How to Get Exact PI Gains from a DC Motor Step Response

Most tutorials tell you to tune PID gains by feel. This video shows the alternative: measure the plant, fit a model, and derive the gains in closed form — no trial and error.

**What's covered:**
- System identification: applying a PWM step, recording the velocity, and fitting a first-order transfer function P(s) = K/(τs+1) using least squares
- Controller design: pole-zero cancellation — placing the PI zero on the motor's pole so the open loop collapses to a pure integrator, giving a first-order closed loop with a freely chosen time constant τ_cl
- Discretisation: forward Euler, 5 ms loop, and the one thing textbooks skip — anti-windup
- Validation: closed-loop step response (τ_cl ≈ 42 ms vs 50 ms design target), PI disturbance rejection vs P-only steady-state error

**Hardware:** Arduino Nano ESP32 · L298N motor driver · brushed DC gear motor 12V · quadrature encoder

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*Timestamps*
0:00 Intro
0:53 System identification
2:08 Controller design — pole-zero cancellation
3:18 C++ implementation & anti-windup
3:56 Validation — Step Response & Disturbance Rejection (PI vs. P-only)

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#controlsystems #embeddedsystems #arduino #pid #motorscontrol

Видео How to Get Exact PI Gains from a DC Motor Step Response канала Transient Torque