PID — proportional term

Summary¶

The proportional term (P) of a PID controller applies a correction proportional to the current error: large error produces large correction, small error produces small correction. P is the primary stiffness of the flight controller — too low and the drone drifts and responds sluggishly, too high and it oscillates rapidly. P alone cannot eliminate steady-state error (a drone that needs constant slight correction to fly level will always be slightly off) — that is the job of the integral term. For libdrone's mapping role, P is tuned conservatively: responsive enough to reject wind, not so aggressive that it fights itself during slow survey transects.

Concept¶

What proportional means¶

The proportional term multiplies the current error by a constant gain K_P:

P_output = K_P × error

Where error = setpoint − measured_value (desired rotation rate minus actual rotation rate in degrees/second).

If the drone is 10°/s away from the commanded rate, and K_P = 50, the correction output is 500. If the drone is 2°/s away, the correction is 100. The controller applies exactly as much correction as the error requires — proportionally.

The residual offset problem¶

A purely proportional controller always leaves a small residual error. Here is why: as the drone approaches the setpoint, the error shrinks, so the correction shrinks. At some point, the correction is just barely large enough to overcome the forces holding the drone off setpoint (friction, steady wind, slight mass imbalance). At that point, the system reaches equilibrium — but slightly off the setpoint. The correction exactly balances the disturbance, but the drone is not quite at the commanded attitude.

This residual offset is called steady-state error. In practice it means the drone consistently flies at a slightly wrong attitude unless the pilot applies a permanent stick input. The I term (integral) is designed to eliminate this. → See pid-integral-term.

P too low: sluggish and drifting¶

When K_P is too low, even a large error produces only a small correction. The drone responds slowly to disturbances — wind pushes it off course and it takes a long time to return. Manual stick inputs feel mushy. The drone oscillates slowly, never snapping to the commanded attitude.

In a Blackbox trace, low P shows as large, slow gyro excursions that gradually damp out over many cycles.

P too high: rapid oscillation¶

When K_P is too high, even a small error produces a large, aggressive correction. The drone overshoots the setpoint, overcorrects, overshoots again — oscillating at high frequency. The oscillation frequency is approximately the natural frequency of the airframe-motor system. At extreme P values, the oscillation becomes self-sustaining and the drone is unflyable.

In a Blackbox trace, high P shows as a rapid, sustained oscillation on all axes, visible in both the gyro trace and the motor output trace.

Correct P: crisp, settled, no oscillation¶

Correctly tuned P produces a response that reaches the setpoint quickly and settles without visible oscillation. Stick inputs feel direct and proportional. Wind gusts are rejected promptly. There is no sustained ringing after a disturbance.

Reference¶

P effects on flight behaviour¶

P and the pendulum natural frequency¶

The correct P gain is related to the airframe's natural frequency (determined by its moment of inertia and the pendulum effect). Lowering the CG (as in V2.4.6 vs V2.14) increases the natural frequency → requires slightly different P tuning. Start from documented baseline values and adjust from Blackbox evidence, not by feel alone. → See pendulum-stability.

Procedure¶

P tuning sequence (Betaflight)¶

1. Set I and D to zero (or very low). Work on P in isolation.
2. Hover and observe stability. Introduce a sharp disturbance (brisk pitch input, hand-wave near the drone).
3. If drone oscillates continuously: lower P by 10–15%.
4. If drone drifts slowly: raise P by 10–15%.
5. Target: drone snaps back from a disturbance and settles in 1–2 oscillation cycles without sustained ringing.
6. Once P is set, restore I and D before further tuning.
7. Verify result in Blackbox: gyro trace should show clean, damped response to step inputs.

Rationale¶

Why P is the first term to tune¶

P sets the fundamental gain of the control loop — the relationship between error magnitude and correction magnitude. I and D modify P's behaviour (I removes steady-state error, D prevents overshoot), but they cannot compensate for a badly set P. Starting with P correct before adding I and D is the standard practice because the interactions are easier to understand one term at a time.

Why libdrone tunes P conservatively¶

libdrone spends most of its flight time in GPS position hold at low speed. In this regime, the disturbances are slow-moving (wind, thermal drift) and the control demands are modest. Aggressive P tuned for freestyle flying would produce unnecessary motor activity, heat, and vibration during steady-state hover. Conservative P keeps the flight smooth and the motors cool during long mapping missions, accepting slightly slower transient response that is invisible in practice.

Connections¶

requires: - closed-loop-control related: - pid-integral-term - pid-derivative-term - pendulum-stability leads_to: - pid-integral-term - pid-derivative-term