how can I get 5 parameters in using the optimization tool of an equation

how can i optimize the 5 parameters of the following equation,

have to determine the c_1,c_2,m_1,m_2,r_s,r_p. the actual vaule is given;c_1=170.80; % [AK^(-3)],c_2=18.8e-3; % [AK^(-5/2)],m_1=1.00; % [ ], m_2=2.00; % [ ]

r_s=50e-4; % [Ohm], r_p=5;

given the parameters, t=25; %temperature (C),,i_ph=3.113; %phase current [A],e_g=1.12; %band gap [eV], e=1.6*10^-(19); %electronvolt [j]

k=1.38*10^-(23), %Boltzmann constant [JK^(-1)], U=(0:0.001:0.6); %voltage [V]

Answer 1

[Jannatul Ferdous Tania]

for optimaization one parameter i got,

clear,clc

t=25; %temperature (C)

T=t+273; %temperature (K)

i_ph=3.113; %phase current [A]

e_g=1.12; %band gap [eV]

c_01=170.80; %co-efficient of saturation current [AK^(-3)]

m_1=1.00; %diode factor

e=1.6*10^-(19); %electronvolt [j]

k=1.38*10^-(23); %Boltzmann constant [JK^(-1)]

U=(0:0.001:0.6); %voltage [V]

% Ut=(k*T)/e;

Ut=0.0257

I= i_ph - (c_01 * T^3 * exp(-((e_g*e)/(k*T)))) .* (exp(U./(m_1*Ut))-1);

plot(U,I,'linewidth',2.5,'DisplayName','real curve');

axis([0,0.6,0,3.5]);

xlabel('Spannung U');

ylabel('Strom A');

grid on;

% legend show

hold on

% c_01_guess=870.80; %co-efficient of saturation current [AK^(-3)]

%

% I= i_ph - (c_01_guess * T^3 * exp(-((e_g*e)/(k*T)))) .* (exp(U./(m_1*Ut))-1);

% plot(U,I,'linewidth',2.5,'DisplayName','guessed curve');

%first define optimization variables

c_01=optimvar('c_01');

m_1=optimvar('m_1');

%create expression for the objective function, which is the square to minimize

fun=i_ph - (c_01 * T^3 * exp(-((e_g*e)/(k*T)))) .* (exp(U./(m_1*Ut))-1);

obj=sum((fun - I).^2);

%create an optimized problem with the function obj

lsqproblem = optimproblem("Objective",obj)

%for the problem based appraoch, specify the initial point as a structure,with the variable names and fields of the structure

x0.c_01 = [870.8]

x0.m_1 = [1.2]

%Review the problem formulation

show(lsqproblem)

%solving problem using Isqnonlin

[sol,fval] = solve(lsqproblem,x0)

%Plot the resulting solution and original data

% figure

responsedata = evaluate(fun,sol);

plot(U,I,'r*',U,responsedata,'b-');

% plot(U,responsedata,'black--','DisplayName','responsedata')

legend('Original Data','Fitted Curve')

legend show

axis([0,0.6,0,3.5]);

xlabel('Spannung U');

ylabel('Strom A');

grid on;

% display solved c_01 value

disp(sol.c_01)

disp(sol.m_1)

Answer 2

[Alan Weiss]

I would not write the sum of squares explicitly. Instead, formulate your problem as an EquationProblem and solve that. You can have five variables in the problem as easily as one. Of course, with just one equation and five variables, it is unlikely that there is a unique solution. But perhaps I misunderstand the problem.

Alan Weiss

MATLAB mathematical toolbox documentation