Zero-order hold in Simulink - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding Zero-Order Hold Output Behavior

In Simulink, a Zero-Order Hold (ZOH) block samples and holds the input signal at discrete time intervals. What best describes the output signal behavior of a ZOH block?

A The output signal is a linear interpolation between consecutive input samples.

B The output signal is a continuous-time signal that matches the input exactly.

C The output signal is a delayed version of the input signal with no change in shape.

D The output signal is a piecewise constant signal that holds the last sampled input value until the next sample.

💡 Hint

Think about how the ZOH maintains the input value between sampling instants.

The Zero-Order Hold block holds the input value constant between sampling points, producing a step-like output signal.

❓ Predict Output

intermediate

Output Values from a Zero-Order Hold Block

Given a discrete input signal sampled at 1 Hz with values [2, 4, 6, 8] at times t = 0, 1, 2, 3 seconds respectively, what will be the output of a Zero-Order Hold block at t = 2.5 seconds?

Simulink

Input samples: t=0s:2, t=1s:4, t=2s:6, t=3s:8
Sampling rate: 1 Hz
Query: Output at t=2.5s

A 7

B 6

C 8

D 4

💡 Hint

Remember that ZOH holds the last sampled value until the next sample.

At t=2.5s, the last sample was at t=2s with value 6, so the output holds this value until t=3s.

❓ data_output

advanced

Simulating Zero-Order Hold Output Data

Consider a continuous-time input signal defined as sin(2πt) sampled at 5 Hz. Using a Zero-Order Hold block, what is the output value at t = 0.22 seconds?

Simulink

Sampling frequency = 5 Hz (sampling interval = 0.2s)
Input signal: sin(2πt)
Samples at t=0s, 0.2s, 0.4s, ...
Find output at t=0.22s

A sin(2π × 0.4) ≈ 0.5878

B sin(2π × 0.22) ≈ 0.9877

C sin(2π × 0.2) ≈ 0.9511

D sin(2π × 0) = 0

💡 Hint

Zero-Order Hold output holds the last sampled value until the next sample.

At t=0.22s, the last sample was at t=0.2s, so output equals sin(2π × 0.2) ≈ 0.9511.

🔧 Debug

advanced

Identifying the Cause of Output Signal Distortion with Zero-Order Hold

A Simulink model uses a Zero-Order Hold block with a very large sample time on a rapidly changing input signal. The output appears distorted and delayed. What is the most likely cause?

A The sample time is too large, causing the output to hold outdated values for too long.

B The Zero-Order Hold block is incorrectly connected to the input signal.

C The input signal is continuous and cannot be sampled by a Zero-Order Hold block.

D The Zero-Order Hold block requires a smaller input amplitude.

💡 Hint

Think about how sample time affects the output signal's responsiveness.

A large sample time means the output holds each sampled value for a long time, causing distortion and delay when the input changes quickly.

🚀 Application

expert

Choosing Sample Time for Zero-Order Hold in Control Systems

In a digital control system, you use a Zero-Order Hold block to convert a discrete control signal to continuous time. The system has a bandwidth of 50 Hz. Which sample time for the Zero-Order Hold block is most appropriate to avoid aliasing and maintain control accuracy?

A Sample time of 0.005 seconds (200 Hz sampling rate)

B Sample time of 0.02 seconds (50 Hz sampling rate)

C Sample time of 0.1 seconds (10 Hz sampling rate)

D Sample time of 0.5 seconds (2 Hz sampling rate)

💡 Hint

Recall the Nyquist sampling theorem and how sample rate relates to system bandwidth.

To avoid aliasing, the sampling frequency should be at least twice the system bandwidth. For 50 Hz bandwidth, sample at >100 Hz. 200 Hz (0.005s) is appropriate.

Practice

1.

What is the main function of a Zero-order hold block in Simulink?

easy

A. It converts continuous signals to discrete signals.

B. It differentiates the input signal continuously.

C. It integrates the input signal over time.

D. It holds the input value constant between sample times.

Solution

1. Step 1: Understand the role of Zero-order hold and compare options

   The Zero-order hold block keeps the input value constant during the sample period. It does not differentiate, integrate, or convert continuous to discrete signals.

2. Final Answer:

   It holds the input value constant between sample times. -> Option D

3. Quick Check:

   Zero-order hold = hold input constant [OK]

Hint: Remember: zero-order hold means 'hold value constant' [OK]

Common Mistakes:

• Confusing zero-order hold with differentiation or integration
• Thinking it converts continuous to discrete signals
• Assuming it changes the signal value continuously

2.

Which of the following is the correct way to set the fixed sample time parameter in a Zero-order hold block in Simulink?

easy

A. Set sample time to a positive number like 0.1 seconds.

B. Set sample time to -1 for inherited sample time.

C. Set sample time to 0 for continuous operation.

D. Set sample time to a negative number other than -1.

Solution

1. Step 1: Understand sample time settings and evaluate options

   Fixed sample time must be a positive number (e.g., 0.1s) to specify hold duration. -1 inherits from input; 0 means continuous (no hold); other negatives invalid.

2. Final Answer:

   Set sample time to a positive number like 0.1 seconds. -> Option A

3. Quick Check:

   Sample time positive number = correct setting [OK]

Hint: Sample time must be positive for zero-order hold [OK]

Common Mistakes:

• Using zero or negative sample times incorrectly
• Confusing inherited sample time (-1) with explicit sample time
• Setting sample time to continuous (0) for discrete hold

3.

Consider this Simulink model snippet using a Zero-order hold block with sample time 0.5 seconds. The input signal is a step that changes from 0 to 1 at time 0.3 seconds. What will be the output of the Zero-order hold block at time 0.7 seconds?

medium

A. 0.5

B. 0

C. 1

D. Undefined

Solution

1. Step 1: Analyze sample intervals and input timing

   With sample time 0.5s, samples at 0, 0.5, 1.0s. Step changes at 0.3s, so input(0)=0, input(0.5)=1. At 0.7s (in [0.5,1.0)), holds 1.

2. Final Answer:

   1 -> Option C

3. Quick Check:

   Output holds last sampled input = 1 [OK]

Hint: Output holds input at last sample time before current time [OK]

Common Mistakes:

• Thinking sample at 0.5s captures 0 despite change at 0.3s
• Ignoring sample time intervals
• Confusing step change time with sample time

4.

In a Simulink model, a Zero-order hold block is set with sample time 0.2 seconds. The output signal is not holding values as expected and changes continuously. What is the most likely cause?

medium

A. Sample time is set to 0 (continuous) instead of 0.2.

B. Input signal is discrete, so hold is unnecessary.

C. Zero-order hold block is connected incorrectly.

D. Sample time is set to a negative number other than -1.

Solution

1. Step 1: Identify cause of continuous output behavior

   If sample time=0, block operates continuously (follows input without holding). Other causes less likely to produce continuous change.

2. Final Answer:

   Sample time is set to 0 (continuous) instead of 0.2. -> Option A

3. Quick Check:

   Continuous sample time = no hold [OK]

Hint: Check sample time is positive, not zero [OK]

Common Mistakes:

• Ignoring sample time setting
• Assuming input signal type causes issue
• Misconnecting blocks without checking parameters

5.

You want to convert a discrete sensor signal sampled every 0.1 seconds into a continuous signal for further processing in Simulink. Which approach using a Zero-order hold block is correct?

Choose the best option.

hard

A. Do not use Zero-order hold; use a continuous integrator instead.

B. Set the Zero-order hold sample time to 0.1 seconds to hold each sample value constant until the next sample.

C. Set the Zero-order hold sample time to -1 to inherit sample time from input.

D. Set the Zero-order hold sample time to 0 to make the output continuous.

Solution

1. Step 1: Understand goal and evaluate ZOH configurations

   Goal: hold discrete samples constant between 0.1s intervals for continuous output. Set Ts=0.1s matches sensor rate. Ts=0 continuous (no hold); -1 inherits (risk mismatch); integrator changes values.

2. Final Answer:

   Set the Zero-order hold sample time to 0.1 seconds to hold each sample value constant until the next sample. -> Option B

3. Quick Check:

   Sample time = sensor rate for correct hold [OK]

Hint: Match hold sample time to sensor sample interval [OK]

Common Mistakes:

• Setting sample time to zero for hold
• Using inherited sample time without checking input
• Replacing hold with integrator incorrectly