Integrating over a step function

Hello everyone,

I´m currently working on a little program where I read some data from an Ecxel Sheet and plot a cooling curve from it with some mathematical equotions. Until now i have only used one value (scalar) for my power profile P and PC. Now i want to integrate a power profile from an excel sheet, which is not an scalar anymore but rather a step function. My problem is now that i dont know how to finish the code as i dont know how to implement the step function into the integral. I have to plot 2 different curves given from to 2 different results, thats why it is doubled.

Thanks in advance.

the profile is given below, on the left the time in seconds is given and on the right side the Power profile.

% The file should be in the currently used Matlab folder
% Please enter the .xlsx data and the desired measurement (Fit) of the examined chip
values = xlsread('AAA', 'Fit 1');

% The file should be in the currently used Matlab folder
% Please enter the .xlsx data and measurement of the coupled thermoelement
valuesC = xlsread('Kopplung', 'Fit 1');

% Please enter the power profile
PowerValues = xlsread('LeistungImpuls4Chips', 'Chip4_P');
 
cooling_time = values(:,1)';

Fitted_Curve = values(:,3)';
 
R_F = values(:,4);
R_F = R_F(~isnan(R_F))';
 
C_F = values(:,5);
C_F = C_F(~isnan(C_F))';

Tmax = max(values(:,2));

P = @(t) 303,839733;

cooling_timeC = valuesC(:,1)';

Fitted_CurveC = valuesC(:,3)';
 
R_FC = valuesC(:,4);
R_FC = R_FC(~isnan(R_FC))';
 
C_FC = valuesC(:,5);
C_FC = C_FC(~isnan(C_FC))';

TmaxC = max(valuesC(:,2));

PC = @(k) 827,2826177;


%Time = values3(:,2)';
%Power = values3(:,1)';

%Calculation of the derived Zth values
dZ_th = @(t) 0;
for v = 1:length(R_F)
dZ_th = @(t) dZ_th(t) + exp(-t / (R_F(v) * C_F(v))) / C_F(v);
end

dZ_thC = @(k) 0;
for l = 1:length(R_FC)
dZ_thC = @(k) dZ_thC(k) + exp(-k / (R_FC(l) * C_FC(l))) / C_FC(l);
end

%Calculation of the temperature curve
T_j_scalar_t = @(t) integral(@(tau) P(tau) .* dZ_th(t - tau), 0, t);
T_j = arrayfun(@(t)T_j_scalar_t(t), cooling_time);


T_j_scalar_tC = @(k) integral(@(lambda) PC(lambda) .* dZ_thC(k - lambda), 0, k);
T_jC = arrayfun(@(k)T_j_scalar_tC(k), cooling_timeC);


%reversing the temperature curve
T_i =   (Tmax - T_j);
semilogx(cooling_time, T_i)
hold on


T_iC =   (TmaxC - T_jC);
semilogx(cooling_timeC, T_iC)
hold on


T_all = (T_i + T_iC)
semilogx(cooling_time, T_all)
hold on


%Calculation of Zth curve
%Zth_norm =   (Tmax - T_j) ./P(cooling_time);
%semilogx(cooling_time, Zth_norm)
%hold on

%Zth2_norm =   (Tmax2 - T_j2) ./P(cooling_time2);
%semilogx(cooling_time2, Zth2_norm)
%hold off

xlabel("Time in s");
ylabel("Temperature")

legend('T_i','T_iC','T_all')

[Torsten]

So which values should P and Pc in your code take ?

E.g., is P = 800 only for t = 200 and 0 else ? Then the usual "integral" will give you a value of 0 for

T_j_scalar_t = @(t) integral(@(tau) P(tau) .* dZ_th(t - tau), 0, t);

[David Sicic]

The value for P is at t = 0 P = 0, then at 200 it rises to 800 and at 250 it falls back to 0.

[David Sicic]

So we have from t = 200 - t = 250 P = 800.

[Torsten]

Then

P = @(t) 800.*(t>=200).*(t<=250)

[David Sicic]

but how about if i have an complex system, with over 1500 inputs for the power profile?

I attached the excel table for a more complex power profile

[Torsten]

P = @(t) interp1(t_Excel,P_Excel,t)

where t_Excel and P_Excel are the Excel columns for time and corresponding Power input, respectively.

[David Sicic]

Im getting now quite a big error message

Error using matlab.internal.math.interp1

The sample points must be finite.

[Torsten]

Then your vectors t_Excel and/or P_Excel contain NaN, Inf or -Inf values.

Further take care that t_Excel is ordered (either ascending or descending).

Further the interpolation will return NaN if the t-value with which it is called is not in between t_Excel_min and t_Excel_max.