1、NASA Technical Paper 1043 of a Light Airplane Robkrt L. Cannaday and William T. Suit DECEMBER 1977 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECH LIBRARY KAFB, NM 11II1llIllllllllIllllllllllllllllllllllHllll OL342b5 NASA Technical Paper 1043 Ef
2、fects of Control Inputs on the Estimation of Stability and Control Parameters of a Light Airplane Robert L. Cannaday and William T. Suit Langley Research Center Hampton, Virginia National Aeronautics and Space Administration Scientific and Technical information Office 1977 l- Provided by IHSNot for
3、ResaleNo reproduction or networking permitted without license from IHS-,-,-SUMMARY The maximum likelihood parameter estimation technique was used to extract values of stability and control derivatives from flight test data obtained from a light, single-engine, low-wing airplane. The flight tests con
4、sisted of 9 runs in which the stabilator was used to excite the longitudinal motions and 28 runs in which the rudder and ailerons were used to excite lateral motions. The vari- ous control inputs were initiated from trimmed level flight with a trimmed air- speed of about 46 m/sec and an initial alti
5、tude of about 600 m. The consistency of the derivative estimates as it relates to various inputs was investigated to determine the inputs which provide the most information for identification. Three criteria were used in this investigation: the ensemble variance, the estimated Cram and the airplane
6、was instrumented to record control-surface movements and airplane responses to these movements. The variables recorded for this study were obtained from an onboard instru- mentation package. The range of each instrument used to record the pertinent variables is given in table 11. The accelerations,
7、angular rates, and angular attitudes were recorded continuously, whereas the airspeed, angle of attack, angle of sideslip, and control-surface positions were recorded sequentially by use of a commutator which sampled each variable 20 times per second. Airspeed, angle of attack, and angle of sideslip
8、 were measured on a boom that was located near the wing tip and extended 3/4 E ahead of the wing leading edge. (See fig. 2.) The flight tests were divided into two groups: those in which the longitu- dinal modes were excited and those in which the lateral modes were excited. No flaps were used durin
9、g the flight tests and all.tests were initiated from trimmed level flight. The test procedure was as follows: The pilot turned on the data recording equipment, made specific control inputs, allowed airplane responses to settle out, and then turned off the recording equipment. This sequence con- stit
10、uted a data run. The tests were conducted in smooth air to minimize process noise from gusts. The throttle was held fixed during the runs to minimize any changes in thrust so that the only disturbing force on the airplane was due to the control input. Since angle-of-attack oscillations during the te
11、sts were generally less than To peak to peak, these variations were considered minimal, although the reader should note possible thrust change effects on Cxa and Cza as stated in appendix A. A total of 37 flight test runs were made, 9 runs concentrating on longitu- dinal dynamics and the remainder c
12、oncentrating on lateral dynamics. The length of the runs ranged from about 20 to 50 sec. Since the.object of the flight test was to evaluate the relative effectiveness of various inputs for parameter esti- mation, all test runs were initiated from approximately the same condition of trimmed level fl
13、ight. The flight condition was between approach and cruise air- speed (approximately 40 percent power). For the longitudinal tests, the mean initial trimmed airspeed was 45.3 m/sec with a standard deviation of 1.7 m/sec and the initial altitude was 641 m with a standard deviation of 57 m. For the la
14、teral tests, the mean initial trimmed airspeed was 45.8 m/sec with a standard deviation of 1.6 m/sec, and the initial altitude was 564 m with a standard devi- ation of 24 m. Effects of variations in airspeed and altitude were considered to be negligible and were ignored in the processing and analysi
15、s of the data. It was necessary to apply corrections to some of the data before processing with the identification algorithm. Airspeed was corrected for position error and altitude (assuming standard temperature) to obtain true airspeed. Then air- speed, angle of attack, and angle of sideslip were c
16、orrected for upwash and Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-resolved into velocity components u, v, and w by using the relationships developed in appendix B. The control-surface positions were measured at the respective cables in the vici
17、nity of the cockpit. Because Some of the data were commutated, it was necessary to reconstruct the data between data points by lin- ear interpolation and then sample simultaneously to avoid time-shift errors due to commutation. The continuous data were sampled digitally by using a zero- phase Ormsby
18、 filter (ref. IO). The accelerometers were considered to be located on the airplane center of gravity in the X-Y plane but their z-position relative to thewairplane center of gravity was unknown. The computer program used for identification had the option of identifying the z-position of the Y-accel
19、erometer; so this variable was activated in the algorithm for the appropriate maneuvers. Therefore, the accelerometer data were not corrected to the center-of-gravity position before being examined by use of the identification algorithm. A brief description of the identification algorithm is contain
20、ed in appendix C. CONTROL INPUTS Various control inputs were used to determine dependence of parameter con- sistency on the inputs. Some of the inputs were suggested by several input design studies (refs. 6, 7, and 8) and others were inputs common to flight test- ing. The inputs used in this study w
21、ere not the optimal inputs of these studies but were simplified forms. For the identification of the longitudinal parameters, three basic types of inputs were attempted: the stabilator square wave, sine wave, and rapid rise followed by slower decay. The square-wave input (input A, fig. 3) was chosen
22、 because it was thought to contain the frequency content necessary to excite the short-period mode. The period and amplitude (stabilator travel) were chosen for ease of pilot implementation, as well as to keep pitch-attitude changes within 5O to IOo of trim. The stabilator sine-wave input (input B,
23、fig. 3) is often used to characterize a second-order system. The stabilator rapid rise followed by slower decay (input C, fig. 3) was an attempt to approxi- mate an input form suggested by reference 6. For lateral identification, inputs consisted of rudder or ailerons applied individually or a seque
24、ntial combination of both. (See fig. 4.) Switching-type (square-wave) inputs were recommended in several references (for example, refs. 7 and 8) as an approximation to the optimal input; therefore, square-wave inputs were attempted, although the switching times and amplitudes used for the tests were
25、 not optimal. Both sine- and square-wave forms were investigated for each control. The resulting inputs were rudder square wave (input Dl, rudder sine wave (input E), aileron square wave (input F), and aileron sine wave (input GI. Rudder inputs alone do not provide adequate excitation of the lateral
26、 modes for parameter identification (ref. 11). To provide better excitation than single controls (rudder or ailerons individually) can produce, combinations of rudder and ailerons were used sequentially. That is, the aileron inputs were imple- mented followed immediately by rudder inputs or rudder i
27、nputs were followed by aileron inputs. The resulting sequential inputs were rudder square wave fol- 7 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-lowed by aileron square wave (input HI, rudder sine wave followed by aileron sine wave (input I), ai
28、leron square wave followed by rudder square wave (input J), and aileron sine wave followed by rudder sine wave (input K). Typical time histories of these inputs can be seen in figure 4. Several repeat runs were made for each input in an effort to obtain the desired input form. Inspection of the data
29、 for each input form showed that none of the input repeats excelled over the others, so all the runs were used for analysis. For the longitudinal inputs, this resulted in five repeats of input A and two of B and C. For the lateral inputs, D and E each had four repeats, F had two, G had four, H had f
30、ive, I had three, J had four, and K had two. CRITERIA USED FOR EVALUATING INPUTS The results from each of the several different control inputs were examined before presenting a set of stability and control derivative values which best described the subject airplane. In determining which inputs provi
31、ded the most consistent identification of the parameter values, three criteria were consid- ered: ensemble variance of the parameter estimates, estimated Cram for input B, from 0.93 to 0.96; and for input C, from 0.84 to 0.91. Also, for input B, run 6 exhibited relatively high correlations for some
32、of the other parameters also. Based on parameter correla- tions, input C appeared to offer slightly improved identification. The form of input C was loosely patterned after the optimal input of reference 6, which was based on criteria related to the trace and determinant of the Fisher information ma
33、trix. This matrix is the inverse of the parameter covariance matrix. Based on the three criteria considered, none of the three longitudinal inputs clearly offered better identification than the other two. Effects of Various Lateral Control Inputs The lateral parameter values obtained from the flight
34、 data are shown in figure 6 and table V. The lateral data are presented in the same format as that used for the longitudinal data. Note that no attempt was made to identify aile- ron control derivatives with rudder inputs or rudder control derivatives with aileron inputs. A visual inspection of the
35、data reveals that inputs with rudder alone (D and E) generally gave the least consistent estimates of the parameters except for the rudder control derivatives. Correspondingly, ailerons alone (inputs F and G) generally provided more consistent estimates than the rudder alone. For one of the aileron
36、runs (run 22 of input GI, however, the parameter estimates were considerably out of line for the rolling- and yawing-moment parameters. An examination of the time history of run 22 showed that the period of the input was about 2 sec longer than the other runs for input G, although the basic form was
37、 the same. This long input period may not have properly excited the airplane dynamics and thus may have resulted in some identification problems. Parameter correlations for run 22 were exceptionally high and are discussed subsequently. Due to the problems encountered with run 22, the associated para
38、meter values were omitted from the computation of the statistics shown in the lower half of figure 6. To investigate lateral inputs as they relate to consistent identification, the three criteria - ensemble variance, uncertainty level, and parameter correla- tions - were again used as for the longit
39、udinal parameters. In order to determine whether input form affected consistency, results from inputs D and E, and F and G were compared by using the variance criterion (F-test). For rudder input forms, D generally provided more consistent esti- mates than E but only CyB, Cygr, and Cn were significa
40、ntly more consistent (80-percent level). In no case did input E provide significantly greater consis- tency in the parameter estimates than input D. This result seems to indicate that, for rudder inputs, rudder square waves provided the better identification. For aileron inputs, F provided more cons
41、istent estimates than G (sine waves). Input F demonstrates significantly greater consistency for CY8) CYp, CB and Cqa than input G. Therefore, it appears that square-wave inputs provided r 10 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-the more c
42、onsistent estimates for ailerons also, but uncertainty levels (esti- mated Cram only Cygr was identified as significantly more consistent and this was for input I. Therefore, based on the information examined thus far, it is difficult to conclude whether order makes any difference. The next criterio
43、n to be considered in evaluating input effectiveness for identification purposes was the uncertainty level, or estimated Cram = -pv + qu + g cos e cos 4 + + CZc,(a - at1 + cz 1 qa 2m q 2v c1 = tan-1 w U 16 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-
44、APPENDIX A The values of the lateral states v, p, r, and used in the longitudinal equations were the flight-measured quantities. Since thrust changes are not explicitly modeled in the equations of motion, Cia of equation (AI) and Cia of equation (A2) are not necessarily pure Cx, and Cza but may
45、contain small contributions due to changes in thrust. There- fore, Cia and Cia, as determined in this study, are given by Since, in this study, thrust was held constant and the angle-of-attack changes were no more than 7O peak to peak, the contributions of thrust to Cia and Cia were considered minim
46、al. The equations used to compute the lateral motions were + = -ru + pw + g cos 8 sin + 1 p + cyB + cyr 2v rb 2m 17 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-APPENDIX A v = $2 + v2 + w2 (A161 The values of longitudinal states u, w, q, and 8 use
47、d in the lateral equa- tions were the flight-measured quantities. The equations were used to compute the airplane state responses. The computed responses were then compared with the recorded responses from the flight tests and the differences were used to update the parameters (stability and control
48、 derivatives) to improve the fit. The longitudinal measured and computed responses, or states, used in the algorithm for this study were u, w, q, 0, ax, and az. The lateral states used were v, p, r, , and ay. An abbreviated discussion of the identifica- tion algorithm is given in appendix C. 18 Prov
49、ided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-APPENDIX B TRANSFORMATION OF MEASURED V, a, AND B The boom on which the dynamic pressure, angle of attack, and angle of side- slip were measured was located at the left wing tip parallel to the airplane X body axis. The sensing elements were located about 3/4 E ahea
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