parameter optimization in function

Hi!

I have written a code in which a nonlinear pendulum is modelled. Now with measured data from a pendulum I would like to optimize my damping coefficient so that the model in matlab fits the measured data. Since the damping coeficient is in a separate function file I do not know how to tackle this. See script in attachment.

In F_nonlin the damping coefficient is currently 0.000035 and fits the curve quite well but as mentioned above I would like matlab to optimize this value automattically.

Thanks in advance for the help!

Kind regards, Elon

Answer 1

[Alan Weiss]

Try putting the following code at the end of yours:

[dfinal,resnorm] = fminbnd(@(damping)trytofit(damping,x0,Acc_clean),0.00002,0.00005)


function delta = trytofit(damping,x0,Acc_clean)
tspan = Acc_clean(:,1)/1000-5.017;
[~, S] = ode45(@(t,y) F_nonlin(t,y,damping),tspan,x0);
delta = sum((S - Acc_clean(:,3)).^2,"all");
end

I changed the F_nonlin code as follows:

function dx = F_nonlin(~,x,Bfactor)
% Derivative function for a nonlinear pendulum model.
%
% States:
%   x(1):   theta
%   x(2):   d theta/dt
% system parameters:
g = 9.81;   % gravitational constant (m/s^2)
m = 1.042;   % mass pendulum
L = 0.210;   % length pendulum
M = m*L; 
K = m*g; %iets met g
B = Bfactor * 2 * sqrt(M*K); %0.000035 for fitted line
dx(1,1) = x(2);
dx(2,1) = -( K*sin(x(1)) + B*x(2)*abs(x(2)) ) / M;

I get the result dfinal = 3.1459e-05, pretty close to what you have.

My code searches for a minimum of the sum of squares of differences between the simulated pendulum and the data you have. The only thing it varies is the damping (Bfactor in F_nonlin, a scalar), so I use fminbnd to get the minimum.

Of course, it is possible I made an error somewhere, but I think that you see how I put the parameter Bfactor in the simulation to give something that a solver can vary to search for a minimum.

Alan Weiss

MATLAB mathematical toolbox documentation

[Elon Hendriksen]

Thanks Alan! I am going to try this out now

[Elon Hendriksen]

I see now that you have removed the L variable from the F_nonlin function, now that wont run the ode45 in my main code right?

[Alan Weiss]

I don't know what you mean. You had a null L variable that you were passing in; it didn't do anything because you redefined the L variable inside the code, so the passed value was ignored. Feel free to rearrange things if you like, but I gave you working, tested code.

Alan Weiss

MATLAB mathematical toolbox documentation

[Torsten]

In your code, L is an input variable to F_nonlin and you immediately overwrite that input by setting L to 0.21. One of these settings is superfluous.

Answer 2

[Rajiv Singh]

See also Classical Pendulum: Some Algorithm-Related Issues - MATLAB & Simulink Example (mathworks.com)