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Control Engineering I · Week 04 · Connecting Transfer Functions and Blocks

English translation

Edit the code and response fields in your own copy. Name: ⟦enter here⟧ / Student ID: ⟦enter here⟧

How to run

In Live Editor, click inside the code and run the current section with Run Section (Windows/Linux Ctrl+Enter, Mac ⌘+Enter). Run executes the entire document. Edit the explanations and response fields directly.
Initially run from the top, and rerun any section whose values you change. If an undefined-variable error occurs, run the preceding sections first. Outputs appear below or to the right of the code.
Environment: MATLAB Online and Control System Toolbox. Simulink is also required to run the Simulink model.

1. Construct the transfer function

Enter coefficients in descending powers.
Prediction before running: ⟦enter here⟧
G=tf(1,[1 2 5]);
T=feedback(G,1);
disp(G);disp(T);
assert(abs(dcgain(G)-.2)<1e-10);
Do it yourself:
  1. Substitute M=2M=2, b=3b=3, and k=6k=6 into the mechanical model's transfer function 1/(Ms2+bs+k)1/(Ms^2+bs+k) to create a MATLAB model.
  2. Write the transfer function used and record dcgain(G) beside the hand-calculated 1/k1/k. State whether the two values agree.
% ✍ Your code: add your own code below.
Changed condition: ⟦enter here⟧
Observed result: ⟦enter here⟧
Differences from the prediction and their causes: ⟦enter here⟧

2. Block connections and responses

Compare using the same time axis.
Prediction before running: ⟦enter here⟧
G=tf(1,[1 2 5]);T=feedback(G,1);t=0:.01:10;
figure;step(G,T,t);legend('Open-loop','Unity feedback');grid on;
Do it yourself:
  1. Keep the baseline G=tf(1,[1 2 5]) and connect negative feedback with H=2H=2.
  2. Write the closed-loop transfer function simplified by hand beside the result of feedback(G,2).
  3. Write and compare the denominator coefficients of both equations in the same order of powers. Also mark which coefficients differ from the case H=1H=1.
% ✍ Your code: add your own code below.
Changed condition: ⟦enter here⟧
Observed result: ⟦enter here⟧
Differences from the prediction and their causes: ⟦enter here⟧

3. Open the Simulink model

Open the accompanying .slx in MATLAB Drive, or build the same model as shown below.
Prediction before running: ⟦enter here⟧
modelName='Control_Engineering_1_Week04_Block_Model';
if isfile([modelName '.slx'])
open_system(modelName);
else
disp('블로그 자료 모음에서 Week04 .slx 파일을 같은 폴더에 받으세요.');
end
Do it yourself:
  1. Connect Step → Transfer Fcn → Scope in Simulink. Set the numerator to [1] and denominator to [1 2 5] to match the baseline G=tf(1,[1 2 5]).
  2. Run with Step time=0, Final value=1, and Stop time=10.
  3. Present the Scope output beside MATLAB's step(G,0:0.01:10) curve. Use the same time range and output-axis range, and state whether the final values and curve shapes agree. This block diagram corresponds to G without feedback.
% ✍ Your code: add your own code below.
Changed condition: ⟦enter here⟧
Observed result: ⟦enter here⟧
Differences from the prediction and their causes: ⟦enter here⟧

Practice through repetition and check before submission

Summarize the three conditions compared in the preceding hands-on activities below. You do not need to repeat experiments already completed. Predictions may state increasing or decreasing trends instead of exact values.
Repetition 1 — Condition: ⟦enter here⟧ / Prediction: ⟦enter here⟧ / Actual result: ⟦enter here⟧
Trial 2 — Condition: ⟦enter here⟧ / Prediction: ⟦enter here⟧ / Observation: ⟦enter here⟧
Trial 3 — Condition: ⟦enter here⟧ / Prediction: ⟦enter here⟧ / Observation: ⟦enter here⟧
Optional:
Example: changing the coefficient order in a transfer-function denominator
  1. Create the baseline tf(1,[1 2 5]) and a separate model tf(1,[5 2 1]) with reversed coefficient order.
  2. Write each denominator polynomial and DC gain side by side. Change only the denominator vector to [1 2 5] so that s2+2s+5s^2+2s+5.
Include code, actual outputs and plots, and your own interpretation. Submit through KLAS; check the semester schedule and latest announcements for the deadline.
Filename: Name_StudentID_Week4.mlx.