Filtering and Fusion based Reconstruction of Angle of Attack N Shantha Kuar Scientist, FMC Division NAL, Bangalore 7 E-ail: nskuar@css.nal.res.in Girija G Scientist, FMC Division NAL, Bangalore 7 E-ail: ggirija@css.nal.res.in Abstract This paper presents a schee to provide analytical redundancy for angle of attack sensor which is an iportant feedback for flight control syste of a high perforance aircraft / issile and also for aircraft stall warning syste. The filtering and fusion schee for reconstruction of angle of attack utilizes the rigid body kineatic equations of the aircraft and the data fro INS and air data coputer in an extended Kalan filter. The schee is ipleented in MATLAB / SIMULINK environent and validated with both flight siulator data as well as flight data. The schee provides an additional source of angle of attack which is reliable and reasonably accurate. Noenclature u, v, w Velocity coponents along aircraft body axis p, q, r Aircraft angular rates A x, Ay, Az Aircraft linear acceleration along body axis N z, N y Aircraft noral and lateral acceleration, Aircraft roll and pitch attitude, Aircraft angle of attack and angle of sideslip h,q, Aircraft altitude, dynaic pressure and air density C L, C L Aircraft aerodynaic coefficients a Coputed angle of attack fro altitude rate and Euler angles a Coputed angle of attack fro noral acceleration, weight and aerodynaic derivatives a Coputed angle of sideslip fro N y gain derivative g Acceleration due to gravity s, wt Aircraft wing reference area and weight N y gain N y to gain derivative subscript denotes easureents.ˆ denotes estiate Introduction Angle of attack (AOA) and angle of sideslip (AOS) provide inforation about the flow condition of the aircraft. It can contribute to flight safety by supporting avoidance of critical conditions like probleatic stalling behavior of the aircraft and can be an aid concerning departure characteristics. For unstable aircraft, AOA inforation fors an iportant feedback signal in the flight control syste (FCS). Also the stall warning syste (SWS) in transport aircraft uses the AOA signal to copute the stall argin which is directly proportional to the ratio of true AOA to stall AOA. Thus, both fighter as well transport aircraft require AOA inforation for all their ission requireents. In general, AOA and AOS are easured by vanes or pressure probes. They have to be placed outside the fuselage and at a proper location outside the flow field in order to provide correct indications of AOA. If vanes are used, they have to be ounted on nose boos on the fuselage and they are usually susceptible to daages particularly at high speed. Further, regular aintenance is required to ensure proper operation. The sensors, their installation and aintenance are a costly affair. It is andatory to have sensor redundancy in aircraft for AOA easureent since it is an essential feedback signal for FCS. Hence, in this paper, a schee to provide analytical redundancy for AOA is presented. National Conference on Range Technology (NACORT) ITR, Chandipur
There are several approaches for deterining the AOA and AOS based on data fro the inertial navigation syste (INS) instead of aerodynaic sensors. In this paper, an approach featuring estiation of AOA and AOS by filtering and fusion of INS data and air data coputer outputs through the aircraft rigid body kineatics is presented. The goal is to achieve a redundant, reliable source of AOA and AOS inforation all the tie with reasonable accuracy. An extended Kalan filter is ipleented for filtering and fusion of INS and airdata sensor outputs and the schee is ipleented in MATLAB / SIMULINK environent and validated with light transport aircraft flight siulator data as well as real data fro a fighter aircraft. The concept and schee presented here can be easily extended and utilized for other aerospace guidance and testing systes. AOA and AOS reconstruction schee AOA estiation has two iportant requireents, naely, speed and accuracy. Speed of estiation is a critical requireent for in-flight real tie application for flight control usage of AOA as well as for pilot inforation. AOA and AOS can be estiated with high degree of accuracy fro the easureents fro inertial navigation syste. Fusing the outputs of three acceleroeters, three rate gyros and air data coputer (total velocity, dynaic pressure and altitude), the AOA and AOS can be estiated through aircraft rigid body kineatic equations[,]. Thus it is purely an analytical ethod of reconstructing AOA and AOS without utilizing inforation fro external devices like flow vanes. Kalan filter algorith is used to estiate the AOA and AOS as it is recursive in nature and suitable for online data processing. The state and easureent equations of the filter are given below. State Equations: u A x q w r v g sin v Ay r u p w g sin cos w A z p v q u g cos cos p q sin tan r cos tan q cos r sin h u sin v sin cos w cos cos Measureent Equations: V u v w q u v w h h () tan w a u tan w a u () sin v a u v w where sin a sin sin cos cos h (3) sin V a sin cos sin sin cos cos cos g Nz cos cos s a CL Ny gain Ny wt q CL () a () N y gain is taken fro the lookup table given as a function of dynaic pressure In this odel it is assued that all the easureents are bias free and are at the aircraft centre of gravity. Appropriate changes in the kineatic odel can be incorporated to estiate the bias in the easureents as augented states. Figure shows the scheatic diagra of the AOA and AOS estiation schee. In Kalan filter, analytically obtained redundant AOA ( a & a ) and redundant AOS ( a ) are used as observations to estiate the relevant aircraft states. Fro the estiated (filtered) states, the AOA and AOS are coputed as given below: ˆ sin w ˆ ˆ tan uˆ vˆ uˆ vˆ wˆ where uˆ, vˆ & wˆ are the estiated states fro the filter. 3 MATLAB / SIMULINK ipleentation () The reconstruction of AOA and AOS is realized and studied in MATLAB / SIMULINK environent 3. Analytical AOA and AOS Analytical redundant AOA and AOS are obtained fro INS and airdata coputer outputs using equations (3, National Conference on Range Technology (NACORT) ITR, Chandipur
p, q, r A x, A y, A z V, q h N z, Wt, C L, C L, g, S N y, N y V q h gain Figure : AOA and AOS reconstruction schee & ) [3]. These equations are ipleented in SIMULINK and the output of this ipleentation has been independently checked with respective reference values (true values in case of flight siulator data and vane angles in case of real data). It has been noted in the reference [3] and confired here that the redundant AOA derived fro altitude rate and Euler angles (equation 3) are very accurate wherever there is no gust or turbulence. However in the presence of vertical gust/turbulence, the redundant AOA derived using N z, weight, CL and C L (equation ) is relatively better. This is because sufficient inforation of vertical gust/turbulence is captured in N z easureent. 3.3 Kalan Filter a State Equations & Filter Tie Update u w Kalan filter algorith is introduced into the SIMULINK block as S-function. The filter odel consists of two coponents, a nonlinear kineatic state odel and a nonlinear easureent odel. The state odel predicts the states ( u, v, w,,, h ) fro one instant of tie to the next instant based on the input data fro the acceleroeters and rate gyros. The easureent odel corrects this prediction with the reference easureents obtained fro the air data sensors and analytically coputed AOA and AOS (equations, 3 a a v h Measureent Equations & Filter Measureent Update ˆ ˆ and ). The ipleentation details of Kalan filter are given in reference []. The filter is anually tuned and its perforance is tested by plotting and checking:. AOA and AOS with true AOA and AOS (vane outputs in case of flight data).. filter odel outputs with easureents 3. Filter residual with bounds Re where R e is the innovation variance. Auto correlation of the residual with bounds where N is the no. of saples, (to confir the whiteness of the residual) Validation Results.9 N AOA and AOS estiation schee is initially validated with light transport aircraft flight siulator data. Sae set of siulated data used for evaluation of INS based AOA estiation schee for stall warning syste by autopilot tea [3] is being used here for validation of the present schee. Two sets of data are considered one with only elevator input and the other with elevator input and with vertical gust of /s. The results obtained fro the first set of siulated data (i.e. without gust) are shown in figures (a) to (c). Figure (a) shows the estiated outputs of AOA and AOS fro the filter copared with siulated true AOA and AOS along with the analytically coputed AOA and AOS which were used as observables in the Kalan filter. The estiated signals copare well with the true AOA and AOS signals. Fig. b shows the residuals of all the observations with bounds and Fig. c shows the autocorrelation function with bounds. It is clear that all the residuals are well within their theoretical bounds and the autocorrelation function shows that the residuals satisfy the whiteness test. Thus, the proposed schee indicates satisfactory perforance when the aircraft flight is in cal air. Figure 3 shows the AOA and AOS estiates fro the light transport aircraft siulator data generated with elevator and vertical gust. During the presence of vertical gust, since a (obtained fro N z, weight, CL and CL ) is relatively better copared to a (obtained fro attitudes and altitude rate), the easureent noise covariance of these observations in the Kalan filter are rescheduled giving ore ephasis to a observation (with lower easureent noise covariance). Thus whenever vertical gust is present it is possible to reconstruct AOA with reasonable accuracy without odeling of gust using this schee. However, this ethod would require soe kind of an indication of the presence of gust. National Conference on Range Technology (NACORT) ITR, Chandipur
Tht (deg) Tht (deg) AOA AOS Phi (deg) Phi (deg) Alt AOA qbar (N/) qbar (N/) Phi Tht V qbar V (/s) V (/s) Beta (deg) Beta (deg) AOS (deg) Alt () Alt () Analytical (Hdot, Attitudes) Analytical (Nz, Weight) Measured Vs Outputs.. Residual with bounds -. - -..... -. -. -. -. Analytical -.... -. -. - -. Figure (a): Reconstructed AOA and AOS trajectories Measured Vs Outputs Measured Residual with bounds -. -. Figure (b): Continued.. -. -. - -... 3 3 -.... -..... 3..... -........... -..... - -. Lag -. -. Lag Figure (b): Kalan filter perforance check (Filter residuals with bounds) Figure (c): Kalan filter perforance check (Autocorrelation of residual for whiteness test) National Conference on Range Technology (NACORT) ITR, Chandipur
AOS (deg) Analytical (Hdot, Attitudes) Analytical (Nz, Weight) Vane Analytical Analytical - Presence of gust -... Analytical.. -. -. -. 3 Figure : Reconstructed AOA fro level acceleration aneuver of flighter aircraft -. -. Figure 3: Reconstructed AOA and AOS trajectories in the presence of vertical gust Figures and show the reconstruction of AOA fro the real (flight) data of a fighter aircraft fro different aneuvers. Here the vane output which is found to be accurate (after correcting by kineatic consistency check) is taken as reference. Results indicate that the proposed algorith successfully reconstruct the AOA despite noisy data. It can be seen that the reconstructed AOA is reasonable accurate even when one of the analytical redundant observation ( a ) not being very accurate. Concluding Rearks A schee based on filtering and fusion using an extended Kalan filter to provide analytical redundancy for AOA and AOS sensors in an aircraft is presented. The filtering and fusion schee for reconstruction of AOA and AOS utilizes the rigid body kineatic equations of the aircraft and the data fro INS and air data coputer. The schee is validated with aircraft siulator data as well as flight data. The results obtained indicate that the AOA and AOS are reconstructed with reasonable accuracy. The schee can be used to reconstruct AOA and AOS which are critical paraeters during flight eergency situations like landing and also for stall warning. References Vane Analytical Analytical [] Maine R E and Iliff K W, Application of Paraeter Estiation to Aircraft Stability and Control: The Output Error Approach, NASA RP, 9. - 3 Figure : Reconstructed AOA fro roller coaster aneuver of flighter aircraft [] V H Risenberg, V A Vasiliev, V N Paraonov, and V A Sharenskyi, Adaptive syste for aerospace vehicle paraeter and state estiation, Second Braunschweig Aerospace Syposiu on Real-Tie Models for Control, Measureent and Estiation systes, Braunschweig, GERMANY, March 99. [3] G K Singh, Pratia and Shya Chetty, Evaluation of inertial/isu based AOA estiation schees, TM No.: SWS/TM/3, Dec. (Restricted) [] Candy J V, Signal Processing: The Model Based Approach, McGraw Hill International Edition, Singapore, 97 National Conference on Range Technology (NACORT) ITR, Chandipur