• Stands for Proportional Integral Derivative Control.

  • We define a desired set point and a measured process variable . The error is defined

  • It combines three forms of control based on the error. The constants are called gain factors.

    • Proportional Control, defined by the term

    • Integral Control, defined by the term

    • Derivative Control defined by the term

  • The overall control function is then defined by

  • Each control accounts for the temporality of 1

    • Proportional control accounts for the current value of .
    • Integral control accounts for past values of since there could be residual error that persists over time.
    • Derivative control estimates the future value of which aims to reduce the effect of by damping this value.
  • A PID controller is tuned by modifying each of the constants .

  • PID control is not always suitable.

    • They may not scale well when multiple parameters must be considered.
    • They also do not necessarily provide optimal control.
    • It does not, by default, incorporate any knowledge about the system.
    • It works best when the feedback loop is linear and symmetric.

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Footnotes

  1. Although described in the context of controllers for mechanical, this logic of controlling based on current (P), cumulative past (I) and anticipated future (D) values is applicable in a lot of other non-controller related context if we adapt a Cybernetics view and examine the controller as it acts on an entire system (i.e., a human society or an economy)