notes
Loop: unity negative feedback; parallel PID with an ideal
derivative — its impulse kicks at reference jumps are marked with
δ arrows (exact weight, not to scale). Real controllers filter D;
this keeps the algebra identical to the locus.
Locus: poles of 1 + kC(s)G(s), k: 0→∞, PID ratios frozen
at the sliders; ◊ = k = 1 (the current gains). Click a
branch to rescale all three gains onto it.
Ki = 0 removes the controller pole at s = 0 exactly
— P/PD add no phantom integrator.
Stability = every closed-loop pole in Re s < 0; the
feedback moves poles only — closed-loop zeros stay at the
open-loop zeros.