Meaning and mechanism
Proportional terms respond to the current error, integral terms respond to accumulated errors, and the differential term functions to suppress rapid changes or to respond to preceding changes.
Increasing the proportional gain can lead to faster response, but it can also result in increased overshoot and oscillations. Integration reduces persistent errors, but excessive accumulation can degrade the response.
Relationships and conditions
The experiment is controlled by u=Kp e+Ki∫e dt−Kd ḣ. Since the derivative is applied to the measurement height, it distinguishes between the error derivative when the target value changes suddenly, and the derivative of the measurement itself.
The actual controller exhibits output limitations, sensor noise, and delays. A method that significantly increases all gains does not guarantee stability, and tuning must be performed in conjunction with the characteristics of the target.
What to observe in the simulation
Stable integral control removes steady-state error from a constant disturbance.
A 1 kg vertical model with 2 N·s/m drag uses RK4 for 30 s. Baseline hover thrust cancels gravity. Saturation, delay, noise and ground collision are omitted. Final error may differ from steady-state error. Do not imitate real drone flights.
Key relationships and symbols
u = Kp e + Ki∫e dt − Kd ḣ · ḧ + 2ḣ = u + disturbance
| Symbol | Meaning | Unit |
|---|---|---|
| e | setpoint − measured value | Units of the controlled quantity |
| u | Control input | Model input units |
| Kp, Ki, Kd | Gain of each control term | Units appropriate to the term |
Worked example
How is settling time defined?
Time after which error stays within 2% of target · Stable integral control removes steady-state error from a constant disturbance.
Common misconceptions
- It is not possible to determine that the control performance is good simply because the objective has been passed once.