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Actuator Saturation Analysis of a Fly-By-Wire Control System for a Delta-Canard Aircraft

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Actuator Saturation Analysis of a Fly-By-Wire Control System for a Delta-Canard Aircraft DEGREE PROJECT IN VEHICLE ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2020 Actuator Saturation Analysis of a Fly-By-Wire Control System for a Delta-Canard Aircraft ERIK LJUDÉN KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES Author Erik Ljudén <[email protected]> School of Engineering Sciences KTH Royal Institute of Technology Place Linköping, Sweden Saab Examiner Ulf Ringertz Stockholm KTH Royal Institute of Technology Supervisor Peter Jason Linköping Saab Abstract Actuator saturation is a well studied subject regarding control theory. However, little research exist regarding aircraft behavior during actuator saturation. This paper aims to identify flight mechanical parameters that can be useful when analyzing actuator saturation. The studied aircraft is an unstable delta-canard aircraft. By varying the aircraft’s center-of- gravity and applying a square wave input in pitch, saturated actuators have been found and investigated closer using moment coefficients as well as other flight mechanical parameters. The studied flight mechanical parameters has proven to be highly relevant when analyzing actuator saturation, and a simple connection between saturated actuators and moment coefficients has been found. One can for example look for sudden changes in the moment coefficients during saturated actuators in order to find potentially dangerous flight cases. In addition, the studied parameters can be used for robustness analysis, but needs to be further investigated. Lastly, the studied pitch square wave input shows no risk of aircraft departure with saturated elevons during flight, provided non-saturated canards, and that the free-stream velocity is high enough to be flyable. i Sammanfattning Styrdonsmättning är ett välstuderat ämne inom kontrollteorin. Däremot existerar det lite forskning gällande flygplansbeteende vid styrdonsmättning. Syftet med den här rap- porten är att identifiera flygmekaniska parametrar som kan vara användbara vid analys av styrdonsmättning av ett instabilt delta-canard flygplan. Genom att variera flygplan- ets tyngdpunkt och applicera en pulsinmatning i tippled har styrdonsmättning hittats och undersökts närmare med momentkoefficienter, men även med andra flygmekaniska parametrar. De studerade parametrarna har visat sig vara mycket relevanta vid analys av styrdonsmättning och ett enkelt samband mellan mättade styrdon och momentcoefficienter har hittats. Det går till exempel att leta efter plötsliga ändringar i momentkoefficienterna under mättning av styrdon för att hitta potentiellt farliga flygsituationer. De studerade parametrarna kan användas i en robusthetsanalys, men vidare forskning krävs. Den studerade pulsinmatningen i tippled visar även att så länge canarderna inte ligger i mät- tning, trots att elevonerna ligger i mättning, så är det ingen fara att flyga, förutsatt att flyghastigheten är tillräckligt hög. ii Contents 1 Introduction 1 1.1 Background . 1 1.2 Problem . 1 1.3 Purpose . 2 1.4 Goal . 2 1.5 Method . 2 1.6 Limitations . 2 1.7 Outline . 2 2 Theory 4 2.1 Desktop Simulation . 4 2.2 Nonlinearities of Control Systems . 4 2.3 Definition of Lift & Positive Pitching Moment of an Aircraft . 4 2.4 Stability . 5 2.5 Longitudinal Stability . 7 2.6 The Aft-Tail & Tail-First Arrangement . 8 2.7 The Modern Fighter Aircraft . 9 2.8 Control Surface Arrangements . 10 2.9 Aircraft Moment Equation . 11 3 Demonstrator 13 3.1 Deciding Maneuvers . 13 3.2 Angles & Total Moment on The Studied Aircraft . 13 3.3 Moment Coefficients on The Studied Aircraft . 14 3.4 Saturation Prediction . 18 4 Result 19 4.1 The Studied Square Wave Input . 19 4.2 Saturated Region 1 . 20 4.3 Saturated Region 2 . 23 4.4 Two Different Centers of Gravity . 25 5 Discussion 30 6 Conclusion 33 7 Recommendations For Further Research 34 iii Nomenclature , = weight = moment of inertia ! = lift " = total pitching moment ! = lift coefficient !,<0G = maximum lift coefficient < = total pitching moment coefficient d = air density + = airspeed +1 = free-stream velocity ( = wing area 2¯ = wing mean aerodynamic chord @1 = free-stream dynamic pressure ; = distance 6 = gravitational acceleration < = mass U = angle of attack U2A8C = stall angle X = deflection angle \ = pitch angle W = flight path angle @ = pitch angle velocity @¤ = pitch angle acceleration 4;4 = elevons 3;84 = deflection left inner elevon 3;>4 = deflection left outer elevon 3A84 = deflection right inner elevon 3A>4 = deflection right outer elevon 3A = rudder 20= = canards A4BC = collection name for control surface interference, inertia, pitch damping, and aerodynamic leading edge flap effects iv Acronym List FBW Fly-By-Wire c.g center of gravity v 1. Introduction 1.1 Background During the late 19th century some basic theory of aircraft stability appeared and proposed the tail plane to be a basic element of pitch balance, stability, and control. In 1903 the Wright brothers performed the first flight of a motor powered aircraft called the ‘Flyer’. This aircraft was difficult to fly due to pitch instability resulting in major handling difficulties. The Wright brothers realized that the plane would have to bank in a turn and thus decided to twist the Flyer’s wing during flight, causing one half of the wing to produce less lift and the other side to produce more. The aircraft was controlled using wires connected to a hip cradle which moved the rudder and twisted the wing. The elevator control was operated using a lever, which adjusted the pitch of the plane [1]. For several years the standard was to use a cable-operated system. A stick was used to operate both elevators and ailerons through a series of cables and pulleys, while the rudder was moved by foot pedals. With increasing speed and aircraft weight the physical limitations of pilots began to be realized. The only requirement for the cable-operated system was the physical strength of the pilot to control the control surfaces. This problem was solved by integration of technology such as mechanical boosters to help move the control surfaces of large aircraft, and later, hydro mechanical flight control systems got integrated [2]. With the introduction of Fly-By-Wire (FBW) technology in the 1970’s it became possible to use electrical signals for control. Stick signals were converted to electrical signals and transmitted via electrical cables to an on-board computer. In the on-board computer the stick signals together with measured flight condition data got processed to determine the movement of each control surface actuator to provide the ordered flight response [3]. FBW technology is today used frequently within the flight industry. Due to the on-board computer, unintended increases in angle of attack and sideslip can rapidly be detected and automatically be resolved by marginally deflecting the control surfaces in the opposite way while the problem is still small [4]. This has made it possible to purposely build unstable aircraft to gain the advantages of greater agility, as well as shorter take-off and landing distances due to an overall increase in lift compared to a stable aircraft. Since the pilot inputs does not move the control surface actuators directly, but are processed in the on-board computer that determines the final control surface movement, one of many challenges is to understand how such a FBW respond to actuator saturation. In this thesis the behavior of a FBW control system developed for an unstable delta wing aircraft is analyzed in flight envelope regions where actuator saturation occur. The goal is to identify flight mechanical parameters of relevance for analysis of the FBW control system during actuator saturation. 1.2 Problem The control system to be studied is a FBW designed for an unstable delta-canard aircraft. With a saturated control surface, the maximum deflection angle is set, generating its maximum lift force contribution. For an unstable aircraft, saturated control surfaces can potentially be of serious nature if the generated force from the control 1 surfaces is not large enough to counteract the instability of the aircraft. Therefore, it is important to understand how and when actuator saturation occur. The control system is today studied using various simulation programs with and without human pilots where a criteria is used to help determine if the occurrence of saturation can imply a problem or not. However, a better understanding of the FBW response and which flight mechanical parameters that are of relevance to study during actuator saturation are requested. 1.3 Purpose The purpose of this thesis is to identify flight mechanical parameters that are of relevance to study during actuator saturation. 1.4 Goal In this study the following questions will be investigated • Does a simple connection of actuator saturation and flight mechanical parameters exist for the FBW? • Can the flight mechanical parameters be used to determine how robust the aircraft is towards departure from controlled flight? • How does one determine if actuator saturation during flight is a problem or not using flight mechanical parameters? 1.5 Method The data to be analyzed will be generated using a desktop simulator and is run by a script. As a first step, one needs to find typical maneuvers that can cause control surface saturation. Further, regions of flight where saturation occur during flight has to be found in order to finally analyze each case in detail. Since one is interested in the control system behavior, the control system will be tested for flight setups outside of the intended design. Different flight mechanical parameters will be investigated closer in order to understand their connection to actuator saturation. All data gathered from the desktop simulation program will be analyzed using Matlab. 1.6 Limitations In this study, only longitudinal maneuvers are investigated for actuator saturation. The control theory used by the FBW will not be looked into, but will be treated as a black box. Further, the acquired results will not be verified in a real-time simulator. 1.7 Outline This paper starts by introducing background theory in section 2, regarding the used desktop simulator, aircraft stability, moments acting on an aircraft, moment coefficients, and a section explaining the purpose of different control surfaces.
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