ADRC vs PID Explorer — same plant, two controllers, one disturbance
Plant — 2nd order G(s) = b
0
/ (s² + 2ζω
n
s + ω
n
²)
ω
n
2
ζ
0.70
Disturbance
Type
Step at t=1s
Sine 5 rad/s
Ramp + step
Pulse train
Amp
30
Param shift
0%
ADRC — 3 knobs: ω
c
, ω
o
, b
0
ω
c
15
ω
o
60
b
0
100
PID tuning
K
p
8
K
d
1.5
K
i
20
—
ADRC ISE
—
PID ISE
—
ADRC max|u|
—
PID max|u|
Output y(t) —
ADRC
vs
PID
Disturbance — true d(t) vs ADRC estimate f̂(t)
Control signal u(t)
💡
Both controllers tuned for the nominal plant. ADRC estimates and cancels the disturbance; PID relies on its integrator.