Feedback and PID control

Feedback compares what you want with what you measure and uses the difference to act. A toy car that adjusts steering from camera position can reject a side push; a fixed steering command cannot. Define reference r, measured output y_m, and error e = r - y_m. The controller produces u, the plant responds, and the sensor closes the loop. The sign matters: an action intended to reduce positive error must not increase it.

A continuous PID law is u(t) = K_p e(t) + K_i ∫e(t)dt + K_d de/dt. Proportional action reacts to present error. Integral action accumulates persistent error and can remove offset. Derivative action responds to change and can add damping, but it amplifies measurement noise and is often applied to measured output rather than a suddenly changing reference. In sampled code, one simple form uses I_k = I_{k-1} + e_kΔt and D_k = (e_k - e_{k-1})/Δt.

Actuators saturate. A PWM command cannot exceed its allowed range, and a motor driver cannot supply infinite voltage or current. If integration continues during saturation, the stored integral “winds up,” causing prolonged overshoot after the error changes sign. Clamp or condition integration, and record saturation explicitly. A specific build decision for a geared desk robot is to set output limits from driver and motor constraints before increasing K_i.

A common misconception is that PID terms are three magic improvements that should all be increased. More K_p can speed response but also magnify noise or excite oscillation; more K_i can correct bias but erode stability; K_d can become a noise command. Another failure is testing with the mechanism connected before confirming feedback direction. First command a small bounded output, observe sensor sign, and verify that the computed correction opposes displacement. PID does not compensate for an encoder that intermittently disconnects or a mechanically jammed axis.