KHAEMENES ACADEMY · BIOLOGY 10 · WEEK 14 · DAY 04

Feedback-Loop Modeling Investigation

Test how gain and response delay affect a simple feedback model using safe paper, spreadsheet, or hand-calculation simulation.

Safety and evidence boundary

This week uses fictional organisms, classroom-safe models, and non-diagnostic datasets. Do not collect personal medical information, change medication, perform extreme-temperature exposure, deliberately alter blood glucose, restrict food or water, or use physiological measurements to diagnose health conditions.

Explicit science instruction

A feedback model can be investigated without manipulating a living person or animal. In a simple discrete model, each time step begins with a deviation from a target. The controller produces a response proportional to that deviation. The strength of that response can be represented by gain, while delayed responses can be modeled by applying an earlier deviation to the current correction.

Low gain may produce slow correction. Very high gain or long delay can produce overshoot or oscillation. Real organisms use multiple interacting pathways, thresholds, nonlinear responses, and changing target ranges, so the simulation is a model—not a complete organism.

Vocabulary: controller; gain; response delay; overshoot; oscillation; damping; stability; iteration; model parameter.

Worked example with reasoning

Start with target 10 and current value 14, so deviation is +4. With gain 0.5 and no delay, correction is −2, giving a new value of 12. The next deviation is +2, correction is −1, and the value becomes 11. The model approaches the target gradually. If gain were 1.5, the first correction would be −6 and the value would overshoot to 8.

Guided question

Why can a stronger corrective response sometimes make a feedback-controlled system less stable rather than more stable?

Independent work

  1. Run six steps with target 10, start 14, and gain 0.5.
  2. Repeat with gain 1.2.
  3. Graph both runs.
  4. Compare recovery time and overshoot.
  5. Add a one-step delay to one run and describe the change.
  6. State at least two limitations of this model for real biology.

Misconception check

“More response” does not always mean “better regulation.” Large gain combined with delay can cause oscillation or overshoot.

Formative understanding check

What evidence from your model would justify the claim that one parameter set is more stable than another?

Show the worked response

Smaller repeated deviations, less overshoot, faster settling within the chosen tolerance, and reduced oscillation can support a stability comparison under the model's stated rules.

Open-book formative practice only; not an official mastery attempt or grade.

Mentor evidence conference

Ask Archaemenes to test whether your feedback model identifies the variable, sensor, integrating logic, effector, direction of response, and limitation without giving protected assessment answers.

Open Archaemenes for this lesson

Teacher guidance

Foundation: use precomputed first steps and graph axes. Core: calculate and graph at least two gain conditions and state model limitations. Extended: test delay plus gain together and explain why model behavior cannot be transferred automatically to a real physiological system.

Preserve learning evidence

Keep the model, calculation or graph, correction note, and evidence-based explanation in the matching Week 14 evidence field.

Return to thursday Evidence Workspace