WOLFRAM SYSTEM MODELER
DefaultAircraftAircraft model using state-space representation |
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Diagram
Wolfram Language
In[1]:=
SystemModel["Aircraft.StateSpace.FixedWing.DefaultAircraft"]
Out[1]:=
Information
This model compiles a complete aircraft model to be used in the state space modeling environment from the components in the Blocks package. The structure of the complete aircraft model is defined here, and all other complete aircraft models in the FixedWing package extend this model, while having the parameters of the corresponding aircraft.
The parameters are used to derive the longitudinal and lateral stability and control derivatives in the LongitudinalDerivatives and LateralDerivatives blocks, respectively.
Based on the given reference total velocity (refVtot), reference altitude (refAlt) and reference flight path angle (refGamma) parameters in the General parameter tab, the TrimCalculator solves for the reference flight conditions for a steady trimmed flight, around which the linearization is defined. Perturbations from the reference flight conditions to the control actuators are given through the input ports.
The control actuator perturbations together with the reference flight conditions and stability and control derivatives are inputs to the LongitunidalMotion and LateralMotion blocks, which represent the decoupled state space models for aircraft longitudinal and lateral motions for solving the aircraft motion in the local body frame. Finally, the PositionAndOrientation block is used to resolve the aircraft motion in the world frame, which is the output through the position connector.
Parameters (94)
| x0y0 |
Value: {0, 0} Type: Position[2] (m) Description: Initial lateral position of the aircraft (x and y coordinates in world frame) |
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| refVtot |
Value: 100 Type: Velocity (m/s) Description: Total velocity for reference flight condition (Also used as initial velocity) |
| refAlt |
Value: 1000 Type: Height (m) Description: Altitude for reference flight condition (Also used as initial altitude) |
| refGamma |
Value: 0 Type: Angle (rad) Description: Flight path for reference flight condition (Becomes a variable if no propulsion) |
| CDW0 |
Value: Type: Real Description: Drag coefficient of wing-body at zero lift |
| CmW0 |
Value: Type: Real Description: Moment coefficient of wing-body at alpha = 0 |
| CLalphaWing3D |
Value: Type: Real (rad⁻¹) Description: Change in the lift coefficient of the wing-body due to alpha |
| mAC |
Value: Type: Mass (kg) Description: Aircraft mass |
| xCMdry |
Value: Type: Length (m) Description: Aircraft center of mass from wing leading edge at mean chord (positive x-axis towards nose) |
| IxxDry |
Value: Type: MomentOfInertia (kg⋅m²) Description: Aircraft moment of inertia about x-axis |
| IyyDry |
Value: Type: MomentOfInertia (kg⋅m²) Description: Aircraft moment of inertia about y-axis |
| IzzDry |
Value: Type: MomentOfInertia (kg⋅m²) Description: Aircraft moment of inertia about z-axis |
| ARwing |
Value: bWing ^ 2 / SrefWing Type: Real Description: Main wing aspect ratio |
| TRwing |
Value: cWingTip / cWingRoot Type: Real Description: Main wing taper ratio |
| etaWing |
Value: 1 / (Modelica.Constants.pi * ARwing * kdWing * CDW0 + 1 / (0.99 * sdWing)) Type: Real Description: Oswald efficiency factor for main wing |
| sdWing |
Value: 0.9998 + 0.0421 * (wFus / bWing) - 2.6286 * (wFus / bWing) ^ 2 + 2 * (wFus / bWing) ^ 3 Type: Real Description: Fuselage drag factor for main wing |
| Kw |
Value: 1 / (Modelica.Constants.pi * ARwing * etaWing) Type: Real Description: Induced drag factor for main wing |
| bWing |
Value: Type: Length (m) Description: Main wing span |
| cWingTip |
Value: Type: Length (m) Description: Main wing root chord (where wing intersects with fuselage) |
| cWingRoot |
Value: Type: Length (m) Description: Main wing root chord (where wing intersects with fuselage) |
| alphaw0 |
Value: Type: Angle (rad) Description: Zero-lift angle of attack of wing |
| gammaWing |
Value: Type: Angle (rad) Description: Main wing dihedral angle |
| SrefWing |
Value: Type: Area (m²) Description: Main wing reference area |
| xWingAC |
Value: Type: Length (m) Description: Main wing aerodynamic center from wing leading edge at mean chord (positive x-axis towards nose) |
| iWing |
Value: Type: Angle (rad) Description: Main wing incidence angle |
| cWingMean |
Value: Type: Length (m) Description: Main wing mean chord length |
| lambdaWing |
Value: Type: Angle (rad) Description: Main wing sweep angle at 1/4 chord |
| epsilon0 |
Value: Type: Angle (rad) Description: Zero-lift downwash angle |
| CDHT0 |
Value: Type: Real Description: Drag coefficient of horizontal tail at zero lift |
| vHT |
Value: SrefHT / SrefWing * (lHTcm / cWingMean) Type: Real Description: Horizontal tail volume coefficient |
| ARht |
Value: bHT ^ 2 / SrefHT Type: Real Description: Aspect ratio of horizontal tail |
| CLalphaHT3D |
Value: Type: Real (rad⁻¹) Description: Change in the lift coefficient of the horizontal tail due to alpha |
| tauElv |
Value: 1.129 * (Selv / SrefHT) ^ 0.4044 - 0.1772 Type: Real Description: Elevator effectiveness parameter |
| SrefHT |
Value: Type: Area (m²) Description: Horizontal tail reference area |
| lHTcm |
Value: Type: Length (m) Description: Horizontal tail arm length (from aircraft center of mass to 1/4 chord) |
| iHT |
Value: Type: Angle (rad) Description: Horizontal tail incidence angle |
| Selv |
Value: Type: Area (m²) Description: Elevator area |
| bHT |
Value: Type: Length (m) Description: Horizontal tail span |
| kdHT |
Value: -3.333 * 10 ^ (-4) * lambdaHT ^ 2 + 6.667 * 10 ^ (-5) * lambdaHT + 0.38 Type: Real Description: Empirical constant for Oswald efficiency factor for horizontal tail |
| etaHT |
Value: 1 / (Modelica.Constants.pi * ARht * kdHT * CDHT0 + 1 / (0.99 * sdHT)) Type: Real Description: Oswald efficiency factor for horizontal tail |
| sdHT |
Value: 0.9998 + 0.0421 * (dFusHT / bHT) - 2.6286 * (dFusHT / bHT) ^ 2 + 2 * (dFusHT / bHT) ^ 3 Type: Real Description: Fuselage drag factor for horizontal tail |
| lambdaHT |
Value: Type: Angle (rad) Description: Horizontal tail sweep angle at 1/4 chord |
| lVTcm |
Value: Type: Length (m) Description: Vertical tail arm length (from aircraft center of mass to vertical tail 1/4 chord) |
| zVTacCM |
Value: Type: Length (m) Description: z-coordinate w.r.t. aircraft center of mass of center of pressure of vertical tail |
| etaVT |
Value: Type: Real Description: Vertical tail efficiency factor |
| SrefVT |
Value: Type: Area (m²) Description: Vertical tail reference area |
| vVT |
Value: SrefVT / SrefWing * (lVTcm / bWing) Type: Real Description: Vertical tail volume coefficient |
| tauRdr |
Value: 1.129 * (Srdr / SrefVT) ^ 0.4044 - 0.1772 Type: Real Description: Rudder effectiveness parameter |
| Srdr |
Value: Type: Area (m²) Description: Rudder area |
| dFusHT |
Value: Type: Length (m) Description: Fuselage diameter at horizontal tail 1/4 chord |
| wFus |
Value: Type: Length (m) Description: Fuselage maximum width |
| nEng |
Value: Type: Integer Description: Number of engines |
| zTau |
Value: Type: Length (m) Description: z-coordinate w.r.t. aircraft center of mass of thrust line for side (#2-5) engines and single engine |
| zTauMid |
Value: Type: Length (m) Description: z-coordinate w.r.t. aircraft center of mass of thrust line for middle (#1) engine |
| zTauTotal |
Value: if nEng == 3 then (zTau * 2 + zTauMid) / 3 else zTau Type: Length (m) Description: z-coordinate of thrust line |
| Tstatic |
Value: Type: Force (N) Description: Static thrust of one engine at sea level |
| negThrust |
Value: Type: Real Description: Maximum negative thrust (0 to 1 of thrust available) |
| kappa |
Value: Type: Angle (rad) Description: Engine thrust line angle for side (#2-5) engines and single engine |
| deltaElvMax |
Value: Type: Angle (rad) Description: Maximum elevator deflection |
| deltaAilMax |
Value: Type: Angle (rad) Description: Maximum aileron deflection |
| deltaRdrMax |
Value: Type: Angle (rad) Description: Maximum rudder deflection |
| kCnDeltaAil |
Value: Type: Real Description: Empirical factor for the yaw moment derivative due to ailerons. Based on Figure 3.12 in Flight Stability and Automatic Control 2nd Edition |
| tauAil |
Value: 1.129 * (Sail / SrefWing) ^ 0.4044 - 0.1772 Type: Real Description: Aileron effectiveness parameter |
| Sail |
Value: cAil * (yAilTip - yAilRoot) * 2 Type: Area (m²) Description: Aileron area (of both wings) |
| cAil |
Value: Type: Length (m) Description: Aileron average chord |
| yAilRoot |
Value: Type: Length (m) Description: Aileron root y-coordinate w.r.t. fuselage centerline |
| yAilTip |
Value: Type: Length (m) Description: Aileron tip y-coordinate w.r.t. fuselage centerline |
| cAilWingRoot |
Value: Type: Length (m) Description: Local main wing chord at aileron root |
| cAilWingTip |
Value: Type: Length (m) Description: Local main wing chord at aileron tip |
| kdWing |
Value: -3.333 * 10 ^ (-4) * lambdaWing ^ 2 + 6.667 * 10 ^ (-5) * lambdaWing + 0.38 Type: Real Description: Empirical constant for Oswald efficiency factor for main wing |
| epsilonAlpha |
Value: 2 * CLalphaWing3D / (Modelica.Constants.pi * ARwing) Type: Real Description: Change in downwash due to alpha |
| sigmaBeta |
Value: Type: Real Description: Change in sidewash due to beta |
| CLhtDeltaElv |
Value: CLalphaHT3D * tauElv Type: Real (rad⁻¹) Description: C_L_HT_delta_e (Coefficient for change in the lift coefficient of the horizontal tail due to elevator deflection) |
| ClbetaGamma |
Value: Type: Real (rad⁻²) Description: Empirical factor for C_l_beta/gammaWing. -0.66/rad^2 is a decent universal approximation |
| CLdeltae |
Value: SrefHT / SrefWing * etaHT * CLhtDeltaElv Type: Real (rad⁻¹) Description: C_L_delta_e (Coefficient for change in the lift coefficient of entire aircraft due to elevator deflection) |
| CLalpha |
Value: Type: Real (rad⁻¹) Description: Change in the lift coefficient due to alpha |
| CLalphaVT3D |
Value: Type: Real (rad⁻¹) Description: Change in the lift coefficient of the vertical tail due to alpha |
| CDalpha |
Value: Type: Real (rad⁻¹) Description: Change in C_D due to alpha |
| CDM |
Value: Type: Real Description: Change in C_D due to Mach number |
| CMM |
Value: Type: Real Description: Change in C_M due to Mach number |
| Cmdeltae |
Value: -etaHT * vHT * CLhtDeltaElv Type: Real (rad⁻¹) Description: C_m_delta_e (Coefficient for change in pitch moment due to elevator deflection) |
| Cmq |
Value: Cmalphadot / epsilonAlpha Type: Real (rad⁻¹) Description: C_m_q (Coefficient for change in pitch moment due to pitch rate) |
| Cmalphadot |
Value: -2 * etaHT * CLalphaHT3D * vHT * (lHTcm / cWingMean) * epsilonAlpha Type: Real (rad⁻¹) Description: C_m_alphadot (Coefficient for change in pitch moment due to alphadot) |
| Cmalpha |
Value: Type: Real (rad⁻¹) Description: Change in C_M due to alpha |
| CyDeltaRdr |
Value: SrefVT / SrefWing * tauRdr * CLalphaVT3D Type: Real (rad⁻¹) Description: Y-force due to rudder deflection control derivative |
| ClDeltaAil |
Value: 2 * CLalpha * tauAil / (SrefWing * bWing) * (yAilTip ^ 2 / 2 - yAilRoot ^ 2 / 2) * (cAilWingRoot * 2 / 3 * (1 + cAilWingTip / cAilWingRoot + (cAilWingTip / cAilWingRoot) ^ 2) / (1 + cAilWingTip / cAilWingRoot)) Type: Real (rad⁻¹) Description: Roll moment due to aileron deflection control derivative |
| Cldeltar |
Value: SrefVT / SrefWing * abs(zVTacCM) / bWing * tauRdr * CLalphaVT3D Type: Real (rad⁻¹) Description: C_l_delta_r (Coefficient for change in roll moment due to rudder deflection) |
| Cndeltar |
Value: -vVT * etaVT * tauRdr * CLalphaVT3D Type: Real (rad⁻¹) Description: C_n_delta_r (Coefficient for change in yaw moment due to rudder deflection) |
| CyBeta |
Value: -etaVT * SrefVT / SrefWing * CLalphaVT3D * (1 + sigmaBeta) Type: Real (rad⁻¹) Description: Y-force due to sideslip angle stability derivative |
| Cnr |
Value: -2 * etaVT * vVT * lVTcm / bWing * CLalphaVT3D Type: Real Description: C_n_r (Coefficient for change in yaw moment due to yaw rate) |
| Cyr |
Value: -2 * lVTcm / bWing * CyBeta Type: Real (rad⁻¹) Description: C_y_r (Coefficient for change in Y-force due to yaw rate) |
| ClRoll |
Value: -CLalpha / 12 * (1 + 3 * TRwing) / (1 + TRwing) Type: Real (rad⁻¹) Description: C_l_p (Coefficient for change in roll moment due to roll rate) |
| Cnbeta |
Value: etaVT * vVT * CLalphaVT3D * (1 + sigmaBeta) Type: Real (rad⁻¹) Description: C_n_beta (Coefficient for change in yaw moment due to sideslip angle) |
| Clbeta |
Value: ClbetaGamma * gammaWing Type: Real (rad⁻¹) Description: C_l_beta (Coefficient for change in roll moment due to sideslip angle) |
Connectors (7)
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reference |
Type: RefFlightSignalBus Description: Bus for the real signals of the reference flight conditions |
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motion |
Type: MotionSignalBus Description: Bus for the real signals of the linear and angular velocity perturbations resolved in the body frame |
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DdeltaaIn |
Type: RealInput Description: 'input Real' as connector |
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DdeltaTIn |
Type: RealInput Description: 'input Real' as connector |
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DdeltaeIn |
Type: RealInput Description: 'input Real' as connector |
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DdeltarIn |
Type: RealInput Description: 'input Real' as connector |
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position |
Type: PositionSignalBus Description: Bus for the real signals of position, orientation and velocities resolved in the world frame |
Components (21)
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trimCalculator |
Type: TrimCalculator Description: Calculates trimmed conditions for given flight conditions |
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longitudinalMotion |
Type: LongitudinalMotion Description: State space representation of longitudinal motion |
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lateralMotion |
Type: LateralMotion Description: State space representation of lateral motion |
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lateralDerivatives |
Type: LateralDerivatives Description: Calculates lateral stability and control derivatives |
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positionAndOrientation |
Type: PositionAndOrientation Description: Calculates the position, orientation and velocities of the aircraft in the world frame |
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longitudinalDerivatives |
Type: LongitudinalDerivatives Description: Calculates longitudinal stability and control derivatives |
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refVtotExpr |
Type: RealExpression Description: Total velocity of reference flight conditions |
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refAltExpr |
Type: RealExpression Description: Altitude of reference flight conditions |
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refGammaExpr |
Type: RealExpression Description: Flight path of reference flight conditions |
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throttleDynamics |
Type: CriticalDamping Description: Damper for simplified model of throttle dynamics |
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elevatorDynamics |
Type: CriticalDamping Description: Damper for simplified model of elevator dynamics |
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aileronDynamics |
Type: CriticalDamping Description: Damper for simplified model of aileron dynamics |
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rudderDynamics |
Type: CriticalDamping Description: Damper for simplified model of rudder dynamics |
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DeltarLimiter |
Type: Limiter Description: Limits rudder deflection to its assigned limits |
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DeltaaLimiter |
Type: Limiter Description: Limits aileron deflection to its assigned limits |
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deltaElvLimiter |
Type: VariableLimiter Description: Limit the range of a signal with variable limits |
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maxDeltaElv |
Type: RealExpression Description: Upper limit for elevator deflection |
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minDeltaElv |
Type: RealExpression Description: Lower limit for elevator deflection |
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maxDeltaThrot |
Type: RealExpression Description: Upper limit for throttle position |
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minDeltaThrot |
Type: RealExpression Description: Lower limit for throttle position |
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deltaThrotLimiter |
Type: VariableLimiter Description: Limit the range of a signal with variable limits |
Extended by (4)
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Aircraft.StateSpace.FixedWing Model of a general aviation aircraft using state-space representation |
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Aircraft.StateSpace.FixedWing Model of Schweizer SGS 1-36 using state-space representation |
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Aircraft.StateSpace.FixedWing Model of Douglas DC-8 using state-space representation |
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Aircraft.StateSpace.FixedWing Model of Boeing 737-800 using state-space representation |