APPLICATION NOTE

OVERVIEW

PID is an acronym for proportionalband, integral and derivative. Thiscontrol action allows a measurement(process variable) to be controlled ata desired set point by continuouslyadjusting a control output. Thesecontrol parameters act on the erroror deviation between set point andprocess variable.P Proportional Band in %I Integral Time in sec/repeatD Derivative Time in seconds

PROPORTIONAL CONTROL

With proportional band, the controlleroutput changes in “proportion” to theerror between process variable andset point. The amplitude of thechange is adjustable from 1% to999.9%.Control Output = (error) 100

PBRefer to Figure 1 below. Thisexample of a temperature controllershows a proportional band setting of5%.Set point = 500°Measurement range = 0-1000°5% PB = 5% of 1000° = 50°100% output at 475° (2.5% of 1000°)0% output at 525° (2.5% of 1000°)

If the process variable equals the setpoint (500°), there is a 50% output.As the temperature decreases, theproportional band increases theoutput linearly toward 100% as thetemperature falls toward 475°. Theoutput decreases below 50% as thetemperature rises toward 525°.

In this example, a small change intemperature provides a large changein output. If the setting is too smallfor the process dynamics,oscillations will occur and will notsettle at set point. A large PB settingmakes the controller act sluggishand will not respond adequately toupsets. Since proportional controldoes not incorporate the time thatthe error has existed, there willalways be an offset from set point.

Typically, flow or pressurecontrollers have a much larger

proportional setting due to a possiblenarrower measurement range andfast process reaction to a change inthe control output. For example, aflow controller may have an inputrange of 0 to 60gpm and a set pointof 30gpm.Measurement range = 60gpmSet point = 30gpm100% PB = 100% of 60 = 60gpm100% output at 0gpm0% output at 60gpm

PROPORTIONAL + MANUALRESET

To eliminate the inherent offsetobserved with proportional control, amanual reset function can be used.Virtually no process requiresprecisely 50% output to maintain theprocess variable at the set point. Anoffset will be present. Manual resetallows the user to bias the outputaccordingly to compensate for thesteady state offset using P only.Refer to Figure 2 below.

PID Control Tutorial

1000ºManual Reset Adjusted Here

500º Set Point

ProportionalBand

Time

Figure 2

CCUT-G-02A01-01

PROPORTIONAL +AUTOMATIC RESET(INTEGRAL)

Automatic reset or integral actioncorrects for any offset between setpoint and process variableautomatically by shifting theproportional band over a pre-definedtime. The integral time repeats theproportional action over the time set.Integral redefines the outputrequirements at the set point until

Output

0%

100%

Temperature 500º 525º475º

50%

5.0 % Proportional Band Measurement Range: 0 - 1000º

Figure 1

APPLICATION NOTEthe process variable and set pointare equal. Integral engineering unitsvary by controller manufacturer.Some use repeats/minute (resetrate), minutes/repeat orseconds/repeat. In Figure 3 below,seconds/repeat is used. The integralterm is added as follows:

The smaller the integral number, theproportional action will be repeatedmore often. If integral is too small,the process variable will oscillatethrough set point and create erraticcontrol action. If the number is toolarge, the action will be sluggish andunable to compensate for processupsets.

The integral number should beapproximately 5 times the dead/lagtime of the process variable. If theoutput is manually changed, deadtime is defined as the time requiredfor the process variable to initiallyreact after the change. The length oftime that it takes for the processvariable to stabilize at a steady stateis lag time.

Example: 40 sec (dead/lag) x 5 =200 sec/repeat

PROPORTIONAL + INTEGRAL+ DERIVATIVE

Derivative action is used primarily inprocesses with long dead and lagtimes. This control function looks atthe rate of change of the error andadjusts the control output based on

that rate. The derivative termis added to the controlalgorithm as follows:

The amount of derivative added tothe control output is based in timeunits. Figure 4 below shows howderivative acts on the proportionalband. The dashed line shows aproportional only control due to aprocess variable error from set point.

Using derivative (solid line), thecontrol output jumps up, rises in aramp and then falls back toproportional control action when theerror becomes constant. Inessence, it applies the “brakes” onthe process error by quickly shiftingthe proportional band. Derivativehas no effect on the output if theerror is not changing. The derivativeterm should be approximately ¼ theintegral time.

Derivative is typically not used incontrol loops with short dead/lagtime, e. g., flow or pressure. This isan anticipatory action that willcontribute to the inherent instabilityof these fast acting control loops.

Control Output = (error) 100 + 1_∫ (error)dt PB TI

Control Output = (error) 100 + 1_∫ (error)dt + TD (error)d PB TI dt

Output

Time 50 seconds

Derivative Action

Proportional Action

Derivative Time Constant

Error-10%

+10%

Output

Time

Error-10%

+10%

3

Figure

200 sec/repeat

Integr

Propo

Integral

Figure 4

CCUT-G-02A01-01

al Action

rtional Action

Time Constant