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PID Controller: A Simple Control Loop Mechanism

    Proportional-integral-derivative controller calculates feedback
    to reduce the error in the next step.

PID Controller: A Simple Control Loop Mechanism

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
          o current error
          o corrects for error in the previous step
      + integral term
          o sum of errors till now
          o corrects for error in the same direction in the past
      + derivative
          o current derivative of the error
          o can cause instability and not used often
          o or low pass filtering
          o corrects for sudden change in error
  * 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: [                    ]

Extension

  * 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

Related Posts

Constant 1D Kalman Filter Is Exponential Or Cumulative Average

Demo Source Code

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21 May 2021


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