Month: August 2024
جلب الحبيب بالمسك والعنبر – 578385770 : 966 +💞 شيخ روحاني مضمون للزواج
جلب الحبيب بالمسك والعنبر – 578385770 : 966 + شيخ روحاني مضمون للزواج
جلب الحبيب بالمسك والعنبر – 578385770 : 966 + شيخ روحاني مضمون للزواج Read More
رقم هاتف شيخ روحاني – 578385770 : 966 + رقم هاتف معالج روحاني
رقم هاتف شيخ روحاني – 578385770 : 966 + رقم هاتف معالج روحاني
رقم هاتف شيخ روحاني – 578385770 : 966 + رقم هاتف معالج روحاني Read More
جلب الحبيب بالتوكيدات – 578385770 : 966 + رقم هاتف شيخ روحاني
جلب الحبيب بالتوكيدات – 578385770 : 966 + رقم هاتف شيخ روحاني
جلب الحبيب بالتوكيدات – 578385770 : 966 + رقم هاتف شيخ روحاني Read More
جلب الحبيب بعلم الأرقام 34028443 : 973 +❣️ رقم هاتف معالج روحاني
جلب الحبيب بعلم الأرقام 34028443 : 973 +:heavy_heart_exclamation: رقم هاتف معالج روحاني
جلب الحبيب بعلم الأرقام 34028443 : 973 +:heavy_heart_exclamation: رقم هاتف معالج روحاني Read More
شيخ روحاني محترف / 5770 0096657838 / وصفات المحبة المغربية
شيخ روحاني محترف / 5770 0096657838 / وصفات المحبة المغربية
شيخ روحاني محترف / 5770 0096657838 / وصفات المحبة المغربية Read More
Is it possible to implement FOC plant model on Arduino?
I’m trying implement a FOC plant model on Arduino using S32K144 as input pulse generator. I tried looking into some examples but I’m not finding clarity on what blocksets to use.I’m trying implement a FOC plant model on Arduino using S32K144 as input pulse generator. I tried looking into some examples but I’m not finding clarity on what blocksets to use. I’m trying implement a FOC plant model on Arduino using S32K144 as input pulse generator. I tried looking into some examples but I’m not finding clarity on what blocksets to use. power_electronics_control MATLAB Answers — New Questions
Hypervolume computation with PlatEMO
Does anybody know how can i apply this set of code (HV.m) from PlatEMO (https://github.com/BIMK/PlatEMO/blob/1274e2530e1c5afa928f3691c65af7d2f7efe099/PlatEMO/Metrics/HV.m)
I’ve tried to execute it with the population solutions obtained from my algorithm and the optimum values obtained across several benchmark dataset as follows, however the output for hypervolume value that i’ve got is extremely low, what could be the problem?
inputs:
solutions = [43,176,38;43,177,37;42,188,38;46,168,38;43,184,36;42,178,48;42,169,49;42,179,42];
Population.best = struct(‘objs’, []);
% Fill the structure array with the solutions
for i = 1:size(solutions, 1)
Population.best(i).objs = solutions(i, :);
end
optimum = [40, 162, 38 ; 40, 164, 37 ;40, 167, 36; 40,171,36; 40,165,37; 40,169,36 ; 41, 160, 38 ;41, 163, 37 ;42, 157, 40 ;42, 158, 39 ;42, 165, 36 ; 42,162,42 ; 43, 155, 40 ;44, 154, 40 ;45, 153, 42];
hv = HV(Population, optimum);
disp([‘Hypervolume: ‘, num2str(hv)]);
in HV.m:
function score = HV(Population,optimum)
PopObj = vertcat(Population.best.objs);
… and the rest of the code from (https://github.com/BIMK/PlatEMO/blob/1274e2530e1c5afa928f3691c65af7d2f7efe099/PlatEMO/Metrics/HV.m)Does anybody know how can i apply this set of code (HV.m) from PlatEMO (https://github.com/BIMK/PlatEMO/blob/1274e2530e1c5afa928f3691c65af7d2f7efe099/PlatEMO/Metrics/HV.m)
I’ve tried to execute it with the population solutions obtained from my algorithm and the optimum values obtained across several benchmark dataset as follows, however the output for hypervolume value that i’ve got is extremely low, what could be the problem?
inputs:
solutions = [43,176,38;43,177,37;42,188,38;46,168,38;43,184,36;42,178,48;42,169,49;42,179,42];
Population.best = struct(‘objs’, []);
% Fill the structure array with the solutions
for i = 1:size(solutions, 1)
Population.best(i).objs = solutions(i, :);
end
optimum = [40, 162, 38 ; 40, 164, 37 ;40, 167, 36; 40,171,36; 40,165,37; 40,169,36 ; 41, 160, 38 ;41, 163, 37 ;42, 157, 40 ;42, 158, 39 ;42, 165, 36 ; 42,162,42 ; 43, 155, 40 ;44, 154, 40 ;45, 153, 42];
hv = HV(Population, optimum);
disp([‘Hypervolume: ‘, num2str(hv)]);
in HV.m:
function score = HV(Population,optimum)
PopObj = vertcat(Population.best.objs);
… and the rest of the code from (https://github.com/BIMK/PlatEMO/blob/1274e2530e1c5afa928f3691c65af7d2f7efe099/PlatEMO/Metrics/HV.m) Does anybody know how can i apply this set of code (HV.m) from PlatEMO (https://github.com/BIMK/PlatEMO/blob/1274e2530e1c5afa928f3691c65af7d2f7efe099/PlatEMO/Metrics/HV.m)
I’ve tried to execute it with the population solutions obtained from my algorithm and the optimum values obtained across several benchmark dataset as follows, however the output for hypervolume value that i’ve got is extremely low, what could be the problem?
inputs:
solutions = [43,176,38;43,177,37;42,188,38;46,168,38;43,184,36;42,178,48;42,169,49;42,179,42];
Population.best = struct(‘objs’, []);
% Fill the structure array with the solutions
for i = 1:size(solutions, 1)
Population.best(i).objs = solutions(i, :);
end
optimum = [40, 162, 38 ; 40, 164, 37 ;40, 167, 36; 40,171,36; 40,165,37; 40,169,36 ; 41, 160, 38 ;41, 163, 37 ;42, 157, 40 ;42, 158, 39 ;42, 165, 36 ; 42,162,42 ; 43, 155, 40 ;44, 154, 40 ;45, 153, 42];
hv = HV(Population, optimum);
disp([‘Hypervolume: ‘, num2str(hv)]);
in HV.m:
function score = HV(Population,optimum)
PopObj = vertcat(Population.best.objs);
… and the rest of the code from (https://github.com/BIMK/PlatEMO/blob/1274e2530e1c5afa928f3691c65af7d2f7efe099/PlatEMO/Metrics/HV.m) transferred MATLAB Answers — New Questions
Hypervolume indicator with Yi Cao
I am working with Multi-objective optimization problem and i come across with this code (https://www.mathworks.com/matlabcentral/fileexchange/19651-hypervolume-indicator), however, does anyone know how to get the function ‘paretofront’ from the exisiting code to obtain the hypervolume value
thanksI am working with Multi-objective optimization problem and i come across with this code (https://www.mathworks.com/matlabcentral/fileexchange/19651-hypervolume-indicator), however, does anyone know how to get the function ‘paretofront’ from the exisiting code to obtain the hypervolume value
thanks I am working with Multi-objective optimization problem and i come across with this code (https://www.mathworks.com/matlabcentral/fileexchange/19651-hypervolume-indicator), however, does anyone know how to get the function ‘paretofront’ from the exisiting code to obtain the hypervolume value
thanks transferred MATLAB Answers — New Questions
how to display the calling relation ship between simulink function and function caller
hello, as follwoing system shows, how to configure to display the relation ship between function caller an simulink function in the system diagram.hello, as follwoing system shows, how to configure to display the relation ship between function caller an simulink function in the system diagram. hello, as follwoing system shows, how to configure to display the relation ship between function caller an simulink function in the system diagram. simulink function, function caller MATLAB Answers — New Questions
Antlion optimization algorithm for fuel cost optimization
How Can i use the antlion optimizer tool for fuel cost optimization for a thermal power plant If not possible, please i need a matlab code to do thatHow Can i use the antlion optimizer tool for fuel cost optimization for a thermal power plant If not possible, please i need a matlab code to do that How Can i use the antlion optimizer tool for fuel cost optimization for a thermal power plant If not possible, please i need a matlab code to do that antlion optimization MATLAB Answers — New Questions
Migration of system mailboxes from 2013 to 2019?
It is a hybrid environment with exchange 2013. User mailboxes have been migrated to exchange online.
We want to migrate to exchange 2019. do we need to migrate the system mailboxes from exchange 2013 to 2019? Or do I just need to recreate the system mailboxes in exchange 2019?
It is a hybrid environment with exchange 2013. User mailboxes have been migrated to exchange online.We want to migrate to exchange 2019. do we need to migrate the system mailboxes from exchange 2013 to 2019? Or do I just need to recreate the system mailboxes in exchange 2019? Read More
maximum Lyapunov exponent diagram
hello, I’m working on discrete dynamical system in 2 dimesntion
t’m trying to plot a digram a paramete versus the maximum lyapunov exponent, i searched more about it but didn’t reach to anything.
any one have idea or could help me and thank you.hello, I’m working on discrete dynamical system in 2 dimesntion
t’m trying to plot a digram a paramete versus the maximum lyapunov exponent, i searched more about it but didn’t reach to anything.
any one have idea or could help me and thank you. hello, I’m working on discrete dynamical system in 2 dimesntion
t’m trying to plot a digram a paramete versus the maximum lyapunov exponent, i searched more about it but didn’t reach to anything.
any one have idea or could help me and thank you. dynamical system MATLAB Answers — New Questions
Timestep stability in a 1D heat diffusion model
Hi,
I have a 1D heat diffusion code which I was using on a timescale of 10s of years and I am now trying to use the same code to work on a scale of millions of years. Obviously if I keep my timestep the same this will take ages to calculate but if I increase my timestep I encounter numerical stability issues.
My questions are:
How should I approach this problem?
What affects the maximum stable timestep? And how do I calculate this?
Many thanks,
Alex
close all
clear all
dx = 4; % discretization step in m
dt = 0.0000001; % timestep in Myrs
h=1000; % height of box in m
nx=h/dx+1;
model_lenth=1; %length of model in Myrs
nt=ceil(model_lenth/dt)+1; % number of tsteps to reach end of model
kappa = 1e-6; % thermal diffusivity
x=0:dx:0+h; % finite difference mesh
T=38+0.05.*x; % initial T=Tm everywhere …
time=zeros(1,nt);
t=0;
Tnew = zeros(1,nx);
%Lower sill
sill_1_thickness=18;
Sill_1_top_position=590;
Sill_1_top=ceil(Sill_1_top_position/dx);
Sill_1_bottom=ceil((Sill_1_top_position+sill_1_thickness)/dx);
%Upper sill
sill_2_thickness=10;
Sill_2_top_position=260;
Sill_2_top=ceil(Sill_2_top_position/dx);
Sill_2_bottom=ceil((Sill_2_top_position+sill_2_thickness)/dx);
%Temperature of dolerite intrusions
Tm=1300;
T(Sill_1_top:Sill_1_bottom)=Tm; %Apply temperature to intrusion 1
% unit conversion to SI:
secinmyr=24*3600*365*1000000; % dt in sec
dt=dt*secinmyr;
%Plot initial conditions
figure(1), clf
f1 = figure(1); %Make full screen
set(f1,’Units’, ‘Normalized’, ‘OuterPosition’, [0 0 1 1]);
plot (T,x,’LineWidth’,2)
xlabel(‘T [^oC]’)
ylabel(‘x[m]’)
axis([0 1310 0 1000])
title(‘ Initial Conditions’)
set(gca,’YDir’,’reverse’);
%Main calculation
for it=1:nt
%Apply temperature to upper intrusion
if it==10;
T(Sill_2_top:Sill_2_bottom)=Tm;
end
for i = 2:nx-1
Tnew(i) = T(i) + kappa*dt*(T(i+1) – 2*T(i) + T(i-1))/dx/dx;
end
Tnew(1) = T(1);
Tnew(nx) = T(nx);
time(it) = t;
T = Tnew; %Set old Temp to = new temp for next loop
tmyears=(t/secinmyr);
%Plot a figure which updates in the loop of temperature against depth
figure(2), clf
plot (T,x,’LineWidth’,2)
xlabel(‘T [^oC]’)
ylabel(‘x[m]’)
title([‘ Temperature against Depth after ‘,num2str(tmyears),’ Myrs’])
axis([0 1300 0 1000])
set(gca,’YDir’,’reverse’);%Reverse y axis
%Make full screen
f2 = figure(2);
set(f2,’Units’, ‘Normalized’, ‘OuterPosition’, [0 0 1 1]);
drawnow
t=t+dt;
endHi,
I have a 1D heat diffusion code which I was using on a timescale of 10s of years and I am now trying to use the same code to work on a scale of millions of years. Obviously if I keep my timestep the same this will take ages to calculate but if I increase my timestep I encounter numerical stability issues.
My questions are:
How should I approach this problem?
What affects the maximum stable timestep? And how do I calculate this?
Many thanks,
Alex
close all
clear all
dx = 4; % discretization step in m
dt = 0.0000001; % timestep in Myrs
h=1000; % height of box in m
nx=h/dx+1;
model_lenth=1; %length of model in Myrs
nt=ceil(model_lenth/dt)+1; % number of tsteps to reach end of model
kappa = 1e-6; % thermal diffusivity
x=0:dx:0+h; % finite difference mesh
T=38+0.05.*x; % initial T=Tm everywhere …
time=zeros(1,nt);
t=0;
Tnew = zeros(1,nx);
%Lower sill
sill_1_thickness=18;
Sill_1_top_position=590;
Sill_1_top=ceil(Sill_1_top_position/dx);
Sill_1_bottom=ceil((Sill_1_top_position+sill_1_thickness)/dx);
%Upper sill
sill_2_thickness=10;
Sill_2_top_position=260;
Sill_2_top=ceil(Sill_2_top_position/dx);
Sill_2_bottom=ceil((Sill_2_top_position+sill_2_thickness)/dx);
%Temperature of dolerite intrusions
Tm=1300;
T(Sill_1_top:Sill_1_bottom)=Tm; %Apply temperature to intrusion 1
% unit conversion to SI:
secinmyr=24*3600*365*1000000; % dt in sec
dt=dt*secinmyr;
%Plot initial conditions
figure(1), clf
f1 = figure(1); %Make full screen
set(f1,’Units’, ‘Normalized’, ‘OuterPosition’, [0 0 1 1]);
plot (T,x,’LineWidth’,2)
xlabel(‘T [^oC]’)
ylabel(‘x[m]’)
axis([0 1310 0 1000])
title(‘ Initial Conditions’)
set(gca,’YDir’,’reverse’);
%Main calculation
for it=1:nt
%Apply temperature to upper intrusion
if it==10;
T(Sill_2_top:Sill_2_bottom)=Tm;
end
for i = 2:nx-1
Tnew(i) = T(i) + kappa*dt*(T(i+1) – 2*T(i) + T(i-1))/dx/dx;
end
Tnew(1) = T(1);
Tnew(nx) = T(nx);
time(it) = t;
T = Tnew; %Set old Temp to = new temp for next loop
tmyears=(t/secinmyr);
%Plot a figure which updates in the loop of temperature against depth
figure(2), clf
plot (T,x,’LineWidth’,2)
xlabel(‘T [^oC]’)
ylabel(‘x[m]’)
title([‘ Temperature against Depth after ‘,num2str(tmyears),’ Myrs’])
axis([0 1300 0 1000])
set(gca,’YDir’,’reverse’);%Reverse y axis
%Make full screen
f2 = figure(2);
set(f2,’Units’, ‘Normalized’, ‘OuterPosition’, [0 0 1 1]);
drawnow
t=t+dt;
end Hi,
I have a 1D heat diffusion code which I was using on a timescale of 10s of years and I am now trying to use the same code to work on a scale of millions of years. Obviously if I keep my timestep the same this will take ages to calculate but if I increase my timestep I encounter numerical stability issues.
My questions are:
How should I approach this problem?
What affects the maximum stable timestep? And how do I calculate this?
Many thanks,
Alex
close all
clear all
dx = 4; % discretization step in m
dt = 0.0000001; % timestep in Myrs
h=1000; % height of box in m
nx=h/dx+1;
model_lenth=1; %length of model in Myrs
nt=ceil(model_lenth/dt)+1; % number of tsteps to reach end of model
kappa = 1e-6; % thermal diffusivity
x=0:dx:0+h; % finite difference mesh
T=38+0.05.*x; % initial T=Tm everywhere …
time=zeros(1,nt);
t=0;
Tnew = zeros(1,nx);
%Lower sill
sill_1_thickness=18;
Sill_1_top_position=590;
Sill_1_top=ceil(Sill_1_top_position/dx);
Sill_1_bottom=ceil((Sill_1_top_position+sill_1_thickness)/dx);
%Upper sill
sill_2_thickness=10;
Sill_2_top_position=260;
Sill_2_top=ceil(Sill_2_top_position/dx);
Sill_2_bottom=ceil((Sill_2_top_position+sill_2_thickness)/dx);
%Temperature of dolerite intrusions
Tm=1300;
T(Sill_1_top:Sill_1_bottom)=Tm; %Apply temperature to intrusion 1
% unit conversion to SI:
secinmyr=24*3600*365*1000000; % dt in sec
dt=dt*secinmyr;
%Plot initial conditions
figure(1), clf
f1 = figure(1); %Make full screen
set(f1,’Units’, ‘Normalized’, ‘OuterPosition’, [0 0 1 1]);
plot (T,x,’LineWidth’,2)
xlabel(‘T [^oC]’)
ylabel(‘x[m]’)
axis([0 1310 0 1000])
title(‘ Initial Conditions’)
set(gca,’YDir’,’reverse’);
%Main calculation
for it=1:nt
%Apply temperature to upper intrusion
if it==10;
T(Sill_2_top:Sill_2_bottom)=Tm;
end
for i = 2:nx-1
Tnew(i) = T(i) + kappa*dt*(T(i+1) – 2*T(i) + T(i-1))/dx/dx;
end
Tnew(1) = T(1);
Tnew(nx) = T(nx);
time(it) = t;
T = Tnew; %Set old Temp to = new temp for next loop
tmyears=(t/secinmyr);
%Plot a figure which updates in the loop of temperature against depth
figure(2), clf
plot (T,x,’LineWidth’,2)
xlabel(‘T [^oC]’)
ylabel(‘x[m]’)
title([‘ Temperature against Depth after ‘,num2str(tmyears),’ Myrs’])
axis([0 1300 0 1000])
set(gca,’YDir’,’reverse’);%Reverse y axis
%Make full screen
f2 = figure(2);
set(f2,’Units’, ‘Normalized’, ‘OuterPosition’, [0 0 1 1]);
drawnow
t=t+dt;
end time step; heat diffusion MATLAB Answers — New Questions
How to set the theorem of floquet for Linear variational equation with periodic equation?
I’m trying to analyze the stability regions of the equation of motion of a system with periodic coefficients (whirlflutter). I have only written its polynomial equation and examined its roots, but my plot did not match the reference implementation correctly.
If I wanna write the Hill function and use the ode45 code, is it possible for someone to correct my code and my approach to finding the monodromy matrix and calculating the Floquet multipliers?
clc;
clear all;
% Define parameters
N = 2; % Number of blades
I_thetaoverI_b = 2; % Moment of inertia pitch axis over I_b
I_psioverI_b = 2; % Moment of inertia yaw axis over I_b
C_thetaoverI_b = 0.00; % Damping coefficient over I_b
C_psioverI_b = 0.00; % Damping coefficient over I_b
h = 0.3; % rotor mast height, wing tip spar to rotor hub [m]
hoverR = 0.34;
R = h / hoverR; % radius [m]
gamma = 4; % lock number
V_knots = 325; % the rotor forward velocity [knots]
% Convert velocity from [knots] to [meters per second]
% 1 knot = 0.51444 meters per second
V = V_knots * 0.51444;
% Calculate angular velocity in radians per second
omega_rad_s = V / R;
% Convert angular velocity from radians per second to RPM
% 1 radian per second = (60 / (2 * pi)) RPM
Omega = omega_rad_s * (60 / (2 * pi));
freq_1_over_Omega = 1 / Omega;
%the flap moment aerodynamic coefficients for large V
M_b = -(1/10)*V;
M_u = 1/6;
%the propeller aerodynamic coefficients
H_u = V/2;
% Frequency ranges
f_pitch= 5:3:140;
f_yaw= 5:3:140;
divergence_map = [];
Rdivergence_map = [];
unstable = [];
% Modify the loop to iterate over time points
for i = 1:length(f_pitch)
for j = 1:length(f_yaw)
phi_steps = linspace(0, pi, 100); % Time steps within one period
for phi = phi_steps
% Angular frequencies for the current time point
w_omega_pitch = 2 * pi* f_pitch(i);
w_omega_yaw = 2 * pi * f_yaw(j);
K_psi = (w_omega_pitch^2) * I_psioverI_b;
K_theta = (w_omega_yaw^2) * I_thetaoverI_b;
% Define inertia matrix [M]
M_matrix = [I_thetaoverI_b + 1 + cos(2*phi), -sin(2*phi);
-sin(2*phi), I_psioverI_b + 1 – cos(2*phi)];
% Define damping matrix [D]
D11 = C_thetaoverI_b + h^2*gamma*H_u*(1 – cos(2*phi)) – gamma*M_b*(1 + cos(2*phi)) – (2 + 2*h*gamma*M_u)*sin(2*phi);
D12 = h^2*gamma*H_u*sin(2*phi) + gamma*M_b*sin(2*phi) – 2*(1 + cos(2*phi)) – 2*h*gamma*M_u*cos(2*phi);
D21 = h^2*gamma*H_u*sin(2*phi) + gamma*M_b*sin(2*phi) + 2*(1 – cos(2*phi)) – 2*h*gamma*M_u*cos(2*phi);
D22 = C_psioverI_b + h^2*gamma*H_u*(1 + cos(2*phi)) – gamma*M_b*(1 – cos(2*phi)) + (2 + 2*h*gamma*M_u)*sin(2*phi);
D_matrix = [D11, D12;
D21, D22];
% Define stiffness matrix [K]
K11 = K_theta – h*gamma*V*H_u*(1 – cos(2*phi)) + gamma*V*M_u*sin(2*phi);
K12 = -h*V*gamma*H_u*sin(2*phi) + gamma*V*M_u*(1 + cos(2*phi));
K21 = -h*gamma*V*H_u*sin(2*phi) – gamma*V*M_u*(1 – cos(2*phi));
K22 = K_psi – h*gamma*V*H_u*(1 + cos(2*phi)) – gamma*V*M_u*sin(2*phi);
K_matrix = [K11, K12;
K21, K22];
% Compute the system matrices
M11 = M_matrix(1, 1); M12 = M_matrix(1, 2); M21 = M_matrix(2, 1); M22 = M_matrix(2, 2);
D11 = D_matrix(1, 1); D12 = D_matrix(1, 2); D21 = D_matrix(2, 1); D22 = D_matrix(2, 2);
K11 = K_matrix(1, 1); K12 = K_matrix(1, 2); K21 = K_matrix(2, 1); K22 = K_matrix(2, 2);
% Find the roots of the polynomial equation
P0 = M11*M22-M12*M21;
P1 = (- D11*M22*1j – D22*M11*1j + M12*D21*j + D12*M21*j);
P2 = (D11*D22*(1j)^2 – K22*M11 – K11*M22 – D12*D21*(1j)^2 + M12*K21 + M21*K12);
P3 = (D11*K22*1j – D12*K21*1j – D21*K12*1j + D22*K11*1j);
P4 = K11*K22 – K12*K21;
P = roots([P0, P1, P2, P3, P4]);
r = 1 * P;
%Flutter
for k = 1:length(r)
if (real(r(k)) > 0)
if (imag(r(k)) <= 0)
unstable = [unstable; phi, K_psi, K_theta];
% Proximity check for 1/Ω divergence
if abs(real(r(k)) – freq_1_over_Omega) < 0.1
Rdivergence_map = [Rdivergence_map; phi, K_psi, K_theta];
end
end
end
end
%Divergence
if (real(det(K_matrix)) < 0)
divergence_map = [divergence_map; phi, K_psi, K_theta];
end
end
end
end
% Plotting section
figure;
hold on;
scatter(unstable(:,2), unstable(:,3), ‘filled’);
scatter(divergence_map(:,2), divergence_map(:,3), ‘filled’, ‘r’);
scatter(Rdivergence_map(:,2), Rdivergence_map(:,3), ‘filled’, ‘g’);
xlabel(‘K_psi’);
ylabel(‘K_theta’);
title(‘Whirl Flutter Diagram’);
legend(‘Flutter area’, ‘Divergence area’, ‘1/Ω Divergence area’);
hold off;I’m trying to analyze the stability regions of the equation of motion of a system with periodic coefficients (whirlflutter). I have only written its polynomial equation and examined its roots, but my plot did not match the reference implementation correctly.
If I wanna write the Hill function and use the ode45 code, is it possible for someone to correct my code and my approach to finding the monodromy matrix and calculating the Floquet multipliers?
clc;
clear all;
% Define parameters
N = 2; % Number of blades
I_thetaoverI_b = 2; % Moment of inertia pitch axis over I_b
I_psioverI_b = 2; % Moment of inertia yaw axis over I_b
C_thetaoverI_b = 0.00; % Damping coefficient over I_b
C_psioverI_b = 0.00; % Damping coefficient over I_b
h = 0.3; % rotor mast height, wing tip spar to rotor hub [m]
hoverR = 0.34;
R = h / hoverR; % radius [m]
gamma = 4; % lock number
V_knots = 325; % the rotor forward velocity [knots]
% Convert velocity from [knots] to [meters per second]
% 1 knot = 0.51444 meters per second
V = V_knots * 0.51444;
% Calculate angular velocity in radians per second
omega_rad_s = V / R;
% Convert angular velocity from radians per second to RPM
% 1 radian per second = (60 / (2 * pi)) RPM
Omega = omega_rad_s * (60 / (2 * pi));
freq_1_over_Omega = 1 / Omega;
%the flap moment aerodynamic coefficients for large V
M_b = -(1/10)*V;
M_u = 1/6;
%the propeller aerodynamic coefficients
H_u = V/2;
% Frequency ranges
f_pitch= 5:3:140;
f_yaw= 5:3:140;
divergence_map = [];
Rdivergence_map = [];
unstable = [];
% Modify the loop to iterate over time points
for i = 1:length(f_pitch)
for j = 1:length(f_yaw)
phi_steps = linspace(0, pi, 100); % Time steps within one period
for phi = phi_steps
% Angular frequencies for the current time point
w_omega_pitch = 2 * pi* f_pitch(i);
w_omega_yaw = 2 * pi * f_yaw(j);
K_psi = (w_omega_pitch^2) * I_psioverI_b;
K_theta = (w_omega_yaw^2) * I_thetaoverI_b;
% Define inertia matrix [M]
M_matrix = [I_thetaoverI_b + 1 + cos(2*phi), -sin(2*phi);
-sin(2*phi), I_psioverI_b + 1 – cos(2*phi)];
% Define damping matrix [D]
D11 = C_thetaoverI_b + h^2*gamma*H_u*(1 – cos(2*phi)) – gamma*M_b*(1 + cos(2*phi)) – (2 + 2*h*gamma*M_u)*sin(2*phi);
D12 = h^2*gamma*H_u*sin(2*phi) + gamma*M_b*sin(2*phi) – 2*(1 + cos(2*phi)) – 2*h*gamma*M_u*cos(2*phi);
D21 = h^2*gamma*H_u*sin(2*phi) + gamma*M_b*sin(2*phi) + 2*(1 – cos(2*phi)) – 2*h*gamma*M_u*cos(2*phi);
D22 = C_psioverI_b + h^2*gamma*H_u*(1 + cos(2*phi)) – gamma*M_b*(1 – cos(2*phi)) + (2 + 2*h*gamma*M_u)*sin(2*phi);
D_matrix = [D11, D12;
D21, D22];
% Define stiffness matrix [K]
K11 = K_theta – h*gamma*V*H_u*(1 – cos(2*phi)) + gamma*V*M_u*sin(2*phi);
K12 = -h*V*gamma*H_u*sin(2*phi) + gamma*V*M_u*(1 + cos(2*phi));
K21 = -h*gamma*V*H_u*sin(2*phi) – gamma*V*M_u*(1 – cos(2*phi));
K22 = K_psi – h*gamma*V*H_u*(1 + cos(2*phi)) – gamma*V*M_u*sin(2*phi);
K_matrix = [K11, K12;
K21, K22];
% Compute the system matrices
M11 = M_matrix(1, 1); M12 = M_matrix(1, 2); M21 = M_matrix(2, 1); M22 = M_matrix(2, 2);
D11 = D_matrix(1, 1); D12 = D_matrix(1, 2); D21 = D_matrix(2, 1); D22 = D_matrix(2, 2);
K11 = K_matrix(1, 1); K12 = K_matrix(1, 2); K21 = K_matrix(2, 1); K22 = K_matrix(2, 2);
% Find the roots of the polynomial equation
P0 = M11*M22-M12*M21;
P1 = (- D11*M22*1j – D22*M11*1j + M12*D21*j + D12*M21*j);
P2 = (D11*D22*(1j)^2 – K22*M11 – K11*M22 – D12*D21*(1j)^2 + M12*K21 + M21*K12);
P3 = (D11*K22*1j – D12*K21*1j – D21*K12*1j + D22*K11*1j);
P4 = K11*K22 – K12*K21;
P = roots([P0, P1, P2, P3, P4]);
r = 1 * P;
%Flutter
for k = 1:length(r)
if (real(r(k)) > 0)
if (imag(r(k)) <= 0)
unstable = [unstable; phi, K_psi, K_theta];
% Proximity check for 1/Ω divergence
if abs(real(r(k)) – freq_1_over_Omega) < 0.1
Rdivergence_map = [Rdivergence_map; phi, K_psi, K_theta];
end
end
end
end
%Divergence
if (real(det(K_matrix)) < 0)
divergence_map = [divergence_map; phi, K_psi, K_theta];
end
end
end
end
% Plotting section
figure;
hold on;
scatter(unstable(:,2), unstable(:,3), ‘filled’);
scatter(divergence_map(:,2), divergence_map(:,3), ‘filled’, ‘r’);
scatter(Rdivergence_map(:,2), Rdivergence_map(:,3), ‘filled’, ‘g’);
xlabel(‘K_psi’);
ylabel(‘K_theta’);
title(‘Whirl Flutter Diagram’);
legend(‘Flutter area’, ‘Divergence area’, ‘1/Ω Divergence area’);
hold off; I’m trying to analyze the stability regions of the equation of motion of a system with periodic coefficients (whirlflutter). I have only written its polynomial equation and examined its roots, but my plot did not match the reference implementation correctly.
If I wanna write the Hill function and use the ode45 code, is it possible for someone to correct my code and my approach to finding the monodromy matrix and calculating the Floquet multipliers?
clc;
clear all;
% Define parameters
N = 2; % Number of blades
I_thetaoverI_b = 2; % Moment of inertia pitch axis over I_b
I_psioverI_b = 2; % Moment of inertia yaw axis over I_b
C_thetaoverI_b = 0.00; % Damping coefficient over I_b
C_psioverI_b = 0.00; % Damping coefficient over I_b
h = 0.3; % rotor mast height, wing tip spar to rotor hub [m]
hoverR = 0.34;
R = h / hoverR; % radius [m]
gamma = 4; % lock number
V_knots = 325; % the rotor forward velocity [knots]
% Convert velocity from [knots] to [meters per second]
% 1 knot = 0.51444 meters per second
V = V_knots * 0.51444;
% Calculate angular velocity in radians per second
omega_rad_s = V / R;
% Convert angular velocity from radians per second to RPM
% 1 radian per second = (60 / (2 * pi)) RPM
Omega = omega_rad_s * (60 / (2 * pi));
freq_1_over_Omega = 1 / Omega;
%the flap moment aerodynamic coefficients for large V
M_b = -(1/10)*V;
M_u = 1/6;
%the propeller aerodynamic coefficients
H_u = V/2;
% Frequency ranges
f_pitch= 5:3:140;
f_yaw= 5:3:140;
divergence_map = [];
Rdivergence_map = [];
unstable = [];
% Modify the loop to iterate over time points
for i = 1:length(f_pitch)
for j = 1:length(f_yaw)
phi_steps = linspace(0, pi, 100); % Time steps within one period
for phi = phi_steps
% Angular frequencies for the current time point
w_omega_pitch = 2 * pi* f_pitch(i);
w_omega_yaw = 2 * pi * f_yaw(j);
K_psi = (w_omega_pitch^2) * I_psioverI_b;
K_theta = (w_omega_yaw^2) * I_thetaoverI_b;
% Define inertia matrix [M]
M_matrix = [I_thetaoverI_b + 1 + cos(2*phi), -sin(2*phi);
-sin(2*phi), I_psioverI_b + 1 – cos(2*phi)];
% Define damping matrix [D]
D11 = C_thetaoverI_b + h^2*gamma*H_u*(1 – cos(2*phi)) – gamma*M_b*(1 + cos(2*phi)) – (2 + 2*h*gamma*M_u)*sin(2*phi);
D12 = h^2*gamma*H_u*sin(2*phi) + gamma*M_b*sin(2*phi) – 2*(1 + cos(2*phi)) – 2*h*gamma*M_u*cos(2*phi);
D21 = h^2*gamma*H_u*sin(2*phi) + gamma*M_b*sin(2*phi) + 2*(1 – cos(2*phi)) – 2*h*gamma*M_u*cos(2*phi);
D22 = C_psioverI_b + h^2*gamma*H_u*(1 + cos(2*phi)) – gamma*M_b*(1 – cos(2*phi)) + (2 + 2*h*gamma*M_u)*sin(2*phi);
D_matrix = [D11, D12;
D21, D22];
% Define stiffness matrix [K]
K11 = K_theta – h*gamma*V*H_u*(1 – cos(2*phi)) + gamma*V*M_u*sin(2*phi);
K12 = -h*V*gamma*H_u*sin(2*phi) + gamma*V*M_u*(1 + cos(2*phi));
K21 = -h*gamma*V*H_u*sin(2*phi) – gamma*V*M_u*(1 – cos(2*phi));
K22 = K_psi – h*gamma*V*H_u*(1 + cos(2*phi)) – gamma*V*M_u*sin(2*phi);
K_matrix = [K11, K12;
K21, K22];
% Compute the system matrices
M11 = M_matrix(1, 1); M12 = M_matrix(1, 2); M21 = M_matrix(2, 1); M22 = M_matrix(2, 2);
D11 = D_matrix(1, 1); D12 = D_matrix(1, 2); D21 = D_matrix(2, 1); D22 = D_matrix(2, 2);
K11 = K_matrix(1, 1); K12 = K_matrix(1, 2); K21 = K_matrix(2, 1); K22 = K_matrix(2, 2);
% Find the roots of the polynomial equation
P0 = M11*M22-M12*M21;
P1 = (- D11*M22*1j – D22*M11*1j + M12*D21*j + D12*M21*j);
P2 = (D11*D22*(1j)^2 – K22*M11 – K11*M22 – D12*D21*(1j)^2 + M12*K21 + M21*K12);
P3 = (D11*K22*1j – D12*K21*1j – D21*K12*1j + D22*K11*1j);
P4 = K11*K22 – K12*K21;
P = roots([P0, P1, P2, P3, P4]);
r = 1 * P;
%Flutter
for k = 1:length(r)
if (real(r(k)) > 0)
if (imag(r(k)) <= 0)
unstable = [unstable; phi, K_psi, K_theta];
% Proximity check for 1/Ω divergence
if abs(real(r(k)) – freq_1_over_Omega) < 0.1
Rdivergence_map = [Rdivergence_map; phi, K_psi, K_theta];
end
end
end
end
%Divergence
if (real(det(K_matrix)) < 0)
divergence_map = [divergence_map; phi, K_psi, K_theta];
end
end
end
end
% Plotting section
figure;
hold on;
scatter(unstable(:,2), unstable(:,3), ‘filled’);
scatter(divergence_map(:,2), divergence_map(:,3), ‘filled’, ‘r’);
scatter(Rdivergence_map(:,2), Rdivergence_map(:,3), ‘filled’, ‘g’);
xlabel(‘K_psi’);
ylabel(‘K_theta’);
title(‘Whirl Flutter Diagram’);
legend(‘Flutter area’, ‘Divergence area’, ‘1/Ω Divergence area’);
hold off; stability theory, floquet theorem, characteristic multiplier, periodic coeffcients MATLAB Answers — New Questions
similarity gives a message something went wrong try again
I have even tried to reinstall office 365. No luck
I have even tried to reinstall office 365. No luck Read More
Reps in Friedman test
Hi, I want to do Friedman test on a test data where data from an individual has been collected for 18 days. I have 4 groups with 5, 7, 8, and 6 individuals in each group. If I am understanding correctly, then the data should be in the following format:
[D11 D11
D21 D21
D31 D31
D12 D12];
So basically , each column would have 18*n group individuals and each column would represent different group. I want to make sure I am understanding the reqs correctly. Also, how would I represent the reps in this case? The code gives me bad rep number.
Thank you.Hi, I want to do Friedman test on a test data where data from an individual has been collected for 18 days. I have 4 groups with 5, 7, 8, and 6 individuals in each group. If I am understanding correctly, then the data should be in the following format:
[D11 D11
D21 D21
D31 D31
D12 D12];
So basically , each column would have 18*n group individuals and each column would represent different group. I want to make sure I am understanding the reqs correctly. Also, how would I represent the reps in this case? The code gives me bad rep number.
Thank you. Hi, I want to do Friedman test on a test data where data from an individual has been collected for 18 days. I have 4 groups with 5, 7, 8, and 6 individuals in each group. If I am understanding correctly, then the data should be in the following format:
[D11 D11
D21 D21
D31 D31
D12 D12];
So basically , each column would have 18*n group individuals and each column would represent different group. I want to make sure I am understanding the reqs correctly. Also, how would I represent the reps in this case? The code gives me bad rep number.
Thank you. friedman test, non-parametric, statistics MATLAB Answers — New Questions
Windows 11 Insider Preview 10.0.26120.1330 Not
I cannot seem to get this update and the other update along with this caused one of my 2 displays not to work and any video software like AMD, filmora, and adobe not to work anymore on my computer. Something is off and I worked with one of the tech guys with no luck.
I cannot seem to get this update and the other update along with this caused one of my 2 displays not to work and any video software like AMD, filmora, and adobe not to work anymore on my computer. Something is off and I worked with one of the tech guys with no luck. Read More
Combined Discrete-Continuous Simulation In SIMULINK
I am not even sure if that is the right title for this question.
Here’s the question:
How to implement the following dynamic system in Simulink?
Here’s the problem:
Time points are used to establish a uniform time grid on the interval , where the constant step size is . The solver is assumed to be at the beginning of the time step , where the state at the current time , is known, and the objective is to compute the next state through the relation , where is described as follows:
is first transformed to through some algebraic functions,
an IVP is set up with its initial condition set to . This IVP is then solved using a variable step ODE solver from to ,
the solution at time , is then mapped to the next state by some other algebraic mappings.
The following figure shows how the state is propagated thorugh time, in a single step:
In the output, I need the intermediate solutions (denoted by x) in each step, as well as the state variables .This can be easily done in a script, but I am looking for a way to do it in Simulink; which may be trivial problem, but I am really confused at this moment and I can’t really find a way to do it.
In some ways, in each step, the continuous-time subsystem waits for the input to be available, and once it is there, the external solver "waits" for the continuous-time subsystem to locally solve the continuous-time dynamical equations using an adaptive step-size solver, then the external solver receives this subsystem’s output and continuous to perform the remaining functions to produce . I feel like this should be logical workflow of the simulation, but I am not sure how Simulink treats problems of this type.I am not even sure if that is the right title for this question.
Here’s the question:
How to implement the following dynamic system in Simulink?
Here’s the problem:
Time points are used to establish a uniform time grid on the interval , where the constant step size is . The solver is assumed to be at the beginning of the time step , where the state at the current time , is known, and the objective is to compute the next state through the relation , where is described as follows:
is first transformed to through some algebraic functions,
an IVP is set up with its initial condition set to . This IVP is then solved using a variable step ODE solver from to ,
the solution at time , is then mapped to the next state by some other algebraic mappings.
The following figure shows how the state is propagated thorugh time, in a single step:
In the output, I need the intermediate solutions (denoted by x) in each step, as well as the state variables .This can be easily done in a script, but I am looking for a way to do it in Simulink; which may be trivial problem, but I am really confused at this moment and I can’t really find a way to do it.
In some ways, in each step, the continuous-time subsystem waits for the input to be available, and once it is there, the external solver "waits" for the continuous-time subsystem to locally solve the continuous-time dynamical equations using an adaptive step-size solver, then the external solver receives this subsystem’s output and continuous to perform the remaining functions to produce . I feel like this should be logical workflow of the simulation, but I am not sure how Simulink treats problems of this type. I am not even sure if that is the right title for this question.
Here’s the question:
How to implement the following dynamic system in Simulink?
Here’s the problem:
Time points are used to establish a uniform time grid on the interval , where the constant step size is . The solver is assumed to be at the beginning of the time step , where the state at the current time , is known, and the objective is to compute the next state through the relation , where is described as follows:
is first transformed to through some algebraic functions,
an IVP is set up with its initial condition set to . This IVP is then solved using a variable step ODE solver from to ,
the solution at time , is then mapped to the next state by some other algebraic mappings.
The following figure shows how the state is propagated thorugh time, in a single step:
In the output, I need the intermediate solutions (denoted by x) in each step, as well as the state variables .This can be easily done in a script, but I am looking for a way to do it in Simulink; which may be trivial problem, but I am really confused at this moment and I can’t really find a way to do it.
In some ways, in each step, the continuous-time subsystem waits for the input to be available, and once it is there, the external solver "waits" for the continuous-time subsystem to locally solve the continuous-time dynamical equations using an adaptive step-size solver, then the external solver receives this subsystem’s output and continuous to perform the remaining functions to produce . I feel like this should be logical workflow of the simulation, but I am not sure how Simulink treats problems of this type. simulink, simulation MATLAB Answers — New Questions
PivotBy & GroupBy
When will these functions be available in Excel 365? I keep seeing YouTube videos on how to use, but still not available in my version of Excel. I am not part of beta group.
When will these functions be available in Excel 365? I keep seeing YouTube videos on how to use, but still not available in my version of Excel. I am not part of beta group. Read More
شـيخـ روحاني شهير 🔴00.966.540966.983🟢 طلاسم التحصين & المحبة
شـيخـ روحاني شهير :red_circle:00.966.540966.983🟢 طلاسم التحصين & المحبة
، فك السحر ،
رد المطلقة ،
جلب الحبيب،
خواتم روحانية،
عرق السواحل،
فرج الضبعة،
تزويج البائر،
تسهيل الزواج ،
علاج العقم،
تفريق وطلاق ،
طاعة عمياء،
عقد لسان الظالم ،
جلب الحبيب السعودية ،
خ روحاني،
شيخة،
روحانية،
ساحر،
مشعوذ،
سحر أسود،
سحر تفريق،
سحر علوي ،
جلب الحبيب البحرين،
جلب الحبيب عُمان
السعودية
الكويت
قطر
البحرين
الامارات
شـيخـ روحاني شهير :red_circle:00.966.540966.983🟢 طلاسم التحصين & المحبة، فك السحر ،رد المطلقة ،جلب الحبيب،خواتم روحانية،عرق السواحل،فرج الضبعة،تزويج البائر،تسهيل الزواج ،علاج العقم،تفريق وطلاق ،طاعة عمياء،عقد لسان الظالم ،جلب الحبيب السعودية ،خ روحاني،شيخة،روحانية،ساحر،مشعوذ،سحر أسود،سحر تفريق،سحر علوي ،جلب الحبيب البحرين،جلب الحبيب عُمانالسعوديةالكويتقطرالبحرينالامارات Read More