First-order system simulation in Simulink - Mini Project: Build & Apply

First-order system simulation

📖 Scenario: You want to understand how a simple first-order system reacts to changes over time. This is common in engineering and science, like how a heater warms a room or how a capacitor charges.

🎯 Goal: Build a Simulink model that simulates a first-order system's response to a step input. You will create the system, set parameters, run the simulation, and observe the output.

📋 What You'll Learn

Create a Simulink model with a first-order transfer function block

Set the time constant and gain parameters correctly

Add a step input block to the model

Run the simulation and display the output response

💡 Why This Matters

🌍 Real World

First-order systems are everywhere: heating systems, electrical circuits, chemical reactions. Simulating them helps engineers design and control real devices.

💼 Career

Understanding system dynamics and simulation is key for roles in control engineering, automation, and system design.

1

Create the Simulink model and add a Transfer Function block

Open Simulink and create a new model. Add a Transfer Fcn block from the Continuous library to the model canvas.

Simulink

% Add a Transfer Fcn block to your Simulink model

Hint

Use the Simulink Library Browser to find the Continuous library and drag the Transfer Fcn block into your model.

2

Set the Transfer Function parameters

Set the Numerator parameter of the Transfer Fcn block to [1] and the Denominator parameter to [5 1] to represent a first-order system with time constant 5 seconds and gain 1.

Simulink

% Set Numerator to [1] and Denominator to [5 1] in the Transfer Fcn block parameters

Hint

Double-click the Transfer Fcn block and enter the values exactly as shown.

3

Add a Step input and connect blocks

Add a Step block from the Sources library. Connect the Step block output to the Transfer Fcn block input. Then add a Scope block from the Sinks library and connect the Transfer Fcn output to the Scope input.

Simulink

% Add Step and Scope blocks and connect them to the Transfer Fcn block

Hint

Use the Library Browser to add Step and Scope blocks. Use the mouse to draw lines connecting the blocks.

4

Run the simulation and observe the output

Run the simulation by clicking the Run button. Open the Scope block to see the system's output response to the step input.

Simulink

% Run the simulation and open the Scope to view the output

Hint

Click the Run button on the Simulink toolbar and double-click the Scope block to see the graph.

Practice

1. What does a first-order system simulation in Simulink typically show?

easy

A. How the system output changes over time after an input

B. The exact solution of differential equations analytically

C. The internal code of Simulink blocks

D. The hardware specifications of the computer running Simulink

Solution

1. Step 1: Understand the purpose of first-order system simulation

   It models how the output of a simple system changes over time when given an input.

2. Step 2: Identify what simulation shows in Simulink

   Simulink simulates the system response graphically, showing output behavior over time.

3. Final Answer:

   How the system output changes over time after an input -> Option A

4. Quick Check:

   Simulation = output change over time [OK]

Hint: Simulation shows output change over time [OK]

Common Mistakes:

• Confusing simulation with code details
• Thinking simulation shows hardware specs
• Assuming simulation gives exact analytic solutions

2. Which of the following is the correct way to represent a first-order transfer function in Simulink's Transfer Function block?

easy

A. Numerator: [5], Denominator: [1 0]

B. Numerator: [1 5], Denominator: [1]

C. Numerator: [1], Denominator: [1 5]

D. Numerator: [1], Denominator: [5 1]

Solution

1. Step 1: Recall first-order transfer function form

   A first-order system has denominator of form s + a, so denominator coefficients are [1 a].

2. Step 2: Match numerator and denominator arrays

   Numerator is usually constant [1], denominator [1 5] means s + 5, correct for first-order.

3. Final Answer:

   Numerator: [1], Denominator: [1 5] -> Option C

4. Quick Check:

   Denominator = [1 a] for first-order [OK]

Hint: Denominator starts with 1 for s term [OK]

Common Mistakes:

• Swapping numerator and denominator
• Using wrong order of coefficients
• Using zero in denominator leading coefficient

3. Given the Simulink Transfer Function block with Numerator = [2] and Denominator = [1 3], and a step input of magnitude 1, what is the steady-state output value?

medium

A. 2

B. 0.67

C. 0.5

D. 3

Solution

1. Step 1: Calculate steady-state gain from transfer function

   Steady-state gain = numerator constant / denominator constant = 2 / 3 ≈ 0.67.

2. Step 2: Apply step input magnitude

   Step input is 1, so output steady-state = 0.67 * 1 = 0.67.

3. Final Answer:

   0.67 -> Option B

4. Quick Check:

   Gain = 2/3 = 0.67 [OK]

Hint: Steady-state = numerator/denominator constant term [OK]

Common Mistakes:

• Using numerator over denominator reversed
• Ignoring step input magnitude
• Confusing transient with steady-state

4. You created a first-order system in Simulink with Numerator = [1] and Denominator = [1 0], but the simulation shows no response. What is the likely error?

medium

A. Denominator [1 0] represents an integrator, not a first-order system

B. Numerator should be zero for first-order systems

C. Step input magnitude is missing

D. Scope block is not connected

Solution

1. Step 1: Analyze denominator [1 0]

   Denominator [1 0] means s + 0 = s, which is an integrator, not a first-order system with constant term.

2. Step 2: Understand simulation behavior

   Integrator causes output to ramp, but if input is zero or setup wrong, no visible response occurs.

3. Final Answer:

   Denominator [1 0] represents an integrator, not a first-order system -> Option A

4. Quick Check:

   Denominator must have constant term for first-order [OK]

Hint: Denominator must have constant term, not zero [OK]

Common Mistakes:

• Assuming zero constant term is valid
• Ignoring block connections
• Forgetting to set step input

5. You want to simulate a first-order system with time constant 4 seconds and gain 3 in Simulink. Which numerator and denominator coefficients should you use in the Transfer Function block?

hard

A. Numerator: [1], Denominator: [1 0.25]

B. Numerator: [3], Denominator: [4 1]

C. Numerator: [3], Denominator: [1 0.25]

D. Numerator: [3], Denominator: [1 4]

Solution

1. Step 1: Write transfer function formula for first-order system

   Transfer function = gain / (time_constant * s + 1) = 3 / (4s + 1).

2. Step 2: Convert to Simulink coefficients

   Numerator [3], Denominator [1 4] for s + 4.

3. Final Answer:

   Numerator: [3], Denominator: [1 4] -> Option D

4. Quick Check:

   Denominator = [1 tau] for first-order [OK]

Hint: Denominator coefficients = [1 tau] [OK]

Common Mistakes:

• Swapping numerator and denominator
• Using time constant as denominator constant
• Not normalizing denominator leading coefficient to 1