AIAA 95-0744 The Design and Control of an Oblique \Vinged Remote Pilotes Vehicle J.A. Jeffery, C.E. Hall .Jr and J.N. Perkins North Carolina State University Raleigh, NC

33rd Aerospace Sciences Meeting and Exhibit

January 9-1 2,1995 / Reno, NV For permission to copy or republish, contact tho American institute of Aeronautics and Astronautics 370 LEnfant Promenade, S.W., Washington, D.C. 20024

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AI AA-95-0744

The Design and Control of an Oblique Winged Remote Piloted Vehicle

John Jeffery*, Charles Z: llall Jr** , and John N Perklnst iVorrh Cumlrrzu Siure [hzwersi/y, l&dcrglz, Norfh C 'urolnzcr

ABSTRACT

An Oblique Winged Remote Piloted Vehicle was desiLned with a maximum sweep angle of 450. Concurrent Engineering techniques were used in the early design stages to try to reduce, through desi&-, the aerodynamic cross-coupling inherent with an unsymmetric aircraft. Parametric studies were carried out in order to determine how the wing's geometrical characteristics affect the cross coupling, and used to select the wing geometry. Aerodynamic modeling was combined with analytical analysis to give normal and cross-coupled derivatives. The cross coupling was eliminated by the use of a multi-input, multi-output Stability Augmentation System. The gains for the augmentation were found by means of eigenstructure assignment, and the use of dominance metrics to evaluate the effectiveness of various eigenstructures on the decoupling of the system. The resulting aircraft has no cross-coupling apparent to the pilot and has consistent response over the whole sweep range. The control system is robust enough to remain stable for variations in aircraft derivatives and physical characteristics.

* Graduate Student, Dcpt. of Mechanical and Aerospace Engineering, Student Member AlAA

** Assistant Professor, Dept. o f Mechanical and Aerospace Engineering. Member AlAA

t Professor, Dept. of Mechanical and Aerospace Engineering. Associate Fellow AlAA

Copyi&t d:' I994 hy thc Antencan Institute of Aeronautics and Aslronuuticn, Inc. All ri&t f

problems with coupling of roll in pitch maneuvers and a poor response for windup turns (this being the most difficult maneuver performed). With a study using a ground based flight simulator it was shown that a simple rate feedback control aubmentation system using pitch and roll feedback, significantly improved the flight characteristics at sweeps up to 60. Curry and Sim also showed improved aerodynamic performance at Mach numbers up to 1.4 and elimination of the sonic boom at Mach numbers as high as 1.2. The second aircraft is the OWRA which was evaluatcd by Kempel, McNeill, Gilyard and Maine4. This was developed from an F-8 and was used to assess pilots views on the handling, combined with the results found from NASA Ames-Moffett vertical motion simulator. Kempel, et al. found that pilots objected to the high level of lateral acceleration found in pitch maneuvers. Another problem arose with the variation in handling between left and right banked turns, the aircraft had a tendency to roll into turns in the direction of the trailing wing, and out of turns in the direction of the leading wing. The primary cause of lateral acceleration in pitch was found to be the asymmetric sideforce as a function of angle of attack. By using seven motion sensors to feedback roll, pitch and yaw rates along with pitch and roll euler angles the roll due to angle of attack was virtually eliminated and the lateral acceleration was significantly reduced. However the system did not produce favorable pitch to roll decoupling.

The advantages of oblique wings are numerous, including transonic drag benefits and reduced weight due to a single pivot, especially for missions that require long subsonic range and high speed dash capability.

I lowever these advantages cannot be achieved without some drawbacks, namely aerodynamic and inertial cross-coupling not found with symmetric aircraft. The main

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aerodynamic cross-coupling is pitch and roll. This is due to the asymmetric lift on the wing caused by spanwise flow, acting outboard and thus having a large moment arm in both the longitudinal and lateral modes. The cross- coupling generally increases with skew angle. By the use of a multi-input, multi-output (MIMO) control system the aircraft can be de coupled to some extent. Another method of reducing cross-coupling effects is careful d e s i g of the aircraft geometry, especially wing planform and airfoil selection. By knowing the problems that are going to exist from the beginning it is possible to design thc aircraft geometry and weight distribution to minimize the cross-coupling affects and thus require less work from the control system.

Despite most aerodynamic performance benefits occurring at transonic speeds it is still possible to investigate the problems due to asymmetry and the development of the control laws at low subsonic speeds.

THE OBLIQUE WINGED REMOTE PILOTED VEHICLE

The purpose of designing the oblique winged remote piloted vehicle (OWRPV), at North Carolina State University, was to develop an oblique winged aircraft to fly at a maximum skew angle of 450 with minimum cross-coupling apparent to the pilot. The cross-coupling was to be minimized by the use of a stability aubmentation system using a vertical gyro to feedback pitch and roll euler angles, rate transducers to feedback pitch, roll, and yaw rates, and a "bird" to feedback angle of attack, angle of sideslip, and velocity. In order to prevent the control system from having to deal with adversely large cross- coupling derivatives Concurrent Engineering (CE) techniques were used in the design process, especially the seven Management and Planning ( M P ) tools. The aim was not to produce a commercially viable oblique

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winged RPV but to test the design and control theory used.

The first stage was parametric studies using a simplified model, to investigate affects of wing geometry, pivot angle, pivot position and airfoil shape on the cross-coupling at 45". By doing this trends could be found due to altering the wings geometry and as such make i t easier to predict how desibm changes would affect the aircraft's handling characteristics. The aircraft's fuselage was a simple cylinder and was sized along with the fin and tail using tables developed by Roskam'.

A chosen planform alone was then accurately modeled and analyzed to give a quantitative analysis of the wings derivatives. The derivatives found to be satisfactory the wing was combined with a more detailed fuselage sized by simple lofting in order to house the engine and systems whilst keeping wetted area to a minimum. The potential code PMARC6 was then used to give numerical values to a, b, p, q and r derivatives for the whole aircraft.

As the aircraft geometly a weights and balance analysis were carried out. From the weights and balance it was found that all the products of inertia became non zero as the wing was swept thus requiring a complete derivation of the dynamic model using rigid body dynamics. Using modem control theory the whole control system, both open and closed loop, could be loaded into MATLAB' to enable eigenstructure analysis of the whole aircraft over the complete sweep range. The calculation of the gains for the feedback control system was also performed using MATLAB by selecting desired eigenvectors corresponding to eigenvalues which give level 1 handling characteristics. The affects of the feedback gains on the aircraft were compared to the open loop and unswept cases. The final OWRPV can be seen in Figure(1) and the physical characteristics in Table( I ).

PARAMETRIC STUDIES

The main problem with oblique winged

particular the pitch and roll coupling. It is possible through good design to minimize this cross-coupling; however this cannot be done at the cost of all the other aircraft characteristics. Thus it was necessary to perform simple parametric studies using MASX. APAS was chosen due to the ease with which various wing geometries could be analyzed using card files which could be read directly into APAS in order to analyze the sheer number of test cases required.

The APAS studies were carried out for the 450 case as it was assumed that cross- coupling effects would be largest at this sweep angle, and were used to show trends of various geometrical wing characteristics rather than give exact numbers. APAS could only be used to investigate the cross-coupling effects of a on sideforce, and rolling and yawing moments, and the affects of yaw on pitching moment. 'L

The first tests were to investigate the affects of taper ratio, increasing the taper ratio increases all the adverse cross-coupling. However it is necessary to have some taper to enable an elliptical spanwise loading without too much wing-twist. A conservative value of 0.4 was decided upon.

Kroo' explains the need for symmetric leading edge sweep in altering the variation of rolling and pitching moment with a by moving the wing centroid. after study a leading edge sweep of 70 was selected.

Another way of moving the wing centroid during sweep is to alter the position of the wing pivot . Positioning the pivot near the leading edge causes the wing to shift to the right as the right wing is swept forward, the opposite i s true for the pivot positioned near the trailing edge. The selected pivot position was to be at 40% chord, as airfoils tend to

aircraft is the aerodynamic cross-coupling, in L

have a thicker section at this point. The ii

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thicker section gives more room to house the pivot mounting and is a suitable position to - mount the wing spar.

There is a sideforce caused by the wing sweep on the aircraft, due to the force vector of the wing being rotated.. This requires the aircraft to fly at a sideslip and hank angle to balance i t out. One way of avoiding this situation is to hank the wing upon rotation to avoid the whole aircraft having to hank. The advantage of this could not outweigh the manufacturing complications of tilting the pivot and shaping the fuselage to avoid the wing getting stuck when being swept.

In investigating airfoil shapes, 4 geometrical criteria were considered t/c, position of maximum thickness, z/c and position of maximum camber. These studies showed that a 12% thick airfoil seemed to he most favorable changing to an approximately 10% thick airfoil when the wing was swept. From the camber studies the most favorable airfoil seemed to he the NACA 63212,

d however, for the low Reynolds number range of the aircraft this did not have a completely favorable pressure distribution. From an airfoil wish list a new airfoil was designed, based on the NACA 63212 with a more favorable pressure gradient using XFOIL'". The airfoil profile can he seen in Figure(2) with the coordinates shown in Table(2).

WING TIP DESIGN

As one wing was to be swept forwards and one aft, i t was necessary to des@ the tips in such a way that a trailing edge did not become a leading edge upon rotation or that the side of the tip was not placed in the flow. The simplest way to do this was to crank the wing near the tips tapering to a near point. Kroo suggests using asymmetric tips hut this was decided against as this would require S.A.S controls during take-off and landing,

.-,which are the most critical phases of flight.

Also, in order to try to create an elliptical wing loading and to avoid tip stall during take-off and landing the tips were given a washout angle of 20 at the spanwise position of the crank y= 2 3.94ft.

Three tip planforms were investigated with leading edge sweeps of 40",20" and 7". The lift distribution over the three wing planform can he found in Fiyre(3) . From Figure(3) it can he seen, that for the 400 leading edge crank angle case the lift distribution is exaggerated on the forward, right wing tip and drops of rapidly on the trailing, left wing tip. This causes a ncutral point shift of 14% m.a.c. forward between 0" and 45" oblique sweep. With the 7O leading edge tip case, the opposite is true with the lift being biased towards the left, trailing tip. This causes an 11% m.a.c. shift in the neutral point rearward between 0" and 45" oblique. This bias of l i f t in both cases is not only affecting the aircraft about the x-axis but also about the y-axis, causing the pitching moment problems stated. The 200 leading edge tip sweep has a much more even lift distribution and as such the reduced pitching moment shift. Another advantage of an even lift distribution is a reduction in rolling moment

AIRCRAFT MODELING AND DERIVATIVES

Once the tips had been designed i t was necessary to investigate the aircraft as a whole. The fuselage was to he based upon a circular cross-section as much as possible, for ease of manufacture. Modifications were made to the nose section in order to house the engine properly, and at the mid fuselage point for mounting the wing to house the pivot mechanism and to provide a flat base for the wing to pivot upon.

The tail was to taper symmetrically and linearly, this again was done to ease the manufacture. The empennage sizes were

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found using Roskam". The fin was placed with its trailing edge forward of the horizontal tail's trailing edge. So in the event of a stall the turbulent wake shed from the leading edge of the tail would not completely envelop the rudder and thus enabled the rudder to maintain control power.

Each configuration was investigated at a baseline with all angles and rates set to zero, at small angles of attack and sideslip and at small values of pitch, roll, and yaw rates. From these runs the derivatives of all the forces and moments due to these variables can be found assuming linearity due to small angles.

The aircraft was investigated over the whole sweep range. This showed anomalies in pitch and roll cross-coupling, Figure(4), around 200,250 and 300. As the wing sweeps from 200 to 250 there is a greater loss of lift on the leading tip than the trailing due to the angle of leading edge tip sweep. The the result of this differential change in lift on the tips is that the nose down pitching moment and positive rolling moment. As the wing sweeps through to 30 there is a large reduction in the lift on the trailing tip with a smaller reduction on the leading tip due to the trailing edge sweep on the tips. This has the opposite affect to the 200 situation causing an decrease in nose down pitching moment and positive rolling moment. The lift distributions can be found in Figure (5 ) .

All control surfaces were designed with the hinge line parallel to the trailing edge for easier manufacture. For elevator and rudder it was found that the cross coupling was negligible. The main control surface problem is due to the ailerons. These had to be positioned as far outboard as possible to avoid them interacting with the fuselage when the wing is swept at 450. By doing this the ailerons have a larger moment arm in the longitudinal direction as well as the lateral

and have a geater affect on the pitching moment as the wing is swept.

loss of lift is greater than the gain in lift due to the aileron being deflected downwards. This difference in lift increment causes a net loss in l i f t for equal magnitude of left and right aileron deflection. As the wing sweeps the leading aileron becomes less affective and the trailing aileron more affective causing a greater loss in l if t with a positive aileron deflection than a negative one. This lift difference accounts for a different pitching and rolling moment changes between positive and negative aileron deflections.

When an aileron is deflected upwards the L

CONTROL SYSTEM DESIGN

From previous investigations into oblique winged aircraft, the aerodynamic cross- coupling was already known to produce handling difficulties especially the coupling of pitch and roll during banked turns. Previous

benefits of a MIMO control system in reducing the cross-coupling.

The aim of the OWRPV control system was to minimize the cross-coupling affects whilst maintaining the controllability of the aircraft over the whole sweep range. This was to be done using MIMO control, feeding back eight states; namely U, a, q, q, b, $, p and r. The control system was a position controller for pitch and yaw, and a rate controller roll. A block diagam of the system can be found in Figure(6). The upper loop represents the roll rate controller The difference between desired and actual roll rate and angle were fed back through the feedback gain matrix, K. For the position controller the difference between the actual values and zero are fed back through K. The feedforward matrix, F, is used to pre- empt the cross-coupling that will occur when there is a desired pilot control surface deflection and to deflect the other control

work by Kempell et al. has also shown the W

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surfaces required to eliminate it. The feedfonvard is also used to alter the

d magnitude of the pilots desired control surface deflection to maintain a consistent response.

EIGENSTRUCTURE ASSIGNMENT

To reduce the cross-coupling it was necessary to assibm eigenvectors to the System which affect only the states desired. The theory and methodology for this eigenstructure nssibmment and the feedback gain matrix calculation was developed by Andry, Shapiro and ChungI2 which uses the achievable eigenvector. As the dimension of the input matrix is less than that of the system is not possible to specify the entire eigenvector and as such it was necessary to specify only certain elements of the vector. The vectors were chosen so as to try to force the states dominant in a normal mode to 1 and the states in the cross direction to 0 and dlowing the dominant control surface and the

&remaining states in the chosen direction to float. The desired eigenvectors were

Short Phugoid Dutch Rolling States Period Roll Mode

0 0 1: 0.

where x indicates an unspecified component. A value of 1 was also placed on the positions of the dominant control surface for each mode and zeros for the remaining control surfaces. Although each mode has two eigenvalues associated with it, only one vector is required as the two eigenvalues are complex conjugate pairs.

The possibility of achieving the ideal d igenvec to r s was not only dependent upon the

cross-coupling of the aircraft dynamics hut also the value of the desired eigenvalues for each mode and so it was necessary to investigate a range of each modes eigenvalue to minimize cross-coupling. The eigenvalues were varied between values that would producc level 1 handling characteristics with none of the desired eigenvalues matching the existing eigenvalues.

To assess the affect of each eigenvalue combination on the cross-coupling i t was necessary to use some form of metric. White uses a matrix whose columns give the contribution of the output associatcd with thc desired eigenvalue for each input. This was done for all combinations of eigenvalues in the desired range and the combination that gave the minimum value \vas then used to calculate the feedback gain matrix.

Once the desired eigenvalues had been chosen i t was necessary to calculate the gain matrices. These were calculated using a method outlined by Andry et al. The K matrix calculated placed 8 desired eigenvalues and assigned the closest eigenvectors to the desired vectors by a least squares method.

The calculation of the feedfonvard matrix (F) was performed using two methods. For the feedforward due to the position control of pitch angle and angle of sideslip the closed loop steady state values of the crowcoupling control derivatives were found due to control surface inputs of lo. For the control of roll rate it was necessary to find the value of the pitch, roll and yaw rates the response time of the servos, and to solve using those values as the steady state.

AlRCRAFT RESPONSE

The response of the system was investigated for initial pitch and roll rates of look, and elevator, rudder, and aileron deflections of 10 at the individual sweep angles and for initial pitch and roll rates of

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loois as the wing is swept from 00 to 450 and from 450 to 00.

A Runge-Kutta integration technique was used to simulate the response of the aircraft. By updating the elements dependent upon pitch and roll angle each time step i t was possible to produce a non-linear simulation of those elements. For the simulations of sweep range the sweep angle, and corresponding aircraft dynamics, was altered each step by linearly interpolating between the specific d e s i p points.

Jeffely" show the results for the simulations for each of the individual sweep angles. The aircraft response is consistent over the whole sweep range for initial disturbances and control surface deflection. With previous investigations it was found that the largest cross-coupling problem was pitch during roll. This was effectively eliminated on the OWRPV for all sweep angles. Figure(7) shows the results of a + l o aileron deflection with the wing swept at 45".

To find the effectiveness of the control system as the wing is swept it was assumed that the wing would take 5 seconds to sweep over the complete range. The derivatives, feedback, and feedforward matrices were linearly interpolated between the control laws at any point in the sweep range and the discrete points investigated to get the system response. The complete response over the whole sweep range is shown by Jcffery. When the wing is swept from 450 to Oo, with an initial pitch rate of IOOis, the affect of the control system is more apparent, Figure(8). The pitch angle for the controlled system has the same peak value with a time to half amplitude of approximately 2.5s as opposed to 5.5s for the uncontrolled system. The cross- coupling is effectively eliminated, with the angle of sideslip for the controlled system being one fifth of that for the uncontrolled system and a similar affect can he seen for the yaw rate. The roll angle damps out after 1.5s

with the controller and has only reached 112 amplitude for the natural system.

L ROBUSTNESS CHECKS

The robustness of the control system was assessed by investigating the movement of the system's eigenvalues when various parameters werc altered. All alterations were applied to every sweep angle for both positive and negative aileron deflections. A plot of the eigenvalue's real against imaginaly parts, for all situations at all sweep angles, can he found in Figure(9) for the controlled aircraft dynamics. I t can be seen from Figure(9) that there are some unstable eigenvalues on the positive real axis. These positive eigenvalues occur only when the roll damping is halved. This situation however is not cause for much concern, as if the error in calculating CJ,,, was as large as was tested then the whole aerodynamic model could be assumed to he erroneous and would need to be recalculated.

CONCLUSIONS b

It has been shown that by using Concurrent Engineering in the early desibm stages i t was possible to design an Oblique Winged Remote Pilot Vehicle which has consistent handling characteristics over the sweep range 00 to 450. The cross-coupling inherent in an aircraft of this geometry has been eliminated or reduced to magnitudes unnoticeable by the pilot by the use of a MIMO Stability Augnentation System. This gives the aircraft Level 1 handling Characteristics over the whole sweep range. The Stability Aupentation System uses the feedback of U, a, 0, q, P,I$, p and r.

L'

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REFERENCES

d l ) Campbell, J.P and Drake, H.M., "Investigation of Stability and Control Characteristics of an Airplane Model with a Skewed Wing in the Langley Free Flight Tunnel", NACA Technical Note 1208, May 1947. 2) Fantino, R.E., Parsons, E.K., Powell, J.D., and Shevell, R.S., "Effects of Asymmetry on the Dynamic Stability of Aircraft", NASA CR- 142857, 1975 3) Curry, R.E. and Sim, A.G., "Unique Flight Characteristics of the AD-1 Oblique-Wing Research Airplane", AlAA Journal of Aircraft Vol20 NO 6, June 1983 4) Kempel, R., McNeill, W., Gilyard, G., and Maine, T., "A Piloted Evaluation of an Oblique Wing Research Aircraft Motion Simulation With Decoupling Control Laws", NASA TP 2874, November 1988. 5 ) Roskam, J . "Airplane Desi@ Part II", 7oskam Aviation and Engineering

6) Ashby, D., and Dudley, M., Potential Flow Theory and Operation Guide for the Panel Code PMARC, NASA Ames Research Center, California, July 1991 7) MATLAB Users Guide, The Mathworks Inc., Natick, Massachusetts, August 1992 8) Sova, G., and Divan, P., Aerodynamic Preliminar). Analysis System I I Part 11-Users Manual , North American Aircraft Operations, Rockwell International, NASA CR-I 82077 9) Kroo, I., "The Aerodynamic Design of Oblique Wing Aircrafi", AlAA Paper 86-2624, October 1986 10) Drela, M., XFOIL, MIT Department of Aeronautical and Astronautical Engineering, Cambridge, Massachusetts 1 1 ) Roskam, J . "Airplane' Design Part I", Roskam Aviation and Engineering Corporation, Ottawa, Kansas, I988

?) Andry, A.N., Shapiro, E.Y., and Chung, -2., "Eigenstmcture Assignment of Linear

u ' o rpo ra t ion , Ottawa, Kansas, 1988

Systems", IEEE Transactions on Aerospace and Electronic Systems, Vol AES-I9 NO5, September 1983. 13) White, B.A., "Eigcnstructure Assignment By Output Feedback", International Journal of Control, Vol 53 NO. 6. 1991 14) Jeffer)., J.A., "The Design and Control of an Oblique Winged Remote Piloted Vehicle", M.Sc Thesis, Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh. NC, April 1994

l.4 I3 I .E s

Wing reference and actual

Reference and unswept I O ft

Reference and unswept 1.45 ft

lable(2) OWHPV Wing Airfoil

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z I

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e e 8 . 5 1 1.5

Tlnc < * > = Uncontrolled System,

Figure(7) Aircraft Response at 4 5 O Oblique Sweep to Positive Aileron Deflection

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1 5 , I

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- = Uncontrolled System, - - =Controlled System

Figare(8) Aircraft Response to Initial I'itcll Disturbance as Wing is Swept 45' to 0'

Figore(9) Aircraft Dynamics Eigenvalue Movcnlent from Robustness Calculations

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