Here's my attempt at fitting uusing lsqcurvefit from the optimisation toolbox.
First I generate some synthetic data to subsequently fit that follows your curve (since you didn't think to give us any)
Vq1 = 556; % known constant
N = 200; % # of points
t = linspace(0,0.2,N)';
f = 50; % presumably 50 Hz.
% Set values for constants
xd = 1;
xDd = 2;
TDd = 0.1;
TDDd = 0.05;
xDDd = 0.3;
phi = -0.6; % initial phase offset
y = (Vq1/xd+((Vq1/xDd-Vq1/xd))*exp(-t/TDd) + ...
(((Vq1/xDDd)-(Vq1/xDd))*exp(-t/TDDd))).* ...
sin(2*pi*f*t+phi);
plot(t,y,'.-')
Now we are ready to do the fitting:
%% Now use lsqcurvefit
p0 = 3*[1,1,1, 1, 1, 1]'; % guess of parameters
LB = [0,0,0, 0, 0, -5]'; % can put anything here, even -inf.
UB = 10*[1,1,1, 1, 1, 1]';
fun = @(p, t) (Vq1/p(1)+((Vq1/p(2)-Vq1/p(1)))*exp(-t/p(3)) + ...
(((Vq1/p(5))-(Vq1/p(2)))*exp(-t/p(4)))).* ...
sin(2*pi*f*t+p(6));
pfit = lsqcurvefit(fun,p0,...
t,y, ...
LB,UB)
yfit = fun(pfit,t);
plot(t,y,'r.', t,yfit,'b-');
We get a pretty good fit since I start reasonably near the values used to generate the original curve.
