Unit delay block in Simulink - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the purpose of a Unit Delay block in Simulink?

A Unit Delay block stores the input signal and outputs it after one time step, introducing a one-step delay in the signal flow.

intermediate

How does the Unit Delay block differ from a Memory block in Simulink?

The Unit Delay block delays the input by one sample time and updates its output at the sample time, while the Memory block outputs the previous input without delay at the same simulation time step.

beginner

What happens if the Unit Delay block is used at the start of a simulation?

At the start, the Unit Delay block outputs its initial condition value because it has no previous input stored yet.

beginner

Which parameter in the Unit Delay block sets the initial output value?

The 'Initial condition' parameter sets the output value of the Unit Delay block at the first time step of the simulation.

intermediate

Why is the Unit Delay block important in discrete-time systems modeling?

It models the effect of storing and delaying signals by one sample period, which is essential for representing discrete-time dynamics and feedback loops.

What does the Unit Delay block output at the very first simulation step?

A Zero always

B The initial condition value

C The current input signal

D An error message

At the first step, the Unit Delay block outputs the initial condition value because it has no previous input stored yet.

How many time steps does the Unit Delay block delay the input signal?

A Zero

B Two

C One

D Depends on the sample time

The Unit Delay block delays the input signal by exactly one time step.

Which parameter controls the output value of the Unit Delay block at simulation start?

A Sample time

B Output data type

C Delay length

D Initial condition

The 'Initial condition' parameter sets the output value at the start of simulation.

In which type of system is the Unit Delay block most commonly used?

A Discrete-time systems

B Continuous-time systems

C Analog circuits

D Mechanical systems

The Unit Delay block is used to model discrete-time systems by delaying signals by one sample period.

What is the main difference between Unit Delay and Memory blocks in Simulink?

A Unit Delay updates output at sample time; Memory outputs previous input immediately

B Memory delays by two steps; Unit Delay delays by one

C Unit Delay is for continuous signals; Memory is for discrete

D There is no difference

Unit Delay updates output at the sample time, while Memory outputs the previous input without delay at the same time step.

Explain how the Unit Delay block works in a Simulink model and why it is useful.

Think about how signals flow and get delayed in time steps.

Describe the difference between the Unit Delay block and the Memory block in Simulink.

Focus on when each block updates its output.

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