substituting function variable in function handle

i want to substitute y(5) in place of theta and poceed for the ode calculations.

Here is my script

syms theta
A0 = cos(theta).*[1 5 6; 2 9 3; 1 4 5]; 
A =[A0 zeros(3, 2);
    zeros(2, 3) [1 0; 0 1]]
B = tan(2*theta).*[8 5 1 0 0; 1 1 6 0 0; 2 4 7 0 0; 0 0 0 0 0; 0 0 0 0 0]
C = (cos(2*theta)+2).*[8 5 1; 0 1 6; 2 4 7];

myfun = @(t,y)scriptname(t,y,A,B,C);

% dummy values for tspan and y0
tspan = [0 1];
y0 = zeros(1, 5);
An = matlabFunction(subs(A, y(5)))
Bn = matlabFunction(subs(B, y(5)))
Cn = matlabFunction(subs(C, y(5)))

sol = ode45(myfun,tspan,y0);

h = figure;
plot(sol.x,sol.y(i,:));

function dydt = scriptname(t,y,An,Bn,Cn)

inertia = 0.05;
Wr = 2*pi*50;
p =2;
% Cn = double(subs(C,y(5)))
for i=1:3
    I(i,1)=y(i);
end
I
Te = 1/2*p*I'*Cn*I

if t<0.75
    Tl=0;
else
    Tl=7.31;
end

V = [1.4142*400/sqrt(3)*cos(Wr*t);
    1.4142*400/sqrt(3)*cos(Wr*t+2.*pi/3.);
    1.4142*400/sqrt(3)*cos(Wr*t-2.*pi/3.);
    (Te-Tl)/inertia;
    y(4)]

% An = double(subs(A,y(5)))
% Bn = double(subs(B,y(5)))
dydt = An\V-(Bn*y);
end

It is showing the error of "unrecognized function or variable y".

[Stephen23]

Context:

https://www.mathworks.com/matlabcentral/answers/1451984-ode45-is-taking-hours-and-hours-to-compute

@Bathala Teja: you need to pass the function handles to the anonymous function (i.e. An, etc) not the symbolic functions:

https://www.mathworks.com/matlabcentral/answers/1451984-ode45-is-taking-hours-and-hours-to-compute#comment_1734264

[Bathala Teja]

sir can you please rewite my script with your changes?

iam really confused sir please help me out

[Bathala Teja]

hello

anything edited??

Answer 1

[Jaynik]

Hi Bathala,

The error you are encountering occurs because "y" is not defined in the scope where you are trying to substitute "y(5)" for "theta" in matrices "A", "B", and "C". To fix this issue, "y" must first be declared as a symbolic variable. that represents a vector, and then perform the substitution.

You can refer to the following code:

syms theta
syms y [5 1]

A0 = cos(theta).*[1 5 6; 2 9 3; 1 4 5]; 
A =[A0 zeros(3, 2); zeros(2, 3) [1 0; 0 1]];
B = tan(2*theta).*[8 5 1 0 0; 1 1 6 0 0; 2 4 7 0 0; 0 0 0 0 0; 0 0 0 0 0];
C = (cos(2*theta)+2).*[8 5 1; 0 1 6; 2 4 7];

% Substitute theta with y(5) in A, B, C
A_sub = subs(A, theta, y(5));
B_sub = subs(B, theta, y(5));
C_sub = subs(C, theta, y(5));

% Convert the substituted expressions to MATLAB functions
An = matlabFunction(A_sub, 'Vars', {y});
Bn = matlabFunction(B_sub, 'Vars', {y});
Cn = matlabFunction(C_sub, 'Vars', {y});

function dydt = scriptname(t, y, An, Bn, Cn)
    inertia = 0.05;
    Wr = 2*pi*50;
    p = 2

    % Using the An, Bn, and Cn functions with the current state vector y
    A_current = An(y);
    B_current = Bn(y);
    C_current = Cn(y);
    
    I = y(1:3);
    Te = 1/2 * p * I' * C_current * I;

    if t < 0.75
        Tl = 0;
    else
        Tl = 7.31;
    end

    V = [1.4142*400/sqrt(3)*cos(Wr*t);
         1.4142*400/sqrt(3)*cos(Wr*t+2*pi/3);
         1.4142*400/sqrt(3)*cos(Wr*t-2*pi/3);
         (Te - Tl) / inertia;
         y(4)];

    dydt = A_current \ V - (B_current * y);
end

You can refer the following documentation to read more about these functions:

• subs: https://www.mathworks.com/help/releases/R2021a/symbolic/subs.html
• matlabFunction: https://www.mathworks.com/help/releases/R2021a/symbolic/matlabfunction.html

Hope this helps!