How to solve ODEs with symbolic variables using ode45?

I'm trying to solve a system of ODE with 4 equations with symbolic variable as the input. I splitted the code into 3 files.

file name : parameter_pml_freerun0.m

clear
global f Pole ws Rs Rr Lr Ls Lm VLL Tload J B Las Lar vqs vds vqr vdr
f = 50; %frek listrik
Pole = 4; %jumlah pole
ws = 2*f*pi; %kecepatan elektrikal sinkron dalam rad/s
Rs = 1.278; %resistansi stator
Rr = 3.93033; %resistansi rotor
Lr = 0.009549; %induktansi rotor
Ls = Lr; %induktansi stator
Lm = 0.370842; %induktansi magnetisasi
VLL = 380; %tegangan line to line terminal motor
Tload = 11.852;
J = 0.1;
B = 0;
syms t
Las = Ls+Lm; Lar = Lr+Lm; 
%transformasi tegangan abc to dq0
Vm = VLL*sqrt(2)/sqrt(3); %tegangan puncak fasa tanah
Vabc = Vm.*[sin(t); sin(t - 2*pi/3); sin(t + 2*pi/3)];
Park = (2/3).*[cos(0) cos(0 - 2*pi/3) cos(0 + 2*pi/3); sin(0) sin(0 - 2*pi/3) sin(0 + 2*pi/3); 1/2 1/2 1/2];
Vqd0 = Park*Vabc;
vqs = simplify(Vqd0(1,1)); vds = simplify(Vqd0(2,1)); vqr = 0; vdr = 0;

I used this file to store induction motor parameter and do Park transformation in stator reference frames, the transformation returns vqs and vds as symbolic variables

>> vqs
 
vqs =
 
(5458304707397847*sin(t))/17592186044416
 
>> vds
 
vds =
 
(5458304707397847*cos(t))/17592186044416

I stored the set of ODEs in the second file

function [diffy_eqn] = diffy_eqn(ti,statev)
global  Pole ws Rs Rr Lm Tload J B Las Lar vqs vds vqr vdr
lamqs = statev(1);
lamds = statev(2);
lamqr = statev(3);
lamdr = statev(4);
wr    = statev(5);
th    = statev(6);

idr   = (Lm*lamds - Las*lamdr)/(Lm^2 - Lar*Las);
iqr   = (Lm*lamqs - Las*lamqr)/(Lm^2 - Lar*Las);
iqs   = (Lm*lamqr - Lar*lamqs)/(Lm^2 - Lar*Las);
ids   = (Lm*lamdr - Lar*lamds)/(Lm^2 - Lar*Las);

s1 = (vqs - ws*lamds - Rs*iqs);
s2 = (vds + ws*lamqs - Rs*ids);
s3 = (vqr - (ws - wr)*lamdr - Rr*iqr);
s4 = (vdr + (ws - wr)*lamqr - Rr*idr);
Te  = (3/2)*(Pole/2)*(lamqr*idr - lamdr*iqr);
s5 = (Pole/2)*(Te - Tload - B*wr)/J;
s6 = ws;
diffy_eqn = [s1 s2 s3 s4 s5 s6]';

The third file is where i stored the solver

clear
close all
parameter_pml_freerun0
time = [0 7]';
state0 = [0 0 0 0 0 0]';
[tout,yout] = ode45('diffy_eqn',time, state0);

lamqs = yout(:,1);
lamds = yout(:,2);
lamqr = yout(:,3);
lamdr = yout(:,4);
wr    = yout(:,5); 
th    = yout(:,6);

idr   = (Lm*lamds - Las*lamdr)/(Lm^2 - Lar*Las);
iqr   = (Lm*lamqs - Las*lamqr)/(Lm^2 - Lar*Las);
iqs   = (Lm*lamqr - Lar*lamqs)/(Lm^2 - Lar*Las);
ids   = (Lm*lamdr - Lar*lamds)/(Lm^2 - Lar*Las);

T     = (3/2).*(Pole/2).*Lm*(iqs.*idr - ids.*iqr);

ias = cos(th).*ids - sin(th).*iqs;
ibs = cos(th - 2.*pi/3.).*ids - sin(th - 2.*pi/3.).*iqs;
ics = cos(th + 2.*pi/3.).*ids - sin(th + 2.*pi/3.).*iqs;
vas = cos(th).*vds - sin(th).*vqs;
vbs = cos(th - 2.*pi/3.).*vds - sin(th - 2.*pi/3.).*vqs;
vcs = cos(th + 2.*pi/3.).*vds - sin(th + 2.*pi/3.).*vqs;

The solver returned this error code

free_accel
Error using odearguments (line 113)
Inputs must be floats, namely single or double.

Error in ode45 (line 115)
  odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in free_accel (line 7)
[tout,yout] = ode45('diffy_eqn',time, state0);

How can I make the ODEs solvable? I've tried using matlabFunction to the ODEs but that didn't work. Thank you

Answer 1

[Ameer Hamza]

vqs and vds are functions of variable t. To use it with ode45, you need to convert it to numeric functions. Change the line in parameter_pml_freerun0.m to

vqs = matlabFunction(simplify(Vqd0(1,1))); vds = matlabFunction(simplify(Vqd0(2,1))); vqr = 0; vdr = 0;

Since these are functions of variable 't', so you need to use them as functions inside diffy_eqn.m. Change these two lines

s1 = (vqs(ti) - ws*lamds - Rs*iqs);
s2 = (vds(ti) + ws*lamqs - Rs*ids);

And then in your solver script, change these lines too

vas = cos(th).*vds(th) - sin(th).*vqs(th);
vbs = cos(th - 2.*pi/3.).*vds(th) - sin(th - 2.*pi/3.).*vqs(th);
vcs = cos(th + 2.*pi/3.).*vds(th) - sin(th + 2.*pi/3.).*vqs(th);

[Syahadatul Hidayat]

Thank you so much, it worked really well!

[Ameer Hamza]

I am glad to be of help.