Question

Please provide Matlab code.

Components are inconsistencies all components designed to perform at a nominal value, however, due to manufacturing subject to variation from its desired value. are Referring to the diagram above, consider the following: Voltage is specified to be 18 V, tolerance is + 0.5 V Resistors Ri and R2 is specified to be 10 and R3 is specified to be 20 The tolerance on Ri and R2 is + 0.5 (+5 % of nominal) The tolerance on R3 is + 1.0 n (+5% of it's nominal) Simulation of the total resistance, Reg across this circuit 1. Steps: For N 10000, Randomly generate N values for Ri, R2, R3, 10,0) Let Ri Normal =10,o 2 : Normal u -) and R3 Normal u=20, a= 1 was determined by dividing the total range, 10+5 % by 6, (so 99.7 % are Note:For R1 & R2: a within spec, but this does still allow for extreme outliers because occasionally the supplier doesn't catch every bad part. Same for R3 but the tolerance range is wider. F Matlab command: >>N-10000; >R1-random(norm', 10,1/6, [N, 1 ]); After you've generated your R1, R2, and R3 vectors, use You might consider doing this in two steps: equation on page 1 to generate Re 1 1 1 + . + R2 R3 1 then Req Let A=- R A Matlab: ""before the desired operation: To perform operations on vector elements, put a period >>A-1./R1+1./R2+1./R3; A will be a Nxl vector. Now that you've got A, use same syntax to produce the Req vector. For you to hand in: Well labelled histograms of R1, R2, and R3. a. A well labelled histogram of Reg b. Based on the nominal values of RI, R2, and Ra, compute (by hand) the theoretical value for Reg c. Provide the mean and standard deviation of your simulated Reg results. d. The mean of your simulated Rea results is a point estimate for the true mean of Req How does the mean Req from your simulation compare to the theoretical value of Req? e. f. For a very large sample such as this, the 95% confidence interval for the true mean is: Mean of simulation + 1.96*(standard deviation of simulation)/N Compute and provide this confidence interval for the true mean of Req. Is the theoretical value for Reg contained in this interval? ri

Answer 1

close all,
clear all,
clc,

Mu_1=10;
Mu_2=10;
Mu_3=20;

Sigma_1 = 1/6;
Sigma_2 = 1/6;
Sigma_3 = 1/3;

N=1000;

R_1 = random('norm',Mu_1,Sigma_1,[N 1]);
R_2 = random('norm',Mu_2,Sigma_2,[N 1]);
R_3 = random('norm',Mu_3,Sigma_3,[N 1]);

for r=1:N
Req(r) = 1/((1/R_1(r)) + (1/R_2(r)) + (1/R_3(r)));
end

subplot(4,1,1); hist(R_1); title('Histogram Plot - R1'); xlabel('-- Res. Value (Ohms) -->'); ylabel('--- PDF --->');
subplot(4,1,2); hist(R_2); title('Histogram Plot - R2'); xlabel('-- Res. Value (Ohms) -->'); ylabel('--- PDF --->');
subplot(4,1,3); hist(R_3); title('Histogram Plot - R3'); xlabel('-- Res. Value (Ohms) -->'); ylabel('--- PDF --->');
subplot(4,1,4); hist(Req); title('Histogram Plot - Eq. Res. = R1 || R2 || R3'); xlabel('-- Res. Value (Ohms) -->'); ylabel('--- PDF --->');

EqResMean = mean(Req);
EqResSD = std(Req);

disp(['Eq. Res. Mean Value = ',num2str(EqResMean)]);
disp(['Eq. Res. Std. Dev. = ',num2str(EqResSD)]);

Histogram Plot R1 00 200 10.8 10.6 10.4 02 10 9.8 9.8 Res. Value (Ohms)- Histogram Plot R2 00 200 10.6 10.8 10.4 10.2 10 96 Res. Value (Ohms)-> Histogram Plot R3 МПО ПГ 20.5 8.5 19.5 19 Res. Value (Ohms)-> R1 || R2 || R3 Histogram Plot Eq. Res. 200 4 2 4.15 4.1 4.05 85 4 3.95 39 Res. Value (Ohms)->

Matlab Output

Eq. Res. Mean Value = 4.0002
Eq. Res. Std. Dev. = 0.040515
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