to derive one of the N harmonic analog component signals, output on line 50. Each real component signal is multiplied by a cosine wave at a specified harmonic (n) of the rotor rotational rate. Each imaginary component signal is multiplied by a sine wave the same frequency.

0046Each of the N component synthesizers may be pro­grammed to use any of the rotor orders, 1 through N. This selection is accomplished by appropriate jumper connection to the Order (n) Select Bus, 40. In the embodiment of Figure 1, each of the synthesizers uses a separate har­monic order. This is the most probable arrangement for any application, but two or more synthesizers may be locked to the same order, if required.

0047The N separate harmonic components of the desired signal are summed together with an operational amplifier and precision resistors network, comprising the analog summer, 52. The output of this process is the desired analog measurand signal, provided on line 53. The preci­sion resistors utilized in this final summation are housed on the coefficient programming module, 15. This configu­ration permits selectable unequal weights in the final summation. This is deemed desirable as it allows the re-apportionment of computational gains throughout the processing circuits in the event that a significant dif­ference in dynamic range and/or spectral content exists between the input measurands.

0048Excessive analog signal levels can distort the various computed signals in this process. Comparator based overload detectors are distributed throughout the con­troller circuitry to detect and report such exceedances, thus indicating invalid computation. Tests are made in each Fourier coefficient detector each component synthesizer and the final analog summer.

0049Within each of these elements, the dynamic signals are constantly compared against a stable reference voltage equal to 83% of the analog power supply voltage. These comparisons generate a "local" error signal whenever exceedance is detected (and before signal clipping actually occurs). Such comparisons are made at each point where a gain change or signal addition is performed. Each overload detector incorporates a "pulse stretcher" so that even a very brief exceedance will cause an error indica­tion which persists for approximately 5 rotor revolutions.

0050Within each Fourier coefficient detector, two such test points are monitored and their resulting local overload detection logic signals "wire-ORed" to provide a single logical output, signal on line 54. A separately buffered version of this signal drives a local indicator LED. Within each component synthesizer circuit, a single test is performed. Each such module outputs a local over­load signal, on line 55, and has an LED driven by a sepa­rately buffered version of the signal. The output of the analog summer is also monitored. An overload here is indi­ cated on line 56 by local overload signal. Again, a local LED is driven by a separately image of this signal.

0051Overload detection signals are all "active low" signals. These signals are logically merged and inverted by circuit 57 which provides an "active high" Overload Output logic signal on line 58.

0052Fig. 2 illustrates one of eight identical analysis circuit sections 59 which comprise the Fourier Coefficient detector 41 of Fig. 1. The controller returns a Computed Output analog signal on line 53, being the holometric synthesis of a measurand within the rotating rotor system, such as a blade bending moment or strain. This signal faithfully reproduces the dynamic characteris­tics of the target measurand as they occur and must thus be deemed an indirectly transduced measurement. It func­tionally replaces a signal derived by direct transduction in the rotating system and eliminates the attendant signal conduction problems. While the present embodiment returns a single such output, a plurality of such transductions may be accomplished by a single device.

0053The Overload Output signal (line 58) is a logic signal reflecting the presence of distortion producing overloads (signal excesses) anywhere within the Holometric Synthesis computation. This signal is of a logic "low" level for valid operation. A logic "high" indicates that the Computed Output signal may reflect the results of com­putational exceedances and is thus potentially invalid. A plurality of local Overload indicator lamps is also pro­vided, one for each point of potential signal overload.

0054The Holometric Synthesis depends upon temporal synchronization of internally generated sine and cosine waves with the rotative frequency of the rotor. This can be accomplished over the normal range of in-flight rotor speeds. Successful synchronization is reflected by a "high" level of the Lock Output, logic signal (line 37). This signal goes to a logic "low" state whenever such necessary temporal alignment is lost. In this situation, the Computed Output, 3, must be deemed invalid. A local Lock indicator lamp is also provided.

0055The three circuit elements 32, 34, 38 are employed to derive a series of time variant sine and co­sine waves at frequencies 1, 2, 3...N times the rotative speed of the rotor. These are produced as a series of "digital" data words utilized by subsequently discussed processing elements. Each such waveform contains 2048 data words per rotor revolution. Systems can be con­structed using more or less resolute sampling as dictated by analytic requirements specific to the application.

0056In the present embodiment, each such sample word is of 8 bit precision. Systems can be constructed with lesser or greater word lengths. Eight bit precision and the commercial analog components provide a "5% precise" transduction with better than 40 dB of dynamic range. More precise systems of greater dynamic range are feasible using the methods described.

0057The controller of Figure 1 digitally synthesized the first eight harmonics of rotor speed; that is, N=8. A greater or lesser number of terms may be employed with no change in fundamentals. The digital sine and cosine samples are transmitted to the Fourier Coefficient detec­tor circuits 41 and component synthesizer circuits 48 through a simple word parallel Sine/Cosine Data Bus, 39. Data for all the synthesized functions are transmitted in a "time multiplexed" or "interleaved function" fashion. That is, data corresponding to a single rotor angular position for each of the 2N harmonic functions are placed on the bus sequentially. In the present embodiment, these are alternating cosine and sine functions of ascending harmonic order. Higher bandwidth systems may employ alternative parallel bussing of each harmonic function or groups of functions. Alternative orthogonal functions may also be employed. Each of the identical circuit sections of Fourier coefficient detector 36 band limits a single analog input signal X_j, detects its Fourier coefficients a_jR and b_jR with respect to an individual selectable rotor order (rp) and passes DC signals equal to those coeffi­cients to the programming module 44.

0058Analog transducer signals received on line 22 are presented to a band pass filter circuit 60 which serves to filter and AC couple the input data signal received from the transducer. As detailed hereinabove, it is preferable that the controller extract only the 4/rev. or 4P component of the input transducer data signal. As those skilled in the art will note, the above band pass filter introduces essentially no gain error for any order, 1P through 8P. However, a small angle phased error is introduced on the order of -6.5^o for the 4P (4/rev.) signal component. An error of this magnitude has been deemed an acceptable trade-off to eliminate strain gauge bridge amplifier DC signal errors and external signal noise above 150Hz. The averaging filters were set to a time constant nominally equal to the period of rotor revo­lution. This is a component programmable characteristic and may be selected as required by the dynamics and the signal/noise ratio of the examined input signals.

0059Each of the real Fourier coefficients, 13, is computed by multiplying an analog input signal, 1, by the digital cosine wave for the rth harmonic order. This is accomplished by using a four-quadrant multiplying digital to analog conver (DAC). the DAC receives its digital data from bus 39 during the appropriate time as defined by bus 40. The DAC'S analog product is low pass filtered to re­move components at frequency 2rp and to average the resulting coefficient for a selectable time period. This results in a very low frequency signal, instantaneously proportional to the required coefficient. In the case of steady flight condition, this signal is a constant (DC) voltage. Each of the imaginary Fourier Coefficients, is computed in similar manner. The sole difference is that the sine wave at the rth harmonic order is employed.

0060The band limited data signal is applied to both analog inputs of a dual multiplying digital-to-analog con­verter (DAC) circuit 62. A first half 64 of the DAC 62 multiplies the received band limited analog data signal by a digital cosine signal, while a second half 66 multiplies the analog input data signal by a sine signal.

0061The digital sinusoid signals are provided on data bus 68 by the synthesizer. The digital sinusoid signals include orders 1P through 8P. Selection of the desired signal order is dependent on signals received on line 70. In the preferred embodiment, a simple jumper from the digital synthesizer determines which order is utilized, with order 4P selected for the controller of Fig. 1.

0062The signals output from the digital-to-analog converter are currents proportional to the input voltages. The DAC 62 contains internal reference resistors for external voltage to current conversion. The output signals are converted to voltage signals in the conven­tional manner by amplifiers 72 and 74. The output voltage signals reflect "2 quadrant" multiplication of the bi-variant analog input signals with digital codes representing solely positive numbers. Specifically: V_U4p1 = -V_U1p8*(Code_A)/256 0<img file="EP0339833A2_D0008.tif" /> Code_A or Code_B<img file="EP0339833A2_D0009.tif" />256      (15) V_U4p7 = -V_U1p8*(Code_B)/256      (16)

0063In as much as "4 quadrant" multiplication is re­quired, the 8 bit codes presented at data bus 80 to represent bi-variant sinusoids in conventional off-setting binary format. Amplifiers 76 and 78 complete the multipli­cation process by subtracting the analog input signals re­ceived from twice each of the two quadrant product signals, resulting in: V_U4p14= V_U1p8*(Code_A-128)/128      (17) and V_U4p8 = V_U1p8*(Code_B-128)/128      (18)

0064In the preferred embodiment, the digital codes are selectively provided from an Erasable Programmable Read Only Memory (EPROM), described hereinafter, programmed to perform following: Code_A = INTEGER( 128+127*COS(rp))      (19) and Code_B = INTEGER( 128+127*SIN(rp))      (20) As a result, the output voltage signals presented on lines 80 and 82 represent instantaneous product signals having the form: V_U4p14 = (Xj* COS(rp))/2      (21) and V_U4p8 = (Xj* SIN(rp))/2      (22)

0065Each of these signals is averaged by a low pass filter 84. The signals provided therefrom are DC voltages representing the negatives of Fourier coefficients a_JR and b_JR. These signal values reflect the instantaneous change in the coefficients as flight conditions change. The respective Fourier coefficients reflect a moving or expo­nential average over approximately 3 rotor revolutions, matching the processing normally applied to PCM telemeter flight data.

0066Amplifiers 86 and 88 are configured as unity-gain inverters. These amplifiers generate positive signal images of the signals representing Fourier Coefficients a_JR and b_JR. Positive and negative signal images of the Fourier Coefficients are presented to the program board, as described hereinafter. In addition, the computed DC signal levels must be scaled so that the signals are equal in magnitude to the vector values (0 to peak) of the corresponding quadrature signal components at the frequency 4P present in the X_J signal component of the output signal. Therefore, if the analog input signals are free from overload error, the corresponding output signals are likewise error free.

0067In addition to the functions described herein­above, the controller also provides for signal overload protection by means of overload circuitry 90 which perferably comprises conventional comparators and converters configured to detect excursions of the signals in each circuit above a threshold value indicative of an overload. A local indicator of an input overload for the respective signal channel is provided for such detector. This signal is logically configured with all other similar overload signals from the remaining associated circuitry of the Fourier coefficient detector to yield a single global input signal overload indication.

0068For each of the signal channels output from the detector there is a corresponding plurality of signal lines which present signals corresponding to the coefficients generated by the detector. Shown in Fig. 3 are two sets of signal lines 92 and 94. Each set is comprised of four signal lines that present signals whose magnitudes correspond to the plus and minus signals of the Fourier coefficients generated for that channel.

0069Each line is electrically configured with a corresponding resistor which is located on programming board 96. The values of the respective resistors are selected to correspond to the elements in the C matrix pre­viously established by the calibration procedure detailed above. Since the elements of the coefficient matrix are constant, their electrical equivalents are resistors of fixed value. Furthermore, each of the resistors are con­figured at 98 with digital synthesizer in a manner that is detailed hereinafter. The coefficient programming module presents signals on lines 46, 47 (Fig. 1) whose voltages have the form: C_Anbjr = R_{Ref An}/R_Anbjr      (23)

0070Fig. 4 is a schematic illustration of a component synthesis circuit 100; one of six identical such circuits in the preferred embodiment. The component synthesis circuit includes summing amplifiers 102 and 104. Amplifier 102 provides a DC signal voltage equal to the n^th real Fourier Coefficient A_N which describes the amplitude of the cos(np) content in the synthesized output signal Y(t). The signal is formed in accordance with:<maths id="math0007" num=""><img file="EP0339833A2_D0010.tif" /></maths> where R_AJR, R_ANBJRN, R_{ref AN} are values in ohms of progamming resistors found in the corresponding n^th column of the coefficient programming board. Note that the mag­nitudes of these resistors are related to the holometric coefficients C_anajr and C_anbjr such that: C_Anajr = R_{Ref An}/R_Anajr      (26) and C_Anbjr = R_{Ref An}/R_Anbjr      (27)

0071In a similar manner, summing amplifier 104 signals corresponding to the n^th imaginary Fourier Coefficient B_N, describing the amplitude of the sin(np) content in output signal Y(t) in accordance with:<maths id="math0008" num=""><img file="EP0339833A2_D0011.tif" /></maths> and C_Bnajr = R_RefBn/R_Bnajr and (20) C_Bnbjr= R_RefBn/R_Bnbjr      (29)

0072The computed Fourier Coefficients -A_n and -B_n are provided to both the coefficient programming module at 98 as well as the remainder of the component synthesis cir­cuit. The negative image DC signal voltages are indepen­dently applied as analog inputs to dual multiplying digital-to-analog converter (DAC) 108. In a manner similar to the DAC described hereinabove, DAC 108 receives digital inputs from the digital processor that is described hereinafter. The -A_n coefficient is multiplied by a digital image of cos(np). The -B_n coefficient is multiplied by digital image of sin(np). Those digital image signals are received on data bus 39.

0073The rotor order n is determined by signals received on line 110. In the embodiment of Fig. 1 includes 6 of the synthesizer circuits with a single electronic characteristic, the rotor order, differentiat­ing each of the 6 separate sections. Each component syn­thesis circuit section references a different rotor order, n, in a sequence 1 through 6. Although it is preferable to configure the synthesizer circuit sections as described hereinabove, those skilled in the art will note that modi­fications to the selected orders may be made as required by the application.

0074The configuration and operation of DAC 108 is as described above and, represent two quadrant multiplication of the bi-variant analog signal inputs with the digital codes representing solely positive numbers; yielding: V_U4p14 = (Xj* COS(rp))/2      (30) and V_U4p8 = (Xj* SIN(rp))/2      (31) Negative signal images of the n^th order cosine and sine components of the ultimately desired output signal Y(t) are generated by amplifier 112 whose signal voltages have the form: V_U8p8 = -An * Cosine(np)      (32) and V_U8p14= -Bn * Sine(np)      (33)

0075These two signals are added by an inverting summer circuit 114. The summed signal is the n^th order contribution to the final output signal, Y(t), and is pro­vided back to the coefficient programming module at 98 as Y_n(t). Consequently: V_J3p8 = V_U8p1= Vn(t) = An * Cosine(np) + Bn * Sine(np)      (34)

0076This signal is presented on lines 52 and is subjected to overload monitoring by an overload detection circuit 118 whose output signal is presented on lines 120. Circuit 118 is the same as the overload circuit described hereinabove with respect to Fig. 2.

0077Referring now to Fig. 5 there is a schematic illustration of a portion of the analog summer circuit 54 of the controller of Fig. 1. The analog summer circuit performs two disparate analog circuit functions and is not replicated within the controller. The analog summer cir­cuit adds the six signal components Y_n(t) received from the multiplying resolver to form the output signal Y(t) in accordance with:<maths id="math0009" num=""><img file="EP0339833A2_D0012.tif" /></maths> In addition to the Y_n(t) signal components presented on lines 52, amplifier 122 receives signals on lines 124 from the programming board. As detailed above, the resistors installed on the programming board are configured to com­plete an inverting/summation circuit, including amplifier 126, whose output signal on lines 55 corresponds to the desired parameter signal Y(t). In equation 34, R_pn corre­sponds the values of respective order R_p selecting resis­tors 96 located on the programming board.

0078In general, certain orders of the signals output from the multiplying resolver will dominate as compared to others. Maximum precision for the controller is obtained by configuring all of the computed analog voltages to be at or near the full scale voltage level, typically + or -10 volts. For example, it may be desirable, to configure the circuit to provide additional gain in the synthesis of a single constituent component of Y_n(t) and then provide a corresponding attenuation in the analog summer during final summation of the signal.

0079As described hereinabove, each controller circuit provides for signal overload monitoring. In addition to providing for overload monitoring for the output signal from amplifier 122, overload detector circuit 128 provides for "wire ANDing" of all overload signals to output a global overload detection signal on line 57 of all indi­vidual overload signals received on lines 56. These signals are normally at a logic high indicating proper operation. Circuit 130 is conventional, and generates reference voltage for the respective overload circuits.

0080Fig. 6 is a detailed schematic illustration of a portion of a digital processor that is not-replicated in the controller.

0081The period-locked loop with phase assertion (PLLPA) circuit 34 in consort with the multiple Sine/Cosine synthesizer 48 represents a unique approach to the synthesis of period functions synchronously locked to a temporal reference signal. Fig. 6 is a schematic illustration of the circuit 34 of Fig. 1. The PLLPA cir­cuit accepts a period 1/Rev temporal reference signal (line 33) and generates three output logic signals (lines 35, 36, 37). The M/Rev output signal (line 35) is a logic pulse train at a frequency M times that of 1/Rev signal. In the embodiment of Fig. 1 the frequency corresponds to 2048. The Lock output signal is a logic signal that is "high" when signal is at a frequency M times that of the signal on line 31 and "low" in all other circumstances. The Assert Phase or Phase = Zero, line 36, signal is a sharp rise pulse train with the same frequency as 1/Rev, synchronized to signal.

0082The temporal reference signal, (line 31), is typically derived from a mechanical source. This signal is (typically) an imperfect signal, exhibiting slow rise-time and "ringing". This signal is applied to Signal Conditioning Logic, 32, which performs two classical func­tions. Firstly, the circuitry 32 recovers the "rising edge" of the signal through conventional Schmidt triggering. Secondly, it synchronizes this rising edge to that of a system clock signal, line 132, by conventional use of "flipflops" and "AND gates". The resulting logic signal is the Assert Phase output signal. It is also the input to control logic circuit, 134.

0083The System Clock signal is a logic pulse train derived from a conventional crystal oscillator based Clock Generator, 136. The frequency of this oscillator is sig­nificantly greater (i.e. 3 orders of magnitude) than that of the required M/Rev output. This clock signal is applied as an input to Divider, 138, a conventional pre­settable down counter serving as a frequency divider. This circuitry also accepts a digital code, on line 140, representing an integer number, N. The output signal of this divider circuit is a pulse train of frequency equal to the clock frequency divided by N. The constant, N, is derived by the remaining circuitry, 34, so that the frequency of the M/Rev output signal equals M times the frequency of 1/Rev input signal within a prescribed error. N is derived dynamically; this value is updated at the frequency of the 1/Rev input signal. This is accomplished as follows.

0084The System Clock signal is subjected to frequency division by divider circuit 142, a conventional down counter configured to divide by the integer, M. Its out­put signal comprises a pulse train of frequency equal to the clock frequency divided by M. This signal is applied to up counter, 144, as its "clock" imput. Logic control circuit issues certain control signals, on line 146, to cause the accumulated count of counter 144 to be impressed upon the divider,138, as the integer, N.

0085Control logic circuit dictates the following specific action. At each rising edge of the Assert Phase signal, the current accumulation of counter 144 is trans­ferred to storage Latch 148. The counter 144 is reset to zero and enabled to accumulate, again. Thus Latch, 148, retains the period of the signal input on line 31, expressed as a multiple of M System Clock periods. This number is the constant, N, and is reevaluated for each period of the 1/Rev input signal.

0086Immediately after transferring counter 144 output code word on lines 150 to latch 148, the Control Logic, circuit 134 causes Divider,138, to accept latch 148 signal value as its dividing constant, N. This causes the frequency of the M/Rev output signal to be at a frequency M times that of the average of the signal on line 31 during said signal's last period.

0087That is : for an input (1/Rev) signal, of frequency f_in; and a system clock signal of frequency f_clock; the M/Rev output signal will be at a frequency, f_out equal to f_clock/N where: N=f_clock/Mf_in      (36) Thus: f_out=Mf_in      (37)

0088Clearly, quantization error occurs as N and M are restructed to integer values. Nonetheless, the periods of the input and output signals are locked to an integer ratio within the (hardware dependent) precision of the counters 138, 142, and 144. This ratio is re-evaluated and corrected once every cycle of the input signal.

0089The integer, N, is continuously examined by mag­nitude comparator, circuit 152. This circuitry verifies that N remains between two pre-established values, say N_min and N_max. This is signified by the Lock output signal.

0090The comparator circuit, 152, verifies that the input signal remained within a predestined frequency range. In essence, it restricts the lock range to a specific level of precision of counter 144. This permits maintaining output frequency quantization within known error bounds. The counter 144 Overflow output, signal presented on line 154, is used by this circuit to preclude accepting an "aliased" N value due to the counter 144 ex­ceeding its range and "wrapping around".

0091Figure 7 is a simplified schematic illustration of the component synthesizer circuitry 48 of Figure 1. The System Clock, Assert Phase and M/Rev signals are inputs to the multi-frequency synthesizer. This circuit functions to provide a time-multiplexed series of digital sine and cosine signals at harmonics of the input 1/Rev signal. These are output upon a bit parallel Sine/Cosine Data bus, (39 Fig. 1). Required de-multiplexing information is provided upon a separate Order (n) Select bus, (40, Fig. 1).

0092The required sine and cosine (or alternative periodic function) signal values are stored in read-only memory (ROM), 154. A total of 2T such function lists are stored therein. Each list contains M sample values describing functions of 1, 2, 3...T cycles of oscillation. Each list is stored continguously. Thus, the "high order" address bits presented to the ROM determine which list is to be accessed. The lists are arranged in ascending har­monic order with alternating cosine and sine functions. Thus, the lowest addressed list is a first order sine and cosine and the highest addressed list is a Tth order sine wave. Within each list, the data is arranged in phase angle (i.e. time) succession. Hence a linear progression of the "low order" address bits presented to the ROM will read out a signal function in sequence. Other storage schemes may be employed without affecting the fundamental logic of the device.

0093Two counters 156 and 158 form the ROM address. Counter 156 changes at the System Clock rate and forms the Log₂(2T) most significant bits (line 160). Counter 158 forms the remaining least significant bits. These change at a rate of M/Rev (signal on line 35). There are Log₂(M) least significant bits, (line 162).

0094Counters 156 and 158 are controlled by Sequence Logic circuit, 166, which provides control signals on line 164 causing Counter 156 to cycle the High Address bits through the numbers 0 through 2T-1 at the System Clock rate (or a multiple of this rate) for each stable value of the Low Address bit pattern. This circuit sets both counters 156 and 158 to 0 upon each rising edge of the Assert Phase signal.

0095The actions of circuit elements 156, 158 and 160 cause the ROM to be addressed in an orderly interleaved pattern, providing output code words to the Sine/Cosine Data bus. Bursts of 2T words are output to this bus fol­lowing each rising edge of M/Rev signal. The 2T data values are rapidly output following each rising edge of the Assert Phase signal. These are alternating cosine and sine values for phase angle equal to 0, sequenced in in­creasing harmonic order. The bus then remains "quiet" until the next rising edge of M/Rev signal. At this signal rise, the 2T data values associated with phase angle equal to 2TT/M (radians) are output in the same sequence. The data is subsequently output in the same fashion following rise of M/Rev signal. Each such output signal differs in phase angle from its predecessor by 2TTM radians. This sequence continues until the Assert Phase signal causes a reset to 0 phase.

0096Note that quantization errors in the PLLPA and/or frequency variation in the 1/Rev input signal can lead to reading greater or fewer than M angular data sets per 1/Rev period. Such angular truncation is termed the "closure error" and is discussed hereinafter. The bit patterns of the High Address bus indicate the data present on the Sine/Cosine Data bus. The least significant of these is "high" whenever a cosine signal is presented and "low" when a sine is addressed. This signal is incorpo­rated in the Sine/Cosine Data bus as an "A/B select" signal. The remaining Log₂(2T)-1 bits are subjected to "1 of N" encoding by encoder circuit 168. The "1 of N" encoder converts all but the least significant bit of the High Address bus data from a binary number to T separate signals. One of these is uniquely "high" for each har­monic order addressed; the remainder are "low". These sequentially asserted signals form the Order(n)Select bus 40.

0097The PLLPA circuit 34 competes with prior art cir­cuits termed "Phase-locked Loops" (PLL). These perform a similar function but accomplish it by alternate technology. A typical PLL block diagram for frequency multiplication is shown in Figure 8.

0098ρ phase-locked loop circuit 170 contains a voltage controlled oscillator (VCO) 172 which produces a square-wave signal with frequency proportional to its in­put voltage. This control voltage is produced by the filtered output signal of a phase comparator 174 which outputs a voltage proportional to the phase difference between two signals (normally) of the same frequency applied to its inputs, lines 176, 178. Filtration is required to remove harmonic error content in this signal to provide loop stability. One of the inputs to the phase comparator is the "squared-up" image signal of the input signal to be harmonically multiplied, line 180, from signal conditioning circuitry 182. The second is a fre­quency divided signal image of the VOC's output provided by frequency divider circuit 184. When the loop obtains lock, this divided frequency is equal to that of the input signal. If a frequency division of M is employed, the frequency of the V0C output signal (line 186) is then M times that of the input.

0099Some caveats must be noted. Firstly, this type of circuit can lock whenever the two inputs are of harmoni­cally related frequencies. Hence, frequency multiplication by M is not a uniquely possible output. Secondly, the phase between the comparator's inputs is a linear function of frequency unless the low pass filter 188 contains a "free pole" which compromises loop stability. Hence, the multiplied rate signal varies in reference phase M times as rapidly with changes in frequency.

0100Further, a PLL has no inherent means of ascertain­ing that it is in lock. It is possible to compare the filtered phase detector's command voltage signal against the extremes of the VOC's compliance but this merely verifies that the VOC has not been driven to an extreme. As an example, such a test will not detect that the VOC is simply "free-running" in the absence of an input.

0101The present PLLPA circuit solves all of these difficulties and offers several other advantages. Specifically: <ul id="ul0002" list-style="none"><li>(1) The PLLPA circuit does not suffer "harmonic locking".</li><li>(2) The PLLPA circuit maintains a constant phase relationship with frequency.</li><li>(3) The PLLPA circuit has inherent lock indication.</li><li>(4) The "capture" or "acquisition" and "tracking" or "lock" frequency ranges are identical. A PLL will only "capture" a signal within a narrow frequency sub-span of its "tracking" range.</li><li>(5) The PLLPA circuit will acquire an exact lock within one cycle of any input within its "lock" range. No known PLL'S can achieve this.</li><li>(6) The PLLPA circuit is an all digital design with attendent reproducibility, consistency, reliability, simplicity and flexibility. In contrast, PLLs utilize analog as well as digital techniques.</li></ul>

0102As described hereinabove, the synthesizer circuit section generates sinusoidal waveforms which are spectrally pure to better than 40 db. Moreover, the use of long (2048 value) data tables moves any aliased signal images in the output signal to the 10 khz frequency range, well above the analysis range of the measured signals, and at signal magnitudes which are exceptably low.

0103The present synthesizer circuit provides digital sinusoid signals which (1) are not converted to analog waveforms and are used to decompose the received data signal into selected Fourier signal components, and (2) are converted to analog wave forms and are used to recon­struct the desired output signal. Unique to the present controller is circuitry which measures the period of the timing signal (the 1/rev. signal), and generates therefrom a selected number of signals during the timing signal period, (2048 signals per period). In addition, the con­troller provides a forced phase relationship between the synthesized sinusoid signals and the timing signal once per cycle.

0104The "period locked loop with phase assertion" method and apparatus embodied herein with respect to the preferred embodiment represents a significant advance over more traditional "phase lock loop" circuit technology. Those skilled in the art will note that the present period locked loop circuit is characterized by tracking (or capture) and lock ranges which are equal. Conventional phase lock loop circuits have a capture range which is much narrower than the corresponding lock range. Consequently a phase lock loop circuit requires, in the present application, an unacceptably large number of rotor revolutions before capture is accomplished. Since heli­copter blades are operated over a somewhat narrow speed range, the broad lock range provided by conventional phase lock loop circuits is less important. The ability of the present circuit to capture within one revolution is most important, and marks a point of departure of the present invention over the prior art.

0105Moreover, the present circuit inherently provides a digital error signal that indicates when the circuit is not locked to the timing signal. As noted above, as long as the count code value in counter 148 is within a selected range, the circuit is locked. A count code out­side this value results in an error signal. With conven­tional phase locked loop circuits separate circuitry is required to generate an out of lock error signal.

0106While the present period locked loop with phased assertion method and apparatus provides significant advan­tages in the preferred embodiment, those skilled in the art will recognize that the digital synthesizer circuitry can also be synchronized by a high rotor order tachometer signal (e.g. 2048/rev.) rather than a 1/rev. blooper (tachometer) signal. For certain applications, such as the helicopter of Fig. 1, a mechanically generated high order tachometer signal can be configured to provide signal processing and remove the rotor operating speed restrictions, as well as eliminate the need for certain expensive electronics.

0107The period lock loop with phased assertion circuit generates a 2048/rev. signal from a 1/rev. tachometer signal. Quantization errors or closure phase errors in the synthesized signals are the result. The most serious quantization signal error stems from the fact that tachometer signal frequency can only be validated once per revolution. Curves 190,192 in Fig. 9 illustrate an example of the closure phase error in the synthesized tachometer signals when the helicopter rotor is overspeed. A similar error exists when the rotor is underspeed. The synthesized 4/rev. signal is characterized by an instanta­neous discontinuity 194 at the cycle to cycle closure. The difference between actual 1/rev. and the synthesized 1/rev. signals and the corresponding signal harmonics man­ifests itself as an error angle at the time of synthesized tachometer signal update. This is the closure phase error noted above. Note however that rotor speeds which are over or under the bracketed speed constitute an out of lock condition.

0108The closure phase error also exists even when the rotor operates at constant speed within the aforementioned rotor speed range. As detailed hereinabove, the period locked loop with phased assertion circuitry generates signals for 32 different rates of angle advance, one for each of the count codes between counts 192 and 223. Con­sequently, in the preferred embodiment there are 32 precise rates of rotor rotation for which an exact match of angle advance rate and the synthesized (2048/rev.) tachometer signal is possible.

0109In the preferred embodiment the period locked loop with phased assertion provides a closure phase error of less than 2 degrees in magnitude for any rotor speed within the lock range. By restricting the count code to counts in the 192 to 223 range any stable rotor speed within the bracketed 274.3 to 318 rpm lock range results in a closure error of 10 address steps or less. Conse­quently, in the preferred embodiment there is a closure error having a magnitude 1.76 degrees as an upper bound.

0110During rapid accelerations or decelerations of a helicopter rotor within the 295 to 305 rotor rpm operating range, the digital processor detailed hereinabove displays only an eight step or 1.41 degree closure error for those speed transitions between 295 and 305 rpm which are accom­plished in one rotor revolution. With the helicopter rotor operating a constant speed, the closure error is constant and is solely the result of quantized angle advance frequencies in the device. The period locked loop with phased assertion circuitry as described hereinabove is configured so that the period of the synthesized wave­forms (and their frequency) is in exact match with that of the rotor regardless of the closure error. This is the direct ramification of the once per turn phase assertion. In the case of an accelerating rotor, the period of the synthesized function signal lags the period of the rotor by one revolution and the closure error remains constant for a constant rate of change of rpm. Phase error at closure increases to direct proportion to the order synthesized, such that a 1.76 degree error in the fundamental frequency (1/rev.) implies a 10.55 degree error in the sixth harmonic (6/rev.) frequency. The synthesizer circuit of the preferred embodiment performs with an overall precision of about 5% for instantaneous values of its output signal over the entire lock rotor speed range.

0111The HALMARS system detailed hereinabove holomet­rically characterizes the helicopter rotating system so that only a few strains measured on the helicopter fuse­lage can yield the rotating strains and bending moments at any locations on the blades and other rotating parts under transient maneuver as well as steady state flight conditions. This calibration is insensitive to gross weight and sensor location. As such, the present inven­tion is a marked improvement over the known art which rely on sensors positioned with the moving components of interest. In the helicopter of Fig. 1 the HALMARS system removes the need to configure the helicopter with strain gauges on the helicopter blades and slip rings for trans­mission of the sensor signals.

0112Fig. 10 compares flatwise blade bending moments on a measured helicopter blade of Fig. 1 to moments computed by the present invention for level flight at a helicopter speed of 130 knots. Curve 196 corresponds to the measured rotating flatwise blade bending moment, while curve 198 corresponds to that blade bending moment deter­mined using the present invention. The HALMARS system provides load signals which were within 5% of actual load for a variety of flight conditions, including steady and level flight maneuver transients at various roll and pitch rates from a 0.48G pushover to a 2G pullout at 90 knots, as well as maneuver transients at several pitch and heli­copter rolls with rates from a 0.65G pushover to a 1.59G pulloff at maximum velocity.

0113The HALMARS technique detailed hereinabove is not limited in application to helicopters or other aircraft. For example the above analysis can be readily adapted to determine accelerative loads on rotating turbine blades in gas turbine engines, loads in rotating automobile engine components and dynamic loads on aircraft wings. In sum, the present invention allows for a remote determination of strains and loads with any mechanical system having compo­nents which are not amenable to direct, local instrumentation.

0114Similarly, although the invention has been described hereinabove with respect to a preferred embodiment thereof, it should be understood by those skilled in the art that various changes, omissions and additions thereto may be made therein without departing from the spirit and scope of the invention.