Control Systems & Delays Examples

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

Thermostat Simulation

A thermostat simulation showing balancing feedback and time delays.

Level:Beginner

controltime-delaybalancing-loop

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

Bank Renege Simulation

A bank renege simulation where customers join a queue with limited patience and may leave before service if the wait is too long.

Level:Intermediate

queueservicediscrete-eventtime-delay

  • Stocks:queue
  • Flows:served, reneged
  • Probes:wait_time, served, reneged

SIR Model with Vaccination

An SIR vaccination simulation modeling epidemics with optional vaccination.

Level:Intermediate

populationreinforcing-loopbalancing-loopcontrol

  • Stocks:susceptible, infected, recovered
  • Flows:infections, recoveries, vaccinations
  • Feedback Loops:disease spread (reinforcing), herd immunity (balancing)
  • Probes:susceptible, infected, recovered
Advanced - Complex Simulations