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package Flight_Dynamics
extends Modelica.Icons.Package;
class Components
block ForceMoment_Gen
import Modelica.Math.Matrices.*;
import Modelica.SIunits.*;
import Modelica.Blocks.Interfaces.*;
import Modelica.Math.Vectors.*;
parameter Real rho = 1.225;
parameter Real g = 9.81;
parameter Real m = 1043.26;
//1.56 for zagi
parameter Real S_ref = 16.1651;
//reference area
parameter Real C_bar = 1.493;
//average chord
parameter Real b = 10.911;
//span
parameter Real CD0 = 0.036;
//= 0.01631;for Zagi
parameter Real K_drag = 0.0830304;
//for cessna
parameter Real CD_beta = 0.17;
//for cessna
parameter Real CD_alpha = 0.2108;
parameter Real CD_q = 0;
parameter Real CD_delta_e = 0.3045;
//side force
parameter Real Cy_beta = -0.31;
//for cessna
parameter Real Cy_p = -0.037;
//for cessna
parameter Real Cy_r = 0.21;
//for cessna
parameter Real Cy_delta_r = 0.187;
//for cessna
parameter Real Cy_delta_a = 0;
//for cessna
// lift
parameter Real CL0 = 0.25;
//for cessna
parameter Real CL_alpha = 4.47;
//for cessna
parameter Real CL_q = 3.9;
//for cessna
parameter Real CL_delta_e = 0.3476;
//for cessna
// rolling moment
parameter Real Cl_beta = -0.089;
//for cessna
parameter Real Cl_p = -0.47;
//for cessna
parameter Real Cl_r = 0.096;
//for cessna
parameter Real Cl_delta_a = -0.09;
//for cessna
parameter Real Cl_delta_r = 0.0147;
//for cessna
// pitching moment
parameter Real Cm0 = -0.02;
//for cessna
parameter Real Cm_alpha = -1.8;
//for cessna
parameter Real Cm_q = -12.4;
//for cessna
parameter Real Cm_delta_e = -1.28;
//for cessna
// yawing moment
parameter Real Cn_beta = 0.065;
//for cessna
parameter Real Cn_p = -0.03;
//for cessna
parameter Real Cn_r = -0.99;
//for cessna
parameter Real Cn_delta_a = -0.0053;
//for cessna
parameter Real Cn_delta_r = -0.0657;
//for cessna
Real CL;
Real CD;
Real CY;
Real Cl;
Real Cm;
Real Cn;
Real CX;
Real CZ;
RealInput thrust annotation(
Placement(visible = true, transformation(origin = {-110, 0}, extent = {{-20, -20}, {20, 20}}, rotation = 0), iconTransformation(origin = {-110, 0}, extent = {{-20, -20}, {20, 20}}, rotation = 0)));
//Thrust force
RealInput[3] delta annotation(
Placement(visible = true, transformation(origin = {-110, -50}, extent = {{-20, -20}, {20, 20}}, rotation = 0), iconTransformation(origin = {-110, -50}, extent = {{-20, -20}, {20, 20}}, rotation = 0)));
RealInput[3] VAB annotation(
Placement(visible = true, transformation(origin = {-33, 110}, extent = {{-20, -20}, {20, 20}}, rotation = -90), iconTransformation(origin = {-33, 110}, extent = {{-20, -20}, {20, 20}}, rotation = -90)));
//V, alpha, beta
RealInput[3] omega annotation(
Placement(visible = true, transformation(origin = {33, 110}, extent = {{-20, -20}, {20, 20}}, rotation = -90), iconTransformation(origin = {33, 110}, extent = {{-20, -20}, {20, 20}}, rotation = -90)));
//Angular velocities
Real V = VAB[1];
Real alpha = VAB[2];
Real beta = VAB[3];
Real p = omega[1];
Real q = omega[2];
Real r = omega[3];
Real deltaE = delta[1];
Real deltaR = delta[2];
Real deltaA = delta[3];
Real qbar = 0.5 * rho * V ^ 2;
RealOutput Force[3] annotation(
Placement(visible = true, transformation(origin = {110, 33}, extent = {{-20, -20}, {20, 20}}, rotation = 0), iconTransformation(origin = {110, 33}, extent = {{-20, -20}, {20, 20}}, rotation = 0)));
//Thrust force
RealOutput Moment[3] annotation(
Placement(visible = true, transformation(origin = {110, -33}, extent = {{-20, -20}, {20, 20}}, rotation = 0), iconTransformation(origin = {110, -33}, extent = {{-20, -20}, {20, 20}}, rotation = 0)));
//Thrust force
equation
CL = CL0 + CL_alpha * alpha + CL_q * q * C_bar / (2 * V) + CL_delta_e * deltaE;
//CD = CD0+CD_alpha*alpha+((CD_q*q*C_bar)/(2*V))+CD_delta_e*abs(deltaE) ;
CD = CD0 + K_drag * CL ^ 2;
CY = Cy_beta * beta + Cy_p * (p * b) / (2 * V) + Cy_r * (r * b) / (2 * V) + Cy_delta_a * deltaA + Cy_delta_r * deltaR;
//Sideslip coeff
Cl = Cl_beta * beta + Cl_p * (p * b) / (2 * V) + Cl_r * (r * b) / (2 * V) + Cl_delta_a * deltaA + Cl_delta_r * deltaR;
//Rolling coeff
Cm = Cm0 + Cm_alpha * alpha + Cm_q * q * C_bar / (2 * V) + Cm_delta_e * deltaE;
//pitching coeff
Cn = Cn_beta * beta + Cn_p * (p * b) / (2 * V) + Cn_r * (r * b) / (2 * V) + Cn_delta_a * deltaA + Cn_delta_r * deltaR;
//Yawing coeff
CX = (-CD * cos(alpha)) + CL * sin(alpha);
CZ = (-CD * sin(alpha)) - CL * cos(alpha);
Force[1] = thrust * cos(alpha) * cos(beta) - 0.5 * rho * V ^ 2 * S_ref * (CD * cos(beta) - CY * sin(beta));
Force[2] = (-thrust * cos(alpha) * sin(beta)) + 0.5 * rho * V ^ 2 * S_ref * (CY * cos(beta) + CD * sin(beta));
Force[3] = 0.5 * rho * V ^ 2 * S_ref * CL + thrust * sin(alpha);
Moment[2] = Cm * qbar * S_ref * C_bar;
Moment[1] = Cl * qbar * S_ref * b;
Moment[3] = Cn * qbar * S_ref * b;
end ForceMoment_Gen;
block Flight6DOF
import Modelica.Math.Matrices.*;
import SI = Modelica.SIunits;
import Modelica.Blocks.Interfaces.*;
parameter Real g = 9.81;
parameter Real m = 1043.26;
//1.56 for zagi
parameter Real[3, 3] J = {{1285.31, 0.0, 0.0}, {0.0, 1824.93, 0.0}, {0.0, 0.0, 2666.893}};
//12 states
RealOutput[3] omega(start = {0.0, 0.0, 0}) annotation(
Placement(visible = true, transformation(origin = {110, -33}, extent = {{-20, -20}, {20, 20}}, rotation = 0), iconTransformation(origin = {110, -33}, extent = {{-20, -20}, {20, 20}}, rotation = 0)));
//omega
Real OMEGA[3, 3] = skew(omega);
//Skew symmetric matrix form of the angular velocity term
Real V(start = 39.8858);
Real alpha(start = 0.1);
Real beta(start = 0);
RealOutput[3] VAB annotation(
Placement(visible = true, transformation(origin = {110, 33}, extent = {{-20, -20}, {20, 20}}, rotation = 0), iconTransformation(origin = {110, 33}, extent = {{-20, -20}, {20, 20}}, rotation = 0)));
//V, alpha, beta
Real x(start = 0);
Real y(start = 0);
Real z(start = 100);
Real mu(start = 0);
Real gamma(start = 0);
Real chi(start = 0);
RealInput Force[3] annotation(
Placement(visible = true, transformation(origin = {-110, 33}, extent = {{-20, -20}, {20, 20}}, rotation = 0), iconTransformation(origin = {-110, 33}, extent = {{-20, -20}, {20, 20}}, rotation = 0)));
//Thrust force
RealInput Moment[3] annotation(
Placement(visible = true, transformation(origin = {-110, -33}, extent = {{-20, -20}, {20, 20}}, rotation = 0), iconTransformation(origin = {-110, -33}, extent = {{-20, -20}, {20, 20}}, rotation = 0)));
//Thrust force
Real Vdot;
Real alphadot;
Real betadot;
Real[3] omegadot;
Real mudot;
Real gammadot;
Real chidot;
Real xdot;
Real ydot;
Real zdot;
equation
Vdot = der(V);
alphadot = der(alpha);
betadot = der(beta);
omegadot = der(omega);
xdot = der(x);
ydot = der(y);
zdot = der(z);
mudot = der(mu);
gammadot = der(gamma);
chidot = der(chi);
Vdot = 1 / m * (Force[1] - m * g * sin(gamma));
alphadot = omega[2] - 1 / cos(beta) * ((omega[1] * cos(alpha) + omega[3] * sin(alpha)) * sin(beta) - g / V * cos(gamma) * cos(mu) + Force[3] / (m * V));
betadot = omega[1] * sin(alpha) - omega[3] * cos(alpha) + 1 / (m * V) * (Force[2] + m * g * cos(gamma) * sin(mu));
omegadot = inv(J) * (Moment - OMEGA * J * omega);
xdot = V * cos(gamma) * cos(chi);
ydot = V * cos(gamma) * sin(chi);
zdot = -V * sin(gamma);
mudot = omega[1] + tan(gamma) * sin(mu) * omega[2] + tan(gamma) * cos(mu) * omega[3];
gammadot = cos(mu) * omega[2] - sin(mu) * omega[3];
chidot = 1 / cos(gamma) * sin(mu) * omega[2] + 1 / cos(gamma) * cos(mu) * omega[3];
VAB = {V, alpha, beta};
annotation(
uses(Modelica(version = "3.2.2")));
end Flight6DOF;
end Components;
class Test_Cases
model CessnaTrim
// The initial values for delta[2] (elevator), alpha, thrust, and V are obtained by executing Trim_Conditions_Cessna.mo.
parameter Real m = 1043.26;
//1.56 for zagi
parameter Real s = 16.1651;
//reference area
parameter Real cbar = 1.493;
//average chord
parameter Real b = 10.911;
//span
parameter Real W[3] = m * {0, 0, 9.81};
//gravitational force
//parameter Real b= 1.4224, cbar = 0.3302,s = 0.2589;
parameter Real CD0 = 0.036;
//= 0.01631;for Zagi
parameter Real K_drag = 0.0830304;
//for cessna
parameter Real CD_beta = 0.17;
//for cessna
parameter Real CD_alpha = 0.2108;
parameter Real CD_q = 0;
parameter Real CD_delta_e = 0.3045;
//side force
parameter Real Cy_beta = -0.31;
//for cessna
parameter Real Cy_p = -0.037;
//for cessna
parameter Real Cy_r = 0.21;
//for cessna
parameter Real Cy_delta_r = 0.187;
//for cessna
parameter Real Cy_delta_a = 0;
//for cessna
// lift
parameter Real CL0 = 0.25;
//for cessna
parameter Real CL_alpha = 4.47;
//for cessna
parameter Real CL_q = 3.9;
//for cessna
parameter Real CL_delta_e = 0.3476;
//for cessna
// rolling moment
parameter Real Cl_beta = -0.089;
//for cessna
parameter Real Cl_p = -0.47;
//for cessna
parameter Real Cl_r = 0.096;
//for cessna
parameter Real Cl_delta_a = -0.09;
//for cessna
parameter Real Cl_delta_r = 0.0147;
//for cessna
// pitching moment
parameter Real Cm0 = -0.02;
//for cessna
parameter Real Cm_alpha = -1.8;
//for cessna
parameter Real Cm_q = -12.4;
//for cessna
parameter Real Cm_delta_e = -1.28;
//for cessna
// yawing moment
parameter Real Cn_beta = 0.065;
//for cessna
parameter Real Cn_p = -0.03;
//for cessna
parameter Real Cn_r = -0.99;
//for cessna
parameter Real Cn_delta_a = -0.0053;
//for cessna
parameter Real Cn_delta_r = -0.0657;
//for cessna
//Initial conditions. (delta[2], thrust[1] and the others are straightforward)
parameter Real del[3] = {-0.15625, 0, 0};
parameter Real thrust = 1112.82;
Flight_Dynamics.Components.ForceMoment_Gen forceMoment_Gen1 annotation(
Placement(visible = true, transformation(origin = {-18, 4}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
Flight_Dynamics.Components.Flight6DOF flight6DOF1 annotation(
Placement(visible = true, transformation(origin = {24, 4}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
equation
connect(forceMoment_Gen1.omega, flight6DOF1.omega) annotation(
Line(points = {{-14, 16}, {-14, 16}, {-14, 40}, {62, 40}, {62, 0}, {36, 0}, {36, 0}}, color = {0, 0, 127}, thickness = 0.5));
connect(flight6DOF1.VAB, forceMoment_Gen1.VAB) annotation(
Line(points = {{36, 8}, {42, 8}, {42, 32}, {-20, 32}, {-20, 16}, {-22, 16}}, color = {0, 0, 127}, thickness = 0.5));
connect(forceMoment_Gen1.Moment, flight6DOF1.Moment) annotation(
Line(points = {{-6, 0}, {12, 0}, {12, 0}, {14, 0}}, color = {0, 0, 127}, thickness = 0.5));
connect(forceMoment_Gen1.Force, flight6DOF1.Force) annotation(
Line(points = {{-6, 8}, {12, 8}, {12, 8}, {14, 8}}, color = {0, 0, 127}, thickness = 0.5));
forceMoment_Gen1.thrust = thrust;
forceMoment_Gen1.delta = del;
annotation(
experiment(StartTime = 0, StopTime = 100, Tolerance = 1e-3, Interval = 0.001),
uses(Modelica(version = "3.2.2")));
end CessnaTrim;
model CessnaPerturbed
//The initial values for delta[2] (elevator), alpha, thrust, and V are obtained by executing Trim_Conditions_Cessna.mo.
parameter Real m = 1043.26;
//1.56 for zagi
parameter Real s = 16.1651;
//reference area
parameter Real cbar = 1.493;
//average chord
parameter Real b = 10.911;
//span
parameter Real W[3] = m * {0, 0, 9.81};
//gravitational force
//parameter Real b= 1.4224, cbar = 0.3302,s = 0.2589;
parameter Real CD0 = 0.036;
//= 0.01631;for Zagi
parameter Real K_drag = 0.0830304;
//for cessna
parameter Real CD_beta = 0.17;
//for cessna
parameter Real CD_alpha = 0.2108;
parameter Real CD_q = 0;
parameter Real CD_delta_e = 0.3045;
//side force
parameter Real Cy_beta = -0.31;
//for cessna
parameter Real Cy_p = -0.037;
//for cessna
parameter Real Cy_r = 0.21;
//for cessna
parameter Real Cy_delta_r = 0.187;
//for cessna
parameter Real Cy_delta_a = 0;
//for cessna
// lift
parameter Real CL0 = 0.25;
//for cessna
parameter Real CL_alpha = 4.47;
//for cessna
parameter Real CL_q = 3.9;
//for cessna
parameter Real CL_delta_e = 0.3476;
//for cessna
// rolling moment
parameter Real Cl_beta = -0.089;
//for cessna
parameter Real Cl_p = -0.47;
//for cessna
parameter Real Cl_r = 0.096;
//for cessna
parameter Real Cl_delta_a = -0.09;
//for cessna
parameter Real Cl_delta_r = 0.0147;
//for cessna
// pitching moment
parameter Real Cm0 = -0.02;
//for cessna
parameter Real Cm_alpha = -1.8;
//for cessna
parameter Real Cm_q = -12.4;
//for cessna
parameter Real Cm_delta_e = -1.28;
//for cessna
// yawing moment
parameter Real Cn_beta = 0.065;
//for cessna
parameter Real Cn_p = -0.03;
//for cessna
parameter Real Cn_r = -0.99;
//for cessna
parameter Real Cn_delta_a = -0.0053;
//for cessna
parameter Real Cn_delta_r = -0.0657;
//for cessna
//Initial conditions. (delta[2], thrust[1] and the others are straightforward)
parameter Real del[3] = {-0.15625, 0, 0};
parameter Real thrust = 1112.82;
Flight_Dynamics.Components.ForceMoment_Gen forceMoment_Gen1 annotation(
Placement(visible = true, transformation(origin = {-23, 7}, extent = {{-23, -23}, {23, 23}}, rotation = 0)));
Flight_Dynamics.Components.Flight6DOF flight6DOF1 annotation(
Placement(visible = true, transformation(origin = {52, 6}, extent = {{-26, -26}, {26, 26}}, rotation = 0)));
Modelica.Blocks.Sources.RealExpression delta annotation(
Placement(visible = true, transformation(origin = {-142, -5}, extent = {{-26, -47}, {26, 47}}, rotation = 0)));
equation
connect(delta.y, forceMoment_Gen1.delta) annotation(
Line(points = {{-113, -5}, {-50, -5}, {-50, -4}, {-48, -4}}, color = {0, 0, 127}, thickness = 0.5));
connect(forceMoment_Gen1.omega, flight6DOF1.omega) annotation(
Line(points = {{-16, 32}, {-16, 32}, {-16, 78}, {98, 78}, {98, -2}, {80, -2}, {80, -2}}, color = {0, 0, 127}, thickness = 0.5));
connect(forceMoment_Gen1.VAB, flight6DOF1.VAB) annotation(
Line(points = {{-30, 32}, {-28, 32}, {-28, 64}, {84, 64}, {84, 14}, {80, 14}}, color = {0, 0, 127}, thickness = 0.5));
connect(forceMoment_Gen1.Force, flight6DOF1.Force) annotation(
Line(points = {{2, 14}, {22, 14}, {22, 14}, {24, 14}}, color = {0, 0, 127}, thickness = 0.5));
connect(forceMoment_Gen1.Moment, flight6DOF1.Moment) annotation(
Line(points = {{2, 0}, {26, 0}, {26, -2}, {24, -2}}, color = {0, 0, 127}, thickness = 0.5));
forceMoment_Gen1.thrust = thrust;
annotation(
experiment(StartTime = 0, StopTime = 300, Tolerance = 1e-3, Interval = 0.001),
uses(Modelica(version = "3.2.2")));
end CessnaPerturbed;
end Test_Cases;
annotation(
uses(Modelica(version = "3.2.2")));
end Flight_Dynamics;
|
