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.