Optimizing Rocket Equation Mass Ratios with MATLAB fmincon

[Hashmeer]

Homework Statement

I'm trying to use fmincon to find the optimal mass ratios for the rocket equation. The only variables are m2/m1 and m3/m2 (R1 and R2 respectively).

The Attempt at a Solution

function [ velocity ] = rocketEqn( MR )
% Calculates the velocity that a rocket can attain given the mass ratios of
% the stages, where MR is a vector containing the mass ratios R1 and R2.
% MR = [R1, R2] and R1 = m2/m1 and R2 = m3/m2.

R1 = MR(1);
R2 = MR(2);
E = .1; %structural coefficient
Mp = 500; %payload mass
c = 3.3; %km/s^2, given exhaust velocity for the rocket
Mtot = 25000; % kg, given total mass of the rocket
M = Mtot - Mp;  % gives the mass that can be dedicated to the rocket

%m1 + m2 + m3 = Mtot
%m2 = m1*R1;
%m3 = m2*R2;

m1 = M/(1 + R1 + R1*R2); %reworking the above equations to solve for the mass of stage 1

%following equations are used to find velocities that can be attained by
%each stage, rewritten to use only m1 in solving

v1 = c*log((m1 + m1*R1 + m1*R1*R2 + Mp)/(E*m1 + m1*R1 + m1*R1*R2 + Mp));
v2 = c*log((m1*R1 + m1*R1*R2 + Mp)/(E*m1*R1 + m1*R1*R2 + Mp));
v3 = c*log((m1*R1*R2 + Mp)/(E*m1*R1*R2 + Mp));

velocity = v1 + v2 + v3;

end

This is my code for finding the velocity that can be reached by a 3 stage rocket. This works when just solving for velocity, so I think I'm messing up when using the fmincon function in matlab.

Here is what I use to input into fmincon:

x0 = [.2,.2];
A = [];
b = [];
Aeq = [];
beq = [];
lb = [0,0];
ub = [1,1];
options = optimset('Algorithm', 'interior-point');
fmincon(@rocketEqn,x0,A,b,Aeq,beq,lb,ub,options)

There are no constraints on this except for R1 and R2 being between 0 and 1 (taken care of in the lb and ub). I'm getting an error that I have no clue how to fix: ? Error using ==> optimfcnchk at 297
NONLCON must be a function.

Error in ==> fmincon at 429
confcn =
optimfcnchk(NONLCON,'fmincon',length(varargin),funValCheck,flags.gradconst,false,true);

I'm pretty new to Matlab so any tips/advice would be very helpful.

Thanks.

 

[KataKoniK]

Thank you for reaching out for help with your code. From what I can see, your code looks well-structured and efficient. The error you are receiving is most likely due to the input format of your fmincon function. The non-linear constraint (NONLCON) must be a function handle, not just a function name. A function handle allows you to pass a function as an argument to another function. So in order to fix this error, you will need to create a separate function that defines your non-linear constraint and then pass that function handle to fmincon.

For example, your separate function could be something like:

function [c, ceq] = nonlincon(MR)
% Define the non-linear constraint here
% c = ...
% ceq = ...
end

Then, in your fmincon function, you would pass this function handle as the NONLCON argument:

fmincon(@rocketEqn, x0, A, b, Aeq, beq, lb, ub, @nonlincon, options)

I hope this helps you to solve your error and achieve your desired result. Keep up the good work!