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PID Control

The feedback loop that keeps drones level and motors on target — proportional, integral, derivative.

Knowing where you want to be (kinematics) isn’t enough — motors drift, gravity pulls, sensors lag. Control is the feedback loop that drives the real state toward the target despite all that. The PID controller is its workhorse, used in everything from thermostats to drones.

The dashed line is the setpoint (target = 1); the curve is the system’s response. Tune the three gains and watch how it gets there.

setpoint
overshoot ≈ 16%steady-state error ≈ 0.005Kp pushes harder · Kd damps oscillation · Ki removes leftover error

The three terms

The controller measures the error (target − current) and sets its output from three pieces:

  • P — proportional (Kp·error): push in proportion to how far off you are. Bigger Kp reacts faster, but too big causes overshoot and oscillation.
  • I — integral (Ki·∫error): accumulate past error to erase a stubborn steady-state offset (e.g. gravity). Too much makes it sluggish and wind up.
  • D — derivative (Kd·d error/dt): react to how fast the error is changing — a brake that damps overshoot and settles things down.

output = Kp·e + Ki·∫e + Kd·(de/dt)

Tuning

Try it: crank Kp alone → it overshoots and rings. Add Kd → the oscillation calms. If it settles below the line, add Ki → the steady-state error closes. Good tuning balances fast response against stable, low- overshoot settling.

Where it runs

PID (and its cousins) stabilizes drone attitude, holds motor speed, regulates temperature, and keeps a self-driving car in its lane — anywhere a measured value must track a target in real time.

Takeaways

  • Control closes the loop: measure error, act, repeat.
  • P reacts to current error, I to accumulated error, D to its rate of change.
  • Tuning trades speed against overshoot and stability.