Week 2 Assignment · Comparing Step Responses of Physical Models

English translation

First run: Select the start exercise button and sign into your MathWorks account if needed. When repository cloning finishes, this exercise's Control_Engineering_1_Week02_Physical_Models.mlx opens. Run and save it in your workspace. This .mlx Live Script combines explanations, code, and execution results. The current exercise requires Control System Toolbox.

Before practice

01 Motion models already learned

When calculating position with constant-velocity or constant-acceleration equations, what did you assume remained unchanged?

Description

Constant-velocity motion fixes velocity; constant-acceleration motion fixes acceleration. Restricting these changes lets position be calculated with simple equations.
If force changes due to a spring or friction, include that relation in the model. This exercise compares how those forces affect motion.

Review related concepts ↗

02 The model and actual characteristics

If the object becomes heavier or the spring changes, what must change in the model?

Description

Change a parameter representing the mass or spring stiffness. The numbers in the equations relate to the properties of the actual device.
Changing one characteristic at a time makes it easier to identify why the motion changes.

Practice

1. Derive the physical model

Input $u(t)$ is external force [N], and output $y(t)$ is mass displacement [m].

Use the mechanical model's $M=1,\ b=2,\ k=5$ .
Before running the code, mark the force directions and derive the differential equation using Newton's law.
Set the initial conditions to 0, apply the Laplace transform to find $\frac{Y(s)}{U(s)}$ , then calculate the final displacement under a constant force of 1 N.

Compare MATLAB's transfer function and final response with your own equations.
Record this calculation in the prediction field for the baseline case among the three mechanical-model comparisons.

Change one model parameter and explain the physical meaning of the response change.

Submission deadline: 2026-09-10 23:59 (Korean time)
Submission filename and format: Follow the teaching assistant's submission instructions.
Submission location: The corresponding assignment on KLAS. Follow the latest announcement if any changes are announced.

2. Parallel RLC circuit

The baseline values are $R=0.5$ Ω, $L=1$ H, and $C=5$ F. The input is current [A] and the output is voltage [V].

Run the baseline model’s unit-step response, then set parameter to "R", "L", and "C" in turn. For each parameter, rerun the “Change R, L, and C one at a time” code in the practice Live Script with factor=2 and factor=0.5. Keep the two unselected parameters at their baseline values.
Compare peak voltage, oscillation, and convergence between baseline and modified curves for each run. Record the changed parameter, its values before and after the change, and observed differences in the corresponding observation-table row.
For each parameter, explain one observed change in relation to the roles of resistance, inductance, and capacitance. Include a legend identifying conditions and units for time and voltage in the plot.

3. Mass–spring–damper

The row order for each condition is $\begin{bmatrix}M&b&k\end{bmatrix}$ .

Condition	$M$	$b$	$k$
Baseline	1	2	5
Increased damping	1	8	5
Increase spring stiffness	1	2	10

Keep the first row of cases, change the second row to [1 8 5], and the third to [1 2 10]. Run the three responses with the same 1 N step input and time axis.
Place all three curves in one figure, with a legend identifying the conditions and units for time and displacement. In the observation table, describe how peak displacement, presence of oscillations, convergence, and final displacement differ from the baseline curve.
Relate increased damping to the role of $b$ and increased spring stiffness to the role of $k$ . Explain the difference in final displacement using the steady-state force relationship.

Record results

Organize your results in the prediction, observation, and explanation fields in the provided Live Script. The initial comparison array is starter code; adapt it to the assignment's three conditions. Check axes, units, and legends, and explain results in your own words.