When to use PID controller?
- measured value (process variable) is a time series
- ideal value (setpoint) is known
- can correct via a feedback in the next steps
- tuning (training) data is available
- cannot model of the process
- in non-linear systems may not work
- example: cruise control
- process variable = speed
- setpoint = ideal speed
- error = ideal speed - actual speed
- feedback = gas pedal
What is PID controller?
- is sometimes called three-term controller
- tool to stay close to the ideal (control loop mechanism)
- uses distance from setpoint (error) to produce feedback
- error = setpoint - process variable
- defined as sum of 3 terms:
- proportional term
- current error
- corrects for error in the previous step
- integral term
- sum of errors till now
- corrects for error in the same direction in the past
- derivative
- current derivative of the error
- can cause instability and not used often
- or low pass filtering
- corrects for sudden change in error
- proportional term
- mathematical form:
- error: \( e(t) \)
- proportional coefficient: \( K_p \)
- integral coefficient: \( K_i \)
- derivative coefficient: \( K_d \)
- time: \( t \)
- feedback value (control function): \( u(t) \)
- equation: \( u(t) = K_p e(t) + K_i \int_0^t e(t) dt + K_d \frac{de(t)}{dt} \)
Demo
- grey dots represent setpoint
- here: constantly zero
- blue represents original process variable
- uncontrolled process variable
- red represents process variable after corrective feedback
- here: process variable minus feedback
- try changing the input function
- Find the demo source below
sine input function
Kp:
Kd:
Ki:
Self-tuning PID using Kalman filter
- Kalman filter uses linear relationship between measured values
- to estimate true values and uncertainty
- in the paper relationship between the PID parameters defines the Kalman filter tuning
Links to Related Sites
- HN Discussion of this post
- PID Without a PhD for more details on PID
