First-order system simulation in Simulink - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to define the transfer function of a first-order system with gain K and time constant T.

Simulink

sys = tf([[1]], [T 1])

Drag options to blanks, or click blank then click option'

AK

BT

C1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using time constant T in numerator instead of gain K

Using 1 or 0 incorrectly in numerator

The numerator of the transfer function for a first-order system is the gain K.

2fill in blank

medium

Complete the code to simulate the step response of the system 'sys' for 10 seconds.

Simulink

step(sys, [1])

Drag options to blanks, or click blank then click option'

A5

B20

C15

D10

Attempts:

3 left

💡 Hint

Common Mistakes

Using incorrect simulation time

Omitting the simulation time argument

The step response is simulated for 10 seconds as specified.

3fill in blank

hard

Fix the error in the code to correctly define the time vector for simulation from 0 to 10 seconds with 0.1s step.

Simulink

t = [1];

Drag options to blanks, or click blank then click option'

Arange

B0:0.1:10

Clinspace

Darange

Attempts:

3 left

💡 Hint

Common Mistakes

Using Python functions like range or arange

Using vector syntax incorrectly

The colon operator 0:0.1:10 creates linearly spaced vectors and is correct here.

4fill in blank

hard

Fill both blanks to create a transfer function with gain 5 and time constant 2.

Simulink

sys = tf([[1]], [[2] 1])

Drag options to blanks, or click blank then click option'

A5

B2

C1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping gain and time constant

Using 1 or 0 incorrectly in numerator or denominator

The numerator is the gain 5, and the denominator uses the time constant 2 followed by 1.

5fill in blank

hard

Fill all three blanks to simulate the step response of 'sys' over time vector 't' and plot the result.

Simulink

y = step(sys, [1]);
plot([2], [3]);
xlabel('Time (s)');
ylabel('Output');
title('Step Response');

Drag options to blanks, or click blank then click option'

At

By

Dsys

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing order of plot arguments

Using system object instead of output or time vector

Step response is computed over time vector t, then plotted with time t on x-axis and output y on y-axis.

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