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Open-Loop vs Closed-Loop Comparison

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About This MicroSim

This interactive simulation provides a side-by-side comparison of open-loop and closed-loop control systems, demonstrating the fundamental difference in how each architecture handles disturbances.

What You'll Learn

  • Open-loop systems cannot automatically compensate for disturbances - when a disturbance occurs, the output shifts and stays at the wrong value
  • Closed-loop systems use feedback to detect and reject disturbances - the output recovers toward the reference
  • Higher controller gain (K) provides better disturbance rejection but cannot eliminate all error with proportional control alone

How to Use

  1. Start State: Both systems begin at steady state, trying to maintain output y = 1
  2. Apply Disturbance: Click "Apply Disturbance" to introduce a step disturbance at t = 3 seconds
  3. Compare: Observe how the open-loop output shifts permanently while the closed-loop output recovers
  4. Experiment: Adjust the disturbance magnitude and controller gain K to see their effects

Key Observations

System After Disturbance
Open-Loop Output shifts by full disturbance amount and stays there
Closed-Loop Output is deflected but recovers; error reduced by factor of (1+K)

Iframe Embed Code

You can include this MicroSim on your website using the following iframe:

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<iframe src="https://dmccreary.github.io/control-systems/sims/open-vs-closed-loop/main.html"
        height="502px"
        width="100%"
        scrolling="no">
</iframe>

Lesson Plan

Learning Objectives

After completing this activity, students will be able to:

  1. Differentiate between open-loop and closed-loop control architectures based on their response to disturbances
  2. Analyze why feedback enables automatic disturbance rejection
  3. Predict how increasing controller gain affects disturbance rejection capability

Pre-Activity Questions

Before using the simulation, have students predict:

  1. What will happen to each system's output when a disturbance is applied?
  2. Which system do you expect to handle disturbances better? Why?
  3. How might increasing the controller gain change the closed-loop response?

Guided Exploration

  1. Baseline Comparison: Apply the default disturbance (d = 0.3) and note:
  2. The steady-state error for each system

  3. The percentage error reduction achieved by the closed-loop

  4. Gain Investigation: Reset and try different values of K:

  5. K = 1 (low gain)
  6. K = 5 (medium gain)
  7. K = 10 (high gain)

Record the steady-state error for each. What pattern do you observe?

  1. Disturbance Direction: Try both positive and negative disturbances. Does the direction affect the comparison?

Discussion Questions

  1. Why can't the open-loop system compensate for the disturbance?
  2. What information does the closed-loop system have that the open-loop lacks?
  3. Can proportional control alone eliminate all steady-state error? Why or why not?
  4. What real-world systems might you choose to be open-loop vs closed-loop?

Assessment

Have students write a brief explanation (3-4 sentences) of: - Why feedback is essential for disturbance rejection - The role of controller gain in determining rejection capability - A real-world example where feedback control is necessary

Technical Details

Plant Model

Both systems use a first-order plant:

\[G_p(s) = \frac{1}{\tau s + 1}\]

where τ = 1 second (plant time constant).

Open-Loop Configuration

  • Fixed controller gain: Gc = 1 (calibrated for unity output with no disturbance)
  • No feedback path
  • Disturbance directly affects output

Closed-Loop Configuration

  • Proportional controller: Gc = K (adjustable from 1 to 10)
  • Negative feedback with unity sensor gain
  • Closed-loop transfer function: $\frac{K}{\tau s + (1 + K)}$
  • Disturbance rejection: errors attenuated by factor $\frac{1}{1+K}$

Steady-State Analysis

For a unit step reference with disturbance d:

Metric Open-Loop Closed-Loop
Steady-state output 1 + d K/(1+K) + d/(1+K)
Error due to disturbance d d/(1+K)
Error reduction — (1 - 1/(1+K)) × 100%

References

  1. Nise, N. S. (2019). Control Systems Engineering (8th ed.). Wiley.
  2. Franklin, G. F., Powell, J. D., & Emami-Naeini, A. (2019). Feedback Control of Dynamic Systems (8th ed.). Pearson.
  3. Dorf, R. C., & Bishop, R. H. (2017). Modern Control Systems (13th ed.). Pearson.