what is the wrong wtih the “fsolve” function to solve the problem？

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cheng sy 2015-10-10

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https://ww2.mathworks.cn/matlabcentral/answers/247825-what-is-the-wrong-wtih-the-fsolve-function-to-solve-the-problem

评论： cheng sy 2015-10-28

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the figure is the lightning voltage,if the maxium amplitude of it is Um, the green line

crosses the two points:(t1,90%*Um) and (t2,30%*Um),and it intersect at x-axis and horizontal

line of Um。tf is called wave-front time，and the Tt is the half-tail time。Usuallly,we

suppose the voltage can express as the following equation(also double exponential equation):

u(t)=U*ζ*(exp(-a*t)-exp(-b*t)). Now, we know the tf,Tt and U(the maxium amplitude)，

the ζ，a，and b to be solved. this question can be solved by the matlab function fsolve. i

have defined the following fuction in matlab:

%--------------------------------------------------------------------%
    function Vc = imp_f(x,tf,Tt,U)
    %UNTITLED2 Summary of this function goes here
    %   Detailed explanation goes here
    % X is the [a；β；ζ；t1；t2]
    % a/β/ζ are the parameters in function ：i（t）=U*ζ*(exp(-a*t)-exp(-β*t))；
    % t1/t2/Tt/tf：(t1,90%*Um) and (t2,30%*Um) have the same meaning in the previous figure ，U is voltage crest，kV;
    Vc=[tf-(x(4)-x(5))/0.6;                           % tf=(x(4)-x(5))/0.6
        0.3*U-x(3)*(exp(-x(1)*x(5))-exp(-x(2)*x(5))); % cross the point (t2,30%*Um)
        0.9*U-x(3)*(exp(-x(1)*x(4))-exp(-x(2)*x(4))); % cross the point (t1,90%*Um)
        0.5*U-x(3)*(exp(-x(1)*(Tt+1.5*x(5)-0.5*x(4)))-exp(-x(2)*(Tt+1.5*x(5)-0.5*x(4)))); %cross the point  
                                                                                           (Tt+1.5*t2-0.5*t1,50%*Um)
        U-x(3)*(exp(-x(1)*log(x(2)/x(1))/(x(2)-x(1)))-exp(-x(2)*log(x(2)/x(1))/(x(2)-x(1))))];
                                                                                         %cross the maximu value point  
                                                                                            (log(β/a)/(β-a),Um)
    end

then use the following code to find the answer：

%--------------------------------------------------------------------------
tf=1.2;    %
Tt=50;     %
U=1.0;    %
x0=[1;1;1;1;1]; %初值；
[x,fval]=fsolve(@(x) imp_f(x,tf,Tt,U),x0);  % Call solver
%---------------------------------------------------------------

MATLAB give the following wrong answer：

%---------------------------------------------------------------
Error using trustnleqn (line 28)
Objective function is returning undefined values at initial point. FSOLVE cannot continue.
Error in fsolve (line 376)
    [x,FVAL,JACOB,EXITFLAG,OUTPUT,msgData]=...
Error in l_impluse (line 11)
[x,fval]=fsolve(@(x) imp_f(x,tf,Tt,U),x0);  % Call solver
%--------------------------------------------------------------