soniya_shah asked . 2021-10-21

How to solve an equation system using a interp1-variable

% variable definiton
% T                     function argument
% p = f(T)              values are given in form of a 69x2 double
% a | b | c | h         constants / parameters (defined or calculated beforehand)

% equations
% eqn 1
% p = interp1(p(:,1),p(:,2),T)
% eqn 2
% h = a * T + p * (b + c * T)

% As I am used to solve equations with my pocket calculator I quickly found something like this while browsing:

syms T
solve (h == a * T + interp1(p(:,1),p(:,2),T) * (b + c * T),T);

% Unfortunately I do not have the required toolbox to solve equations which is why I need to find a work-around

% my next idea was to use an iteration to solve this (which I did not formulate and test until now)
% it would be something like that though:

for T = 1:100
    p = interp1(p(:,1),p(:,2),T);
    h_iter = a * T + p * (b + c * T);
    if h_iter > h - h_marge | h_iter < h + h_marge
        break
    end
end

% with h_marge being a predefined value for accuracy tolerance

solve , equation , interp1 , iteration , simulink , matlab-function