Motor speed · controls

A DC motor's speed obeys a clean first-order plant: $d o t o m e g a = (K_{v}, u - b, o m e g a - a u_{e} x t l o a d) / J$ , or after some algebra, $G (s) = K / (a u s + 1)$ . The PI controller earns its keep when a load torque suddenly hits — like a cordless drill biting into wood. P alone can hold a speed; only the integrator can recover the speed after a disturbance.

Hold the RPM under load

K_p 2.0 K_i 1.0 load torque (at t=5s) 0.5

peak deviation —

recovery time —

control effort RMS —

SSE after load —

what to try

Set K_i = 0. The motor returns to some speed under load — but not the commanded one. Watch the residual error.
Bring K_i up. The trace climbs back to the setpoint after each load step. The integrator is doing exactly what its name says — accumulating until the error is gone.
K_i too high → overshoot during recovery, then oscillation. The PI sweet spot is small-K_i with a K_p that's bigger than the integrator wants it to be.