Open-loop vs closed-loop systems in Simulink - Performance Comparison

Time Complexity: Open-loop vs closed-loop systems

O(n)

Understanding Time Complexity

We want to understand how the time it takes to run a Simulink model changes when using open-loop or closed-loop systems.

How does adding feedback affect the number of operations as the system grows?

Scenario Under Consideration

Analyze the time complexity of these two simple Simulink setups.

// Open-loop system
Input --> Plant --> Output

// Closed-loop system
Input --> Sum (+/-) --> Plant --> Output
               ^                    |
               |--------------------|

The open-loop system sends input directly to the plant. The closed-loop system adds feedback from output back to input through a summing block.

Identify Repeating Operations

Look at what repeats during simulation steps.

• Primary operation: Calculating plant output each time step.
• How many times: Once per time step in open-loop; plus feedback calculation in closed-loop.

How Execution Grows With Input

As the number of time steps (n) increases, the operations increase.

Input Size (n)	Approx. Operations
10	10 calculations (open-loop), ~20 calculations (closed-loop)
100	100 calculations (open-loop), ~200 calculations (closed-loop)
1000	1000 calculations (open-loop), ~2000 calculations (closed-loop)

Pattern observation: Closed-loop roughly doubles operations per step due to feedback, but both grow linearly with time steps.

Final Time Complexity

Time Complexity: O(n)

This means the time to simulate grows directly with the number of time steps, whether open or closed loop.

Common Mistake

[X] Wrong: "Closed-loop systems always take much longer to simulate because of feedback loops."

[OK] Correct: Feedback adds some extra calculations each step, but the total work still grows linearly with time steps, not exponentially.

Interview Connect

Understanding how feedback affects simulation time helps you design efficient models and explain system behavior clearly.

Self-Check

"What if the plant model inside the loop became more complex with nested loops? How would the time complexity change?"

Practice

1. Which of the following best describes an open-loop system in Simulink?

easy

A. A system that uses sensors to monitor output and correct errors.

B. A system that continuously adjusts output based on feedback.

C. A system that operates without using feedback to adjust its output.

D. A system that always maintains a constant output regardless of input.

Solution

1. Step 1: Understand open-loop system definition

   An open-loop system works without feedback; it does not adjust based on output.

2. Step 2: Compare options to definition

   A system that operates without using feedback to adjust its output. matches this definition exactly, while others describe feedback or constant output.

3. Final Answer:

   A system that operates without using feedback to adjust its output. -> Option C

4. Quick Check:

   Open-loop = no feedback [OK]

Hint: Open-loop means no feedback used to adjust output [OK]

Common Mistakes:

• Confusing open-loop with closed-loop systems
• Thinking open-loop uses feedback
• Assuming open-loop always maintains constant output

2. Which Simulink block is typically used to create a closed-loop system?

easy

A. Gain block

B. Sum block with feedback connection

C. Constant block

D. Scope block

Solution

1. Step 1: Identify closed-loop system structure

   Closed-loop systems require feedback, often created by feeding output back to input using a Sum block.

2. Step 2: Match blocks to feedback role

   Sum block with feedback connection allows error calculation, enabling closed-loop control.

3. Final Answer:

   Sum block with feedback connection -> Option B

4. Quick Check:

   Feedback needs Sum block [OK]

Hint: Closed-loop needs feedback; Sum block enables feedback loop [OK]

Common Mistakes:

• Choosing Gain block which only scales signals
• Selecting Constant or Scope blocks which don't create feedback
• Ignoring the feedback connection requirement

3. Consider this Simulink setup: a Gain block with gain 2 connected directly to input, no feedback. What is the output if input is 3?

medium

A. 3

B. 1.5

C. 0

D. 6

Solution

1. Step 1: Identify system type and operation

   The system is open-loop (no feedback). Output = input * gain.

2. Step 2: Calculate output value

   Output = 3 * 2 = 6.

3. Final Answer:

   6 -> Option D

4. Quick Check:

   Output = input x gain = 6 [OK]

Hint: Multiply input by gain for open-loop output [OK]

Common Mistakes:

• Assuming feedback changes output
• Using input value directly without gain
• Confusing gain with division

4. You have a closed-loop system in Simulink but the output does not stabilize and keeps oscillating. What is the most likely cause?

medium

A. Gain value is too high causing instability

B. Feedback loop is missing

C. Input signal is zero

D. Sum block is not connected

Solution

1. Step 1: Understand oscillation cause in closed-loop

   Oscillations often occur when gain is too high, causing the system to overreact and become unstable.

2. Step 2: Eliminate other options

   Feedback loop missing or Sum block not connected would stop feedback, not cause oscillations. Zero input does not cause oscillations.

3. Final Answer:

   Gain value is too high causing instability -> Option A

4. Quick Check:

   High gain causes oscillation [OK]

Hint: High gain in feedback causes oscillations [OK]

Common Mistakes:

• Thinking missing feedback causes oscillations
• Assuming zero input causes oscillations
• Ignoring gain effect on stability

5. You want to design a Simulink model to maintain room temperature at 22°C despite outside temperature changes. Which system type and feature should you use?

hard

A. Closed-loop system with temperature sensor feedback

B. Open-loop system with timer-based heater control

C. Open-loop system with fixed heater power

D. Closed-loop system without feedback

Solution

1. Step 1: Identify control needs for stable temperature

   Maintaining temperature despite changes requires feedback to adjust heater power.

2. Step 2: Choose system type with feedback

   Closed-loop system with temperature sensor feedback adjusts output based on actual room temperature.

3. Final Answer:

   Closed-loop system with temperature sensor feedback -> Option A

4. Quick Check:

   Stable control needs feedback loop [OK]

Hint: Use feedback to adjust for changing conditions [OK]

Common Mistakes:

• Choosing open-loop which can't adjust to changes
• Ignoring need for sensor feedback
• Selecting closed-loop without feedback