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Open-loop vs closed-loop

An open-loop system applies a fixed input and hopes for the best. A toaster on a timer is open-loop: it heats for two minutes regardless of how brown the bread is. A closed-loop system measures the output and feeds that measurement back to the input. A thermostat is closed-loop: it measures the temperature and turns the heater on or off.

Why feedback stabilizes

Without feedback, any disturbance (a gust of wind, a load change, a modeling error) accumulates unchecked. Feedback subtracts the measured output from the desired reference, producing an error signal. The controller acts on the error, not the raw reference.

If the output is too high, the error goes negative and the controller reduces its effort. If the output is too low, the error goes positive and the controller pushes harder. This negative feedback loop is self-correcting.

The thermostat

Set the desired temperature to 20 degrees C. The sensor measures the room at 18 degrees C, so the error is +2. The heater turns on. As the room warms to 20, the error drops to zero and the heater turns off. If someone opens a window and the room drops to 19, the error becomes +1, and the heater turns on again. That feedback loop maintains the setpoint despite disturbances.

; A simple thermostat simulation
; Closed-loop: heater responds to error between setpoint and room temp

(define setpoint 20.0)
(define room-temp 15.0)
(define heat-rate 0.5)    ; degrees per step when heater is on
(define cool-rate 0.1)    ; degrees per step from heat loss

(define (thermostat temp steps)
  (if (= steps 0)
    (begin (display "Final temp: ") (display temp) (newline))
    (let* ((error (- setpoint temp))
           (heater-on (> error 0))
           (next-temp (if heater-on
                        (- (+ temp heat-rate) cool-rate)
                        (- temp cool-rate))))
      (display "Step: temp=") (display temp)
      (display (if heater-on " heater=ON" " heater=OFF"))
      (display " error=") (display error) (newline)
      (thermostat next-temp (- steps 1)))))

(thermostat room-temp 15)

# Thermostat simulation
setpoint = 20.0
temp = 15.0
heat_rate = 0.5
cool_rate = 0.1

for step in range(15):
    error = setpoint - temp
    heater_on = error > 0
    status = "ON" if heater_on else "OFF"
    print(f"Step {step:2d}: temp={temp:.1f}  heater={status}  error={error:+.1f}")
    if heater_on:
        temp += heat_rate - cool_rate
    else:
        temp -= cool_rate

print(f"Final temp: {temp:.1f}")