Course materials · Control Engineering I

Week 4 · Connecting Transfer Functions and Blocks

English translation

Before practice

01 Problem and goal

What information is needed to understand an object's motion and control it as intended?

Description
  • First specify the desired motion, such as maintaining velocity or changing position.
  • You need current position and velocity, a controllable force, and a relationship describing how that force changes motion.

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02 Level of model detail

When is a simple constant-velocity or constant-acceleration model sufficient, and when is a more detailed model needed?

Description
  • Constant velocity may suffice to estimate distance traveled over a short interval. To describe how an object attached to a spring oscillates and stops, include forces that depend on position and velocity.
  • Start by representing the changes needed for the purpose rather than including every element. Reconsider omitted effects when differences between predictions and observations become significant.

03 Representation and use

What is easier to check by representing the same motion model as both equations and blocks?

Description
  • Equations show relationships between variables; blocks show how signals travel and connect.
  • The same model with the same input and initial conditions should produce the same response. This exercise checks whether different representations implement the same relationship.

Practice

1. Construct the transfer function

  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. State the transfer function used, and record dcgain(G) beside the hand-calculated 1/k1/k. State whether they agree.

2. Block connections and responses

  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 both equations' denominator coefficients in the same power order and compare them. Also identify which coefficients differ from the case H=1H=1.

3. Open the Simulink model

  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.

Submission and saving

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.

Restart the runtime, run all code from the top, then save.

Optional practice

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.