Unit delay block in Simulink

Introduction

The Unit delay block helps you remember the previous value of a signal. It delays the input by one time step, so you can compare or use past data in your model.

When you want to keep track of the last value of a sensor reading in a control system.

When building a system that needs to compare current and previous data points, like detecting changes over time.

When simulating processes that depend on past states, such as filters or feedback loops.

When you want to create a memory effect in your model to analyze time-dependent behavior.

Syntax

Simulink

Unit Delay
- Input: current signal value
- Output: previous signal value
- Delay length: 1 sample time

The block outputs the input from the previous time step.

Initial condition can be set to define the output at the first step.

Examples

The output starts with the initial condition, then shows the previous input values shifted by one step.

Simulink

Input signal: [5, 7, 9, 11]
Unit Delay output: [initial_condition, 5, 7, 9]

Initial output is 0, then outputs previous inputs.

Simulink

Set initial condition = 0
Input: [2, 4, 6]
Output: [0, 2, 4]

Sample Program

This code simulates a unit delay block by shifting the input signal by one time step. The initial output is set to zero. The plot shows how the output lags behind the input by one step.

Simulink

import numpy as np
import matplotlib.pyplot as plt

# Simulate input signal
input_signal = np.array([1, 3, 5, 7, 9])

# Initial condition for unit delay
initial_condition = 0

# Create output array with same length
output_signal = np.empty_like(input_signal)

# Set first output as initial condition
output_signal[0] = initial_condition

# Apply unit delay: output at time t is input at time t-1
for t in range(1, len(input_signal)):
    output_signal[t] = input_signal[t-1]

# Print input and output
print('Input signal: ', input_signal)
print('Unit delay output: ', output_signal)

# Plot signals
plt.plot(input_signal, label='Input Signal')
plt.plot(output_signal, label='Unit Delay Output', linestyle='--')
plt.legend()
plt.title('Unit Delay Block Simulation')
plt.xlabel('Time step')
plt.ylabel('Signal value')
plt.show()

Important Notes

Remember to set the initial condition to avoid unexpected outputs at the start.

The unit delay block is useful for discrete-time systems where signals update step by step.

Summary

The Unit delay block outputs the previous input value, delaying the signal by one step.

It is useful to remember past data in simulations and control systems.

Set the initial condition to control the output at the first time step.

Practice

1. What does the Unit Delay block in Simulink do?

easy

A. Outputs the previous input value, delaying the signal by one step

B. Outputs the current input value without delay

C. Outputs the sum of all past inputs

D. Outputs a random value at each step

Solution

1. Step 1: Understand the function of Unit Delay block

   The Unit Delay block holds the input value and outputs it one time step later, effectively delaying the signal by one step.

2. Step 2: Compare options with the definition

   Only Outputs the previous input value, delaying the signal by one step correctly describes this behavior; others describe different or incorrect behaviors.

3. Final Answer:

   Outputs the previous input value, delaying the signal by one step -> Option A

4. Quick Check:

   Unit Delay = previous input output [OK]

Hint: Remember: Unit Delay outputs last step's input [OK]

Common Mistakes:

• Thinking it outputs current input immediately
• Confusing with blocks that sum inputs
• Assuming it outputs random or initial values only

2. Which of the following is the correct way to set the initial condition of a Unit Delay block in Simulink?

easy

A. Initialize the input signal to zero externally

B. Use a separate Gain block before the Unit Delay

C. Set the 'Initial condition' parameter in the block's dialog box

D. Set the initial condition in the MATLAB workspace only

Solution

1. Step 1: Identify how initial conditions are set in Unit Delay

   The Unit Delay block has a parameter called 'Initial condition' in its dialog box where you specify the output value at the first time step.

2. Step 2: Evaluate the options

   Set the 'Initial condition' parameter in the block's dialog box correctly states this method. Options B, C, and D describe indirect or incorrect ways.

3. Final Answer:

   Set the 'Initial condition' parameter in the block's dialog box -> Option C

4. Quick Check:

   Initial condition set inside block dialog [OK]

Hint: Set initial condition inside Unit Delay block dialog [OK]

Common Mistakes:

• Trying to set initial condition outside the block
• Using other blocks to simulate initial condition
• Assuming MATLAB workspace variable sets it automatically

3. Consider a Unit Delay block with initial condition 0. The input signal over 4 time steps is [1, 3, 5, 7]. What is the output sequence?

medium

A. [1, 3, 5, 7]

B. [0, 1, 3, 5]

C. [1, 1, 3, 5]

D. [0, 0, 1, 3]

Solution

1. Step 1: Understand Unit Delay output behavior

   At each time step, output is the input from the previous step. At step 1, output is initial condition (0).

2. Step 2: Calculate output for each step

   Step 1 output: 0 (initial condition)
   Step 2 output: input at step 1 = 1
   Step 3 output: input at step 2 = 3
   Step 4 output: input at step 3 = 5

3. Final Answer:

   [0, 1, 3, 5] -> Option B

4. Quick Check:

   Output lags input by one step [OK]

Hint: Output is previous input; first output = initial condition [OK]

Common Mistakes:

• Outputting current input instead of previous
• Forgetting initial condition at first step
• Shifting output incorrectly by more than one step

4. You have a Unit Delay block with initial condition 5, but the output starts at 0 instead. What is the likely cause?

medium

A. The initial condition parameter was not set correctly in the block

B. The input signal is zero at the first step

C. The Unit Delay block is connected incorrectly

D. Simulink does not support initial conditions in Unit Delay blocks

Solution

1. Step 1: Analyze the initial condition effect

   The Unit Delay block outputs the initial condition at the first step if set properly.

2. Step 2: Identify why output is zero instead of 5

   If output is zero, likely the initial condition parameter was not set or saved correctly in the block dialog.

3. Final Answer:

   The initial condition parameter was not set correctly in the block -> Option A

4. Quick Check:

   Initial condition must be set inside block [OK]

Hint: Check initial condition parameter inside block dialog [OK]

Common Mistakes:

• Assuming input signal affects initial output
• Thinking connection errors cause initial output zero
• Believing Simulink ignores initial conditions

5. You want to model a system where the output at each step is the sum of the current input and the previous input. How can you use a Unit Delay block to achieve this?

hard

A. Set the initial condition of the Unit Delay block to the sum of inputs

B. Use two Unit Delay blocks in series and sum their outputs

C. Use a Unit Delay block with initial condition zero and multiply by input

D. Add the current input to the output of a Unit Delay block that delays the input by one step

Solution

1. Step 1: Understand the requirement

   The output should be current input plus previous input value.

2. Step 2: Use Unit Delay to get previous input

   A Unit Delay block outputs the previous input. Adding this output to the current input gives the desired sum.

3. Step 3: Evaluate options

   Add the current input to the output of a Unit Delay block that delays the input by one step correctly describes this setup. Options A, B, and D do not produce the required output.

4. Final Answer:

   Add the current input to the output of a Unit Delay block that delays the input by one step -> Option D

5. Quick Check:

   Sum = current input + delayed input [OK]

Hint: Sum current input with Unit Delay output for previous input [OK]

Common Mistakes:

• Using multiple Unit Delay blocks unnecessarily
• Misusing initial condition to store sums
• Multiplying instead of adding signals