Espresso boiler -- cold start and 92 to 96 degC hysteretic thermostat
*
* Thermal/electrical analogy (absolute Celsius temperature):
*   1 V = 1 degC, 1 A = 1 W, 1 F = 1 J/K, 1 ohm = 1 K/W.
* Single well-mixed boiler, initially at room temperature (20 degC).
* Cth = 2500 J/K represents roughly 0.5 L water plus boiler metal.
* A 1200 W heater injects heat; Rloss = 0.25 K/W gives 4 W/K
* heat loss to a fixed 20 degC room. No water draw or sensor lag.
*
* Energy balance: 2500*dT/dt = 1200*heater_on - (T-20)/0.25.
Vambient ambient 0 DC 20
Cthermal boiler 0 2500 IC=20
Rloss boiler ambient 0.25
Bheater 0 boiler I = {1200 * (V(heat_call) > 0.5)}
*
* Stateful thermostat: control = 94 - T.
* Switch closes when control > +2 (T < 92 degC), and opens
* when control < -2 (T > 96 degC); holds its state in between.
* Cold start therefore calls for heat. This is true hysteresis,
* not a memoryless comparator at the midpoint of the band.
Vlogic logic_supply 0 DC 1
Bcontrol control 0 V = {94 - V(boiler)}
Sthermostat logic_supply heat_call control 0 thermostat
Rpulldown heat_call 0 1k
.model thermostat SW(Ron=1 Roff=1e12 Vt=0 Vh=2)
*
* UIC preserves the cold-start thermal capacitor condition rather
* than starting at a DC thermal equilibrium. Limit timestep to
* 0.05 s so ideal thermostat threshold overshoot stays <0.02 degC.
.options reltol=1e-6 abstol=1e-9 vntol=1e-7
.control
save v(boiler) v(heat_call)
tran 0.1 1200 0 0.05 uic
* Output columns: time in seconds, boiler temperature in degC.
set wr_vecnames
set numdgt=9
wrdata boiler_temperature.txt v(boiler)
quit
.endc
.end