Zero-order hold in Simulink

Introduction

A zero-order hold keeps a signal constant between sample points. It helps convert digital signals back to continuous signals smoothly.

When you want to hold a sensor reading steady until the next measurement.

When converting a digital control signal to a continuous signal for a machine.

When simulating sampled data systems in Simulink.

When you need to maintain a value constant over a fixed time interval.

When modeling digital-to-analog converters in control systems.

Syntax

Simulink

Zero-Order Hold block in Simulink

Parameters:
- Sample time: time interval to hold the value

Input: discrete signal
Output: continuous signal held constant over sample time

The block holds the input value constant until the next sample arrives.

Sample time defines how long the value is held.

Examples

This example holds each input value for 0.1 seconds before updating.

Simulink

Set Sample time to 0.1 seconds
Input: discrete signal sampled every 0.1 seconds
Output: continuous signal held constant for 0.1 seconds

This example holds each input value for 1 second, useful for slower systems.

Simulink

Set Sample time to 1 second
Input: discrete signal sampled every 1 second
Output: continuous signal held constant for 1 second

Sample Program

This setup shows how the Zero-Order Hold keeps the sine wave value constant between samples.

Simulink

1. Open Simulink and create a new model.
2. Add a Sine Wave block (source of signal).
3. Add a Zero-Order Hold block.
4. Connect Sine Wave output to Zero-Order Hold input.
5. Set Zero-Order Hold sample time to 0.2.
6. Add a Scope block to visualize output.
7. Connect Zero-Order Hold output to Scope.
8. Run the simulation for 2 seconds.

Observe the Scope output showing the sine wave held constant every 0.2 seconds.

Important Notes

Zero-order hold creates a piecewise constant signal from discrete data.

It is simple but can introduce delay or distortion in some systems.

Useful for digital-to-analog conversion and sampled-data control systems.

Summary

Zero-order hold keeps input values constant between samples.

It converts discrete signals to continuous signals in Simulink.

Sample time controls how long each value is held.

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