finding the solution of a matriciel Differential Equation

Hello all

i have this differential equation (induction machine model)

this is the code

syms i_ds(t) i_dr(t) i_qs(t) i_qr(t) w_r(t)  t  
J=0.024;
p=2;
f=50;
ws=2*pi*f;
ls=0.15;
lr1=0.15;
Lm=0.279;
Cr=10;
% M=(3/2)*Lm;
M=0.143;
Rs=1.15;
Rr1=1.44;   
v_dr=0;
v_qr=0;   
di_ds=diff(i_ds,t);
di_qs=diff(i_qs,t);
di_dr=diff(i_dr,t);
di_qr=diff(i_qr,t);
dw_r=diff(w_r,t);
ode1 =ls*di_ds+M*di_dr ==220*sin(100*pi*t) -Rs*i_ds;
ode2 =ls*di_qs+M*di_qr ==220*sin(100*pi*t-pi/2) -Rs*i_qs;
ode3 =M*di_ds+lr1*di_dr ==v_dr-Rr1*i_dr-M*w_r*i_qs-lr1*w_r*i_qr;
ode4 =M*di_qs+lr1*di_qr ==v_qr-Rr1*i_qr-M*w_r*i_ds-lr1*w_r*i_dr;
ode5 =J*dw_r==(3/2)*p*M*(i_dr*i_qs-i_qr*i_ds)-Cr;
odes = [ode1; ode2; ode3; ode4; ode5]

odes(t) = 

I=[i_ds(0)==0, i_qs(0)==0, i_dr(0)==0, i_qr(0)==0, w_r(0)==0];
yLT =dsolve(odes,I)

Warning: Unable to find symbolic solution.

 
yLT =
 
[ empty sym ]
 

and i having this problem

Warning: Unable to find symbolic solution.

> In dsolve (line 209)

In MAS2 (line 32)

yLT =

[ empty sym ]

[Walter Roberson]

If you ask to dsolve() the first three equations together, then MATLAB thinks about it for a fairly long time...

[Walter Roberson]

When I asked Maple to solve all of them together, it got up to 120 gigabytes of memory before I killed it.

[Abdelkrim]

really

sorry for that

Answer 1

[Torsten]

Your equations cannot be solved analytically using "dsolve". Use a numerical solver instead:

J=0.024;
p=2;
f=50;
ws=2*pi*f;
ls=0.15;
lr1=0.15;
Lm=0.279;
Cr=10;
% M=(3/2)*Lm;
M=0.143;
Rs=1.15;
Rr1=1.44;   
v_dr=0;
v_qr=0;   
Mass = [ls 0 M 0 0;0 ls 0 M 0;M 0 lr1 0 0;0 M 0 lr1 0;0 0 0 0 J];
%fun = @(t,y)[220*sin(100*pi*t)-Rs*y(1);...
%             220*sin(100*pi*t-pi/2)-Rs*y(2);...
%             v_dr-Rr1*y(3)-M*y(5)*y(2)-lr1*y(5)*y(4);...
%             v_qr-Rr1*y(4)-M*y(5)*y(1)-lr1*y(5)*y(3);...
%             (3/2)*p*M*(y(3)*y(2)-y(4)*y(1))-Cr];
fun = @(t,y)inv(Mass)*[220*sin(100*pi*t)-Rs*y(1);...
                       220*sin(100*pi*t-pi/2)-Rs*y(2);...
                       v_dr-Rr1*y(3)-M*y(5)*y(2)-lr1*y(5)*y(4);...
                       v_qr-Rr1*y(4)-M*y(5)*y(1)-lr1*y(5)*y(3);...
                       (3/2)*p*M*(y(3)*y(2)-y(4)*y(1))-Cr];
tspan = [0 0.3];
y0 = [0 0 0 0 0].';
%[T,Y] = ode45(fun,tspan,y0,odeset('Mass',Mass))
[T,Y] = ode45(fun,tspan,y0);
plot(T,Y(:,1))

[Sam Chak]

Hi @Abdelkrim

It seems that your induction machine is unstable. Is this instability intentional, perhaps as part of the simulation to identify the parameters that lead to instability?

tspan = [0 0.3909];

[Abdelkrim]

i dont think so because in simulink the simulation works normaly

[Torsten]

The code is a direct translation of your equations and the results are similar with all ODE solvers available. So I think the equations solved in Simulink must be different from those you posted here.

[Abdelkrim]

I will revisit and revise the equations, as there may be errors in the ones I previously wrote

thank you