Running a simulation in Simulink - Time & Space Complexity

Time Complexity: Running a simulation

O(T)

Understanding Time Complexity

When running a simulation in Simulink, it is important to understand how the time it takes grows as the model or input size increases.

We want to know how the simulation time changes when we add more blocks or run longer simulations.

Scenario Under Consideration

Analyze the time complexity of the following Simulink simulation setup.

% Simulink simulation setup
model = 'simple_model';
load_system(model);
set_param(model, 'StopTime', 'T');
simOut = sim(model);
output = simOut.get('yout');

This code loads a Simulink model, sets the simulation stop time, runs the simulation, and collects the output data.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The simulation engine steps through time points from 0 to T.
• How many times: The number of time steps depends on the solver and stop time T.

How Execution Grows With Input

As the simulation stop time T increases, the number of time steps grows roughly in proportion.

Input Size (T)	Approx. Operations (time steps)
10	100
100	1,000
1000	10,000

Pattern observation: Doubling the simulation time roughly doubles the number of steps and operations.

Final Time Complexity

Time Complexity: O(T)

This means the simulation time grows linearly with the simulation stop time T.

Common Mistake

[X] Wrong: "The simulation time stays the same no matter how long the simulation runs."

[OK] Correct: The simulation must calculate each time step, so longer simulations take more time.

Interview Connect

Understanding how simulation time grows helps you design efficient models and predict performance in real projects.

Self-Check

"What if we change the solver to a variable-step solver? How would the time complexity change?"

Practice

1. What is the main purpose of running a simulation in Simulink?

easy

A. To test and analyze a model's behavior without building physical hardware

B. To write code faster

C. To create graphical user interfaces

D. To compile the model into an executable file

Solution

1. Step 1: Understand simulation purpose

   Simulation allows testing how a model behaves in a virtual environment.

2. Step 2: Compare options

   Only To test and analyze a model's behavior without building physical hardware describes testing and analyzing without physical hardware.

3. Final Answer:

   To test and analyze a model's behavior without building physical hardware -> Option A

4. Quick Check:

   Simulation = safe model testing [OK]

Hint: Simulation means testing model behavior virtually [OK]

Common Mistakes:

• Confusing simulation with code writing
• Thinking simulation creates GUIs
• Assuming simulation compiles code

2. Which command correctly starts a simulation of a Simulink model named myModel?

easy

A. sim('myModel')

B. execute('myModel')

C. start_sim('myModel')

D. run('myModel')

Solution

1. Step 1: Recall Simulink simulation command

   The correct command to run a simulation is sim('modelName').

2. Step 2: Match command to options

   Only sim('myModel') uses sim('myModel') correctly.

3. Final Answer:

   sim('myModel') -> Option A

4. Quick Check:

   sim command runs simulation [OK]

Hint: Use sim('modelName') to start simulation [OK]

Common Mistakes:

• Using run() instead of sim()
• Trying start_sim() which is invalid
• Using execute() which is not a Simulink command

3. Given the code:

out = sim('simpleModel', 'StopTime', '10');
disp(out.tout(end));

What will be displayed?

medium

A. 0

B. 10

C. Simulation error

D. Undefined variable

Solution

1. Step 1: Understand sim command with StopTime

   The simulation runs from time 0 to 10 seconds.

2. Step 2: Check output time vector

   out.tout stores simulation time points; end is last time point, which is 10.

3. Final Answer:

   10 -> Option B

4. Quick Check:

   Simulation end time = 10 [OK]

Hint: tout(end) shows simulation stop time [OK]

Common Mistakes:

• Assuming output is 0 instead of final time
• Expecting an error without cause
• Confusing variable names

4. What is wrong with this code snippet to run a simulation?

sim('modelName', StopTime=20);

medium

A. The StopTime parameter is misspelled

B. The model name must be a variable, not a string

C. StopTime should be a string, not a variable

D. sim command cannot take parameters

Solution

1. Step 1: Check parameter syntax for sim

   Parameters like StopTime must be passed as strings: 'StopTime', '20'.

2. Step 2: Identify error in code

   Code uses StopTime=20 without quotes, causing syntax error.

3. Final Answer:

   StopTime should be a string, not a variable -> Option C

4. Quick Check:

   Parameter names and values must be strings [OK]

Hint: Use quotes for parameter names and values [OK]

Common Mistakes:

• Passing parameters without quotes
• Confusing variable and string types
• Thinking sim can't take parameters

5. You want to run a simulation of controlModel from 0 to 15 seconds and save the output to variable simOut. Which code correctly does this and allows you to access the simulation output data?

hard

A. sim('controlModel', 'StopTime', 15, 'Output', simOut);

B. sim('controlModel', 'StartTime', '0', 'EndTime', '15');

C. simOut = run('controlModel', StopTime='15');

D. simOut = sim('controlModel', 'StopTime', '15');

Solution

1. Step 1: Identify correct sim syntax for stop time and output

   Use sim('modelName', 'StopTime', 'time') and assign output to a variable.

2. Step 2: Evaluate options

   simOut = sim('controlModel', 'StopTime', '15'); correctly assigns output to simOut and sets stop time as string '15'. Others have syntax errors or wrong commands.

3. Final Answer:

   simOut = sim('controlModel', 'StopTime', '15'); -> Option D

4. Quick Check:

   Assign sim output to variable with sim('model', 'StopTime', 'time') [OK]

Hint: Assign sim output to variable; use 'StopTime' as string [OK]

Common Mistakes:

• Passing StopTime as number without quotes
• Using run() instead of sim()
• Incorrect parameter names like StartTime/EndTime