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Development and Optimization of Flight Dynamics, Control Laws and Avionics System for a UAV with a Multi-Scale Optimized Blended Wing Body Configuration

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Development and Optimization of Flight Dynamics, Control Laws and Avionics System for a UAV with a Multi-Scale Optimized Blended Wing Body Configuration Development and Optimization of Flight Dynamics, Control Laws and Avionics System for a UAV with a Multi-scale Optimized Blended Wing Body Configuration Ze Feng (Ted) Gan1, Jiajun (Kevin) Feng2, Fidel Khouli* 3, Mostafa S.A. ElSayed4, and Fred Nitzsche5 Carleton University, Ottawa, Ontario, K1S 5B6, Canada Abstract The research presented in this paper was developed by the multiscale-optimized Blended Wing Body (BWB) Unmanned Aerial Vehicle (UAV) team, an undergraduate capstone project at the Carleton University Department of Mechanical and Aerospace Engineering. The development of the flight dynamics model of the BWB-UAV for stability and control is presented. The stability of the longitudinal and the lateral directional flight modes is examined as a function of flight and design parameters. The design of pole placement and LQR controllers is discussed, and their performance is compared. The PixHawk 2.1 Cube is selected as the flight control unit and the integration of the developed flight dynamics and control laws as a new airframe in the PX4 firmware is described. Parameter optimization and tuning of the flight dynamics model and the control laws using a hardware-in-the-loop simulation setup is presented and discussed. Lessons learned from flight tests, which test the developed firmware using off-the-shelf platforms before migrating to the presented BWB-UAV, and the collected test data are discussed. 1.0 Introduction Blended-wing-body (BWB) aircraft configurations were first sought primarily for military stealth applications (e.g. Northrop Grumman B-2 spirit, Lockheed F-117 Nighthawk), given their small radar and acoustic signature. However, present interest in BWB aircraft by NASA, Boeing, and ACARE (Advisory Council for Aeronautics Research in Europe) involve civilian applications [1, 2]. This is partially because BWB aircraft offer increased payload capacity for passenger and/or cargo transport, without increasing ground footprint relative to a conventional aircraft, thus making them compatible with existing infrastructure. Furthermore, the increased lifting surface area yet reduced total wetted area increases the lift-to-drag ratio. The streamlined geometry also reduces both interference and pressure/form drag, thus reducing fuel consumption [3, 4, 5]. BWB aircraft designs often incorporate numerous control surfaces, engines (enabling distributed propulsion), and even tails for increased maneuverability [2, 4, 5]. When tails are present, they have smaller surface area and moment arm (about the aircraft centre of gravity) relative to conventional aircraft, reducing the tails’ effectiveness in maneuverability. However, this acrobatic maneuverability is not required for cargo transport missions, justifying the design simplicity of two control surfaces (termed elevons because they serve as both elevators and ailerons), one propulsion power plant, and no tail. This configuration poses control challenges, especially due to relying on roll-yaw coupling for yaw control [2, 4, 5]. Although such 2-elevon, tailless, single engine aircraft configurations are common among hobbyist UAVs (e.g. Versa Wing, Skywalker X8, Telink Toro 900), they are less-frequently studied in the academic literature [6, 7, 8], thus motivating the present study. 1 BEng Aerospace Engineering, Carleton University, Ottawa, ON, Canada 2 BEng Aerospace Engineering, Carleton University, Ottawa, ON, Canada 3 Assistant Professor, Department of Mechanical and Aerospace Engineering, Carleton University, Ottawa, ON, Canada * Corresponding author: [email protected] 4 Assistant Professor, Department of Mechanical and Aerospace Engineering, Carleton University, Ottawa, ON, Canada 5 Professor, Department of Mechanical and Aerospace Engineering, Carleton University, Ottawa, ON, Canada 1 2.0 Aircraft Model During the first two years (2017-2019) of the BWB UAV undergraduate capstone project at the Carleton University Department of Mechanical and Aerospace Engineering, the Peregrine-1 UAV was designed based off the commercial off-the-shelf Skywalker X8 UAV. The Skywalker X8 is used for flight tests to verify the aircraft model and controllers; accordingly, it is analyzed in this report, as the Peregrine-1 will be manufactured during the 2019-2020 academic year. The Peregrine-1 has a nearly identical outer mold line (OML) except for a removed front bulge; therefore, its aerodynamic properties are very similar to the Skywalker X8. State space modeling was chosen to model the aircraft dynamics to permit the use of simple conventional linear controllers and decouple longitudinal and lateral uncontrolled dynamics. However, the controlled dynamics are not decoupled, since the elevon inputs are common to both the longitudinal and lateral input vectors. Reconciling differing demanded elevon angles from the longitudinal and lateral controllers is a priority for future work. Given the simple cargo transport mission, the governing equations were linearized about steady level cruise, and gain scheduling was deemed unnecessary. The symbolic longitudinal and lateral state equations were derived to be [9, 10]: 2 ⎡− + 1 − (ℎ − ℎ) − 0 ⎤ α̇ ⎢ ⎥ ⎢ −2 ⎥ q̇ (ℎ − 0.5) 0 0 ̇ = = ⎢ ⎥ ̇ V ⎢ ⎥ 3 θ̇ ⎢ ⎥ − 0 − − ⎢ ⎥ ⎣ 0 1 0 0 ⎦ ⎡ 0 ⎤ 2 2 ⎢ ⎥ ⎢ ⎥ δ ⎢ 0 ⎥ + 2 2 δ ⎢ ⎥ ⎢ 1 ⎥ δ 0 0 ⎢ ⎥ ⎣ 0 0 0 ⎦ ( ) ⎡ − cos ⎤ ̇ ⎢ ⎥ ̇ ⎢ + + + 0 ⎥ ̇ = = ̇ ⎢ ⎥ ̇ ⎢ ⎥ + + + 0 ⎢ ⎥ ⎣ 0 1 tan(θ) 0 ⎦ ⎡ − ⎤ 2 2 ⎢ ⎥ ⎢ ⎥ + − − ⎢ ⎥ + 2 2 2 2 ⎢ ⎥ ⎢ + − − ⎥ ⎢ 2 2 2 2 ⎥ ⎣ 0 0 ⎦ 2 The output equations are redundant, as the output vector is simply the state vector x. The longitudinal state vector consists of angle of attack α, pitch rate q, true airspeed perturbation VT, and pitch angle θ. The lateral state vector consists of sideslip velocity perturbation v, roll rate p, yaw rate r, and roll angle φ. The inputs are left and right aileron deflections (positive down) and , and throttle setting (from 0 to 1) δ. All state variables are perturbations from their equilibrium values; accordingly, the body-centred stability axes serve as the reference coordinate frame. Major assumptions in the state space model include neglecting propeller gyroscopic and unsteady aerodynamic effects. Compressibility effects due to Mach number and elevation were neglected, and the aircraft was assumed to be rigid. The numerical values of each parameter for the Skywalker X8 are listed in Table 1. Table 1: State Space Parameter Values. Parameter Symbol Value Units Notes/Sources True airspeed at steady level cruise 15 m/s Flight tests Dynamic pressure at steady level 1 Pa Assume sea level air density = 1.225 cruise 2 kg/m3, [9] Wing span b 2.1 m Measured Wing mean aerodynamic chord c 0.357 m Measured (MAC) Wing planform reference area S 0.75 m2 CATIA. For a BWB, this is taken as the entire aircraft’s projected area. Total aircraft mass m 3.5 kg Measured on scale; constant for a battery-powered aircraft Centre of gravity (CG) position aft h 0.2 none CATIA of MAC leading edge (LE), divided by c [10] h 0.75 none [10] Value of h for which is zero 0 2 Aircraft moment of inertia about 1.2 kg· m Assume the battery mass is the roll stability axis dominant 2 Aircraft moment of inertia about 0.17 kg· m Assume the battery mass is the pitch stability axis dominant 2 Aircraft moment of inertia about 0.9 kg· m Assume the battery mass is the yaw stability axis dominant 2 Aircraft product of inertia about the 0.9 kg· m Assume the battery mass is aircraft symmetry plane dominant 2 Nameless inertia term ′ − () kg· m [10] 2 Nameless inertia term ′ − () kg· m [10] -1 -2 Nameless inertia term ′ kg · m [10] − () Lift coefficient at equilibrium 0.26 none Aircraft weight cruise Drag coefficient at equilibrium 0.012 none Thrust from flight test cruise Change in lift coefficient with 4.0 rad-1 RANS (Reynolds-averaged Navier- respect to angle of attack Stokes) simulation using SST (shear stress transport) turbulence model in ANSYS CFX 3 Change in pitching moment -0.2 rad-1 RANS in ANSYS CFX coefficient with respect to angle of attack -1 Change in drag coefficient with 0 rad RANS in ANSYS CFX respect to angle of attack Change in lift coefficient with 0.7 rad-1 RANS in ANSYS CFX respect to elevon deflection (both elevons deflected down) Change in pitching moment -0.4 rad-1 RANS in ANSYS CFX coefficient with respect to elevon deflection Change in thrust with respect to 40 N Flight test and motor test; requires throttle setting further testing, but not used for any further calculations Gravitational acceleration g 9.806 m/s2 SI standard Equilibrium pitch angle 0 rad Negligible Change in sideforce coefficient -0.195 rad-1 Inviscid panel methods [7] with respect to sideslip angle Change in sideforce coefficient -0.117 s/rad Inviscid panel methods [7] with respect to roll rate Change in sideforce coefficient 0 s/rad Inviscid panel methods [7] with respect to yaw rate Change in rolling moment -0.0765 rad-1 Inviscid panel methods [7] coefficient with respect to sideslip angle Change in yawing moment 0.04 rad-1 Inviscid panel methods [7] coefficient with respect to sideslip angle Change in rolling moment -0.40 s/rad Inviscid panel methods [7] coefficient with respect to roll rate Change in yawing moment -0.025 s/rad Inviscid panel methods [7] coefficient with respect to roll rate Change in rolling moment 0.025 s/rad Inviscid panel methods [7] coefficient with respect to yaw rate Change in yawing moment -0.1252 s/rad Inviscid panel methods [7] coefficient with respect to yaw rate Negative change in sideforce 0 rad-1 Factor of -1 by convention [7, 10] coefficient with respect to aileron deflection (right elevon up, left elevon down) Change in rolling moment 0.3 rad-1 [7] coefficient with aileron deflection Change in yawing moment 0.0076 rad-1 [7] coefficient with aileron deflection Continue - Table 1 3.0 Uncontrolled Dynamics 3.1 Aircraft Modes The rigid aircraft modes were determined from the eigenvalues of the longitudinal and lateral state matrices (A), and are summarized in Table 2.
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