Integrated design of flight control surfaces and laws for new aircraft configurations Yann Denieul, Joël Bordeneuve-Guibé, Daniel Alazard, Clément Toussaint, Gilles Taquin
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Yann Denieul, Joël Bordeneuve-Guibé, Daniel Alazard, Clément Toussaint, Gilles Taquin. Integrated design of flight control surfaces and laws for new aircraft configurations. IFAC World Congress 2017, Jul 2017, Toulouse, France. pp. 14180-14187, 10.1016/j.ifacol.2017.08.2085. hal-01738089
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http://dx.doi.org/10.1016/j.ifacol.2017.08.2085
Denieul, Yann and Bordeneuve-Guibé, Joël and Alazard, Daniel and Toussaint, Clément and Taquin, Gilles Integrated design of flight control surfaces and laws for new aircraft configurations. (2017) In: IFAC World Congress 2017, 9 July 2017 - 14 July 2017 (Toulouse, France).
Proceedings of the 20th World Congress Proceedings of the 20th World Congress ProceedingsThe International of the Federation 20th World of CongressAutomatic Control The International Federation of Automatic Control TheToulouse, International France, Federation July 9-14, 2017of Automatic Control Toulouse, France, July 9-14, 2017 Toulouse, France, July 9-14, 2017
Integrated design of flight control surfaces Integrated design of flight control surfaces and laws for new aircraft configurations and laws for new aircraft configurations Y. Denieul ∗ J. Bordeneuve-Guib´e ∗∗ D. Alazard ∗∗∗ Y. Denieul ∗ J. Bordeneuve-Guib´e ∗∗ D. Alazard ∗∗∗ Y. Denieul ∗C.J. Toussaint Bordeneuve-Guib´e∗∗∗∗ G. Taquin∗∗ D.† Alazard ∗∗∗ ∗C. Toussaint ∗∗∗∗ G. Taquin∗∗ † ∗∗∗ C. Toussaint ∗∗∗∗ G. Taquin † C. Toussaint ∗∗∗∗ G. Taquin † ∗ PhD Student, University of Toulouse, ISAE-SUPAERO, 10, Av. ∗ PhD Student, University of Toulouse, ISAE-SUPAERO, 10, Av. ∗ PhD Student,Edouard University Belin, of 31055 Toulouse, Toulouse ISAE-SUPAERO, FRANCE 10, Av. ∗ PhD Student,Edouard University Belin, of 31055 Toulouse, Toulouse ISAE-SUPAERO, FRANCE 10, Av. ∗∗ Associated Professor,Edouard Belin, University 31055 of Toulouse Toulouse, FRANCE ISAE-SUPAERO, 10, ∗∗ Associated Professor, University of Toulouse, ISAE-SUPAERO, 10, ∗∗ AssociatedAv. Professor, Edouard University Belin, 31055 of Toulouse,Toulouse FRANCE. ISAE-SUPAERO, 10, ∗∗ AssociatedAv. Professor, Edouard University Belin, 31055 of Toulouse,Toulouse FRANCE. ISAE-SUPAERO, 10, ∗∗∗ Professor,Av. Edouard University Belin, of Toulouse, 31055 Toulouse ISAE-SUPAERO, FRANCE. 10, Av. ∗∗∗ Professor, University of Toulouse, ISAE-SUPAERO, 10, Av. ∗∗∗ Professor,Edouard University Belin, of 31055 Toulouse, Toulouse ISAE-SUPAERO, FRANCE. 10, Av. ∗∗∗ Professor,Edouard University Belin, of 31055 Toulouse, Toulouse ISAE-SUPAERO, FRANCE. 10, Av. ∗∗∗∗ ResearchEdouard Engineer, Belin, ONERA, 31055 Toulouse 2, Av. Edouard FRANCE. Belin, 31055 ∗∗∗∗ Research Engineer, ONERA, 2, Av. Edouard Belin, 31055 ∗∗∗∗ Research Engineer,Toulouse ONERA, FRANCE. 2, Av. Edouard Belin, 31055 ∗∗∗∗ Research Engineer,Toulouse ONERA, FRANCE. 2, Av. Edouard Belin, 31055 † Handling Qualities Expert,Toulouse Airbus FRANCE. Op´erations SAS, 316 route de † Handling Qualities Expert, Airbus Op´erations SAS, 316 route de † Handling QualitiesBayonne, Expert, 31060 Airbus Toulouse Op´erations FRANCE. SAS, 316 route de † Handling QualitiesBayonne, Expert, 31060 Airbus Toulouse Op´erations FRANCE. SAS, 316 route de Bayonne, 31060 Toulouse FRANCE. Abstract: Control architecture sizing is a main challenge for new aircraft design like blended Abstract: Control architecture sizing is a main challenge for new aircraft design like blended Abstract:wing-body design.Control This architecture aircraft configuration sizing is a main typically challenge features for redundantnew aircraft elevons design located like blended at the wing-bodyAbstract: design.Control This architecture aircraft configuration sizing is a main typically challenge features for redundantnew aircraft elevons design located like blended at the wing-bodytrailing edge design. of the This wing, aircraft acting configurationsimultaneously typically on pitch features and roll redundant axes. The elevonsproblem located of integrated at the trailingwing-body edge design. of the This wing, aircraft acting configurationsimultaneously typically on pitch features and roll redundant axes. The elevonsproblem located of integrated at the trailingdesign of edge control of the surface wing, sizes acting and simultaneously flight control on laws pitch for and an unstable roll axes. blended The problem wing-body of integrated aircraft designtrailing of edge control of the surface wing, sizes acting and simultaneously flight control on laws pitch for and an unstable roll axes. blended The problem wing-body of integrated aircraft designis addressed of control here. surface Latest sizes tools and for flightH controlnon-smooth laws for optimization an unstable of blended structured wing-body controllers aircraft are isdesign addressed of control here. surface Latest sizes tools and for flightH∞ controlnon-smooth laws for optimization an unstable of blended structured wing-body controllers aircraft are isused addressed to optimize here. in Latest a single tools step for theH gains∞ non-smooth for both longitudinal optimization and of lateral structured control controllers laws, and are a isused addressed to optimize here. in Latest a single tools step for theH gains∞ non-smooth for both longitudinal optimization and of lateral structured control controllers laws, and are a controlused to allocationoptimize in module, a single while step the minimizing gains∞ for control both longitudinal surfaces total and span. lateral Following control laws, constraints and a controlused to allocationoptimize in module, a single while step the minimizing gains for control both longitudinal surfaces total and span. lateral Following control laws, constraints and a arecontrol ensured: allocation maximal module, deflection while angles minimizing and rates control for 1)surfaces pilot longitudinal total span. Following pull-up 2) constraints pilot bank arecontrol ensured: allocation maximal module, deflection while angles minimizing and rates control for 1)surfaces pilot longitudinal total span. Following pull-up 2) constraints pilot bank angleare ensured: order and maximal 3) longitudinal deflection angles turbulence. and rates Using for this 1) pilot coupled longitudinal approach, pull-up significant 2) pilot gains bank in angleare ensured: order and maximal 3) longitudinal deflection angles turbulence. and rates Using for this 1) pilot coupled longitudinal approach, pull-up significant 2) pilot gains bank in termsangleorder of outer and elevons 3) longitudinal span compared turbulence. to the Using initial this layout coupled are demonstrated, approach, significant while closed-loop gains in termsangleorder of outer and elevons 3) longitudinal span compared turbulence. to the Using initial this layout coupled are demonstrated, approach, significant while closed-loop gains in handlingterms of outer qualities elevons constraints span compared are guaranteed. to the initial layout are demonstrated, while closed-loop handlingterms of outer qualities elevons constraints span compared are guaranteed. to the initial layout are demonstrated, while closed-loop handling qualities constraints are guaranteed. Keywords: Integrated design, Flight Control Law, Aircraft, H control, Dynamics, BWB Keywords: Integrated design, Flight Control Law, Aircraft, H∞ control, Dynamics, BWB Keywords: Integrated design, Flight Control Law, Aircraft, H∞ control, Dynamics, BWB Keywords: Integrated design, Flight Control Law, Aircraft, H∞ control, Dynamics, BWB 1. INTRODUCTION already addressed∞ in a previous work Saucez and Boiffier 1. INTRODUCTION already addressed in a previous work Saucez and Boiffier 1. INTRODUCTION already(2012). addressed in a previous work Saucez and Boiffier (2012). Among other disruptive aircraft configurations, the Blended Then(2012). concerning control surfaces area sizing, two phenom- Among other disruptive aircraft configurations, the Blended Then concerning control surfaces area sizing, two phenom- AmongWing-Body other (BWB) disruptive was aircraft identified configurations, for years as a the promising Blended enaThen have concerning a combined control detrimental surfaces area effect sizing, both two on actuators phenom- Wing-Body (BWB) was identified for years as a promising enaThen have concerning a combined control detrimental surfaces area effect sizing, both two on actuators phenom- Wing-Bodycandidate for (BWB) the future was identified of civil aviation for years Liebeck as a promising (2004). massena have and a power combined consumption detrimental Roskam effect (1985). both on On actuators the one candidate for the future of civil aviation Liebeck (2004). massena have and a power combined consumption detrimental Roskam effect (1985). both on On actuators the one candidateThe rationale for the for futurethis game-changing of civil aviation configuration Liebeck (2004). is as hand,mass and trailing power edge consumption elevons induce Roskam high (1985).aerodynamic On the hinge one The rationale for this game-changing configuration is as hand,mass and trailing power edge consumption elevons induce Roskam high (1985).aerodynamic On the hinge one Thefollows: rationale instead for of this considering game-changing separate configuration geometrical com- is as momentshand, trailing due toedge their elevons large induce area. On high the aerodynamic other hand, hinge high follows: instead of considering separate geometrical com- momentshand, trailing due toedge their elevons large induce area. On high the aerodynamic other hand, hinge high follows:ponents insteadfor each of basic considering function separateof an aircraft, geometrical namely com-Lift, deflectionmoments due rates to result their large from area. the longitudinal On the other stabilization hand, high ponents for each basic function of an aircraft, namely Lift, deflectionmoments due rates to result their large from area. the longitudinal On the other stabilization hand, high Transport,ponents for Control each basicand functionPropulsion of an, the aircraft, BWB namely gathersLift, the ofdeflection an unstable rates configuration. result from the Indeed longitudinal the Airbus stabilization BWB fea- Transport, Control and Propulsion, the BWB gathers the ofdeflection an unstable rates configuration. result from the Indeed longitudinal the Airbus stabilization BWB fea- Transport,three former Control functionsand intoPropulsion a single, the lifting BWB surface. gathers As the a turesof an unstablea negative configuration. static margin, Indeed specially theAirbus at low speed BWB (seefea- three former functions into a single lifting surface. As a turesof an unstablea negative configuration. static margin, Indeed specially theAirbus at low speed BWB (seefea- threeconsequence former of functions this functions into a merging, single lifting an overall surface. improved As a sectiontures a negative2.2), i.e. statican unstable margin, short-period specially at mode. low speed For that (see consequence of this functions merging, an overall improved sectiontures a negative2.2), i.e. statican unstable margin, short-period specially at mode. low speed For that (see consequenceefficiency is expected, of this functions implying merging, significant an overall gains in improved terms of reasonsection it2.2), requires i.e. an a unstable permanent short-period Stability mode. Augmentation For that efficiency is expected, implying significant gains in terms of reasonsection it2.2), requires i.e. an a unstable permanent short-period Stability mode. Augmentation For that efficiencyfuel consumption is expected, Mart´ınez-Val implying significant and P´erez gains (2005); in terms Liebeck of Systemreason it (SAS) requires in order a permanent to guarantee Stability adequate Augmentation safety and fuel consumption Mart´ınez-Val and P´erez (2005); Liebeck Systemreason it (SAS) requires in order a permanent to guarantee Stability adequate Augmentation safety and fuel(2004); consumption Qin et al. Mart´ınez-Val (2004); Bolsunovsky and P´erez et al. (2005); (2001). Liebeck This handlingSystem (SAS) qualities. in order However to guarantee it was shown adequate in asafety previous and (2004); Qin et al. (2004); Bolsunovsky et al. (2001). This handlingSystem (SAS) qualities. in order However to guarantee it was shown adequate in asafety previous and (2004);paper focuses Qin et on al. an (2004); Airbus Bolsunovsky long-range BWB et al. configuration. (2001). This studyhandling Denieul qualities. et al. However (2015a) it that was the shown more in unstable a previous an paper focuses on an Airbus long-range BWB configuration. studyhandling Denieul qualities. et al. However (2015a) it that was the shown more in unstable a previous an paper focuses on an Airbus long-range BWB configuration. aircraft,study Denieul the faster et al. its (2015a) control that surfaces the more need unstable to move an in Major challenges yet to be solved before a potential entry aircraft,study Denieul the faster et al. its (2015a) control that surfaces the more need unstable to move an in Major challenges yet to be solved before a potential entry orderaircraft, to maintain the faster the its equilibrium control surfaces under disturbance. need to move This in Majorinto service challenges include yet control-relatedto be solved before issues a potential Roman et entry al. orderaircraft, to maintain the faster the its equilibrium control surfaces under disturbance. need to move This in into service include control-related issues Roman et al. effectorder to is maintain even increased the equilibrium on the BWB,under disturbance. for elevons This lack into(2000). service These include issues first control-related originate from issues the Roman nature of et the al. effectorder to is maintain even increased the equilibrium on the BWB,under disturbance. for elevons This lack (2000). These issues first originate from the nature of the longitudinaleffect is even lever increased arm with on therespect BWB, to center for elevons of gravity lack (2000).control These devices issues used first for thisoriginate configuration: from the nature the BWB of the is longitudinaleffect is even lever increased arm with on therespect BWB, to center for elevons of gravity lack control devices used for this configuration: the BWB is (CG).longitudinal During lever preliminary arm with design respect phase, to center control of surfaces gravity controlcontrolled devices with multi-control used for this surfaces, configuration: also named the BWB elevons, is (CG).longitudinal During lever preliminary arm with design respect phase, to center control of surfaces gravity controlled with multi-control surfaces, also named elevons, pitch(CG). efficiency During preliminary should then design be sought phase, to control be maximized, surfaces controlledusually spanning with multi-control the whole surfaces, trailing-edge also named and acting elevons, as pitch(CG). efficiency During preliminary should then design be sought phase, to control be maximized, surfaces usually spanning the whole trailing-edge and acting as forpitch instance efficiency byshould increasing then control be sought surfaces to be area maximized, as much usuallypitch and spanning roll devices. the whole Among trailing-edge challenges implied and acting by this as forpitch instance efficiency byshould increasing then control be sought surfaces to be area maximized, as much pitch and roll devices. Among challenges implied by this asfor possible, instance which by increasing is conflicting control with surfaces previously area mentioned as much pitchtechnology, and roll new devices. handling Among qualities challenges criteria implied are required by this asfor possible, instance which by increasing is conflicting control with surfaces previously area mentioned as much technology, new handling qualities criteria are required requirementas possible, which on hinge is conflicting moments with limitation. previously mentioned technology,in order to take new intohandling account qualities the combined criteria are authority required of requirementas possible, which on hinge is conflicting moments with limitation. previously mentioned in order to take into account the combined authority of requirement on hinge moments limitation. incontrol order surfaces to take on into longitudinal account the and combined lateral axes. authority This was of Bothrequirement large hinge on hinge moments moments and limitation.high deflection rates have control surfaces on longitudinal and lateral axes. This was Both large hinge moments and high deflection rates have control surfaces on longitudinal and lateral axes. This was Botha direct large impact hinge on moments FCS sizing and and high secondary deflection power rates have con- This work is supported by ANRT and AIRBUS. a direct impact on FCS sizing and secondary power con- This work is supported by ANRT and AIRBUS. a direct impact on FCS sizing and secondary power con- This work is supported by ANRT and AIRBUS. a direct impact on FCS sizing and secondary power con- Copyright © 2017 IFAC 14745 Copyright © 2017 IFAC 14745 Copyright © 2017 IFAC 14745 10.1016/j.ifacol.2017.08.2085
10.1016/j.ifacol.2017.08.2085 2405-8963 Proceedings of the 20th World Congress Proceedings of the 20th World Congress ProceedingsThe International of the Federation 20th World of CongressAutomatic Control The International Federation of Automatic Control TheToulouse, International France, Federation July 9-14, 2017of Automatic Control Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Toulouse, France, July 9-14, 2017 Toulouse, France, July 9-14, 2017
sumption. Indeed as stated by Garmendia et al. Garmen- This paper is organized as follows: in section 2 the flight Integrated design of flight control surfaces dia et al. (2014), secondary power for FCS PFCS may be dynamics models are presented. Then section 3 introduces Integrated design of flight control surfaces evaluated in a preliminary way by the equation (1): the strategy for parameterizing the elevons total span, and and laws for new aircraft configurations obtaining a parametrized state-space representation suit- and laws for new aircraft configurations ncontrols able for optimization. The integrated design and control P = HMmax.θ˙max (1) Y. Denieul ∗ J. Bordeneuve-Guib´e ∗∗ D. Alazard ∗∗∗ FCS i i problem of computing structured longitudinal / lateral Y. Denieul ∗ J. Bordeneuve-Guib´e ∗∗ D. Alazard ∗∗∗ i=1 Y. Denieul ∗C.J. Toussaint Bordeneuve-Guib´e∗∗∗∗ G. Taquin∗∗ D.† Alazard ∗∗∗ control laws gains together with optimal elevons size is ∗C. Toussaint ∗∗∗∗ G. Taquin∗∗ † ∗∗∗ C. Toussaint ∗∗∗∗ G. Taquin † C. Toussaint ∗∗∗∗ G. Taquin † presented in section 4, and results are discussed in section max ˙max ∗ PhD Student, University of Toulouse, ISAE-SUPAERO, 10, Av. where HMi and θi are the maximum hinge moment 5. ∗ PhD Student, University of Toulouse, ISAE-SUPAERO, 10, Av. ∗ PhD Student,Edouard University Belin, of 31055 Toulouse, Toulouse ISAE-SUPAERO, FRANCE 10, Av. and maximum deflection rate of the i-th control surface re- ∗ Edouard Belin, 31055 Toulouse FRANCE ∗∗ Associated Professor,Edouard Belin, University 31055 of Toulouse Toulouse, FRANCE ISAE-SUPAERO, 10, spectively, and ncontrols is the number of control surfaces. ∗∗ Associated Professor, University of Toulouse, ISAE-SUPAERO, 10, 2. AIRCRAFT FLIGHT DYNAMICS AND CONTROL ∗∗ AssociatedAv. Professor, Edouard University Belin, 31055 of Toulouse,Toulouse FRANCE. ISAE-SUPAERO, 10, ∗∗ AssociatedAv. Professor, Edouard University Belin, 31055 of Toulouse,Toulouse FRANCE. ISAE-SUPAERO, 10, At preliminary design phase, when actuators sizing is not ∗∗∗ Professor,Av. Edouard University Belin, of Toulouse, 31055 Toulouse ISAE-SUPAERO, FRANCE. 10, Av. ∗∗∗ Professor, University of Toulouse, ISAE-SUPAERO, 10, Av. yet frozen, deflection rate is a direct consequence of control In this section the models used in sections 3 and 4 ∗∗∗ Professor,Edouard University Belin, of 31055 Toulouse, Toulouse ISAE-SUPAERO, FRANCE. 10, Av. ∗∗∗ Professor,Edouard University Belin, of 31055 Toulouse, Toulouse ISAE-SUPAERO, FRANCE. 10, Av. laws design. Also the traditional way of sizing conventional for design, control and simulation are described. The ∗∗∗∗ ResearchEdouard Engineer, Belin, ONERA, 31055 Toulouse 2, Av. Edouard FRANCE. Belin, 31055 ∗∗∗∗ Research Engineer, ONERA, 2, Av. Edouard Belin, 31055 control surfaces considers simplified open-loop handling configuration studied in this paper is a long-range BWB ∗∗∗∗ Research Engineer,Toulouse ONERA, FRANCE. 2, Av. Edouard Belin, 31055 ∗∗∗∗ Research Engineer,Toulouse ONERA, FRANCE. 2, Av. Edouard Belin, 31055 qualities criteria, such as roll rate target for the ailerons whose planform results from optimization studies on high- † Handling Qualities Expert,Toulouse Airbus FRANCE. Op´erations SAS, 316 route de † Handling Qualities Expert, Airbus Op´erations SAS, 316 route de or pitch rate target for the elevator. Such an approach speed performance with constraints on low-speed pitching † Handling QualitiesBayonne, Expert, 31060 Airbus Toulouse Op´erations FRANCE. SAS, 316 route de † Bayonne, 31060 Toulouse FRANCE. is no more valid for BWB control surface sizing due to moment Meheut et al. (2012). The focus of this work is the Bayonne, 31060 Toulouse FRANCE. the natural pitch instability: control surface areas may sizing of control surfaces; thus, the planform is considered Abstract: Control architecture sizing is a main challenge for new aircraft design like blended constant. The planform and initial control surfaces layout Abstract: Control architecture sizing is a main challenge for new aircraft design like blended be largely sized by stabilization requirements, so sizing wing-bodyAbstract: design.Control This architecture aircraft configuration sizing is a main typically challenge features for redundantnew aircraft elevons design located like blended at the are visible on Figure 2(a). wing-bodyAbstract: design.Control This architecture aircraft configuration sizing is a main typically challenge features for redundantnew aircraft elevons design located like blended at the requires considering control laws at the early design phase. trailingwing-body edge design. of the This wing, aircraft acting configurationsimultaneously typically on pitch features and roll redundant axes. The elevonsproblem located of integrated at the trailingwing-body edge design. of the This wing, aircraft acting configurationsimultaneously typically on pitch features and roll redundant axes. The elevonsproblem located of integrated at the Control laws design in turn depends on control surfaces designtrailing of edge control of the surface wing, sizes acting and simultaneously flight control on laws pitch for and an unstable roll axes. blended The problem wing-body of integrated aircraft designtrailing of edge control of the surface wing, sizes acting and simultaneously flight control on laws pitch for and an unstable roll axes. blended The problem wing-body of integrated aircraft effectiveness. This coupled problem is known in control 2.1 Linear Model of Flight Dynamics Equations isdesign addressed of control here. surface Latest sizes tools and for flightH controlnon-smooth laws for optimization an unstable of blended structured wing-body controllers aircraft are community as plant-controller optimization or integrated isdesign addressed of control here. surface Latest sizes tools and for flightH∞ controlnon-smooth laws for optimization an unstable of blended structured wing-body controllers aircraft are isused addressed to optimize here. in Latest a single tools step for theH gains∞ non-smooth for both longitudinal optimization and of lateral structured control controllers laws, and are a design and control. Classical way of handling this problem isused addressed to optimize here. in Latest a single tools step for theH gains∞ non-smooth for both longitudinal optimization and of lateral structured control controllers laws, and are a In order to perform control laws synthesis and linear analy- controlused to allocationoptimize in module, a single while step the minimizing gains∞ for control both longitudinal surfaces total and span. lateral Following control laws, constraints and a controlused to allocationoptimize in module, a single while step the minimizing gains for control both longitudinal surfaces total and span. lateral Following control laws, constraints and a involves an iterative approach: effectors are sized based sis, Flight Dynamics equations are linearized around equi- arecontrol ensured: allocation maximal module, deflection while angles minimizing and rates control for 1)surfaces pilot longitudinal total span. Following pull-up 2) constraints pilot bank arecontrol ensured: allocation maximal module, deflection while angles minimizing and rates control for 1)surfaces pilot longitudinal total span. Following pull-up 2) constraints pilot bank on engineering rules, then a control law is designed. If librium flight points. These initial equilibria are computed angleare ensured: order and maximal 3) longitudinal deflection angles turbulence. and rates Using for this 1) pilot coupled longitudinal approach, pull-up significant 2) pilot gains bank in angleare ensured: order and maximal 3) longitudinal deflection angles turbulence. and rates Using for this 1) pilot coupled longitudinal approach, pull-up significant 2) pilot gains bank in requirements are not met, then the sizing is changed for the following conditions: zero flight path angle, sideslip termsangleorder of outer and elevons 3) longitudinal span compared turbulence. to the Using initial this layout coupled are demonstrated, approach, significant while closed-loop gains in termsangleorder of outer and elevons 3) longitudinal span compared turbulence. to the Using initial this layout coupled are demonstrated, approach, significant while closed-loop gains in based on the existing control law, and so on. However and bank angle. At a given flight operating conditions in termshandling of outer qualities elevons constraints span compared are guaranteed. to the initial layout are demonstrated, while closed-loop it is proved Fathy et al. (2001) that beyond being time- handling qualities constraints are guaranteed. terms of mass (m), Mach number (M) and altitude (H), handling qualities constraints are guaranteed. consuming, this approach may miss the optimum because the 3-axis model state-space representation reads: Keywords: Integrated design, Flight Control Law, Aircraft, H control, Dynamics, BWB of the tightly coupled nature of the problem. Consequently, Keywords: Integrated design, Flight Control Law, Aircraft, H∞ control, Dynamics, BWB Keywords: Integrated design, Flight Control Law, Aircraft, H∞ control, Dynamics, BWB several approaches are seeking solving these combined Keywords: Integrated design, Flight Control Law, Aircraft, H∞ control, Dynamics, BWB X˙ = AX + BU + B w (2) ∞ problems in a single step. ”Plant-controller optimization” w z 1. INTRODUCTION already addressed in a previous work Saucez and Boiffier 1. INTRODUCTION already addressed in a previous work Saucez and Boiffier was studied in a variety of domains, such as chemistry Y = CX + DU + D w (3) 1. INTRODUCTION already(2012). addressed in a previous work Saucez and Boiffier w z (2012). Ricardez-Sandoval et al. (2009), autonomous underwater Among other disruptive aircraft configurations, the Blended Then(2012). concerning control surfaces area sizing, two phenom- vehicles Silvestre et al. (1998) and astronautics Alazard T Among other disruptive aircraft configurations, the Blended Then concerning control surfaces area sizing, two phenom- where X =[δV δα q δθ β p r φ] is the state vector AmongWing-Body other (BWB) disruptive was aircraft identified configurations, for years as a the promising Blended enaThen have concerning a combined control detrimental surfaces area effect sizing, both two on actuators phenom- et al. (2013); Denieul et al. (2015b,a). Wing-Body (BWB) was identified for years as a promising enaThen have concerning a combined control detrimental surfaces area effect sizing, both two on actuators phenom- composed of δV = V Ve the relative airspeed with Wing-Bodycandidate for (BWB) the future was identified of civil aviation for years Liebeck as a promising (2004). massena have and a power combined consumption detrimental Roskam effect (1985). both on On actuators the one − candidate for the future of civil aviation Liebeck (2004). massena have and a power combined consumption detrimental Roskam effect (1985). both on On actuators the one In the field of aeronautics two complementary approaches respect to the equilibrium speed, δα = α αe and candidateThe rationale for the for futurethis game-changing of civil aviation configuration Liebeck (2004). is as hand,mass and trailing power edge consumption elevons induce Roskam high (1985).aerodynamic On the hinge one − The rationale for this game-changing configuration is as hand,mass and trailing power edge consumption elevons induce Roskam high (1985).aerodynamic On the hinge one were studied. The first method considers integrating a δθ = θ θe relative angle of attack and pitch attitude Thefollows: rationale instead for of this considering game-changing separate configuration geometrical com- is as momentshand, trailing due toedge their elevons large induce area. On high the aerodynamic other hand, hinge high − follows: instead of considering separate geometrical com- momentshand, trailing due toedge their elevons large induce area. On high the aerodynamic other hand, hinge high stability and control module into a multidisciplinary op- with respect to the equilibrium respectively, sideslip β and follows:ponents insteadfor each of basic considering function separateof an aircraft, geometrical namely com-Lift, deflectionmoments due rates to result their large from area. the longitudinal On the other stabilization hand, high ponents for each basic function of an aircraft, namely Lift, deflectionmoments due rates to result their large from area. the longitudinal On the other stabilization hand, high timization (MDO) process Perez et al. (2006). A second p, q, r rotation rates of the aircraft with respect to the ponentsTransport, for Control each basicand functionPropulsion of an, the aircraft, BWB namely gathersLift, the ofdeflection an unstable rates configuration. result from the Indeed longitudinal the Airbus stabilization BWB fea- Transport, Control and Propulsion, the BWB gathers the ofdeflection an unstable rates configuration. result from the Indeed longitudinal the Airbus stabilization BWB fea- more control-oriented approach takes advantage of opti- earth reference frame in roll, pitch and yaw respectively. Transport,three former Control functionsand intoPropulsion a single, the lifting BWB surface. gathers As the a turesof an unstablea negative configuration. static margin, Indeed specially theAirbus at low speed BWB (seefea- T T three former functions into a single lifting surface. As a turesof an unstablea negative configuration. static margin, Indeed specially theAirbus at low speed BWB (seefea- mization tools developped for controllers design in order U = [∆δm , δn] is the control vector composed of threeconsequence former of functions this functions into a merging, single lifting an overall surface. improved As a sectiontures a negative2.2), i.e. statican unstable margin, short-period specially at mode. low speed For that (see T consequence of this functions merging, an overall improved sectiontures a negative2.2), i.e. statican unstable margin, short-period specially at mode. low speed For that (see to simultaneously optimize a controller and some meaning- ∆δm = [∆δmi] ,i=1...10 with ∆δmi = δmi δme consequenceefficiency is expected, of this functions implying merging, significant an overall gains in improved terms of reasonsection it2.2), requires i.e. an a unstable permanent short-period Stability mode. Augmentation For that − efficiency is expected, implying significant gains in terms of reasonsection it2.2), requires i.e. an a unstable permanent short-period Stability mode. Augmentation For that ful physical parameters. Niewoehner and Kaminer (1996) the relative deflection of the i th elevon control surface efficiencyfuel consumption is expected, Mart´ınez-Val implying significant and P´erez gains (2005); in terms Liebeck of Systemreason it (SAS) requires in order a permanent to guarantee Stability adequate Augmentation safety and − fuel consumption Mart´ınez-Val and P´erez (2005); Liebeck Systemreason it (SAS) requires in order a permanent to guarantee Stability adequate Augmentation safety and optimized in a single loop a longitudinal controller and with respect to the equilibrium position. Each of the 10 fuel(2004); consumption Qin et al. Mart´ınez-Val (2004); Bolsunovsky and P´erez et al. (2005); (2001). Liebeck This handlingSystem (SAS) qualities. in order However to guarantee it was shown adequate in asafety previous and (2004); Qin et al. (2004); Bolsunovsky et al. (2001). This handlingSystem (SAS) qualities. in order However to guarantee it was shown adequate in asafety previous and elevator control surface using linear matrix inequalities elevons is actuated independently, through a control al- (2004);paper focuses Qin et on al. an (2004); Airbus Bolsunovsky long-range BWB et al. configuration. (2001). This studyhandling Denieul qualities. et al. However (2015a) it that was the shown more in unstable a previous an paper focuses on an Airbus long-range BWB configuration. studyhandling Denieul qualities. et al. However (2015a) it that was the shown more in unstable a previous an (LMI) framework. More recently, nonsmooth optimization location strategy presented in 4.2. Elevons layout shown Majorpaper focuses challenges on an yet Airbus to be long-range solved before BWB a potential configuration. entry aircraft,study Denieul the faster et al. its (2015a) control that surfaces the more need unstable to move an in in Figure 2(a) is ordered in the control vector as follows: Major challenges yet to be solved before a potential entry aircraft,study Denieul the faster et al. its (2015a) control that surfaces the more need unstable to move an in methods enabling structured linear varying paremeters intoMajor service challenges include yet control-relatedto be solved before issues a potential Roman et entry al. orderaircraft, to maintain the faster the its equilibrium control surfaces under disturbance. need to move This in δm =[LDQ1 ...LDQ5, RDQ1 ...RDQ5]. Con- intoMajor service challenges include yet control-relatedto be solved before issues a potential Roman et entry al. orderaircraft, to maintain the faster the its equilibrium control surfaces under disturbance. need to move This in (LPV) controllers were applied to the longitudinal inte- i,i=1...10 (2000).into service These include issues first control-related originate from issues the Roman nature of et the al. effectorder to is maintain even increased the equilibrium on the BWB,under disturbance. for elevons This lack trol vector also contains rudder deflection δn. While two (2000).into service These include issues first control-related originate from issues the Roman nature of et the al. effectorder to is maintain even increased the equilibrium on the BWB,under disturbance. for elevons This lack grated design and control problem Lhachemi et al. (2015). control(2000). These devices issues used first for thisoriginate configuration: from the nature the BWB of the is longitudinaleffect is even lever increased arm with on therespect BWB, to center for elevons of gravity lack rudders are visible on the configuration of Figure 2(a) control(2000). These devices issues used first for thisoriginate configuration: from the nature the BWB of the is longitudinaleffect is even lever increased arm with on therespect BWB, to center for elevons of gravity lack controlledcontrol devices with multi-control used for this surfaces, configuration: also named the BWB elevons, is (CG).longitudinal During lever preliminary arm with design respect phase, to center control of surfaces gravity We propose to extend this approach to longitudinal / lat- (LDR and RDR), it was chosen for sake of clarity to controlledcontrol devices with multi-control used for this surfaces, configuration: also named the BWB elevons, is (CG).longitudinal During lever preliminary arm with design respect phase, to center control of surfaces gravity usuallycontrolled spanning with multi-control the whole surfaces, trailing-edge also named and acting elevons, as pitch(CG). efficiency During preliminary should then design be sought phase, to control be maximized, surfaces eral integrated design and control of a BWB by optimizing group them as a single control with twice the efficiency usuallycontrolled spanning with multi-control the whole surfaces, trailing-edge also named and acting elevons, as pitch(CG). efficiency During preliminary should then design be sought phase, to control be maximized, surfaces pitchusually and spanning roll devices. the whole Among trailing-edge challenges implied and acting by this as forpitch instance efficiency byshould increasing then control be sought surfaces to be area maximized, as much together a three-axes control laws and control surfaces of one rudder; the aim of our study is indeed not to pitchusually and spanning roll devices. the whole Among trailing-edge challenges implied and acting by this as forpitch instance efficiency byshould increasing then control be sought surfaces to be area maximized, as much technology,pitch and roll new devices. handling Among qualities challenges criteria implied are required by this asfor possible, instance which by increasing is conflicting control with surfaces previously area mentioned as much total span, using nonsmooth optimization techniques for size vertical surfaces but only elevons. The output vector technology,pitch and roll new devices. handling Among qualities challenges criteria implied are required by this asfor possible, instance which by increasing is conflicting control with surfaces previously area mentioned as much intechnology, order to take new intohandling account qualities the combined criteria are authority required of requirementas possible, which on hinge is conflicting moments with limitation. previously mentioned fixed structure controllers. The main contribution of this Y =[N ,q,β,p,r,φ]T is composed of the vertical load intechnology, order to take new intohandling account qualities the combined criteria are authority required of requirementas possible, which on hinge is conflicting moments with limitation. previously mentioned z controlin order surfaces to take on into longitudinal account the and combined lateral axes. authority This was of requirement on hinge moments limitation. paper is to optimize in a single step the control surfaces factor Nz and the measured state variables. Finally turbu- controlin order surfaces to take on into longitudinal account the and combined lateral axes. authority This was of Bothrequirement large hinge on hinge moments moments and limitation.high deflection rates have control surfaces on longitudinal and lateral axes. This was Both large hinge moments and high deflection rates have span, the control allocation module, and flight control lence effect is included as a vertical velocity wz expressed control surfaces on longitudinal and lateral axes. This was Botha direct large impact hinge on moments FCS sizing and and high secondary deflection power rates have con- This work is supported by ANRT and AIRBUS. a direct impact on FCS sizing and secondary power con- laws, in order to guarantee longitudinal and lateral han- in the earth reference frame, under the assumption that it This work is supported by ANRT and AIRBUS. a direct impact on FCS sizing and secondary power con- This work is supported by ANRT and AIRBUS. a direct impact on FCS sizing and secondary power con- dling qualities constraints with a minimum control surfaces acts as an increment of angle of attack. The model used Copyright © 2017 IFAC 14745 size. for turbulence is described in section 2.3. Copyright © 2017 IFAC 14745 Copyright © 2017 IFAC 14745 14746 Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017
elevons span is presented. This part aims at obtaining a Poles for H=30000 ft, mass=200000 kg 0.5 0.85 continuously parametrized state-space representation, so 0.993 0.985 0.97 0.93 0.75
0.4 0.997 DR that the continuous optimizer presented in section 4 may use the continuous variable representing elevons size as an 0.3 0.999 0.75 optimization variable. 0.2 PH ) -1 1 0.1 PR 3.1 Geometric Parametrization of Control Surfaces Span 5 4 3 2 1 SPI 0 0.65 Mach
-0.1 1 Outer elevons total span is chosen as a plant Figure- Imaginary Axis (seconds -0.2 of-merit to be minimized. More precisely a variable η 0.999 SP -0.3 representing the ratio of outer elevons total span compared to the initial control surfaces span is introduced. On Figure -0.4 0.997
0.993 0.985 0.97 0.93 0.75 2(a) initial elevons layout, corresponding to parameter -0.5 0.45 -5 -4 -3 -2 -1 0 1 2 Real Axis (seconds-1) value η = 1 is presented. This initial layout features five control surfaces on each side of the wing spanning the whole trailing edge, except a gap between elevon 1 and 2 Fig. 1. Poles of aircraft dynamics for backward CG. for engine pylon integration – elevons are numbered from 2.2 Modes Analysis inboard to outboard. Elevons relative chord is limited in x wise position by cabin integration for elevon 1, and by For a given Aircraft configuration, the coefficients of state- rear− spar for elevons 2 to 5. So it was decided: (i) elevon space matrices (Eq. (2) and (3) depends on the flight 1 is constant, (ii) relative chord and span are constant for conditions (m, M and H). The modes of the eight-states elevons 2 to 5 (split equally on the outer wing), (iii) the aircraft dynamics presented in Eq. (2) are depicted in number of elevons is constant. Elevons number is mostly Figure 1. For sake of clarity poles are shown only for one a failure cases problem that is out of scope of our study. mass and altitude, with Mach number varying between It is then clear that 0 η 1, η = 1 corresponding 0.45 to 0.85. The main point to retain from Figure 1 is the ≤ ≤ strong instability of the short-period (SP) oscillation and to initial elevons layout and η = 0 corresponding to the a poorly damped dutch roll mode (DR). lack of any control surface on the outer wing. Examples of layouts for η =0.8 and η =0.4 are presented on Figures 2.3 Turbulence Model 2(b) and 2(c) respectively.
A Dryden continuous turbulence model is used for simu- 3.2 Computation of Aerodynamic Models as a function of lating vertical continuous turbulence wz. A band-limited the Control Surface Span η white noise ew is passed through a forming filter approxi- mating the Dryden velocity spectra. The transfer function For a given flight condition (m, M and H), the coefficients has the following expression from Standard (1990): of state-space matrices (Eq. (2) and (3) depends on the
√3Lz Aircraft configuration parameter (reduced to η in this wz 2Lz 1+ V s Hw (s)= (s)=σz (4) study) through the aerodynamic coefficients. Since the z e πV Lz 2 w (1 + V s) plan-form and the airfoils are kept constant for all con- where V is the aircraft airspeed, Lz is the vertical tur- figurations, the varying coefficients are the control surface bulence scale length that was set to 500 m and S is te aerodynamic coefficients which impact only the control reference area. effectiveness matrix: B = B(η). 2.4 Actuators Model Computation of aerodynamic model for different pa- rameter values of η is described in this section. The A second-order actuators model accounting for their band- goal is to obtain state-space representations continuously width and damping is used: parametrized by elevon span parameter η. Process to y ω2 obtain such a continuous approximation is presented on act 0 Figure 3. A first step is to compute calibrated aerodynamic = 2 2 (5) uact s +2ξω0s + ω0 models for discrete values of η, namely for values between A single bandwidth and damping of respectively ω0 = 0.1 and 1 with steps of 0.1. For that purpose the Athena 1.4Hz and ξ =0.8 was used. Previous studies considered Vortex Lattice (AVL) software Drela and Youngren (2006) allocating different bandwidth for all control surfaces De- was used together with calibration factors coming from the nieul et al. (2015a,b), however this is out of the scope of supposedly known aerodynamic coefficients of the initial present paper. A 100 ms delay (approximated by a second- BWB design. This method combines the advantages of fast order Pad´efilter) accounting for sensors, computers and data generation through light CFD computation, and far data processing is included in the control law synthesis better accuracy than AVL direct output through accurate and simulation. Actuators and delay are visible on control knowledge on a reference configuration. It provides a set law structure of Figure 5. of control effectiveness matrices Bηk for N sampled values η of η: η = [0.1, , 1]. 3. PARAMETRIC REPRESENTATION OF CONTROL k k,k=1:N ··· SURFACES SPAN VARIATION Once aerodynamic coefficients are computed and cali- brated for discretized values of η, the final step consists in In this section a process for obtaining a continuous approx- obtaining an approximation of the function B(η). For that imation of control surfaces efficiencies for varying outer purpose it was chosen to work with the Linear Fractional
14747 Proceedings of the 20th IFAC World Congress Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Toulouse, France, July 9-14, 2017 elevons span is presented. This part aims at obtaining a Poles for H=30000 ft, mass=200000 kg 0.5 0.85 continuously parametrized state-space representation, so 0.993 0.985 0.97 0.93 0.75
0.4 0.997 DR that the continuous optimizer presented in section 4 may use the continuous variable representing elevons size as an 0.3 0.999 0.75 optimization variable. 0.2 PH LDQ3 LDQ2 RDQ2 RDQ3 )
-1 LDQ1 1 0.1 PR 3.1 Geometric Parametrization of Control Surfaces Span LDQ4 RDQ4 5 4 3 2 1 SPI 0 0.65 LDQ5 LDR RDR RDQ5
Mach RDQ1
-0.1 1 Outer elevons total span is chosen as a plant Figure- (a) η =1 (b) η =0.8 (c) η =0.4 Imaginary Axis (seconds -0.2 of-merit to be minimized. More precisely a variable η 0.999 SP -0.3 representing the ratio of outer elevons total span compared Fig. 2. Elevons size for different values of parameter η. to the initial control surfaces span is introduced. On Figure -0.4 0.997
0.993 0.985 0.97 0.93 0.75 2(a) initial elevons layout, corresponding to parameter -0.5 0.45 Reference Aircraft -5 -4 -3 -2 -1 0 1 2 Real Axis (seconds-1) value η = 1 is presented. This initial layout features five Aerodynamic Model control surfaces on each side of the wing spanning the whole trailing edge, except a gap between elevon 1 and 2 Fig. 1. Poles of aircraft dynamics for backward CG. for engine pylon integration – elevons are numbered from Aircraft with varying AVL APRICOT 2.2 Modes Analysis inboard to outboard. Elevons relative chord is limited in elevons span Aerodynamic Calibrated Aerodynamic Toolbox x wise position by cabin integration for elevon 1, and by Geometrical Model Computation Models LFR Approximation η =0:1:1 − η =0:1:1 For a given Aircraft configuration, the coefficients of state- rear spar for elevons 2 to 5. So it was decided: (i) elevon mass Mach H space matrices (Eq. (2) and (3) depends on the flight 1 is constant, (ii) relative chord and span are constant for mass Mach H conditions (m, M and H). The modes of the eight-states elevons 2 to 5 (split equally on the outer wing), (iii) the η aircraft dynamics presented in Eq. (2) are depicted in number of elevons is constant. Elevons number is mostly Figure 1. For sake of clarity poles are shown only for one a failure cases problem that is out of scope of our study. LFR function of mass and altitude, with Mach number varying between elevons span 0.45 to 0.85. The main point to retain from Figure 1 is the It is then clear that 0 η 1, η = 1 corresponding to initial elevons layout≤ and η≤= 0 corresponding to the strong instability of the short-period (SP) oscillation and mass Mach H a poorly damped dutch roll mode (DR). lack of any control surface on the outer wing. Examples of layouts for η =0.8 and η =0.4 are presented on Figures Fig. 3. Process for obtaining LFR approximation of state-space representations as a function of η parameter. 2.3 Turbulence Model 2(b) and 2(c) respectively.
∆ = η In 4. INTEGRATED DESIGN AND CONTROL A Dryden continuous turbulence model is used for simu- 3.2 Computation of Aerodynamic Models as a function of η lating vertical continuous turbulence wz. A band-limited the Control Surface Span η M In this section the integrated design and control problem white noise ew is passed through a forming filter approxi- of simultaneously minimizing elevons span parameter η mating the Dryden velocity spectra. The transfer function For a given flight condition (m, M and H), the coefficients while satisfying handling qualities and maneuverability Fig. 4. Linear Fractional Representation of B(η). has the following expression from Standard (1990): of state-space matrices (Eq. (2) and (3) depends on the constraints is developed. √ Aircraft configuration parameter (reduced to η in this w 2L 1+ 3Lz s Representation (LFR) framework, because this represen- z z V study) through the aerodynamic coefficients. Since the Hwz (s)= (s)=σz L (4) tation is suited to the optimizer coming from the control 4.1 Structure of Control Laws ew πV (1 + z s)2 plan-form and the airfoils are kept constant for all con- V community presented in section 4. Moreover efficient al- figurations, the varying coefficients are the control surface where V is the aircraft airspeed, Lz is the vertical tur- gorithms for approximating a set of numerical data as an aerodynamic coefficients which impact only the control As stated in section 2.2, longitudinal instability on this bulence scale length that was set to 500 m and S is te LFR were developed by Onera Roos et al. (2014). An LFR effectiveness matrix: B = B(η). BWB requires a SAS to make it flyable. Moreover lateral reference area. is a model where all fixed dynamics are gathered in a single control laws are also mandatory to enhance lateral han- 2.4 Actuators Model Computation of aerodynamic model for different pa- linear time-invariant plant M, whereas uncertainties or dling qualities. Considering both these longitudinal and rameter values of η is described in this section. The varying parameters are contained in a block-diagonal ma- lateral / directional control laws is moreover necessary for A second-order actuators model accounting for their band- goal is to obtain state-space representations continuously trix ∆ (see Figure 4). Polynomial and rational expressions a proper sizing of control surfaces. A main contribution width and damping is used: parametrized by elevon span parameter η. Process to are for instance easily convertible into LFR. of this paper is indeed to provide a methodology for obtain such a continuous approximation is presented on simultaneous longitudinal, lateral and directional control y ω2 More precisely, the problem is that of finding an LFR act = 0 (5) Figure 3. A first step is to compute calibrated aerodynamic laws synthesis of arbitrary structure, whereas this problem 2 2 approximating as closely as possible state-space represen- uact s +2ξω0s + ω0 models for discrete values of η, namely for values between is usually treated by decoupling longitudinal from lateral tations computed for different values of η. Uncertainties A single bandwidth and damping of respectively ω0 = 0.1 and 1 with steps of 0.1. For that purpose the Athena / directional axes. Here a typical fly-by-wire FCS archi- are not considered in this study, so the ∆ block is only 1.4Hz and ξ =0.8 was used. Previous studies considered Vortex Lattice (AVL) software Drela and Youngren (2006) tecture is considered. Pilot provides inputs in terms of composed of η parameter repeated n times. It was decided allocating different bandwidth for all control surfaces De- was used together with calibration factors coming from the η to restrict search for LFR approximations to polynomial commanded load factor Nzc, bank angle φc and sideslip nieul et al. (2015a,b), however this is out of the scope of supposedly known aerodynamic coefficients of the initial approximations in order to keep the LFR order n as βc. Control law feedback features C∗ and Y ∗ structure for present paper. A 100 ms delay (approximated by a second- BWB design. This method combines the advantages of fast η small as possible. From a physical perspective this can longitudinal and lateral/directional control respectively, order Pad´efilter) accounting for sensors, computers and data generation through light CFD computation, and far be justified by the fact that control surfaces efficiencies whose structure is provided in Favre (1994). More pre- data processing is included in the control law synthesis better accuracy than AVL direct output through accurate should vary smoothly with respect to their span. The cisely: and simulation. Actuators and delay are visible on control knowledge on a reference configuration. It provides a set least-squares routine lsapprox from APRICOT library on C law structure of Figure 5. of control effectiveness matrices B for N sampled values ∗ structure is composed of load factor Nz and pitch ηk Matlab Roos et al. (2014) was used. A 5-th order polyno- • η of η: η = [0.1, , 1]. rate q feedback, together with an integrator for zero 3. PARAMETRIC REPRESENTATION OF CONTROL k k,k=1:N mial approximation of the 8 11 B(η) matrix leads to an steady-state tracking error and a direct feedthrough ··· × SURFACES SPAN VARIATION Once aerodynamic coefficients are computed and cali- LFR with nη = 20. Maximum root-mean-square (RMS) is gain. Output of the law is an equivalent elevator order 3 2 brated for discretized values of η, the final step consists in 9.36.10− and maximum local absolute error is 2.01.10− . δmequi. In this section a process for obtaining a continuous approx- obtaining an approximation of the function B(η). For that lsapprox instead of orthogonal least-squares olsapprox Y ∗ structure features lateral / directional state feed- imation of control surfaces efficiencies for varying outer purpose it was chosen to work with the Linear Fractional routine was used for it achieves higher accuracy. • back, namely sideslip β, yaw rate r, bank angle φ and
14747 14748 Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017
roll rate p. An integrator is added to keep zero steady- pitch roll Kalloc Kalloc 0 state sideslip, as well as a bank angle order direct pitch roll Kalloc = K K 0 (9) alloc alloc feedthrough gain. Outputs of this law are equivalent 00− Kyaw aileron and rudder order δl and δn respec- alloc equi equi tively. This means we impose a symmetrical and anti-symmetrical All the gains involved in the C∗ and Y ∗ structured deflection of the elevons for a pitch and roll order respec- controllers are gathered in K as decision variables. A tively, and a yaw order is allocated to the rudder only. general overview of control law structure is visible on By incorporating this physical knowledge of the control Figure 5. As already mentioned, control laws outputs allocation structure, the number of variables within Kalloc are equivalent elevator, aileron and rudder orders, which is reduced from 33 to 11 variables. are independent from control surfaces architecture. These equivalent orders are then converted into control surfaces deflections thanks to a control allocation module described 4.3 Simultaneous Three-Axes Control Law Synthesis in next section. Integrated design and control of the BWB presented in this paper follows a two-steps scheme: 4.2 Control Allocation Model (1) A first control laws synthesis computes gains for an arbitrarily fixed η value. The problem consists in Control allocation is the problem of converting equivalent minimizing the difference between a reference model orders, computed by the control law, into control orders and the closed-loop aircraft. The output of this step is when there are more effectors than axes to control. For a the optimum value of the H criterion. This section comprehensive survey of control allocation methods, please is devoted to describing this∞ first step. refer to the work by Johansen and Fossen (2013). In our (2) Output of step 1 is used to put a constraint on max- study a control allocation module needs to be incorporated imal value of the H criterion, in order to guarantee in order to convert equivalent elevator, aileron and rudder satisfactory closed-loop∞ behavior while optimizing the deflections (δmequi, δlequi, δnequi) into actual control sur- elevons size η and control law gains. This step is faces deflections (δmi,i=1...10, δn). described extensively in next section. Mathematically, the control allocation problem is that of As stated previously, simultaneously optimizing control finding a deflections vector u satisfying: surfaces size η and control law gains requires setting a constraint – in the optimization sense – that ensures an Cmδm ... Cmδm Cmδn Cmδm δmequi 1 10 equi adequate closed-loop behavior of the optimal solution. Clδm ... Clδm Clδn u = Clδl δlequi 1 10 equi This constraint was set as a maximal admissible value of Cnδm ... Cnδn Cnδn Cnδn δnequi 1 10 equi an H criterion, value which must be computed through ∞ B1(η) a first synthesis. The H criterion and its optimal value (6) computation are described∞ now. where B1(η) is the matrix of elevons gradients in pitch, A three-channels model-reference tracking scheme was roll and yaw respectively, which all depend from parameter used. This scheme consists in minimizing the difference T η.[Cmδmequi Clδlequi Cnδnequi ] is a vector of equivalent between a reference dynamics model and the closed-loop gradients as seen by the control law. These values may aircraft, from the H norm point of view. If the reference be set arbitrarily without loss of generality, we chose model is perfectly∞ matched by the closed-loop in the equivalent values of 1 on all axes. Then a classical solution whole frequency-domain, then the optimal H value is of equation 6 is the Moore-Penrose pseudo-inverse: zero. However this is practically infeasible due∞ to physical limitations, as a consequence the optimal value is always above zero. δmequi u = Kalloc(η) δlequi (7) Here model-reference tracking is written as minimizing the δnequi H norm of a three-input three-output transfer function T T 1 between∞ pilot inputs (Nz ,φ ,β ) and outputs (z ,z ,z ) with Kalloc(η)=B1 (B1B1 )− (8) c c c 1 2 3 the differences between reference dynamics outputs and actual closed-loop signals (Nz, φ, β). For a proper def- As comprehensively discussed in section 4.3, our process inition of signals please refer to Figure 5. In our case features two steps. In the first step, three-axes gains are multi-channel transfer has several advantages over mul- computed for a fixed η value; in this step the pseudo- tiple single-input single-output (SISO) transfers. First off- inverse control allocation from equation (8) is used. During diagonal terms are implicitly set to zero. Hence resulting the second step, three-axes control law gains and η param- control law will totally decouple all three axes, namely eter are simultaneously optimized. In this step, K is alloc longitudinal from lateral / directional, but also lateral no more fixed, but is a variable for the optimization. By from directional – turns are performed with zero sideslip doing this, the design space is widened, and a truly optimal – and directional from lateral – “pedal” inputs imply no strategy with respect to the imposed handling qualities bank –. Couplings between all axes are explicitly taken into constraints can be chosen by the optimizer. account by the control law, which a SISO approach would More precisely, in order to limit the number of variables not. A single constraint on the H norm of this multi- ∞ for the optimization, Kalloc is parameterized as follows: channel transfer ensures an adequate closed-loop behavior
14749 Proceedings of the 20th IFAC World Congress Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Toulouse, France, July 9-14, 2017
ref roll rate p. An integrator is added to keep zero steady- pitch roll 2 N + z1 K Kalloc 0 !0 z alloc 2 2 state sideslip, as well as a bank angle order direct K = pitch roll (9) s +2ξ0!0s+!0 − alloc Kalloc Kalloc 0 feedthrough gain. Outputs of this law are equivalent − yaw Reference pitch dynamics 00Kalloc aileron and rudder order δlequi and δnequi respec- 1 φref + z2 tively. (1+s=τ )(1+s=τ ) This means we impose a symmetrical and anti-symmetrical rp sp − All the gains involved in the C∗ and Y ∗ structured deflection of the elevons for a pitch and roll order respec- Reference roll dynamics tively, and a yaw order is allocated to the rudder only. 2 controllers are gathered in K as decision variables. A !dr βref + z3 s2+2ξ ! s+!2 general overview of control law structure is visible on By incorporating this physical knowledge of the control dr dr dr − Figure 5. As already mentioned, control laws outputs allocation structure, the number of variables within Kalloc Reference yaw dynamics are equivalent elevator, aileron and rudder orders, which is reduced from 33 to 11 variables. η Nz are independent from control surfaces architecture. These q equivalent orders are then converted into control surfaces LFR Aircraft ∗ δmequi 2 β C Law δm i =1::10 ! deflections thanks to a control allocation module described 4.3 Simultaneous Three-Axes Control Law Synthesis Nzc K i act u Representation alloc 2 2 Delay p in next section. δn s +2ξact!acts+!act φc Integrated design and control of the BWB presented in δlequi Actuators model r β ∗ δn this paper follows a two-steps scheme: c Y Law equi e 1+ p3Lz w φ w 2Lz Ve s z σ 2 z πVe Lz 4.2 Control Allocation Model q (1+ V s) (1) A first control laws synthesis computes gains for an e arbitrarily fixed η value. The problem consists in Turbulence model Control allocation is the problem of converting equivalent minimizing the difference between a reference model orders, computed by the control law, into control orders and the closed-loop aircraft. The output of this step is when there are more effectors than axes to control. For a the optimum value of the H criterion. This section comprehensive survey of control allocation methods, please is devoted to describing this∞ first step. Fig. 5. Closed-loop representation for integrated design and control optimization. refer to the work by Johansen and Fossen (2013). In our (2) Output of step 1 is used to put a constraint on max- study a control allocation module needs to be incorporated imal value of the H criterion, in order to guarantee on all three axes. An equivalent formulation with SISO 4.4 Definition of the Optimization Problem in order to convert equivalent elevator, aileron and rudder satisfactory closed-loop∞ behavior while optimizing the transfers would require nine constraints. deflections (δmequi, δlequi, δnequi) into actual control sur- elevons size η and control law gains. This step is In our study the closed-loop reference values are fixed and Once the optimumγ ˆ of the H criterion is computed, faces deflections (δmi,i=1...10, δn). described extensively in next section. ∞ ∞ are given in table 1. The optimization problem for simul- it is used as a constraint on the H norm of the multi- ∞ Mathematically, the control allocation problem is that of As stated previously, simultaneously optimizing control taneous three-axes control laws synthesis simply reads: channel transfer for the combined optimization problem. finding a deflections vector u satisfying: surfaces size η and control law gains requires setting a init init More precisely the integrated design and control problem min T(Nzc,φc,βc) (z1,z2,z3) P (η ), K, Kalloc =ˆγ constraint – in the optimization sense – that ensures an K → ∞ ∞ of this study is that of finding a minimal η such that: Cmδm ... Cmδm Cmδn Cmδm δmequi 1 10 equi adequate closed-loop behavior of the optimal solution. such that: (10) Clδm1 ... Clδm10 Clδn u = Clδlequi δlequi Deflections and deflection rates in response to maneu- This constraint was set as a maximal admissible value of • Cnδm ... Cnδn Cnδn Cnδn δnequi p, pole of P (s): vers do not exceed prescribed limits. 1 10 equi an H criterion, value which must be computed through ∀ ∞ Re(p) MinDecay, Re(p) MinDamping. p ; Closed-loop behavior is optimal. B1(η) a first synthesis. The H criterion and its optimal value ≤− ≤− | | K internally stabilizes P (η) • (6) computation are described∞ now. The latter point is solved by ensuring that the H norm of ∞ K being a vector containing all control law gains defined in the multi-channel transfer T(Nz ,φ ,β ) (z ,z ,z )(η) is where B (η) is the matrix of elevons gradients in pitch, c c c 1 2 3 ∞ 1 A three-channels model-reference tracking scheme was section 4.1. The additional constraints ensure that closed- kept under its optimal valueγ ˆ whatever→ η. Once the op- roll and yaw respectively, which all depend from parameter used. This scheme consists in minimizing the difference ∞ T loop poles have a damping of at least 0.5 (MinDamping), timum valueγ ˆ for a fixed η is known from the optimiza- η.[Cm Cl Cn ] is a vector of equivalent ∞ δmequi δlequi δnequi between a reference dynamics model and the closed-loop and a real part of at least 0.2 (MinDecay). Even though tion described in section 4.3, the optimization problem of gradients as seen by the control law. These values may aircraft, from the H norm point of view. If the reference those constraints may seem redundant with the reference finding the best possible closed-loop behavior translates be set arbitrarily without loss of generality, we chose ∞ model is perfectly matched by the closed-loop in the model tracking objective, it was found that it helps the into a single constraint satisfaction problem. This elegant equivalent values of 1 on all axes. Then a classical solution whole frequency-domain, then the optimal H value is optimizer to converge and to control indirectly the integral formulation allows minimizing an other objective, – η in of equation 6 is the Moore-Penrose pseudo-inverse: ∞ zero. However this is practically infeasible due to physical terms dynamics. our case – while designing appropriate control law gains limitations, as a consequence the optimal value is always to ensure a satisfactory closed-loop behavior on all axes. above zero. To solve this optimization problem, the systune routine δmequi Apkarian (2012) from Matlab Robust Control Toolbox was Constraints on maneuverability are cast as constraints on u = K (η) δlequi (7) alloc Here model-reference tracking is written as minimizing the used. This routine allows tuning of fixed-order structured the H norm of adequate transfer functions, similarly to δnequi H norm of a three-input three-output transfer function controllers, so it can handle physical parameters optimiza- the work∞ of Niewoehner and Kaminer (1996). Therefore T T 1 between∞ pilot inputs (Nz ,φ ,β ) and outputs (z ,z ,z ) with Kalloc(η)=B1 (B1B1 )− (8) c c c 1 2 3 tion combined with control gains computation. Couplings these constraints are root-mean-square (RMS) and not the differences between reference dynamics outputs and between control and design problem are therefore taken temporal. Following constraints are ensured: actual closed-loop signals (Nz, φ, β). For a proper def- As comprehensively discussed in section 4.3, our process into account directly in a single optimization. Moreover inition of signals please refer to Figure 5. In our case Maximum deflections and deflections rate in response features two steps. In the first step, three-axes gains are it is well suited to mathematical particularities of the multi-channel transfer has several advantages over mul- • to a pilot pull-up. This is ensured through constraint computed for a fixed η value; in this step the pseudo- optimization problem in equation (10), namely the non- tiple single-input single-output (SISO) transfers. First off- on following H norms: inverse control allocation from equation (8) is used. During smooth behavior of the H norm. Optima found by the ∞ ∞ 1 max diagonal terms are implicitly set to zero. Hence resulting ∆δmmax TNzc u∆Nzc 1 and the second step, three-axes control law gains and η param- algorithm are only local, consequently several initializa- i → ∞ ≤ control law will totally decouple all three axes, namely 1 max eter are simultaneously optimized. In this step, Kalloc is tions should be performed in order to ensure the globality ˙ max TNzc u˙ ∆Nzc 1 respectively, with longitudinal from lateral / directional, but also lateral δmi → ∞ ≤ no more fixed, but is a variable for the optimization. By of the solution. max max from directional – turns are performed with zero sideslip ∆δmi = δmi δme. doing this, the design space is widened, and a truly optimal Maximum deflections− and deflections rate in re- – and directional from lateral – “pedal” inputs imply no Parameter ω0 τrp τsp ωdr • strategy with respect to the imposed handling qualities 1 sponse to severe longitudinal turbulence. This is en- bank –. Couplings between all axes are explicitly taken into Value (ad.s− ) 1 1.6 1.9 0.4 constraints can be chosen by the optimizer. sured through constraint on following H norms: account by the control law, which a SISO approach would Table 1. Reference model (ξ0 = ξdr =0.7). 2 2 ∞ ∆δmmax Tew u 1 and ˙ max Tew u˙ 1 More precisely, in order to limit the number of variables not. A single constraint on the H norm of this multi- i → ∞ δmi → ∞ ∞ ≤ ≤ for the optimization, Kalloc is parameterized as follows: channel transfer ensures an adequate closed-loop behavior respectively.
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Maximum deflections and deflections rate in re- roll order, hence all roll criteria are equally saturated. • sponse to φmax bank angle order. This is en- Pitch being not limiting on this flight point, only two sured through constraint on following H norms: pairs of elevons are used for pitch control. This behavior is 1 max ∞ ∆δmmax Tφc uφ 1 and confirmed by looking at the optimized allocation matrix: i → ∞ ≤ 1 max max T φ 1 respectively. δm˙ φc u˙ i → ∞ ≤ 0.023 0.3811 0 Chosen values for the sizing are: 0.0116 0.3811 0 max ˙ max max max δm = 25◦, δm = 60◦/s,∆Nzc =1.5g, φc = 0.000 0.3811 0 45◦. 0.000 0.3811 0 0.000 0.3811 0 opt The combined optimization problem is finally summarized K = 0.023 0.3811 0 (13) in Tab. 2 and is extensively described in Denieul (2016). alloc − 0.0116 0.3811 0 − 0.000 0.3811 0 5. RESULTS − 0.000 0.3811 0 − 0.000 0.3811 0 In this section the results of the integrated design and 0.000− 0.000 0.006 control process are analyzed. 6. CONCLUSION 5.1 Integrated Design and Control on a Single Flight Point A new method for sizing control surfaces of an unstable Integrated design and control with tunable allocation blended wing-body using closed-loop handling qualities applied to the flight point M.35, H = 3300ft, m = 300T criteria was presented. This method consists in simulta- gives following results: neously optimizing the longitudinal and lateral control ηopt =0.3885 (11) laws, as well as a control allocation module, while min- imizing the control surface areas under handling qualities gBest =0.9998 (12) constraints. From a sizing perspective, we have shown that the studied Airbus BWB configuration can adequately be controlled on all three axes with only 60% of the initial control surfaces span, with normal laws and full control authority, with reasonable hypotheses on the actuators, sensors and delays chain. Future work will extend such a procedure to the full flight envelope. Temporal criteria instead of frequency – root-mean-square – criteria will be also investigated. Finally alternative optimizers could be considered for solving this coupled problem; simulation- based routines such as genetic algorithms could be worth examining.
REFERENCES Alazard, D., Loquen, T., de Plinval, H., and Cumer, C. (2013). Avionics/Control co-design for large flexible space structures. In AIAA Guidance, Navigation, and Control (GNC) Conference, Guidance, Navigation, and Control and Co-located Conferences. American Institute of Aeronautics and Astronautics. Apkarian, P. (2012). Tuning Controllers Against Multiple Design Requirements. In System Theory, Control and Computing (ICSTCC), 2012 16th International Confer- ence on, 1–6. IEEE. Bolsunovsky, A., Buzoverya, N., Gurevich, B., Denisov, V., Dunaevsky, A., Shkadov, L., Sonin, O., Udzhuhu, A., and Zhurihin, J. (2001). Flying wing—problems and decisions. Aircraft Design, 4(4), 193–219. Fig. 6. Bar diagram of normalized constraints values after Denieul, Y. (2016). Preliminary Design of Control Sur- optimization with tunable allocation, ηopt =0.3885. faces and Laws for Unconventional Aircraft Configu- rations. M´emoire de th`ese,ISAE-Supa´ero, Toulouse, A 61% decrease of the control surfaces span is achieved France. compared to the initial layout, while still satisfying all Denieul, Y., Alazard, D., Bordeneuve, J., Toussaint, C., handling qualities constraints – i.e. gBest < 1. More pre- and Taquin, G. (2015a). Interactions of Aircraft Design cisely Figure 6, gathering all handling qualities constraints and Control: Actuators Sizing and Optimization for an at the optimum, indicates that on this flight point the Unstable Blended Wing-Body. In AIAA Atmospheric roll constraint is limiting. As a consequence, the optimal Flight Mechanics Conference, AIAA Aviation. American allocation is to distribute equally among all elevons the Institute of Aeronautics and Astronautics, Dallas, TX.
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Maximum deflections and deflections rate in re- roll order, hence all roll criteria are equally saturated. Function / Variable Description Quantity • sponse to φmax bank angle order. This is en- Pitch being not limiting on this flight point, only two minimize η Outer elevons total span sured through constraint on following H norms: pairs of elevons are used for pitch control. This behavior is with respect to K Control law gains 16 ∞ 1 max Kalloc Control allocation matrix 11 ∆δmmax Tφc uφ 1 and confirmed by looking at the optimized allocation matrix: i → ∞ ≤ η Outer elevons total span 1 1 max 1 V max Tφc u˙ φ 1 respectively. e δm˙ subject to ∆δmmax TNzc u∆α g zα 1 Maximum deflection in response to longi- 5 i → ∞ ≤ i → ∞ ≤ 0.023 0.3811 0 tudinal order. Chosen values for the sizing are: 0.0116 0.3811 0 1 Ve max ˙ max TNzc u˙ ∆α g zα 1 Maximum deflection rate in response to 5 max ˙ max max δmi → ∞ ≤ δm = 25◦, δm = 60◦/s,∆Nzc =1.5g, φc = 0.000 0.3811 0 longitudinal order. 2 45◦. 0.000 0.3811 0 ∆δmmax Tew u 1 Maximum deflection in response to longi- 5 i → ∞ ≤ 0.000 0.3811 0 tudinal turbulence The combined optimization problem is finally summarized opt 2 K = 0.023 0.3811 0 (13) ˙ max Tew u˙ 1 Maximum deflection rate in response to 5 alloc δmi → ∞ ≤ in Tab. 2 and is extensively described in Denieul (2016). 0.0116 −0.3811 0 longitudinal turbulence 1 max − ∆δmmax Tφc uφ 1 Maximum deflection in response to bank 5 0.000 0.3811 0 i → ∞ ≤ 5. RESULTS − order. 0.000 0.3811 0 1 max − ˙ max Tφc u˙ φ 1 Maximum deflection rate in response to 5 0.000 0.3811 0 δmi → ∞ ≤ − bank order. In this section the results of the integrated design and 0.000 0.000 0.006 1 T(Nz ,φ ,β ) (z ,z ,z ). 1 Optimal closed-loop performance. 1 c c c → 1 2 3 γˆ ∞ ≤ control process are analyzed. p, p pole of P (s): ∞ Closed-loop poles location. 1 ∀ 6. CONCLUSION Re(p) MinDecay, Re(p) MinDamping. p ≤− ≤− | | 5.1 Integrated Design and Control on a Single Flight Point K internally stabilizes P (η) A new method for sizing control surfaces of an unstable Table 2. Integrated design and control optimization problem. Integrated design and control with tunable allocation blended wing-body using closed-loop handling qualities applied to the flight point M.35, H = 3300ft, m = 300T criteria was presented. This method consists in simulta- gives following results: neously optimizing the longitudinal and lateral control Denieul, Y., Bordeneuve, J., Alazard, D., Toussaint, C., ities. Journal of Guidance, Control, and Dynamics, and Taquin, G. (2015b). Integrated Design and Con- 19(2), 445–452. ηopt =0.3885 (11) laws, as well as a control allocation module, while min- imizing the control surface areas under handling qualities trol of a Flying Wing Using Nonsmooth Optimization Perez, R., Liu, H., and Behdinan, K. (2006). A Mul- gBest =0.9998 (12) constraints. From a sizing perspective, we have shown that Techniques. In J. Bordeneuve, A. Drouin, and C. Roos tidisciplinary Optimization Framework for Control- the studied Airbus BWB configuration can adequately be (eds.), Advances in Aerospace Guidance, Navigation and Configuration Integration in Aircraft Conceptual De- controlled on all three axes with only 60% of the initial Control, 475–489. Springer International Publishing. sign. Journal of Aircraft, 43(6), 1937–1948. control surfaces span, with normal laws and full control Drela, M. and Youngren, H. (2006). AVL Aerodynamic Qin, N., Vavalle, A., Le Moigne, A., Laban, M., Hackett, authority, with reasonable hypotheses on the actuators, Analysis, Trim Calculation, Dynamic Stability Analysis, K., and Weinerfelt, P. (2004). Aerodynamic consid- sensors and delays chain. Future work will extend such Aircraft Configuration Development. erations of blended wing body aircraft. Progress in a procedure to the full flight envelope. Temporal criteria Fathy, H., Reyer, J., Papalambros, P., and Ulsov, A. Aerospace Sciences, 40(6), 321–343. instead of frequency – root-mean-square – criteria will be (2001). On the Coupling Between the Plant and Con- Ricardez-Sandoval, L., Budman, H., and Douglas, P. also investigated. Finally alternative optimizers could be troller Optimization Problems. In American Control (2009). Simultaneous design and control of chemical considered for solving this coupled problem; simulation- Conference, 2001. Proceedings of the, volume 3, 1864– processes with application to the Tennessee Eastman based routines such as genetic algorithms could be worth 1869 vol.3. process. Journal of Process Control, 19(8), 1377–1391. examining. Favre, C. (1994). Fly-by-wire for commercial aircraft: the Roman, D., Allen, J., and Liebeck, R. (2000). Aero- Airbus experience. International Journal of Control, dynamic Design Challenges of the Blended-Wing-Body REFERENCES 59(1), 139–157. Subsonic Transport. In 18th Applied Aerodynamics Con- Garmendia, D.C., Chakraborty, I., Trawick, D.R., and ference. AIAA. Alazard, D., Loquen, T., de Plinval, H., and Cumer, C. Mavris, D.N. (2014). Assessment of Electrically Actu- Roos, C., Hardier, G., and Biannic, J.M. (2014). Poly- (2013). Avionics/Control co-design for large flexible ated Redundant Control Surface Layouts for a Hybrid nomial and rational approximation with the APRICOT space structures. In AIAA Guidance, Navigation, and Wing Body Concept. In 14th AIAA Aviation Tech- Library of the SMAC toolbox. In Control Applications Control (GNC) Conference, Guidance, Navigation, and nology, Integration, and Operations Conference, AIAA (CCA), 2014 IEEE Conference on, 1473–1478. Control and Co-located Conferences. American Institute Aviation. American Institute of Aeronautics and Astro- Roskam, J. (1985). Airplane Design Part VI: Preliminary of Aeronautics and Astronautics. nautics. Calculation of Aerodynamic, Thrust and Power Charac- Apkarian, P. (2012). Tuning Controllers Against Multiple Johansen, T.A. and Fossen, T.I. (2013). Control teristics. DARcorporation, Kansas. Design Requirements. In System Theory, Control and allocation- a survey. Automatica, 49(5), 1087–1103. Saucez, M. and Boiffier, J.L. (2012). Optimization of En- Computing (ICSTCC), 2012 16th International Confer- Lhachemi, H., Saussie, D., and Zhu, G. (2015). A gine Failure on a Flying Wing Configuration. In AIAA ence on, 1–6. IEEE. structured -based optimization approach for integrated Atmospheric Flight Mechanics Conference, Guidance, Bolsunovsky, A., Buzoverya, N., Gurevich, B., Denisov, plant and self-scheduled flight control system design. Navigation, and Control and Co-located Conferences. V., Dunaevsky, A., Shkadov, L., Sonin, O., Udzhuhu, Aerospace Science and Technology, 45(0), 30–38. AIAA, Minneapolis, Minnesota. A., and Zhurihin, J. (2001). Flying wing—problems and Liebeck, R.H. (2004). Design of the Blended Wing Body Silvestre, C., Pascoal, A., Kaminer, I., and Healey, A. decisions. Aircraft Design, 4(4), 193–219. Subsonic Transport. Journal of Aircraft, 41(1), 10–25. (1998). Plant-Controller Optimization with Applica- Fig. 6. Bar diagram of normalized constraints values after Denieul, Y. (2016). Preliminary Design of Control Sur- Mart´ınez-Val, R. and P´erez, E. (2005). Medium Size Fly- tions to Integrated Surface Sizing and Feedback Con- optimization with tunable allocation, ηopt =0.3885. faces and Laws for Unconventional Aircraft Configu- ing Wings. von Karman Institute for Fluid Dynamics. troller Design for Autonomous Underwater Vehicles rations. M´emoire de th`ese,ISAE-Supa´ero, Toulouse, Meheut, M., Arntz, A., and Carrier, G. (2012). Aerody- (AUVs). In American Control Conference, volume 3, A 61% decrease of the control surfaces span is achieved France. namic Shape Optimizations of a Blended Wing Body 1640–1644. compared to the initial layout, while still satisfying all Denieul, Y., Alazard, D., Bordeneuve, J., Toussaint, C., Configuration for Several Wing Planforms. In AIAA, Standard, M. (1990). Flying Qualities of Piloted Aircraft. handling qualities constraints – i.e. gBest < 1. More pre- and Taquin, G. (2015a). Interactions of Aircraft Design volume 10, 3122. American Institute of Aeronautics and Technical report, MIL-STD-1797A, Department of De- cisely Figure 6, gathering all handling qualities constraints and Control: Actuators Sizing and Optimization for an Astronautics, New Orleans, Louisiana. fense. at the optimum, indicates that on this flight point the Unstable Blended Wing-Body. In AIAA Atmospheric Niewoehner, R.J. and Kaminer, I. (1996). Integrated roll constraint is limiting. As a consequence, the optimal Flight Mechanics Conference, AIAA Aviation. American Aircraft-Controller Design using Linear Matrix Inequal- allocation is to distribute equally among all elevons the Institute of Aeronautics and Astronautics, Dallas, TX.
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