Espresso boiler - cold start and 92-96 degC hysteretic thermostat
*
* Lumped thermal/electrical analogue (absolute temperature in degC):
*   1 V = 1 degC, 1 A = 1 W, 1 F = 1 J/K, 1 ohm = 1 K/W.
*   Cthermal stores heat; Rloss conducts heat to ambient; Bheater adds heat.
* Assumptions: well-mixed boiler, fixed water mass, no brewing/steam draw,
* instantaneous heater and temperature sensor, constant ambient at 20 degC.
* 2000 J/K represents about 0.4 L water plus the metal boiler assembly.
* 1200 W heater; 0.5 K/W insulation gives 148 W loss at 94 degC.
*
.param Tamb=20 Cth=2000 Rth=0.5 Pheater=1200

* Thermal plant: Cth*dT/dt = Pheater*call - (T-Tamb)/Rth.
Vambient ambient 0 DC {Tamb}
Rloss boiler ambient {Rth}
Cthermal boiler 0 {Cth} IC={Tamb}
Bheater 0 boiler I={Pheater}*V(call)

* Stateful thermostat, NOT a single-threshold comparator:
* error = 94-T; switch closes above +2 (T<92), opens below -2 (T>96),
* and remembers its previous state throughout the 92-96 degC deadband.
* ON sets the cold-start state; the cold error also requests heat.
Vlogic logic 0 DC 1
Berror error 0 V=94-V(boiler)
Sthermostat logic call error 0 TSTAT ON
Rcall call 0 1meg
.model TSTAT SW(Ron=1m Roff=1e12 Vt=0 Vh=2)
* Switch/load ratio makes call effectively 1 when on, 0 when off.

.options reltol=1e-5 abstol=1e-9 vntol=1e-6
.control
set noaskquit
set wr_singlescale
set wr_vecnames
* Seconds: 1200 s = 20 min; max step 0.05 s resolves switching edges.
* UIC preserves the capacitor's 20 degC initial condition, avoiding a
* hot DC operating-point start in this hysteretic feedback system.
tran 0.1 1200 0 0.05 uic
let boiler_temperature_C = v(boiler)
* Two columns (with header): time in seconds, boiler temperature in degC.
wrdata boiler_temperature.txt boiler_temperature_C
.endc
.end