Why not heat exactly to the setpoint and stop?

Real sensors lag, and heat keeps flowing after the actuator turns off. Without hysteresis or a modulating valve, the system would chatter—rapidly cycling on and off—which is inefficient and hard on equipment.

Is this the same mathematics as the PID cart demo?

Same family of ideas—error-driven feedback—but thermal plants are slow, often dominated by long time constants, so proportional-only or PI loops are common and derivative action must be filtered against sensor noise.

What does thermal mass change in the plots?

Larger capacitance slows temperature swings, smoothing disturbances but delaying response. It is analogous to a larger time constant in an RC circuit.

Do smart thermostats violate these basics?

They add scheduling, occupancy sensing, and sometimes weather prediction, but the core still closes a loop between measured temperature and actuator commands.

Thermostat: on/off vs PID

First-order room: on/off hysteresis vs continuous PID heater power.

About this model

A thermostat implements temperature regulation with hysteresis or proportional control: heating or cooling runs until the measured temperature crosses a setpoint band, preventing rapid on-off chattering from sensor noise. Simple bang-bang control flips at high and low thresholds; more advanced digital thermostats approximate PID behavior or model predictive schedules. The simulator connects the *control law* to the *thermal inertia* of a room or vessel—capacity, losses to ambient, and actuator power limit how quickly temperature can change. Idealizations often use a first- or second-order thermal model without spatial gradients, assuming a single well-mixed temperature and instantaneous actuator response. Students see why overshoot appears when gain is too aggressive, why deadband saves wear on compressors, and why feed-forward (weather, occupancy) improves comfort in real products.

Who it's for: Introductory control or HVAC students linking household thermostats to feedback concepts taught with the PID and governor simulators.

Key terms

Setpoint
Hysteresis
Bang-bang control
Deadband
Thermal inertia
Heat loss
Feedback
Overshoot

How it works

First-order room model: dT/dt = −k(T−T_amb) + P·u with u ∈ [0,1] heater power. On/off control uses hysteresis around the setpoint to avoid chattering. PID smoothly modulates power and usually settles with less overshoot when gains are tuned.

Frequently asked questions

Why not heat exactly to the setpoint and stop?: Real sensors lag, and heat keeps flowing after the actuator turns off. Without hysteresis or a modulating valve, the system would chatter—rapidly cycling on and off—which is inefficient and hard on equipment.
Is this the same mathematics as the PID cart demo?: Same family of ideas—error-driven feedback—but thermal plants are slow, often dominated by long time constants, so proportional-only or PI loops are common and derivative action must be filtered against sensor noise.
What does thermal mass change in the plots?: Larger capacitance slows temperature swings, smoothing disturbances but delaying response. It is analogous to a larger time constant in an RC circuit.
Do smart thermostats violate these basics?: They add scheduling, occupancy sensing, and sometimes weather prediction, but the core still closes a loop between measured temperature and actuator commands.

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