How does feedback stabilise a room’s temperature?
Element · Relation · Boundary
Room, heater, sensor, controller and environment are elements. Measurement, heat input and loss are different relations. The reference is a controller goal, not a physical centre. The boundary must retain outward heat-loss interfaces.
Effect · Time · Feedback
The sensor measures T; the controller compares it to r and adjusts u. The deviation changes later temperature and the next measurement. In a simplified model assume constant capacity C > 0 and loss coefficient k > 0. Those assumptions limit scope. With u = K(r − T), K > 0 gives linear feedback.
C · dT/dt = −k(T − Tout) + u
u = K(r − T)
δT(t) = δT(0) · exp(−(k + K)t/C)With constant environment and reference and ideal delay-free control, deviations decay because (k + K)/C > 0. This is a derivation within this linear model, not validation of all ADL feedback. The equilibrium need not equal the reference exactly.
Limits of the claim
Sensor errors, delay and bounded power can change behaviour. A drawn loop without parameters does not support stability.
Test
Measure response to a disturbance against the predicted decay and record conditions. Systematic mismatch refutes this simplified model’s suitability.
Source
Sources support the mathematical or technical foundations. Their connection to ADL is the interpretation disclosed here.