Document
NASA Technical Memorandum 102758
HOT-BENCH SIMULATION OF THE ACTIVE FLEXIBLE WING WIND-TUNNEL MODEL CAREY So BUTTRILL JACOB A. HOUCK NOVEMBER 1990 (NASA-TU-I02ISo) HOT-BF_CH SIMULATION OF N91-21144 TH_ ACTIVE FLCXT3L3 WING WIqD-TUNNEL MODEL (NASA) i4 p CSCL OIC G_/OB
N/ A
National Aeronautics and Space Adminislration Langley Research Center Itamolon, Virginia 23665 I r _ i HOT-BENCH SIMULATION OF THE ACTIVE FLEXIBLE WIN(; WIND-TUNNEL MODEL Carey S. Buttrill* and Jacob A. ttouck** NASA Langley Research Center Hampton, Virginia 23665-5225 Abstract h integration step size, seconds control surface hinge moment, in-lbs I IM 8 Two simulations, one batch and one real-time, of an k8 actuator steady state gain aeroelastically scaled wind-tunnel model were developed.
[-Kf.]
diagonal modal stiffness matrix, Kf(i,i) = mio_i 2 The wind-tunnel model was a full-span, free-to-roll model of an advanced fighter concept. The batch simulation was used I-Mr.]
diagonal modal mass matrix, Mf(i,i) = mi to generate and verify the real-time simulation and to test candidate control laws prior to implementation. The real-time [M cf] matrix of control mode to elastic mode inertial simulation supported hot-bench testing of a digital controller, coupling which was developed to actively control the elastic dynamic pressure, Ibs/in 2 deformation of the wind-tunnel model. Time scaling was d rate limit required for hot-bench testing. The wind-tunnel model, the s Laplace variable math models for the simulations, the techniques employed to {Uk} vector input at time t=kh reduce the hot-bench time-scale factor, and the verification V airspeed, in/sec (6696 in/see at Mach = .5) procedures are described.
state x state vector at time t=kh {xk} Nomenclature 8i generalized coordinate - control mode i first-order pole of typical actuator transfer function, a8 ;a damping of second-order denominator term of rad/sec typical actuator transfer function, rad/sec ff. • a(-Frli I _I) generalized coordinate - elastic mode i rli A ff [ k ] nfxnf matrix where AOO,j) - output of Dryden turbulence transfer function _g 3rlfk) , negative density, 1.146x 10 .7 lbs-sec2/'m 4 or slinches]'m 3 P force coefficient on the ith elastic mode due to kth RMS turbulence intensity, in/see Og time derivative of jib elastic mode, k = 0,1,2 Gaussian random number 1)
ff .. )
A ff frequency of second-order denominator term of [ m+2 ] nf×nf matrix where Am+20,J) = _..::au_, effect of t.08 typical actuator transfer function, tad/see jth elastic mode rate on the derivative of the mth break frequency of turbulence transfer function, _g unsteady aerodynamic lag state associated with the (2n)(l 7.32) rad/sec ilia flexible mode, m = 1 ..... ntag break frequency of anti-aliasing transfer function, ]t,i a A_C(i,j) a(-Frli / q) force on i th elastic mode due (2n)(25.0) rad/sec a k) ' matrix [l column vector {} to k th time derivative of jlJacontrol mode, k = 0,1,2 Subscripls A d /_- j " re(i,') _ a( -Fai / _) a aerodynamic [ k] arl(k) , opposing hinge moment on aa anti-aliasing J _t_ anti-symmetric i th control mode due to k th time derivative of jth c commanded elastic mode g quantity associated with turbulence [A],[B] general continuous system dynamic matrices tag aerodynamic "lag" quantity [C],[D] lin linear neg negative wing chord, 39.76 in pos positive Frli nl no toad total generalized force on elastic (flexible) mode i [F],[G] general discrete system dynamic matrices STALl. actuator dynamic stall value [Go] discrete system input matrix applied to {Uk} sy symmetric [G1] discrete system input matrix applied to [Uk+ t } 0 quantity associated with position 1 quantity associated with rate
rG .]
diagonal modal damping matrix, Gf(i,i) = .03 2 quantity associated with acceleration * Senior Member, AIAA 8 quantity associated with actuator ** Associate Fellow, AIAA testing is undertaken, both the model and the tunnel are at Su_rscripts risk.
f associated with elastic (flex) mode equations ff effect on elastic due to elastic (flex-flex) Wind-Tunnel Model fc effect on elastic due to control (flex-control) fg effect on elastic due to gust input (flex-gust) C Figure 1 shows the AFW model mounted in the LaRC associated with control mode equations cf Transonic Dynamics Tunnel during the November 1989 test.
effect on hinge moment due to flex (control-flex) The sting mount has an internal ball bearing arrangement that effect on hinge moment due to control effect on hinge moment due to gust input allows the model to roll +1- 145 ° about the sting axis. The cg fuselage is connected to the sting with a hydraulically Abbreviations powered pivot so that the model can be remotely pitched from AB2 Adams-Bashforth second-order predictor approximately -1.5 ° to +13.5 °. Destabilizing mass ballast AFW Active Flexible W'mg was added to each wingtip so that the model would flutter CAMAC Computer Automated Measurement and Control within the operating envelope of the TDT[2I. The tip ballast ISAC Interaction of Structures, Aerodynamics, and serves to lower both the first-bending and the first-torsion Controls elastic mode frequencies, with the predominant effect on the LaRC Langley Research Center first-torsion mode. The result is that the In'st-torsion and the LEI Leading Edge Inboard first-bending elastic modes combine to form the primary LEO Leading Edge Outboard flutter mechanism at a lower dynamic pressure than was the PPU Peripheral Processor Unit case for the original model (with no tip ballas0. The tip pounds per square foot psf ballast can also be rapidly decoupled in pitch from the wingtip RK2 Runge-Kutta second-order predictor-corrector by releasing a hydraulic brake. When decoupled, the tip P_S root-mean-square ballast is restrained in pitch by a soft spring. Decoupling the RVDT Rotary Variable Differential Transducer tip ballast proved to be an effective flutter stopper during TDT LaRC Transonic Dynamics Tunnel testing, providing a significant safety margin. For the flutter T_ Trailing Edge Inboard TED Trailing Edge Outboard Introduction The simulations described in this paper were developed as part of the ongoing Active Flexible Wing Wind-Tunnel Test Program,ll,2,31 a collaborative effort between NASA Langley Research Center and Rockwell International Corporation.
Three wind-tunnel tests have been completed and the final test is scheduled for February 1991. The program objective is the validation of analysis and synthesis methodologies as applied to the multi-function control of a sophisticated aeroelastic wind-tunnel model. The control functions being investigated include suppression of flutter, roll performance maximization, and load alleviation. Only the simulation models developed to support flutter suppression are discussed in this paper.
Flutter is a potentially explosive dynamic instability that can Figure 1.- AFW model mounted in the I.aRC Transonic occur when a sufficiently flexible wing begins to extract Dynamics Tunnel.
energy from the fluid stream. During the most recent tunnel entry, completed in November 1989, flutter suppression was successfully demonstrated at a dynamic pressure 24 percent above a measured open-loop flutter point.J2,31 13 Accelerometers Simulation Roles _J 2 per tip bldlmat )t_I,% .o5 Two distinct, but interrelated, simulations were developed to support the AFW test program, a batch simulation and a real-time simulation. The batch simulation served as a "truth" model, and was used to: (1) evaluate the control laws to 6 DOF forceLi l_ predict performance and establish gain and phase margins; (2) provide models and data files for the real-time hot-bench simulation; and (3) verify the real-time simulation.
/ 8 Strain gages2x'_L... 8 RVDT's for control The real-time simulation of the model/wind-tunnel
/
environment served to verify the functionality of the digital controller system in a hot-bench laboratory. End-to-end Roll rate gyro 2 outboard verification and debugging of the complex, one-of-a-kind digital controller system was essential, since whenever flutter Figure 2.- Instrumentation of the AFW model.
ORIGINAL PAGE IS ORIGINAL PAGE OF POOR OU#,LITY BLACK AND WHITE PHOTOGRAPH suppression tests conducted in the November 1989 test, the behavior, a real-time display (figure 4) was developed on an roll brake was engaged, so that the model was not free to roll. ADAGE graphics computer. The display presents model pitch and roll, control surface deflections, and total structural Figure 2, a drawing of the model, illustrates the locations of the control surfaces and selected instrumentation. There deformation of the simulated wind-tunnel model. The display are 8 control surfaces and 13 accelerometers. With the is based on a finite-element structural model of the test article.
A subset of the finite-element structural nodes were used to addition of the tip ballast, two wing accelerometers, previously co-located with the leading edge inboard control highlight the main body, wings, and the eight control surfaces, were moved to the tip ballasts. Reference 4 surfaces. The dashed line represents the undeformed describes in detail the AFW wind-tunnel model prior to configuration. The deformations can be exaggerated for ease adding the tip ballast. The input/output signal list for both the of viewing by a factor set at the console.
wind-tunnel model and the supporting simulations is given in Simulalion Time Scaling Appendix A.
--- The AFW hot-bench simulation operated at a time scale slower than 1:1 (real time). Time-scale is a function of the llot-Bench Laboratory integration step (h) and the computer frame ('13. If T is larger The AFW hot-bench simulation set-up, depicted than h, the simulation runs at l:(T/h) "slow." Since there was schematically in figure 3, utilized the central real-time facility no human operator in the hot-bench loop, a time scale other at LaRC[S]. The LaRC real-time facility consists of nodes or than 1:1 could be accommodated. Several factors prevented the AFW hot-bench simulation from operating in real time.
simulation sites that communicate by means of a 50-megabit- The control computer was scheduled to run at 200 Hz in the per-second fiber-optic digital-data network. The various simulation nodes on the network included two Control Data wind-tunnel. To avoid excessive digitally induced time delays, the hot-bench simulation needed to update at least Cyber 175 computers, engineering control consoles, various twice for each digital controller frame, requiring a 400 Hz rate aircraft cockpits, and motion base hardware. For the AFW for the simulation if it were to run in real time. The minimum hot-bench simulation, one Cyber 175 was used to integrate frame time available on the Cyber 175 real-time clock was 5 the equations of motion. An Adage graphics computer, used milliseconds (200 Hz). The simulation model itself was in this study, communicates directly with a Cyber 175 sufficiently complex that a computational frame of at least through a port. New Terabit Eagle 1000 graphics computers, 12.5 milliseconds (80 Hz) was required. Furthermore, since currently being installed at LaRC, will communicate over the there are cmly two Cyber real-time computers and many real- fiber-optic network as another simulation node. Communi- time jobs, the hot-bench simulation often shared a Cyber 175 cations with the digital controller occurred over analog lines in the same manner as when the controller was connected to the with another job. With only one half of the Cyber computing wind-tunnel model at the LaRC TDT.
power available, the 80 Hz simulation update rate would be further reduced to 40 Hz. Time-scale must, therefore, be an easily adjusted parameter for any dynamic component in the Real-Time Graphics hot-bench loop.
To assist in visualizing the simulated model dynamic -- NASA/Rockwell Interface -- _ Control Computer "--i Filters 1 Aliasing CYBER 175 / Integrate equations of motion PPU
/
Port m _Rack q I"""'_ __ _ AID l Site Rack Graphics Computer
I
Real-time image generation ] Video link General //,,4 Simulation Console Date entry _ I Aviation High Speed crate Cockpit Optical Strip charts Network Figure 3.- Schematic of the FW hot-bench simulation laboratory.
Figure 4.- Adage generated real-time wireframe image of the simulated AFW model.
theory was used. These models were combined with Digital Controller Apparatus empirical data to form a "whole aircraft" model wherein left The control computer consisted of a SUN 3/160 and right actuators were modeled individually.
workstation augmented with a digital signal processor, a floating point array processor, and analog/digltal conversion AtTluators boards.12,6l During both hot-bench and tunnel testing, signals Frequency responses for the eight individual actuators to and from the digital controller go through a Rockwell- were measured with the wing elastic motion restrained. In the NASA interface box. The interface box has several functions, frequency range of interest, third-order transfer functions, one of which is to house anti-aliasing filters that condition the with parameters optimized in a least square sense, produced signals from the wind-tunnel model before being sampled by good fits with measured frequency response data. In general, the digital controller. Because of the time scaling, the anti- right and left members of an actuator pair required different aliasing filters in the interface box were bypassed during hot- parameters to achieve a good fit and were so modeled.
bench testing (figure 1). The anti-aliasing filter dynamics All the actuator transfer functions had the following form, were included in the hot-bench simulation. Since the control laws were digitized assuming an update rate of 200 Hz in the wind tunnel, when the hot-bench simulation ran at 1 :n slow, 8(s) the controller was clocked at (200/n) Hz to be dynamically equivalent.
8c(s) (s+as)(s 2 + 2_8o3/is + ¢o_) In addition to its primary function of implementing a selected control law at 200 Hz, the digital controller performed a variety of support functions. Static checks, where k 8 is the steady state gain, a8 is the first-order pole dynamic data acquisition and storage, and sine-sweeps were location, _ is the damping of the complex pair, and t_ is the performed. Data from 20 second sine-sweeps were shipped frequency of the complex pair. The second-order complex to another computer wherein both open-loop and closed-loop pair results from the compressibility of the hydraulic fluid plant estimations were performed.[ 71 together with compliance of the structure. The first-order pole reflects the dynamics of hydraulic fluid flowing through a Simulation Math Model small orifice whose size is regulated by position feedback error. Rate limits, as a function of load, were specified by the Linear aeroelastic descriptions for the symmetric and anti- manufacturer and result from the maximum rate that hydraulic symmetric boundary conditions were generated using a set of fluid can pass through a small orifice for a given difference aeroservoelastic design and analysis programs developed at between supply and chamber pressures. The first-order pole the LaRC called ISAC, short for "Interaction of Structures, part of the transfer function was then a reasonable place to Aerodynamics, and Controls"lSl. Doublet lattice aerodynamic apply rate limits. An initial, linear rate was first calculated as --IF- fits rms rate (sy) Post-test L---G estimate - [] - fits rms position (sy) sy for G - - O- fits rms rate (as) (pre-test) as -" O" fits rms position (as) Turbulence Intensity, Post-test estimate G for G
(in/see)
sy
-o---0
O as
(pre-tes0
300 350 150 200 250 Dynamic Prcssure, psf Figure 5.- Turbulence intensities u_d for simulation.
surfaces were obtained they were resolved into symmetric and follows, anti-symmetric components that became inputs into the _0t/n = k8 ap (Se-x0) aeroelastic equations.
Positive and negative rate limits based on no-load rate limits Turbulence Model modified by hinge moment were formed, A turbulence model based on the Dryden atmospheric turbulence modellgl was used. A break frequency of 17.23 Hz for the turbulence transfer function was used to rlpos= (r/n?_/1-(IIMs/HMSsTAL L) approximate the expected wind-tunnel turbulence. Resonance peaks at 10 Hz were observed in tunnel data from prior entries r/neg =- (r[nl)_/l+(HMb/] IMSSTALL) and 10-11 Hz was the predicted flutter frequency. A break frequency of 17.23 Hz produces a peak magnitude at 10 Hz in where the hinge moment, HM 8, is positive for an external load the Dryden transfer function. The state equations used for resisting positive actuator motion, and HMSSTALL represents each symmetry are, the maximum load the actuators can overcome. Note thai an • 2 3/2 Tl% aiding load will produce a rate limit larger than the no-load X'g = -2COgXg - t0gXg + OgCOg rate limit, rlnr An aiding load could occur for a leading edge surface. The positive and negative limits were imposed on the where, x)is a Gaussian random process that is sampled and linear rate xotin as follows, held every TX)seconds, tog is the break frequency in radians/second, aod Og is the RMS intensity. In both the batch and hot-bench simulations, T_) is the integration step X0 = _Otin otherwise size. The factor ofT_/2 applied to the input 9 arises from the r/po s if xOlin > rlpo s r/neg if xOlin < rlneg inherently band-limited nature of a digital simulation. The random process that produces _ can be interpreted as white The state xo was then used as a command to the second-order noise being passed through a perfect (l/2Ta;) Hz band-pass portion of the actuator transfer function filter. The output equations are, = 082 (x O" _i) - 2 _5_8 _i _g = Xg+ _g and _g = _g+ _f3 k.g Once the position, velocity, and acceleration ot" the control
tog
Prior to the November 1989 entry, an overall intcnsity and apply to either symmetric or anti-symmetric motion. The level of 12 in/sec was estimated for the tunnel turbulence. It flexible modes are augmented with control modes that was decided to allocate the turbulence between the symmetric represent control surface deflection. The control modes have and anti-symmetric models based on an 85/15 percent zero stiffness. A low frequency subset of the elastic modes of distribution. The following symmetric and anti-symmetric free vibration from a large-order structural model are typically intensities resulted used in an aeroelastic formulation. For the AFW simulations, the number of retained flexible modes per symmetry was 6gsy = 10.2 in/see Ogas = 1.8 in/see always between 7 and 10, inclusive. The flexible modes are orthogonal to each other so the mass and stiffness matrices are When the model is in the tunnel with a flutter-suppression diagonal. Modal damping of 0.03 is assumed for each mode.
control law engaged and subjected only to natural turbulence The in-vacuo equations were augmented with generalized as excitation, control surface activity results. Analysis of data generated in the November 1989 tunnel test revealed that the acrodynamic force coefficient matrices, [Q(j_)], that are RMS control surface activity predicted by simulation was functions of frequency. The functions, [Q(jco)], can be much higher than actually experienced in the tunnel. Three approximatedltO,111 by matrix expressions that are rational in different flutter control laws were tested in the Novembcr the Laplace variable, s. The "least square"llO,11] form of 1989 tunnel test and all generally resulted in the same approximation is given by observed RMS levels and the same degree of overprediction by the simulation. By making the turbulence intensities (Gg) A [Q(s)] = [A0] + [A1]I:s + [A2]('Cs) 2 functions of dynamic pressure, simulation-predicted RMS levels can be brought into agreement with observed data. An n/ag example of this process is shown in figure 5 for the flutter (2) suppression control law that achieved the highest dynamic pressure. The intensities required to bring batch-simulation- m=!
generated RMS results for both commanded control positions and control rates into agreement with experimental data are plotted in figure 5 as functions of dynamic pressure. For each where z = (_c/2V) and ntag is 1,2,3 or 4, depending on the symmetry, one intensity function corrects the RMS rate order of the fit. Equations (1) and (2) can be combined to predictions and the other corrects the RMS deflection produce the time domain aeroelastic equations (3) in table 1, predictions. Since only one intensity exists per symmetry, wherein the second-order, in-vacuo equations were either the RMS rate results or the RMS position results, but augmented with unsteady aerodynamic "lag" states arising not both, can be matched. The solid lines (one per symmetry) from the denominator term being summed in equation (2).
on figure 5 represent a fitted line biased upwards. The Control surface positions, rates, and accelerations along with upward bias favors overprediction, which is conservative and turbulence are treated as external inputs. The vectors {_ } preferable, if small. The solid lines on figure 5 are given by the following functions, are nfxl, nf f t both where is the number of retained and Xam J elastic modes. Equations (3) are used to solve for the elastic mode accelerations, {_ }, which can be integrated to find the Ogsy = 0.4 + 1.0 (1-'_) Ogas = 1.6 + 2.4 (1-_) rates and displacements. Equations (4) in table 1 are used to calculate actuator hinge moments. A positive hinge moment in this case resists positive actuator motion. The derivative where q has units ofpsf. These estimates are configuration calculations indicated in equations (3) and (4) were performed dependent and should not be be regarded as a final characterization of turbulence in the TDT. for each symmetry in the simulations. The symmetric and anti-symmetric components of the final accelerometer outputs were resolvcd into right and left components before output.
Agroglastic F_.uation$ The aeroelastic equations in a frequency domain format Anti-Aliasing Filters are given by [8,1o,11] For all the simulations, the dynamics of the anti-aliasing filters on the 40 primary outputs were simulated. For the tunnel test, both single-pole filters with a break frequency of 25 Hz and fourth-order Butterworth filters with break
*JC°L 0 * 0 0 5
frequencies of 100 Hz, had been assembled and were available. Only the single-pole filters were used in the November 1989 tunnel test. The single pole anti-aliasing filters are given by,
+ tCo ,)l IQ o )J J LsJ
xfs) 1 (1) u(s)- (s/O_aa)+l QCg(jco) J_, v ) where Oaa is the break frequency in radians/second.
These equations consist of the standard in-vacuo second-order matrix structural equations (mass, damping, and stiffness) Table 1 Aeroelastic and Ilinge Moment Equations (3) C-_ [ m+2] [Am+2] ){i } { fg /_ 1 {_n}+ _m X_m}+( Aff fc =- Am+2} (m=1,4) (4) [Am+21 [A_+ 2] _ =- ACg Pre-Test and Post-Test Models effectively test the control laws. The aerodynamic data arrays in the simulation are strong functions of Mach in the 0.8 to When the initial batch simulation was being developed, it was assumed the test would be conducted in Freon in the 0.8 0.9 range. To interpolate each element of the aerodynamic data arrays according to Mach would require excessive CPU to 0.9 Mach range, and a real possibility existed of holding time. Therefore, the approach used in the both the pre-test Mach constant during a test run and bleeding in Freon to raise batch and hot-bench simulations was to leave Mach and the density of the test medium. It was also expected that some airspeed fixed and to vary the density to achieve a change in of the control laws would be scheduled on dynamic pressure in which case both the batch and hot-bench simulations would dynamic pressure.
need to be able to vary dynamic pressure during a run to Table 2 Pre-Test and Post-Test Simulation Math Models ........ ' I Pre-test {1-!ag) Post-test (4-lag) State Catesodes Symmetric flexible mode positions and velocities 16 Sym aero lag states associated w/the flexible modcs 8 Sym aero lag states associated w/the control modes 4 Symmetric turbulence states 2 2O Anfi-sym flexible mode positions and velocities 14 Anti-sym aero lag states associated w] the flexible modes 7 Anfi-sym aero lag states associated w/the control modes 4 Anti-sym turbulence states 2 57 156 Total aeroelastie states Actuator states, 3 per actuator, 8 actuators 24 Anti-aliasin_ filters on 40 channels 40 121 220 Total states the anti-aliasing filter states were formed. The vector of state Some months prior to the 1989 tunnel entry, the use of Freon as a test medium was forbidden, and it was determined derivatives was integrated numerically with no assumptions that the test would be conducted with air as the test medium in of linearity. Once current-time flexible mode accelerations were calculated from the current-time positions and velocities, the 0.2 to 0.5 Mach range. In this Mach range the an Adams-Bashforth second-order (AB2) predictor method aerodynamic matrices are virtually constant with respect to Mach. Furthermore, in the actual wind-tunnel test, the tunnel was used to predict the velocities at the next time step. These predicted velocities were then used in a trapezoidal integration was not evacuated to any degree. Dynamic pressure, Math, scheme to generate predicted flexible mode positions. To wit: and airspeed were all changing as the fan speed was gradually increased. In the post-test implementation, density was left fixed, while airspeed was varied to replicate a given TDT rl(t+h) = _(t) + 1 ( 3 _(t)-_(t-h) ) dynamic pressure.
As seen in table 2, the number of states in the post-test I fi(t) ) Tl(t+h) = H(t) + _ (_(t+h) + simulation math model is almost twice the number required in the pre-test math model. The post-test model uses 20 elastic Using this modified AB2-based method, accuracy comparable modes instead of i5. For the post-test model, a 4-1ag least- to the Runge-Kutta second-order predictor-corrector formula square aerodynamic fit is employed (n/as=4) instead of the (RK2) used in the batch simulation was achieved with a l-lag fit used in the pre-test model. As seen in equations (3) single-pass formula. Note that the RK2 formulation requires and (4) and table 2, the choice of nlag has a dramatic impact two derivative evaluations per time step, whereas AB2 is a on the number of states.
single-pass formula which gives up some gain accuracy for phase accuracy and is typically used in real-time applications.
Batch Simulation Implementation The integration step of 1/2000 seconds used in the pre-test hot-bench simulation was small enough that the batch and The structure of the batch simulation is identical to the hot-bench simulation results compared favorably.
simulation math model as described by differential equations.
The anti-aliasing filters were handled separately from the The state derivatives are all calculated explicitly from the aeroelastic and actuator states. A scalar form of the state states (outputs of integrators). The state derivatives are transition equations for a constant input over the interval was collected in a vector and integrated with a Runge-Kutta used. For the single-pole anti-aliasing filters given by, second-order predictor-corrector method. The integration step used in the batch simulation is 1/2000 seconds. As indicated in figure 6, an integration step of 1/1600 seconds x(s) 1 results in a small change in predicted response with u(s)- (s/Oaa)+ 1 significant degradation occurring for larger steps. In addition to the actuator, turbulence, aeroelastie, and filter dynamics, the constant input state transition equation is the batch simulation also simulates the digital controller. The effects of computational delay and quantization are modeled.
x(t+h) = e-(Oaah)x(t) + (1-e-(Oaah))u(t) Pre-Test Hot-Bench Implementation As seen in equations (3), calculating the accelerations of The pre-test hot-bench simulation was implemented in a the elastic modes requires solving a matrix equation involving manner very similar to the batch simulation. State vectors the mass matrix. If the mass matrix is constant, an inversion (and associated state derivative vectors) that included all but can be performed prior to a run (in a "reset" mode) and the
3/
I mh--,ll_o I • i : 2-t-t - - -h:_/,ooo I........... ":!_: ........ ::'"i" !
/I ..... _=;_o I i:! i!:: :: m M 1 -_- .................. ; ............. , ..... _..;t._ ...... ,_..,..: ....... _........ ;,.
/ _. ,'_' :' , _ _, :'" ' tn . ,' ,/' :# _ b : q ' '
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-tO < -I ............... l ................... II ...... _xg ....... -;L-; ........ if'..:.....
._.
[.-.
-20 -' l" ........ :!!-: ........ ....................
z0a,), ho = Inooo ] i 1 .... J.-- -3 ........ i i .30 0 0.l 0.2 0 O.l 0.2 Time, _onds Time, seconds Figure 6.- Effect of step sizes on batch simulation response.
The post-test implementation method, wherein the hot- results simply stored for use as the integ_'ation proceeds. The bench simulation is updated by data extracted from the batch mass matrix for the flexible modes, ['M'Z'.],(see equation (1)) simulation, is depicted schematically in figure 7. The second- is both constant and diagonal, and its inversion is trivial. The order part of the third-order actuator models can be lumped s-plane formulation used for the unsteady aerodynamic states, with the remaining linear dynamics. The box in figure 7, however, augments the mass matrix with a fully populated labeled "Aeroelastic, Hinge Moment, and load Equations," represents the state equations of table I together with matrix, [A_Z], that is a function of Mach number. The total algebraic output equations to estimate the required mass matrix becomes accelerometer outputs, strain gage outputs, and pressure _2 transducer outputs from the states. Together with the 16 [M] = ['Mf.l + p (_-) [Affl states associated with the second-order part of 8 actuator transfer functions and N (57 pre-tes4 156 post-tes0 states from the aeroelastic model, a coupled linear system of N+16 (5) states, 10 inputs (8 actuator and 2 noise), and 40 outputs can be extracted from the "linear" portion of the batch simulation.
To implement the pre-test math model using the post-test state =([I]+[A])['M f] transition method required no model reduction on the extracted model, i.e., the simulation calculations could be completed in the same 1/80 second real-time clock frame used If the density of the test medium, p, is to be varied from the by the pre-test simulation, resulting in a time scale of 1:5. To simulation control console without losing time maintain a 1:5 time scale ratio while implementing the large synchronization, then the mass matrix equation must be post-test math model will require model reduction techniques solved at each derivative evaluation. Because the elements of to be applied to the extracted model. Reduction methods [A] in equation (5) were much smaller than unity, the utilizing internal balancing techniques are being investigated.
following approximation was successfully used for the Once the model has been reduced, the state transition model inverse of the mass matrix, based on an integration step of 1/400 seconds is calculated.
The nonlinear portion involves only eight states, one from each actuator. Each state is integrated numerically with an integration step of 1/1600 seconds. Four integration steps are made to predict the value of the input to the coupled linear system at time (k+l)h where h = 1/400 seconds. Since input When checked against the exact answer for maximum to the coupled linear system at time (k+l)h is now available, a anticipated values for p, induced errors for the pre-test model trapeT_oidal state transition scheme can be employed. Let were less than the precision available in the analog/digital {Uk} denote the quantity {u(kh)}. Given the linear dynamic converters used in the simulation loop.
system Prior to the November 1989 test, an integration step size of 112000 seconds and a compute frame of 1/80 seconds were {_} = [A](x} +[B]{u} required for the hot-bench simulation. A compute frame of 1/80 seconds was achieved only if the AFW simulation was if the ramp input signal, the only job on a Cyber 175. Thus, at best, the hot-bench simulation ran 25 (2000/80) times slower than real time, i.e., {Uk+1}-{uk} at a time scale of 1:25. A 1:25 time scale, however, proved to {u(t)} = {uk} + (t-kh) h be burdensome while testing the controller performance evaluation mode. Sine sweeps taking 20 seconds in the is defined over the interval tunnel would take over 8 minutes in the hot-bench lab.
Modifications to the hot-bench simulation implementation, kh < t < (k+l)h discussed in the next section, allowed the simulation to use a 1/400 second integration step, allowing a 5-fold improvement then the following exact solution for {x} at time t = (k+l)h in time scale.
exists Post-Test Hot-Bench Implementation {Xk+l} = [F]{x k} + [O0l{Uk}+[O,l{Uk+t} The post-test hot-bench simulation implementation was where, driven by the need to reduce the time-scale factor to something closer to real time together with the need to IF] = e [A]h accommodate the larger post-test models. If the hot-bench simulation is restricted to a fixed tunnel operating point for a [Gol = (e[A]h[Ah] t - [Ah] -I - e[A]h)[-A]l[ B] (6) given run, i.e., density, Mach, and airspeed are held fixed, then once the rate limiting is performed on the actuator [Gl] = ([I]- e[A]h[Ah] l + [Ah]I)[-A]'I[B] (7) transfer functions, the remaining dynamics in the simulation are linear. By utilizing a state transition method of Note that discretization on these dynamics, the hot-bench integration step has been increased by a factor of 5, from 112000 to 1/400 [O] --[Oo]+ [Gl]= ([l]- e [A]h ) [-A]'I[B] seconds.
Batch Simulation portion Hinge Moments Input (volts) Rate Limit Uncoupled Linear Coupled Linear Dynamics .,.-,., Dynamics Outputs (volts) Aerolastic Hinge Moment. IB ccelerations and Load ctuator positions Actuator oments Equations (Linear part) ending Torsion Hinge I h = 1/'2000 seconds I i Extract Linear Model at fixed dynamic pressure ([A] [B] [CI [D] {E}) • Perform Model Reduction (if required) Integrate derivatives I T • Scalar discretization of of 8 rate-limited Input [17INk+ [G0]Uk + [GI]Uk+I I anti-aliasingfilters Outputs actuator states by ] X k+l = (volts) (volts) cycling 4 times I • Convert from E +
[ClX +
through fast inner ] Yk+l = engineering units k+t [D]Uk+I I to volts loop. i [ h = 1/400 seconds _ h = 1/400 seconds L h=l/1600 seconds ] I Figure 7.- Data flow from the batch to the hot-bench simulation.
which corresponds to the result one expects to see for [G] if u(t) is assumed to be constant over the interval ([A]h)e [A]h = e[A]h[A]h kh < t < (k+l)h the equations for [Go] and [G1] can be put into a form that can be calculated if [A] has zero eigenvalues. Thus, Clearly, the direct evaluation of [Go] and [G1] using equations (6) and (7) will not work if [A] is singular, as would occur if [A] included rigid body modes with zero eigenvalues. However, using the Taylor series expansion _.w('I) p ([A]h) p'2 h [B] [G°] = I _p=2 I I e[A]h e [A]h = [I] + [A]h + _([A]h) 2 + ..¢ (8)
X
= Z _.i ([A]h) p [B] [G1] = .__..# p=o • p=2 and recognizing that References
The matrices [Go] and [GI]can be calculated by summing the
above series until the next term is under some tolerance.
I. Noll, T.; et al.: Aeroservoelastic Wind-Tunnel When applied to the pre-test model, procedures to sum the Investigations Using the Active Flexible Wing Model - series def'med by equations (8) converged without difficulty.
Status and Recent Accomplishments. NASA TM- The anti-aliasing filters are applied individually to each 101570 and AIAA Paper 89-1168. Presented at the output signal, which results in a diagonal system. The anti- AIAA/ASME/ASCF./AHS 30111Structures, Structural aliasing filters are therefore not lumped with the coupled Dynamics, and Materials (SDM) Conference in Mobile, linear system to avoid making full matrix operations. The Alabama, April 1989.
anti-aliasing filter dynamics are digitized in a sequential manner utilizing a scalar form of the trapezoidal state .
Perry, B.; Mukhopadhyay, V.; Hoadley, S.; Cole, S.; transition method described above. For single pole anti- Buttrill, C.; and Houck, J.: Digital-Flutter-Suppression- aliasing filters given by System Investigations for the Active Flexible Wing Wind-Tunnel Model. NASA TM-102618 and AIAA Paper 90-1074. Presented at the AIAA/ASME/ASCE/- x(s) 1 AHS 31 st Structures, Structural Dynamics, and Materials u(s)- (s/co,D+l (SDIvO Conference in Long Beach, CA, April 1990.
.
the state transition equations are Cole, S.; Perry, B.; and Miller, G: An Overview of the Active Flexible Wing Program. Presented at the Fourth Workshop on Computational Control of Flexible x(t+h) = e'(t°aah)x(t) + g0u(t) + glu(t+h) Aerospace Systems, Williamsburg, VA, July 11-13, 1990.
where 4.
Miller, G: Active Flexible Wing (AFW) Technology.
go = "e'(Oaah)(eO_ah) "1 + (°-hah)-I "e-(O_aah) (9) NA-87-1515L, 1987.
gl = 1 + e'(°_h)(_h) -1 - (O_aah)1 (i0) .
Crawford, D.; Cleveland, J., and Staib, R.: The Langley Advanced Real-Time Simulation (ARTS) System Status Report. AIAA-88-4595-CP, September 1988.
Note that the term (-[A] "1[B]) in (6) and (7) becomes unity in equations (9) and (10).
. Hoadley, S.; Buttrill, C.; McGraw, S. and Houck, J."
Development, Simulation Validation, and Wind-Tunnel Verification Testing of a Digital Controller System for Flutter Suppression. Presented at the Fourth Workshop on The hot-bench simulation was verified by comparing time Computational Control of Flexible Aerospace Systems, history results with the batch simulation. Trajectories were Williamsburg, VA, July 11-13, 1990.
found to match within the width of plotted lines. The open- .
loop plant dynamics of the batch simulation were verified by Pototzky, T.; Wieseman, C.; Hoadley, S. and comparison with ISAC-generated linear models. For each Mukhopadhyay, V.: Development and Testing of Methodology for Evaluating the Performance of Multi- symmetry, a linear model was extracted from the batch Input Multi-Output Digital Control Systems. AIAA simulation using finite differencing. A batch-generated Paper 90-3501. Presented at the AIAA Guidance, symmetric model and an ISAC-generated symmetric model Navigation, and Control Conference in Portland, had different numbers of states because of the way the Oregon, August 20-22, 1990.
actuators were handled. The batch-derived model had dynamics for eight right and left control surfaces and the .
Peele, E. and Adams, W.: A Digital Program for ISAC model had dynamics for only four symmetric control Calculating the Interaction Between Flexible Structures, deflections. The corresponding batch and ISAC linear Unsteady Aerodynamics, and Active Controls. NASA models were compared by overlaying the gain and phase TM-80040, January 1979.
frequency response of each input/output pair. The agreement between ISAC-generated and batch-simulation-derived . Hoblit, F.: Gust Loads on Aircraft: Concepts and frequency responses was excellent. Applications, AIAA Education Series, American Institute of Aeronautics and Astronautics, Inc., Washington, DC, 1988.
Concluding Remarks 10.
Tifrany, S.; and Adams,W.: Nonlinear Programming Two simulations, one batch and one real-time, of an Extensions to Rational Function Approximation Methods aeroelastically scaled wind-tunnel model were described. The for Unsteady Aerodynamic Forces Which Allow Variable batch simulation was used to generate and verify the real-time Selection of Constraints, NASA TP-2776, May 1988.
simulation and to test candidate control laws prior to implementation on the control computer. The real-time ll.
Tiffany, S.; and Karpel, M.: Aeroservoelastic Modeling simulation supported hot-bench testing of a digital controller and Applications Using Minimum-State Approximations developed to actively control the elastic deformation of the of the Unsteady Aerodynamics. NASA TM-101574 and wind tunnel model. Tune scaling required for hot-bench AIAA Paper 89-1188. Presented at the AIAA/ASME/- testing was discussed. Substantial improvement in the time ASCE/AHS 301!a Structures, Structural Dynamics, and scale ratio was achieved by application of state transition Materials (SDM) Conference in Mobile, AL, April 1989.
methods.
Appendix A - lnput/Ouput List for AFW Wind-Tunnel Model and Simulations Table A.1 Simulation and Wind-Tunnel Model Inputs and Scalin_ Volts/Unit nldmlz No. i__.a!
0.375 degrees streamwlse 1 Left LEO actuator command, + leading edge down 0.375 2 Left LEI actuator command, + leading edge down degrees streamwlse 0.375 degrees streamw_se 3 Right LEI actuator command, + leading edge down 0.375 degrees streamw_se 4 Right LEO actuator command, + leading edge down 0.375 5 Left TEO actuator command, + trailing edge down degrees streamw_se 0.375 degrees streamw_se 6 Left TEI actuator command, + trailing edge down 0.375 degrees streamwlse 7 Right TEl actuator command, + trailing edge down 0.375 degrees streamwlse 8 Right TEO actuator command, + trailing edge down Table A.2 Simulation and Wind-Tunncl Model Outputs and Scalin[ Units No. _ Volts/Unit 1 Left LEO actuator position, RVDT, + leading edge down 0.375 degrees streamwtse 2 Left LEI actuator position, RVDT, + leading edge down 0.375 degrees streamw_se degrees streamw_se 3 Right LEI actuator position, RVDT, + leading edge down 0.375 degrees streamw_se 4 Right LEO actuator position, RVDT, + leading edge down 0.375 degrees streamw_se 5 Left TEO actuator position, RVDT, + trailing edge down 0.375 degrees streamw_se 6 Left TEl actuator position, RVDT, + trailing edge down 0.375 degrees streamw_se 7 Right TEl actuator position, RVDT, + trailing edge down 0.375 degrees streamw_se 8 Right TEO actuator position, RVDT, + trailing edge down 0.375 degrees 9 Model pitch actuator position, RVDT, + nose up 0.375 degrees 10 Model roll position, + right wing down 0.0555 11 Left LEO co-located accelerometer, + up 0.5 g 12 Right LEO co-located accelerometer, + up 0.5 g 13 Left TEO co-located accelerometer, + up 0.5 g 14 Left TEI co-located accelerometer, + up 0.5 g g 15 Right TEI co-located accelerometer, + up 0.5 16 Right TEO co-located acccleromcter, + up 0.5 g 17 Left wingtip accelerometer, + up 0.5 g 18 Right wingtip accelerometer, + up 0.5 g 19 Left store-mounted accelerometer, + up 0.5 g 20 Right store-mounted accelerometer, + up 0.5 g 21 Fuselage accelerometer # 1, + up 1.0 g 22 Fuselage accelerometer # 2, + up 1.0 g 23 Fuselage accelerometer # 3, + up 1.0 g 24 Roll rate, + right wing down 0.0224 deg/sec in-lb 25 Left outboard bending moment, + tip up 0.00244 in-lb 26 Left inboard bending moment, + tip up 0.000477 in-lb 27 Right inboard bending moment, + tip up 0.000553 in-lh 28 Right outboard bending moment, + tip up 0.002820 in-lb 29 Left outboard torsion moment, + leading edge up 0.00611 in-lb 30 Left inboard torsion moment, + leading edge up 0.000112 in-lb 31 Right inboard torsion momelit, + leading edge up 0.000106 in-lb 32 Right outboard torsion moment, + leading edge up 0.00702 in-lb 33 Left LEO actuator hinge moment, + leading extge up 0.014760 in-lb 34 Left LEI actuator hinge moment, + leading edge up 0.014144 in-lb 35 Right LEI actuator hinge moment, + leading edge up 0.014155 in-lb 36 Right LEO actuator hinge moment, + leading edge up 0.020503 in-lb 37 Left'lEO actuator hinge moment, + trailing edge up ').026917 in-lb 38 Left TEl actuator hinge moment, + trailing edge up 9.014592 in-lb 39 Right TEI actuator hinge moment, + trailing edge up 3.013616 in-lb 40 Right TEO actuator hinge moment, + trailing edge up 0,028341 Mach number 41 Wind Tunnel Mach number 10.0 PSI 42 Wind Tunnel Dynamic Pressure .006945 Report Documentation Page NdlO_,,31 A_o_r_[_y=£5 fin(] 2. Government Accession No. 3. Recipient's Catalog No.
1. Report No.
NASA TM-I02758 4. Title and Subtitle 5. Report Date Hot-Bench Simulation of the Active November 1990 Flexible Wing Wind-Tunnel Model 6. Performing Organization Code 7. Author(s) 8, Performing Organization Report No.
Carey S. Buttrill Jacob A. Houck i01 'Work Unit No.
505-64-20-01 9. Performing Organization Name and' Address 11. Contract or Grant No.
NASA Langley Research Center Hampton, VA 23665-5225 13, Ty_ of Report aod Period Coverod 12. Sponsoring Agency Name and Address Technical Memorandum National Aeronautics and 14. Sponsoring ._gency Code Space Administration Washington, DC 20546-0001 15. Supplementary Notes Simulation Presented as AIAA Paper No. 90-3121 at the AIAA Flight Technologies Conference, September 17-19, 1990, Dayton, Ohio.
i6. Abstract Two simulations, one batch and one real-time, of an aeroelastically scaled wind-tunnel model were developed. The wind-tunnel model was a full-span, free-to-roll model of an advanced fighter concept. The batch simulation was used to generate and verify the real-time simulation and to test candidate control laws prior to implementation. The real-time simulation supported hot-bench testing of a digital controller, which was developed to actively control the elastic deformation of the wind-tunnel model. Time scaling was required for hot-bench testing. The wind-tunnel model, the math models for the simulations, the techniques employed to reduce the hot-bench time-scale factor, and the verification procedures are described.
18. Distribution Statement 17. Key"Words (Suggested by Author(s)) Unclassified - Unlimited Flexible, Simulation, Subject Category 08 Aircraft, Real-time 22. Price 21 No. of pages 20. Security Classif. (of this page) 19. Security Classif. [of this report) 13 A0 3 Unclassified Unclassified NASA FORM 1626 OCT 86