Matlab solving ODE applied to State Space System, inputs time dependent - matlab

Question

I've got at State System, with "forced" inputs at bounds. My SS equation is: zp = A*z * B. (A is a square matrix, and B colunm)
If B is a step (along the time of experience), there is no problem, because I can use
tevent = 2;
tmax= 5*tevent;
n =100;
dT = n/tmax;
t = linspace(0,tmax,n);
u0 = 1 * ones(size(z'));
B = zeros(nz,n);
B(1,1)= utop(1)';
A = eye(nz,nz);
[tt,u]=ode23('SS',t,u0);
and SS is:
function zp = SS(t,z)
global A B
zp = A*z + B;
end
My problem is when I applied a slop, So B will be time dependent.
utop_init= 20;
utop_final = 50;
utop(1)=utop_init;
utop(tevent * dT)=utop_final;
for k = 2: tevent*dT -1
utop(k) = utop(k-1) +(( utop(tevent * dT) - utop(1))/(tevent * dT));
end
for k = (tevent * dT) +1 :(tmax*dT)
utop(k) = utop(k-1);
end
global A B
B = zeros(nz,1);
B(1,1:n) = utop(:)';
A = eye(nz,nz);
I wrote a new equation (to trying to solve), the problem, but I can't adjust "time step", and I don't get a u with 22x100 (which is the objective).
for k = 2 : n
u=solveSS(t,k,u0);
end
SolveSS has the code:
function [ u ] = solveSS( t,k,u0)
tspan = [t(k-1) t(k)];
[t,u] = ode15s(#SS,tspan,u0);
function zp = SS(t,z)
global A B
zp = A*z + B(:,k-1);
end
end
I hope that you can help!

Answer 1

You should define a function B that is continuously varying with t and pass it as a function handle. This way you will allow the ODE solver to adjust time steps efficiently (your use of ode15s, a stiff ODE solver, suggests that variable time stepping is even more crucial)
The form of your code will be something like this:
function [ u ] = solveSS( t,k,u0)
tspan = [t(k-1) t(k)];
[t,u] = ode15s(#SS,tspan,u0,#B);
function y = B(x)
%% insert B calculation
end
function zp = SS(t,z,B)
global A
zp = A*z + B(t);
end
end