Whitespace

1 files changed, 89 insertions, 89 deletions

diff --git a/uav_model.m b/uav_model.m
index 7b2bf9d..2ae4d96 100644
--- a/uav_model.m
+++ b/uav_model.m
@@ -31,25 +31,25 @@ alpha = [alpha_1; alpha_2; alpha_3; alpha_4];
 % positive / negative with respect to the roll / pitch axis to which they
 % are attached to. Reference table:
 %
-%   angle     attached axis   lift force direction
-%                             when angle is positive
-%   -------   -------------   ----------------------
-%   alpha_1   pos. x axis      y direction
-%   alpha_2   pos. y axis     -x direction
-%   alpha_3   neg. x axis      y direction
-%   alpha_4   neg. y axis     -x direction
+%  angle   attached axis   lift force direction
+%                           when angle is positive
+%  -------   -------------   ----------------------
+%  alpha_1   pos. x axis    y direction
+%  alpha_2   pos. y axis   -x direction
+%  alpha_3   neg. x axis    y direction
+%  alpha_4   neg. y axis   -x direction
 
 % Rotation matrix to change between frames of reference:
 % multiplying by R moves from the inertial frame to the body frame
 % to go from body frame to inertial frame use R transpose (R is SO(3))
 R = [
-	cos(theta) * cos(psi), cos(theta) * sin(psi), -sin(theta);
-	(sin(phi) * sin(theta) * cos(psi) - cos(phi) * sin(psi)), ...
-		(sin(phi) * sin(theta) * sin(psi) + cos(phi) * cos(psi)), ...
-		sin(phi) * cos(theta);
-	(cos(phi) * sin(theta) * cos(psi) + sin(phi) * sin(psi)), ...
-		(cos(phi) * sin(theta) * sin(psi) - sin(phi) * cos(psi)), ...
-		cos(phi) * cos(theta);
+  cos(theta) * cos(psi), cos(theta) * sin(psi), -sin(theta);
+  (sin(phi) * sin(theta) * cos(psi) - cos(phi) * sin(psi)), ...
+    (sin(phi) * sin(theta) * sin(psi) + cos(phi) * cos(psi)), ...
+    sin(phi) * cos(theta);
+  (cos(phi) * sin(theta) * cos(psi) + sin(phi) * sin(psi)), ...
+    (cos(phi) * sin(theta) * sin(psi) - sin(phi) * cos(psi)), ...
+    cos(phi) * cos(theta);
 ];
 
 % Matrix to relate Euler angles to angular velocity in the body frame
@@ -79,7 +79,7 @@ nu = omega / pi * sqrt(k_T  / (2 * a * rho));
 
 % Aerodynamic force caused by flaps in body frame
 F_flap = @(alpha, uvec_n) rho * S * nu^2 / 2 * (...
-	(c_d * alpha^2 + c_0) * uvec_z + c_l * alpha * uvec_n);
+  (c_d * alpha^2 + c_0) * uvec_z + c_l * alpha * uvec_n);
 
 F_1 = F_flap(alpha_1, uvec_y);
 F_2 = F_flap(alpha_2, uvec_x);
@@ -94,12 +94,12 @@ tau_4 = cross((d * uvec_z - a/3 * uvec_y), F_4);
 
 % Total force acting on the UAV in the body frame
 F = R * (m * g * uvec_k) ... % gravity
-	- k_T * omega^2 * uvec_z ... % thrust
-	+ F_1 + F_2 + F_3 + F_4; % flaps	
+  - k_T * omega^2 * uvec_z ... % thrust
+  + F_1 + F_2 + F_3 + F_4; % flaps  
 
 % Total torque acting on the UAV in the body frame
 tau = J_r * omega * R * cross(uvec_k, Omega) + ... % gyroscopic procession
-	tau_1 + tau_2 + tau_3 + tau_4; % flaps
+  tau_1 + tau_2 + tau_3 + tau_4; % flaps
 
 % State space form with state variable xi and input u
 %
@@ -115,10 +115,10 @@ u = [alpha; omega];
 
 % Right hand side of dynamics dxi = f(xi, u)
 f = [
-	Pdot;
-	R' * F / m; % translational dynamics
-	U * Omega; 
-    inv(J) * (tau - cross(Omega, J * Omega)); % rotational dynamics
+  Pdot;
+  R' * F / m; % translational dynamics
+  U * Omega; 
+  inv(J) * (tau - cross(Omega, J * Omega)); % rotational dynamics
 ];
 
 % ------------------------------------------------------------------------
@@ -126,10 +126,10 @@ f = [
 
 % Equilibrium point
 xi_eq = [
-	params.linearization.Position;
-	params.linearization.Velocity;
-	params.linearization.Angles;
-	params.linearization.AngularVelocities;
+  params.linearization.Position;
+  params.linearization.Velocity;
+  params.linearization.Angles;
+  params.linearization.AngularVelocities;
 ];
 u_eq = params.linearization.Inputs;
 
@@ -139,31 +139,31 @@ B = subs(jacobian(f, u), [xi; u], [xi_eq; u_eq]);
 
 % Insert values of parameters
 phy = struct(...
-	'g', params.physics.Gravity, ...
-	'rho', params.physics.AirDensity ...
+  'g', params.physics.Gravity, ...
+  'rho', params.physics.AirDensity ...
 );
 A = subs(A, phy);
 B = subs(B, phy);
 
 mech = struct(...
-	'm', params.mechanical.Mass, ...
-	'a', params.mechanical.DuctRadius, ...
-	'b', params.mechanical.DuctHeight, ...
-	'd', params.mechanical.FlapZDistance, ...
-	'J_1', params.mechanical.InertiaTensor(1, 1), ...
-	'J_2', params.mechanical.InertiaTensor(2, 2), ...
-	'J_3', params.mechanical.InertiaTensor(3, 3), ...
-	'J_r', params.mechanical.GyroscopicInertiaZ ...
+  'm', params.mechanical.Mass, ...
+  'a', params.mechanical.DuctRadius, ...
+  'b', params.mechanical.DuctHeight, ...
+  'd', params.mechanical.FlapZDistance, ...
+  'J_1', params.mechanical.InertiaTensor(1, 1), ...
+  'J_2', params.mechanical.InertiaTensor(2, 2), ...
+  'J_3', params.mechanical.InertiaTensor(3, 3), ...
+  'J_r', params.mechanical.GyroscopicInertiaZ ...
 );
 A = subs(A, mech);
 B = subs(B, mech);
 
 aero = struct(...
-	'k_T', params.aerodynamics.ThrustOmegaProp, ...
-	'S',   params.aerodynamics.FlapArea, ...
-	'c_d', params.aerodynamics.DragCoefficients(1), ...
-	'c_0', params.aerodynamics.DragCoefficients(2), ...
-	'c_l', params.aerodynamics.LiftCoefficient ...
+  'k_T', params.aerodynamics.ThrustOmegaProp, ...
+  'S',   params.aerodynamics.FlapArea, ...
+  'c_d', params.aerodynamics.DragCoefficients(1), ...
+  'c_0', params.aerodynamics.DragCoefficients(2), ...
+  'c_l', params.aerodynamics.LiftCoefficient ...
 );
 A = subs(A, aero);
 B = subs(B, aero);
@@ -196,51 +196,51 @@ eigvals = eig(A);
 % Check system controllability / stabilizability
 Wc = ctrb(sys);
 if rank(Wc) < nx
-	fprintf('Linearized system has %d uncontrollable states!\n', ...
-		(nx - rank(Wc)));
-		
-	% Is the system at least stabilizable?
-	unstabilizable = 0;
-	for i = 1:nx
-		if real(eigvals(i)) >= 0
-			% PBH test
-			W = [(A - eigvals(i) * eye(size(A))), B];
-			if rank(W) < nx
-				% fprintf('  State %d is not stabilizable\n', i);
-				unstabilizable = unstabilizable + 1;
-			end
-		end
-	end
-	if unstabilizable > 0
-		fprintf('Linearized system has %d unstabilizable modes!\n', ...
-			unstabilizable);
-	else
-		fprintf('However, it is stabilizable.\n');
-	end
+  fprintf('Linearized system has %d uncontrollable states!\n', ...
+    (nx - rank(Wc)));
+    
+  % Is the system at least stabilizable?
+  unstabilizable = 0;
+  for i = 1:nx
+    if real(eigvals(i)) >= 0
+      % PBH test
+      W = [(A - eigvals(i) * eye(size(A))), B];
+      if rank(W) < nx
+        % fprintf('  State %d is not stabilizable\n', i);
+        unstabilizable = unstabilizable + 1;
+      end
+    end
+  end
+  if unstabilizable > 0
+    fprintf('Linearized system has %d unstabilizable modes!\n', ...
+      unstabilizable);
+  else
+    fprintf('However, it is stabilizable.\n');
+  end
 end
 
 % Check  system observability / detectability
 Wo = obsv(sys);
 if rank(Wo) < nx
-	fprintf('Linearized system has %d unobservable state!\n', ...
-		(nx - rank(Wo)));
-	% is the system at least detectable?
-	undetectable = 0
-	for i = 1:nx
-		if real(eigvals(i)) >= 0
-			% PBH test
-			W = [C; (A - eigvals(i) * eye(size(A)))];
-			if rank(W) < nx
-				undetectable = undetectable + 1;
-			end
-		end
-	end
-	if undetectable > 0
-		fprintf('Linearized system has %d undetectable modes!\n', ...
-			undetectable);
-	else
-		fprintf('However, it is detectable.')
-	end
+  fprintf('Linearized system has %d unobservable state!\n', ...
+    (nx - rank(Wo)));
+  % is the system at least detectable?
+  undetectable = 0
+  for i = 1:nx
+    if real(eigvals(i)) >= 0
+      % PBH test
+      W = [C; (A - eigvals(i) * eye(size(A)))];
+      if rank(W) < nx
+        undetectable = undetectable + 1;
+      end
+    end
+  end
+  if undetectable > 0
+    fprintf('Linearized system has %d undetectable modes!\n', ...
+      undetectable);
+  else
+    fprintf('However, it is detectable.')
+  end
 end
 
 % ------------------------------------------------------------------------
@@ -250,21 +250,21 @@ model = struct();
 
 % Function to compute the rotation matrix
 model.FrameRot = @(pitch, roll, yaw) ...
-	subs(R, [phi, theta, psi], [pitch, roll, yaw]);
+  subs(R, [phi, theta, psi], [pitch, roll, yaw]);
 
 % Equations of non-linear model (algebraic)
 model.nonlinear = struct(...
-	'State', xi, ...
-	'Inputs', u, ...
-	'Dynamics', f ...
+  'State', xi, ...
+  'Inputs', u, ...
+  'Dynamics', f ...
 );
 
 % Linearized dynamics (numerical)
 model.linear = struct(...
-	'Nx', nx, 'Nu', nu, 'Ny', ny, ... % number of states, inputs, and outputs
-	'State', xi, 'Inputs', u, ... % state and input variables
-	'StateEq', xi_eq, 'InputEq', u_eq, ... % where the system was linearized
-	'StateSpace', sys ... % state space object
+  'Nx', nx, 'Nu', nu, 'Ny', ny, ... % number of states, inputs, and outputs
+  'State', xi, 'Inputs', u, ... % state and input variables
+  'StateEq', xi_eq, 'InputEq', u_eq, ... % where the system was linearized
+  'StateSpace', sys ... % state space object
 );
 
 end