Control Systems & Delays Examplesllms.txt

Control system models demonstrate how feedback tries to reach a goal in the face of delays. Sensors lag or actions take time to take effect, creating oscillations and overshoot.

From thermostats to goal-seeking decay, these examples reveal how tuning gain, delay, and set points stabilizes or destabilizes a system. They connect real-world controllers with the time lags that challenge them.

Select an example to explore it in the playground.

Beginner - Introductory Models

Goal-Seeking Decay

A goal-seeking decay simulation modeling exponential approach toward a target.

Level: Beginner

decaygoalbalancing-loopexponentialcontrolfirst-order-dynamicstime-delay

  • Stocks: level
  • Flows: approach_rate
  • Feedback Loops: goal-seeking (balancing)
  • Probes: level, approach_rate
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Thermostat Simulation

A bang-bang thermostat reading a delayed sensor overshoots and rings; shorten the delay and it settles.

Level: Beginner

controltime-delaybalancing-loop

  • Stocks: indoor_temp
  • Flows: heat_gain, heat_loss
  • Feedback Loops: controller chasing set-point (balancing)
  • Probes: indoor_temp, error, heater_on
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Intermediate - Classic Dynamics

SIR Model with Vaccination

An SIR epidemic at the threshold: vaccinating past the herd-immunity line pushes effective R0 below 1 and the outbreak fizzles.

Level: Intermediate

populationreinforcing-loopbalancing-loopcontrol

  • Stocks: susceptible, infected, recovered
  • Flows: infections, recoveries
  • Feedback Loops: disease spread (reinforcing), susceptible depletion / herd immunity (balancing)
  • Probes: susceptible, infected, recovered, r_eff
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