No Description of Error for ode45

I am trying to use the ode45 function to plot the response of the output y(t) for

where all inputs are step functions with initial conditions

and .

I think most of my code is correct, but I am having an issue with line 21. I am receiving this error message:

Error in Problem_7_A (line 21)
[t,x]=ode45(odefun,time_int, x0);

However, there is no description, so I am unsure what the error is and I don't know how to fix it.

My code is pasted below.

clc; % clear command window
syms x t; % create symbolic variables x and t

% define system parameters
sp.a=4; % coefficient on ydot term
sp.b=3; % coefficient on y term
sp.c=2; % coefficient on ycubed term

% define initial conditions
x0=zeros(2,1); % define matrix size
x0(1)=1; % initial position y(0)=x0(1)=1
x0(2)=0; % initial velocity ydot(0)=x0(2)=0


% define time interval for solution
tinitial=0; % set initial time
tfinal=10; % set final time
time_int=[tinitial tfinal]; % define time interval bounds

% call the ode45 function
[t,x]=ode45(odefun,time_int, x0);

% plot solution x(t)
figure(1); hold on; % create figure
plot(t,x(:,1),'LineWidth',2); % plot time on x axis and response on y axis
th=title('Output Response Using ode45'); % set title
xh=xlabel('$t$ [s]'); % set x axis label
yh=ylabel('$y(t)$'); % set y axis label

% customize fonts
set(th,'FontSize',15); % set font size for title
set(xh,'FontSize',15); % set font size for x axis
set(yh,'FontSize',15); % set font size for y axis
set(xh,'Interpreter','latex'); % interpret characters using LaTeX markup
set(yh,'Interpreter','latex'); % interpret characters using LaTeX markup
fh=gca; % get current axes
set(fh,'FontSize',15); % set font size for axes

function dx = odefun(t,x,sp)

% for readability, extract system parameters from sp
a=sp.a; % coefficient on ydot term
b=sp.a; % coefficient on y term
c=sp.c; % coefficient on ycubed term

u=t; % STILL NEED TO CHANGE TO STEP FUNCTION H(T)
dx=zeros(2,1); % initialize vector of states (here 1D)

x1=x(1);
x2=x(2);

% use state variable ODE to calculate dx
dx(1)=x2;
dx(2)=(-a*x2)+(-b*x1)+(-c*x1*x1*x1)+(-x2*x1*x1)+u;

end

Answer 1

[James Tursa]

Looks like your odefun needs additional inputs that you are not providing. E.g., try changing this

[t,x]=ode45(odefun,time_int, x0);

to this

[t,x]=ode45(@(t,x)odefun(t,x,sp),time_int, x0); % also pass sp

Also, note that the following line accomplishes nothing and can be removed (you don't use syms variables for ode45):

syms x t; % create symbolic variables x and t

[Peyton Schroeder]

That fixed my problem! Thanks for your help. My only question is: why do we remove sp from that line? In some of the examples I have seen, sp is included there, but I will admit I don't fully understand the purpose of using system parameters.

[James Tursa]

"... why do we remove sp from that line ..."

I don't understand. I added sp to the line in question ... I didn't remove it.