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Stands for Proportional Integral Derivative Control.
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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
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Integral Control, defined by the term
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Derivative Control defined by the term
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The overall control function is then defined by
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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.
- Proportional control accounts for the current value of
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A PID controller is tuned by modifying each of the constants
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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.
Links
Footnotes
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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) ↩