National-instruments PID Control Toolkit 371685C-01 Manuale Utente Scaricare il pdf (Pagina 10)

PID Algorithms

This chapter explains the fast PID, precise PID, and autotuning algorithms.

The PID Algorithm

The PID controller compares the setpoint (SP) to the process variable (PV) to obtain the error

(e), as follows:

e = SP – PV

Then the PID controller calculates the controller action, u(t), as follows. In this equation, K

is the controller gain.

If the error and the controller output have the same range, –100% to 100%, controller gain is

the reciprocal of proportional band. T

is the integral time in minutes, also called the reset

time, and T

is the derivative time in minutes, also called the rate time. The following formula

represents the proportional action.

The following formula represents the integral action.

The following formula represents the derivative action.

ut() K

----

etd

∫

------

⎝⎠

⎜⎟

⎛⎞

t() K

t() =

-------

etd

∫

t() K

-------

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National-instruments PID Control Toolkit 371685C-01 Manuale Utente Pagina 10