Zero-order hold in Simulink - Mini Project: Build & Apply

Zero-order Hold Simulation in Simulink

📖 Scenario: Imagine you are working on a digital control system where sensor data is sampled at discrete times. To hold the sensor value constant between samples, you use a zero-order hold (ZOH) block. This project will guide you through setting up a simple Simulink model to simulate a zero-order hold on a signal.

🎯 Goal: You will build a Simulink model that uses a Zero-Order Hold block to hold the input signal constant between sample times and observe the output signal behavior.

📋 What You'll Learn

Create a time vector representing the simulation time

Create a sample time variable for the zero-order hold

Add a Zero-Order Hold block with the specified sample time

Simulate the model and display the output signal

💡 Why This Matters

🌍 Real World

Zero-order hold is used in digital control systems to maintain a constant signal value between sampling times, which is common in sensor data processing and digital-to-analog conversion.

💼 Career

Understanding zero-order hold and Simulink simulation is important for control engineers, embedded systems developers, and anyone working with digital signal processing or automation.

1

Create the simulation time vector

Create a variable called t that is a vector from 0 to 10 with increments of 0.1 seconds.

Simulink

# Create the time vector t from 0 to 10 with step 0.1
# Your code here

Hint

Use the colon operator to create a vector: start:step:end

2

Define the sample time for the Zero-Order Hold

Create a variable called Ts and set it to 0.5 to represent the sample time for the zero-order hold block.

Simulink

t = 0:0.1:10;
# Define the sample time Ts as 0.5 seconds
# Your code here

Hint

Assign 0.5 to the variable Ts using the equals sign.

3

Add and configure the Zero-Order Hold block

In your Simulink model, add a Zero-Order Hold block and set its sample time parameter to the variable Ts.

Simulink

t = 0:0.1:10;
Ts = 0.5;
% Add Zero-Order Hold block and set sample time to Ts
% Your code here (in Simulink environment)

Hint

Open Simulink, drag the Zero-Order Hold block into your model, and set its sample time to Ts in the block parameters.

4

Simulate the model and display the output

Run the simulation and use a Scope block to observe the output of the Zero-Order Hold block. Print the message 'Simulation complete: output observed in Scope.'

Simulink

t = 0:0.1:10;
Ts = 0.5;
% Run the simulation and display output
% Your code here

Hint

Use fprintf to print the message after simulation.

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