Transfer function block in Simulink - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a Transfer Function block in Simulink?

A Transfer Function block represents a system using a ratio of polynomials in the Laplace variable s. It models how input signals are transformed to output signals in linear time-invariant systems.

beginner

How do you specify a Transfer Function in the block parameters?

You enter the numerator and denominator coefficients as vectors. For example, numerator [1 3] means 1*s + 3, denominator [1 5 6] means s² + 5*s + 6.

intermediate

Why is the Transfer Function block useful in control systems?

It helps simulate and analyze system behavior like stability and response to inputs, without needing to write differential equations manually.

intermediate

What happens if the denominator polynomial has roots with positive real parts?

The system is unstable because the output will grow without bound over time, which can be seen in the simulation results.

advanced

Can the Transfer Function block handle time delays directly?

No, the Transfer Function block models rational functions of s only. Time delays require special blocks like the Transport Delay block.

What does the numerator vector in a Transfer Function block represent?

A Coefficients of the denominator polynomial in s

B Coefficients of the numerator polynomial in s

C Initial conditions of the system

D Time delay values

The numerator vector contains coefficients for the polynomial in the numerator of the transfer function.

If the denominator polynomial has roots with positive real parts, what does it indicate?

A The system is stable

B The system is time delayed

C The system has no output

D The system is unstable

Roots with positive real parts cause the system output to grow over time, indicating instability.

Which variable is used in the Transfer Function block to represent the Laplace transform?

A s

B z

C t

D x

The Laplace variable is denoted by s in transfer functions.

Can the Transfer Function block model nonlinear systems?

A No, only linear time-invariant systems

B Only if time delays are included

C Yes, directly

D Only with initial conditions

Transfer Function blocks model linear time-invariant systems only.

How do you enter the denominator polynomial s² + 4s + 3 in the Transfer Function block?

A [4 3]

B [1 3 4]

C [1 4 3]

D [3 4 1]

The denominator vector lists coefficients from highest to lowest power: s² coefficient 1, s coefficient 4, constant 3.

Explain how to set up a Transfer Function block in Simulink to model a system with transfer function (s + 2)/(s² + 3s + 2).

Think about how polynomials translate to coefficient vectors.

Describe what the Transfer Function block output tells you about system behavior when you simulate a step input.

Consider what happens to the output signal after a sudden input change.

Practice

1. What does the Transfer Function block in Simulink represent?

easy

A. A mathematical model using numerator and denominator polynomials

B. A block that generates random signals

C. A tool for drawing system diagrams

D. A block that stores data values

Solution

1. Step 1: Understand the Transfer Function block purpose and compare options

   The Transfer Function block models system behavior mathematically using polynomials. Only a mathematical model using numerator and denominator polynomials correctly describes the block.

2. Final Answer:

   A mathematical model using numerator and denominator polynomials -> Option A

3. Quick Check:

   Transfer Function = numerator/denominator polynomials [OK]

Hint: Remember: Transfer function = output/input ratio [OK]

Common Mistakes:

• Confusing with signal generator blocks
• Thinking it stores data instead of modeling
• Assuming it draws diagrams

2. Which of the following is the correct way to enter a transfer function with numerator [1 3] and denominator [1 5 6] in the Simulink Transfer Function block?

easy

A. Numerator: [1 3], Denominator: [1 5 6]

B. Numerator: 1/3, Denominator: 1/5/6

C. Numerator: (1,3), Denominator: (1,5,6)

D. Numerator: {1 3}, Denominator: {1 5 6}

Solution

1. Step 1: Recall Simulink syntax for polynomials and match options

   Simulink requires vectors in square brackets for numerator and denominator coefficients. Only Numerator: [1 3], Denominator: [1 5 6] uses square brackets and space-separated coefficients correctly.

2. Final Answer:

   Numerator: [1 3], Denominator: [1 5 6] -> Option A

3. Quick Check:

   Use square brackets for polynomials [OK]

Hint: Use square brackets for coefficient vectors [OK]

Common Mistakes:

• Using slashes or commas instead of spaces
• Using parentheses or braces instead of brackets
• Entering fractions instead of vectors

3. Given a Transfer Function block with numerator [2] and denominator [1 4 4], what is the expected system type?

medium

A. First-order system

B. Third-order system

C. Second-order system

D. Zero-order system

Solution

1. Step 1: Determine system order from denominator degree and match to options

   The denominator polynomial [1 4 4] has 3 coefficients, so degree is 2 (order = degree of denominator). A second-order system corresponds to denominator degree 2.

2. Final Answer:

   Second-order system -> Option C

3. Quick Check:

   Order = degree of denominator polynomial = 2 [OK]

Hint: System order = degree of denominator polynomial [OK]

Common Mistakes:

• Counting number of coefficients instead of degree
• Confusing numerator degree with system order
• Assuming order from numerator length

4. You entered numerator [1 0] and denominator [1 -2 1] in a Transfer Function block, but the simulation shows unexpected oscillations. What is the likely cause?

medium

A. Numerator should have more coefficients

B. Simulation time is too short

C. Transfer Function block does not support negative coefficients

D. Incorrect sign in denominator coefficients causing instability

Solution

1. Step 1: Analyze denominator polynomial for stability and identify cause

   The denominator [1 -2 1] corresponds to (s-1)^2, which has poles at s=1 (right half-plane), causing instability. Incorrect sign in denominator coefficients leads to this.

2. Final Answer:

   Incorrect sign in denominator coefficients causing instability -> Option D

3. Quick Check:

   Poles in right half-plane cause oscillations [OK]

Hint: Check denominator signs for stability [OK]

Common Mistakes:

• Assuming numerator length causes oscillations
• Believing negative coefficients are unsupported
• Ignoring pole locations

5. You want to model a system with transfer function \( \frac{5s + 10}{s^2 + 3s + 2} \) in Simulink. How should you enter the numerator and denominator coefficients in the Transfer Function block?

hard

A. Numerator: [10 5], Denominator: [1 3 2]

B. Numerator: [5 10], Denominator: [1 3 2]

C. Numerator: [5 10], Denominator: [1 2 3]

D. Numerator: [5 10], Denominator: [3 2 1]

Solution

1. Step 1: Identify numerator and denominator coefficients in descending powers of s

   Numerator is 5s + 10, so [5 10]; denominator s^2 + 3s + 2, so [1 3 2].

2. Final Answer:

   Numerator: [5 10], Denominator: [1 3 2] -> Option B

3. Quick Check:

   Coefficients match polynomial terms in order [OK]

Hint: List coefficients from highest to lowest power [OK]

Common Mistakes:

• Reversing coefficient order
• Mixing up numerator and denominator
• Using incorrect coefficient values