28TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES
CONTROL ALLOCATION FOR AIRCRAFTS WITH MULTIPLE CONTROL EFFECTORS DURING TAKEOFF AND LANDING PHASES
Liu Yan*, Gao Zhenghong*, Chen Xing* *School of Aeronautics, Northwestern Polytechincal University, 710072, Xi’an, P.R.China [email protected]; [email protected]; [email protected]
Keywords: Control allocation, multiple control effectors, control effector superiority, flight performance, takeoff and landing
Abstract flight performance will be affected. [2] Besides, multiple control effectors also means that the This paper discusses the control allocation control effectiveness of a single control effector problem for aircrafts with multiple control is relatively limited which will easily cause the effectors during takeoff and landing phases. actuators to saturate and hinder the flying Based on the analysis results of performance qualities. indices during takeoff and landing phases, a The flight performance requirements and the control effector superiority evaluation method is corresponding control allocation problem vary proposed, and further an optimized control from different flight phases. Takeoff and landing allocation model is formalized for increased are two critical phases of aircraft operation. [3] flight performance. The flight performances during these two As a case study, the control effector phases play an important role in determining the superiority and takeoff/landing performance size of the airport and have a significant effect parameters of a typical canard-delta wing on flight safety as well as landing gear load. aircraft are evaluated. The simulation results Compared with free-flight condition, the show that the control allocation model operating process and the forces acting on the formalized in this paper can efficiently make use aircraft during takeoff and landing are more of the takeoff and landing performance complicated, which leads to more complex potentials of the target aircraft, which indicates control allocation problems. that the control effector superiority evaluation In order to make full use of the takeoff and method and control allocation model we landing performance potentials, the control proposed are sound and effective. allocation problems during takeoff and landing phases will be discussed in this paper to achieve increased flight performances. 1 Introduction Modern aircrafts are usually equipped with 2 Control Allocation Problem multiple control effectors in order to achieve desired flight performances. As a consequence, The goal of control allocation is to find a set of the number of control effectors tends to be permissible control effector deflections to greater than the number of control parameters, achieve desired control effects. The input is the which results in an infinite number of solutions. total control effect to be produced, i.e., the Therefore, there needs to be an effective method virtual control input vR()t k . The output is the for solving the control allocation problem for m aircrafts with multiple control effectors. [1] true control input uR()t , where km [4]. When the control effectors deflect, not only For linear systems, the moments but also the lift and drag, i.e. the Bu()tt v () (1)
1 Liu Yan, Gao Zhenghong, Chen Xing
where the control effectiveness matrix B To satisfy the performance requirements of is a km matrix with a rank of k . aircrafts with multiple control effectors, control To incorporate actuator position and rate effectors which are participated in control constraints, it is required that: should be selected on the basis of evaluating the
uuumin ()t max (2) superiority of control effectors.
ρmin u()t ρmax (3) Since the control allocator is usually 3.1 Performance Requirements implemented as part of a time-discrete control The most important performance indices of system, it is reasonable to approximate the time takeoff and landing phases include takeoff derivative as ground run distance, landing ground roll uu()ttT ( ) distance, liftoff speed and touchdown speed [5]. u()t (4) T The first two parameters are directly related to where T is the sampling time. Combining the range of the airport. Additionally, higher (2) ~ (4) yields liftoff velocity requires a longer takeoff distance. uuu()tt () ()t (5) Touchdown velocity will affect the landing uuu()ttT max{ , ( )Tρ } safety as well as the landing gear load [6]. min min (6) uuu()ttT min{ , ( )Tρ } max max 3.2 Superiority of Control Effectors Equation (1) constrained by (5) constitutes the standard formulation of the linear control During the takeoff phase, the aircraft needs allocation problem. high lift and noseup pitching moment [6]. Bu v Because of the low dynamic pressure, the (7) uuu aerodynamic drag is negligible relative to the There are three possible outcomes for takeoff thrust. control allocation problems: [4] During the landing phase, before 1. No solution exists touchdown, the aircraft also needs high lift and 2. One unique solution pitching up moment. The aerodynamic drag can 3. An infinite number of solutions not be ignored because of the low landing thrust. This paper focuses on the third case which After touchdown, to minimize the ground roll is typical in control allocation for aircrafts with distance, the aircraft needs low lift and high multiple control effectors. drag. In addition, due of the low dynamic pressure, the control effectiveness of 3 Superiority of Control Effectors aerodynamic control effectors is relatively low, and the actuator positions and rates of the For aircrafts with multiple control effectors, all control effectors are easy to saturate. the control effectors have the ability to control Specifically, for takeoff and landing before the aircraft. In other words, they all have a touchdown, the superiority of control effectors certain influence on the flight performance can be formalized as when activated. However, it does not PaRaRaR （8） necessarily mean that they have to be involved iLLimmirlrli in control for all flight phases. If the control For landing after touchdown, the effectors are used inappropriately, the flight superiority of control effectors can be given by PaRaR performances potential will not be fully utilized. iLLiDDi （9）
Besides, from the angle of reliability and where Pi is the superiority parameter of complexity of the flight control system, the the i-th control effector. number of control effectors simultaneously Cmi involved in flight control should be as few as Rmi C possible. m 0
2 CONTROL ALLOCATION FOR AIRCRAFTS WITH MULTIPLE CONTROL EFFECTORS DURING TAKEOFF AND LANDING PHASES
C GLLLcos L i enen RLi (10) CL 0 2cossin(NP2 T )
CDi where L is the lift increment (per unit) RDi n CD 0 produced by deflection of control effectors
CL 0 and CD 0 are the lift and drag ahead of the center of gravity (CG), such as canard; L is the lift increment (per unit) coefficient increment per unit deflection of the e reference control effector. Reference control produced by deflection of control effectors aft effector could be anly control effector of the of CG, such as elevator and/or elevon. aircraft. C iL and CDi are the lift and drag coefficient increment per unit deflection of the i-th control effector.
aaLmr,, aland aD are the weighting parameters of the lift, pitching up control effectiveness, rate limit and drag characteristics respectively. The weighting parameters depend on the performance requirements, aerodynamic Fig. 1 Force acting on aircraft with TV during takeoff characteristics of the aircraft and each control ground run effector, and the actuator performance. For a given equation, the weighting parameters satisfy The net pitching moment: that aaaa,,, [0,1], and their sum equals MM0 () M (en ) M ( ) LmrlD (11) to 1. PxNxsin(Tt )v 22 ( mgHcg ) In the following section, we will formalize where the control allocation model for the takeoff and M ()n pitching moment increment landing phases respectively. due to the deflection of control effectors ahead of CG 4 Control Allocation Model M ()e pitching moment increment After specifying the performance requirements due to the deflection of and control effectors participated in control, a control effectors aft of CG pitching moment when proper allocation method should be selected to M 0 build the control allocation model. 0 and no clean configuration M () pitching moment increment 4.1 Takeoff due to AOA
A typical takeoff phase consists of three steps: 1) xtv horizontal distance between with the engine producing maximum thrust, the the TV nozzle and CG aircraft is accelerated to the takeoff speed; 2) PsinTtv xpitching moment generated after reaching the takeoff speed, the aircraft is by TV rotated noseup so that the angle of attack (AOA) x mg horizontal distance between increases to generate sufficient lift for liftoff; 3) main gear and CG the aircraft starts climbing to the obstacle height Hcg height of CG (11.5m). [3] 2Nx2 mg pitching moment generated The force acting on aircraft with thrust by reaction of main gear vectoring (TV) during two gear takeoff ground 2NH2 cg pitching moment generated run is shown in Fig. 1. [7] by friction of main gear The vertical forces are According to the takeoff performance requirements specified in Section 3, maximum 3 Liu Yan, Gao Zhenghong, Chen Xing
lift can be formalized as the object function, and max(LLP sin enen T linear programming is selected as the allocation DDP cos ) method [8][9]. Therefore, the control allocation enen T model for takeoff can be formalized as follows: sin(TTTmin ) sin sin(max ) (14) max (LLP sin ) nene T eeemin max M ()enMP () sin( T ) xtv nnnmin max M MNxH() 2 ( ) 02mg cg (12) sin(TTTmin ) sin sin( max ) 5 Simulations eeemin max We use the ADMIRE (Aero-Data Model in nnnmin max Research Environment) developed by FOI, [10] All the deflections are positive if they are as the simulation platform. Control allocation deflected downward. for takeoff and landing phases are realized and evaluated on the basis of control allocation 4.2 Landing models built in this paper. 4.2.1 Before Touchdown Before touchdown, an increase in lift and drag is required. Hence, the lift and drag increments generated by control effector deflections can be selected as the object function for control allocation using the linear programming method. Therefore, the control allocation model for landing before touchdown can be formalized as: Fig. 2 Layout of the example aircraft max(LLP sin enen T As shown in Fig. 2, the aerodynamic DDPcos ) control surfaces of ADMIRE include: two enen T close-coupled canards, four elevons, a leading- MM0 () M (ne ) M ( ) edge flap (LEF) and a rudder. The maximal Pxsin(Tt ) v (13) allowed deflections and angular rate of the control surfaces are given in Table 1. sin(TTTmin ) sin sin( max ) Table 1 Control surface deflection limits eeemin max Control Angular Min. Max. Surface Rate nnnmin max Canard -55° 25° ±50°/s 4.2.2 After Touchdown Rudder -30° 30° ±50°/s Elevon -25° 25° ±50°/s After touchdown, to minimize the ground roll LEF -10° 30° ±20°/s distance, the lift should be minimized, while the TV -25° 25° ±25°/s drag and friction forces should be maximized. Decreasing the lift can lead to an increase in the This paper focuses on the longitudinal reaction and eventually the friction force; In problem. The canards/elevons are considered as other words, minimum lift is coincident with one canard/elevon deflecting respectively. 2/)( maximum friction force. Besides, during ground rclcn (15) roll, the moment problem can be ignored. Hence, ( loeliee rie roe 4/) the control allocation model for landing after touchdown can be built as 5.1 Choosing Control Effectors
4 CONTROL ALLOCATION FOR AIRCRAFTS WITH MULTIPLE CONTROL EFFECTORS DURING TAKEOFF AND LANDING PHASES
The weighting parameters aaaLmr,, l for takeoff increase the lift coefficient. If TV nozzle and landing before touchdown are selected as deflects upward during landing after touchdown, 0.4, 0.4 and 0.2 respectively. The weighting it will increase the landing gear reaction and parameters aa, for landing after touchdown friction forces. From the highest superiority to LD the lowest, the control effector sequence for can be selected based on the braking friction, takeoff is TV (upward), canard, elevon, and and are set to 0.4 and 0.6 in our simulation. leading edge flap. The sequence for landing Since the forces and moments generated by before touchdown is the same as takeoff, but the thrust vectoring do not vary with the velocity of superiority parameters are different because of the aircraft, V 60 m/s is taken as the rence variations in thrusts. The sequence for landing speed in our simulation. after touchdown is elevon (upward), canard Choosing elevon as the reference control (upward) and TV (upward). effector, the superiority parameters at takeoff speed are given in Tables 2 to 4. 5.2 Takeoff Table 2 Superiority parameters for takeoff R R R Table 5 gives the liftoff velocity and ground run Control L i mi rl i P i distance under different control allocation effector aL 0.4 am 0.4 arl 0.2 Canard 0.032 0.35 1 0.35 configurations. Elevon 1 -1 1 0.2 As indicated in Table 5, for a given elevon LEF -0.024 -0.022 0.4 0.06 deflection, the aircraft can obtain high lift TV(down) 0.43 -6.53 0.5 -2.34 coefficients under larger elevon deflects.s TV(up) -0.43 6.53 0.5 2.54 Meanwhile, large downward elevon deflection Table 3 Superiority parameters for landing will generate significant nosedown pitching before touchdown moment, which will make the aircraft hard to R R R Control L i mi rl i P pitch up, and increase the ground run distance. effector i aL 0.4 am 0.4 arl 0.2 Upward TV nozzle deflection allows the elevon Canard 0.032 0.35 1 0.35 to have a larger downward deflection, which Elevon 1 -1 1 0.2 will increase the lift coefficient and decrease the LEF -0.024 -0.022 0.4 0.06 liftoff speed and ground run distance. TV(down) 0.04 -0.61 0.5 -0.13 Idle Table 5 Simulation results of takeoff performance TV(up) -0.04 0.61 0.5 0.33 Elevon TV Liftoff Ground Run Idle (deg) (deg) Speed (m/s) Distance (m) TV(down) 0.43 -6.53 0.5 -2.34 0 0 93.15 491 Maximum 4 0 94.48 505.27 TV(up) -0.43 6.53 0.5 2.54 8 0 95.16 513.71 Maximum optimal 0 82.91 391.75 Table 4 Superiority parameters for landing optimal optimal 74 301 after touchdown 30
20 RL i RD i Control effector P i o / n
aL 0.4 aD 0.6 10 Canard (down) -0.056 0.57 0.319 0 Canard (up) 0.0323 0.6 0.373 Elevon (down) -1 1 0.2 0246810 Elevon (up) 1 1 1 0
TV (down) -0.04 0.02 -0.004 o -10 / e
TV (up) 0.04 0.02 0.028 -20 As shown in Tables 2 to 4, if the TV nozzle -30 deflects upward during takeoff and landing 0246810 before touchdown, it will generate significant t / s noseup pitching moment, and elevon will be Fig. 3 Control effector deflections without TV during allowed to deflect a larger downward angle to ground run 5 Liu Yan, Gao Zhenghong, Chen Xing
30 upward to increase noseup pitching moment. 20 o
/ With the increasing velocity and AOA, the lift
e 10 0 will increase while the main gear reaction and
30 02468 nosedown pitching moment will decrease. As a 20 result, the upward elevon deflection decreases to o /
n 10
get higher lift coefficient. 0 As shown in Fig. 4, after reaching the 02468 0.0 takeoff speed, canard deflects to the maximum
o -0.1
/ downward angle to increase lift and noseup
tv -0.2 -0.3 pitching moment; TV nozzle deflects upward to -0.4 02468 generate noseup pitching moment; elevon t / s deflects downward to increase lift coefficient. Fig. 4 Control effector deflections with TV during ground As the velocity increases, the aerodynamic lift run and pitching moment will grow accordingly. Figure 3 and 4 give the takeoff simulation Because the control effectiveness of TV does results without and with TV using the control not vary with the velocity, the required TV allocation model built in Section 4. nozzle deflection will increase. As shown in Fig. 3, after reaching the As indicated by Table 5, the optimized takeoff speed, the canard deflects to the control allocation model improves takeoff maximum downward angle to increase lift and performance significantly. noseup pitching moment; the elevon deflects Table 6 Performance of landing before touchdown with idle thrust Without TV With TV AOA Elevon Touchdown Speed Elevon TV Touchdown (deg) (deg) (m/s) (deg) (deg) Speed (m/s) 5 9.95 81.59 11.49 -25 79.81 8 11.14 69.12 13.30 -25 67.60 12 10.93 58.48 13.98 -25 57.18 15 12.30 52.76 16.04 -25 51.59 Table 7 Performance of landing before touchdown with maximum thrust Without TV With TV AOA Elevon Touchdown Speed Elevon TV Touchdown (deg) (deg) (m/s) (deg) (deg) Speed (m/s) 5 9.95 81.59 28.38 -25 67.5 8 11.14 69.12 30 -17.25 59.11 12 10.93 58.48 30 -12.13 51.68 15 12.30 52.76 30 -9.44 47.88 At idle thrust, although the thrust is low, 5.3 Landing the control effectiveness of TV is sufficient as compared to aerodynamic control effectors. The 5.3.1 Before Touchdown nozzle can deflect upward to generate noseup pitching moment, and the elevon is allowed to Table 6 and 7 show the landing simulation deflect downward to increase lift coefficient. results using the control allocation model built This indicates that using TV can reduce the in Section 4 with idle and maximum thrust touchdown speed, which is reflected from the respectively. simulation results shown in Table 6. As shown in Tables 6 to 7, when TV is not At maximum thrust, as a result of higher used, the throttle has no effect on the touchdown control effectiveness, TV can generate higher speed. Lift coefficient will increase while the noseup pitching moment, and elevon is allowed touchdown speed will decrease as AOA to deflect a larger downward angle to get a increases regardless of the use of TV. higher lift coefficient. Hence, using TV can
6 CONTROL ALLOCATION FOR AIRCRAFTS WITH MULTIPLE CONTROL EFFECTORS DURING TAKEOFF AND LANDING PHASES reduce the touchdown speed significantly. [4] Ola Harkegard. Backstepping and control allocation Besides, because of the high control with application to flight control. PhD thesis, effectiveness, the required nozzle angle is Linkoping University, 2003 [5] Department of Defence. Glossary of Definitions, smaller than idle thrust. ground rules, and mission profiles to define air 5.3.2 After Touchdown vehicle performance capability. MIL-STD-3013, 2003 Table 8 gives the simulation results of landing [6] Jin Changjiang, Fan Liqin. Flight dynamics – flight performance calculation. 1990 after touchdown. The reference touchdown [7] Shui Qingcai, Wang Xinhua. A mathematical model speed is 48m/s; the braking friction factor is 0.4, used to calculate the takeoff performance for an and rolling friction factor is 0.02. aircraft. Flight Dynamics. Vol.19, No.4, 2001 Both the upward deflection of elevon and [8] Zhang Jianzhong, Xu Shaoji. Linear Programming. canard can reduce landing ground roll distance 1990 by decreasing lift coefficient while increasing [9] Susan A. Frost, Marc Bodson, Diana M. Acosta. Sensitivity analysis of linear programming and drag coefficient. Elevon is relatively more quadratic programming algorithms for control effective as indicated by the simulation results. allocation. AIAA 2009-1936 Because of the low thrust, the effect of TV is [10] Lars Frossell, Ulrik Nilsson. ADMIRE the aero-data limited. model in a research environment 4.0. Swedish Defence Research Agency (FOI), FOI-R-1624-SE, Table 8 Performance of Landing after touchdown 2005 Control effector Landing Ground Roll (m) No Deflection 330.5 Elevon (up to max) 277.6 Copyright Statement Canard (up to max) 301.2 TV (up to max) 316.9 The authors confirm that they, and/or their company or Elevon + Canard + TV 249.9 organization, hold copyright on all of the original material The simulation results of landing ground included in this paper. The authors also confirm that they have obtained permission, from the copyright holder of roll in Table 8 agree well with the trends of the any third party material included in this paper, to publish superiority parameters in Table 4. it as part of their paper. The authors confirm that they give permission, or have obtained permission from the copyright holder of this paper, for the publication and 5. Conclusion distribution of this paper as part of the ICAS2012 proceedings or as individual off-prints from the This paper discussed the control allocation proceedings. problem during takeoff and landing phases. The control allocation models were formalized and an aircraft was used for verification. The simulation results indicate that he control allocation model built in this paper can fully utilize the takeoff and landing performance potentials.
References
[1] Ken Bordignon. Constrained control allocation for systems with redundant control effectors. PhD thesis, Virginia Polytechnic Institute and State University, 1996 [2] Fang Baorui. The aerodynamic configuration design of aircraft. 1997 [3] Bandu N. Pamadi. Performance, stability, dynamics, and control of airplanes. AIAA Education Series. 2004
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