How to plot intermediate variables of a function used by ode45 solver

Question

Thayumanavan 2013-7-29

1
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/83439-how-to-plot-intermediate-variables-of-a-function-used-by-ode45-solver

Sir, I am calling ode45 for integrating a diff equation say x'=(1/(H))*(2x)

Main Program:

x0=0.1; final_time=1; [t,x]=ode45(@myfunc,[0,final_time],x0);% ODE Call plot(t(:,1),x(:,1))% plotting the state variable main ends

Function Program:

function dv=myfunc(t,x) H=1.0; Te=2*x(1);% intermediate calculations/variables for my differential equations %The Differential Equation dv=[(1/(H))*(Te)];

But i want to plot the intermediate variables say Te in this case.But ode returns t,x alone.How to plot the intermediate variables that was used in the integration process.

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Answer 1

Jan 2013-7-29

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/83439-how-to-plot-intermediate-variables-of-a-function-used-by-ode45-solver#answer_93012

在 MATLAB Online 中打开

You can prepare your function such, that it replies the wanted value according to a special trigger method and accepts vectors as input also:

function dv = myfunc(t, x, flag)
H  = 1.0;
Te = 2 * x(:, 1)
dv = Te ./ H;      % Btw, No addition square brackets
if nargin == 3
  dv = Te;
end

Now run the integration at first:

[t,x] = ode45(@myfunc,[0,final_time],x0);

and obtain the internal variable afterwards:

Te = myFunc(t, x, 'flag');

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Thayumanavan 2013-8-3

在 MATLAB Online 中打开

Sir ,I got answer for the problem that i asked help.But for simplicity i gave that differential equation.But my code is little bit different with many variables.I am attaching the main program and my function.Please help me to plot Te and Vpcc intermediate variable.

Main Code: clear all clc;

% Time Tspan =[0 10]; X0=[0.7; 1.0151; 157 ];

options=odeset('RelTol',1e-3,'AbsTol',1e-6);

%solving the differential Equation [t,x]=ode45(@dvdt,Tspan,X0,options);

%Plotting the figures figure subplot(5,1,1) plot(t(:,1),x(:,1)) xlabel('t'); ylabel('Eprime'); title('Dynamic Wind Time Response ') grid on

subplot(5,1,2) plot(t(:,1),x(:,2)) xlabel('t'); ylabel('Delta') grid on

wradsec=x(:,3); wmech=(60*wradsec)/(2*pi); wpu=wmech/1500;

subplot(5,1,3) plot(t(:,1),wradsec) xlabel('t'); ylabel('Omega') grid on

% Plotting of Intermediate Variables as per Your Idea subplot(5,1,4) op= dvdt(t, x, 'flag'); plot(t(:,1),op(1,:)) xlabel('t'); ylabel('Vterminal') grid on

subplot(5,1,5) plot(t(:,1),op(2,:)) xlabel('t'); ylabel('ElectromagneticTorque') grid on

Function code: function dv=dvdt(t,x,flag)

Xs=0.0754;Xr=0.0326;H=0.20; Rl=0.0083;Rcon=0.0089;Xl=0.033;Xcon=0.01789; Vdinf=1.0;Vqinf=0.0;wspu=157.0; T=0.7855;Xdash=0.1076;D=6.4165; Rt=Rl+Rcon;Xt=Xl+Xcon; xtrans=Xt+(D/Xr); detm=(Rt*Rt)+(xtrans*xtrans); J1=-xtrans;J2=-Rt;J3=-Rt;J4=xtrans; iq=(1/detm)*((J3*((x(1)*cos(x(2)))-Vqinf))+(J4*((-x(1)*sin(x(2)))-Vdinf))); id=(1/detm)*((J2*((-x(1)*sin(x(2)))-Vdinf))+(J1*((x(1)*cos(x(2)))-Vqinf))); Vq=(1/Xr)*((D*id)+(Xr*x(1)*cos(x(2)))); Vd=(-1/Xr)*((D*iq)+(Xr*x(1)*sin(x(2)))); Vdpc=(-Rcon*id)+(Xcon*iq)+Vdinf; Vqpc=(-Rcon*iq)-(Xcon*id)+Vqinf; VPCC=sqrt((Vdpc*Vdpc)+(Vqpc*Vqpc));% Intermediate Variable 1 t1=(Vq*cos(x(2)))-(Vd*sin(x(2))); t2=(Vq*sin(x(2)))+(Vd*cos(x(2))); t3=((Vd*cos(x(2)))+(Vq*sin(x(2)))); Te=(x(1)*t3/Xdash); % Intermediate Variable 2

%The Diffenrential Equation 
       dv=[ (1/T)*((-Xs*x(1)/Xdash)+(((Xs-Xdash)/Xdash)*t1)); % My 1st Differential Equation
           (x(3)-wspu)-(((Xs-Xdash)*t2) /(Xdash*T*x(1)));    %My 2nd  Differential Equation  
           (wspu/(2*H))*(Tm+Te)]; %  My 3rd Differential Equation
 if nargin == 3
  dv = [VPCC;
       Te];

end

You copy paste the code execute and suggest me to plot Te,Vpcc.Thanks

Thayumanavan 2013-8-3

在 MATLAB Online 中打开

clear all clc; % Time Tspan =[0 10]; X0=[0.7; 1.0151; 157 ];

options=odeset('RelTol',1e-3,'AbsTol',1e-6);

%solving the differential Equation [t,x]=ode45(@dvdt,Tspan,X0,options);

%Plotting the figures figure subplot(5,1,1) plot(t(:,1),x(:,1)) xlabel('t'); ylabel('Eprime'); title('Dynamic Wind Time Response ') grid on

subplot(5,1,2) plot(t(:,1),x(:,2)) xlabel('t'); ylabel('Delta') grid on

wradsec=x(:,3); wmech=(60*wradsec)/(2*pi); wpu=wmech/1500;

subplot(5,1,3) plot(t(:,1),wradsec) xlabel('t'); ylabel('Omega') grid on

% Plotting of Intermediate Variables as per Your Idea subplot(5,1,4) op= dvdt(t, x, 'flag'); plot(t(:,1),op(1,:)) xlabel('t'); ylabel('Vterminal') grid on

subplot(5,1,5) plot(t(:,1),op(2,:)) xlabel('t'); ylabel('ElectromagneticTorque') grid on

Function Code: function dv=dvdt(t,x,flag)

Xs=0.0754;Xr=0.0326;H=0.20; Rl=0.0083;Rcon=0.0089;Xl=0.033;Xcon=0.01789; Vdinf=1.0;Vqinf=0.0;wspu=157.0; T=0.7855;Xdash=0.1076;D=6.4165; Rt=Rl+Rcon;Xt=Xl+Xcon; xtrans=Xt+(D/Xr); detm=(Rt*Rt)+(xtrans*xtrans); J1=-xtrans;J2=-Rt;J3=-Rt;J4=xtrans; iq=(1/detm)*((J3*((x(1)*cos(x(2)))-Vqinf))+(J4*((-x(1)*sin(x(2)))-Vdinf))); id=(1/detm)*((J2*((-x(1)*sin(x(2)))-Vdinf))+(J1*((x(1)*cos(x(2)))-Vqinf))); Vq=(1/Xr)*((D*id)+(Xr*x(1)*cos(x(2)))); Vd=(-1/Xr)*((D*iq)+(Xr*x(1)*sin(x(2)))); Vdpc=(-Rcon*id)+(Xcon*iq)+Vdinf; Vqpc=(-Rcon*iq)-(Xcon*id)+Vqinf; VPCC=sqrt((Vdpc*Vdpc)+(Vqpc*Vqpc));% Intermediate Variable 1 t1=(Vq*cos(x(2)))-(Vd*sin(x(2))); t2=(Vq*sin(x(2)))+(Vd*cos(x(2))); t3=((Vd*cos(x(2)))+(Vq*sin(x(2)))); Te=(x(1)*t3/Xdash)% Intermediate Variable 2 Tm=1.0;

%The Diffenrential Equation 
       dv=[ (1/T)*((-Xs*x(1)/Xdash)+(((Xs-Xdash)/Xdash)*t1)); % My 1st Differential Equation
           (x(3)-wspu)-(((Xs-Xdash)*t2) /(Xdash*T*x(1)));    %My 2nd  Differential Equation  
           (wspu/(2*H))*(Tm+Te)]; %  My 3rd Differential Equation
 if nargin == 3
  dv = [VPCC;
       Te];

end

Little change in code .i forgot to give 1 parameter .You pls simulate and tell me what change i need to do in the code to get plot of Te,Vpcc

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Answer 2

Shashank Prasanna 2013-7-29

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/83439-how-to-plot-intermediate-variables-of-a-function-used-by-ode45-solver#answer_93006

You can define an output function (outputfcn) that will be called after each iteration.

http://www.mathworks.com/help/matlab/ref/odeset.html#f92-1016858

you can specify that in the options structure. In your custom output function you can use a plot command with a hold on in order to plot all you intermediate values.