Robust Fly-by-Wire under Horizontal Tail Damage

Dlamini, Zinhle (2016-12)

Thesis (DPhil)--Stellenbosch University, 2016.


ENGLISH ABSTRACT: Aircraft damage modelling was conducted on a Boeing 747 to examine the effects of asymmetric horizontal stabiliser loss on the flight dynamics of a commercial fly-by-Wire (FBW) aircraft. Change in static stability was investigated by analysing how the static margin is reduced as a function of percentage tail loss. It is proven that contrary to intuition, the aircraft is longitudinally stable with 40% horizontal tail removed. The short period mode is significantly changed and to a lesser extent the Dutch roll mode is affected through lateral coupling. Longitudinal and lateral trimmability of the damaged aircraft are analysed by comparing the tail-loss-induced roll, pitch, and yaw moments to available actuator force from control surfaces. It is presented that the aircraft is completely trimmable with 50% tail loss. Robustness of a generic C* FBW control system is investigated by analysing how characteristic eigenvalues move as a result of damage, and comparison to the non-FBW aircraft is made. Furthermore, the extent of stabiliser loss that the system can successfully handle, without loss of acceptable performance, is identified. A handling qualities evaluation is presented to provide an understanding of how the pilot would perceive the damaged aircraft. The results of the study show that a generic FBW system improves robustness such that the aircraft is stable with 50% horizontal stabiliser loss. With 50% damage, the aircraft is controllable but unsafe to fly and may be unable to effectively complete its mission task. The damaged FBW aircraft is formulated into an H2 control problem. Convex optimisation techniques are employed to represent the problem as a linear matrix inequality and a solution is synthesised through the interior point method. An analysis of the state feedback gains is carried out to ascertain a suitable control strategy to minimise the in fluence of disturbance on longitudinal dynamics. It is proven that pitch angle feedback provides good disturbance rejection in the low frequency range, however, it attenuates the control signal at higher frequencies thus resulting in loss of robustness. By comparison with a different class of aircraft it is shown that pitch angle feedback is only advantageous for aircraft with slow closed-loop longitudinal poles. The generic C* fly-by-wire system is augmented to include pitch angle feedback and thus creates a novel system, the C* FBW. This system is compared to the original C* and its advantages and disadvantages presented. For the case of 50% damage, the phugoid poles of the system are stable whilst the short period poles are within level 2 handling qualities. A small loss in robustness is, however, observed for the short period poles. It is shown through an alternative control strategy that improvement of short period robustness can be achieved by increasing the system gain, however, this destabilises the marginally stable phugoid poles of the aircraft. The original contributions presented in this thesis are in the field of flight dynamics and robust control. An analysis of change in dynamics due to horizontal tail damage is carried out in a method that provides visibility to changes in trim and manoeuvrability of the aircraft after damage. An evaluation of FBW robustness against this kind of damage is presented as well as change in handling qualities. A novel approach of analysing disturbance rejection capabilities of an aircraft with available actuators through a more robust combination of feedback states is discussed. From this analysis a new FBW control law is developed and its robustness evaluated. Through a comparison with an ideal system the limiting factors to improving the robustness of the B747 class of aircraft are identified.

AFRIKAANSE OPSOMMING: Vliegtuigskade op ‘n Boeing 747 is gemodelleer om die effek van asimmetriese verlies van die horisontale stabiliseerder op die vlugdinamika van ‘n kommersiële vliegtuig met ‘n elektroniese beheerstelsel (fly-by-wire) te toets. Die verandering in statiese stabiliteit is ondersoek deur te analiseer hoe die statiese marge verminder as ‘n funksie van die persentasie stertverlies. Dit word bewys dat die vliegtuig longitudinaal stabiel is met 40% van die horisontale stert verwyder. Die kort-periode fase word beduidend deur die skade verander. Die Nederlandse kanteling wyse (Dutch roll mode) word tot ‘n mindere mate geaffekteer deur laterale koppeling. Die longitudinale en laterale ewewig-instelbaarheid (trimmability) van die beskadigde vliegtuig is geanaliseer deur die kanteling, helling en verdraaiing (roll, pitch, and yaw) weens stertverlies te vergelyk met die beskikbare aktueerder krag vanaf beheeroppervlaktes. Dit word bevind dat die vliegtuig ten volle ewewig-instelbaar is met 50% stertverlies. Die robuustheid van ‘n generiese C* elektroniese beheerstelsel is ondersoek deur te analiseer hoe die eiewaardes verander weens skade; ‘n vergelyk word getref met die vliegtuig sonder ‘n elektroniese beheerstelsel. Die vlak van stabiliseerderverlies wat die stelsel suksesvol kan hanteer, sonder om aanvaarbare verrigting te verminder, word bepaal. ‘n Hanteringskwaliteit evaluasie word voorgestel om te help verduidelik hoe die vlieënier die skade sal ervaar. Die resultate van hierdie studie dui daarop dat ‘n generiese elektroniese beheerstelsel robuustheid verbeter, wat tot gevolg het dat die vliegtuig stabiel sal bly selfs met 50% horisontale stabiliseerder verlies. Met 50% skade is die vliegtuig steeds beheerbaar maar onveilig om te vlieg. Die beskadigde vliegtuig, met elektroniese beheerstelsel, word as ‘n H2 beheerprobleem geformuleer. Konvekse optimaliseringstegnieke word gebruik om die probleem as ‘n lineêre matriks ongelykheid voor te stel. ‘n Oplossing word bewerkstellig met behulp van die interne punt metode. ‘n Analise van die toename in toestand terugvoer word gedoen om ‘n toepaslike beheerstrategie vas te stel wat die invloed van versteuring op die longitudinale dinamika tot ‘n minimum sal beperk. In die studie word bewys dat die hellingshoekterugvoer goeie versteuringsverwerping verskaf onder lae frekwensies. Dit verswak wel die beheersein onder hoë frekwensies wat dus lei tot ‘n verlies aan robuustheid. In vergelyking tot ‘n ander vliegtuigklas word dit bewys dat hellingshoek-terugvoer slegs voordelig is vir vliegtuie met stadige geslotelus longitudinale pole. Die generiese C* elektroniese beheerstelsel is aangepas om hellingshoek-terugvoer in te sluit en skep dus ‘n nuwe stelsel—die C* elektroniese beheerstelsel. Hierdie stelsel word vergelyk met die oorspronklike C* stelsel en die voor- en nadele word bespreek. Met 50% skade is die langperiode (phugoid) pole van die stelsel stabiel, terwyl die kort-periode pole binne vlak-2 hanteringskwaliteit is. ‘n Klein verlies aan robuustheid word wel waargeneem vir die kort-periode pole. Deur ‘n alternatiewe beheerstrategie word gewys dat ‘n verbetering in kort-periode robuustheid bereik kan word deur die stelsel toename te verhoog. Dit destabiliseer hoewel die marginaal stabiele lang-periode pole van die vliegtuig. Die oorspronklike bydraes van hierdie studie is in die veld van vlugdinamika en robuuste beheer. ‘n Analise van die verandering in dinamika weens horisontale stertskade is uitgevoer met ‘n metode wat sigbaarheid verleen aan die veranderings in ewewiginstelbaarheid en beweeglikheid na skade aan die vliegtuig. ‘n Evaluasie van elektroniese beheerstelselrobuustheid en veranderings in die hanteringseienskappe, na hierdie tipe skade, is voorgelê. ‘n Nuwe benadering is bespreek oor die analisering van ‘n vliegtuig, met beskikbare aktueerders, se vermoë om versteurings te verwerp by wyse van ‘n meer robuuste kombinasie van terugvoer toestande. Vanuit hierdie analise is ‘n nuwe elektroniese beheerstelselwet ontwikkel. Die robuustheid van hierdie nuwe wet is ook geevalueer. Die beperkende faktore om die robuustheid van die Boeing 747 vliegtuigklas te verbeter word identifiseer deur middel van vergelyking met ‘n ideale stelsel.

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