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PID CONTROLLER

MAPUA INSTITUTE OF TECHNOLOGY  School of Chemical Engineering & Chemistry 

Process Control & Instrumentation

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OUTLINE

• Important Concepts

• Process Time Lags

• PID Control Algorithms

• Selection Of Control Action

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PROCESS CONTROL

• Definition 

 – the physical regulation of a

process to maintain aparticular process variable

as close as possible to a

desired value.

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4 BASIC COMPONENTS IN A 

FEEDBACK CONTROL LOOP

Refining Process (Plant)

1. Process

3. Controller 

Set Point (SV)

Controlled

Variable (CV)

Operator 

2. Measuring Element 4. Final Control Element

Process Variable (PV)

Manipulated

Variable (MV)

Load

Variable

Controller Output

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• Feedback Control = PID Control

 where

OUT(t) = controller output, 0 - 100% OUTdesign = design (steady state) controller output

OUT = control adjustment 

FEEDBACK CONTROL ALGORITHM

OUT(t) = OUTdesign + OUT 

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• P = Proportional Control Action

• I = Integral Control Action

• D = Derivative Control Action

PID CONTROL ALGORITHM

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• control adjustment is proportional to the

magnitude of the error

 where

OUT = control adjustment, %

Kc = Proportionality Constant (Gain or Sensitivity)

e = ERROR = Set Point (SP) - Process Variable (PV) 

Proportional Control Action

OUT = (Kc)(e) 

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• control adjustment is proportional to the

time integral of the error

 where

OUT = control adjustment, %

I 

= Integral Time Constant, time 

Integral Control Action

OUT = (Kc)/(I) (e)dt 

0

t

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• control adjustment is proportional to the rate

of change of the error

 where

OUT = control adjustment, %

D 

= Derivative Time Constant, time 

Derivative Control Action

OUT = (Kc)(D)(de/dt) 

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• P - Proportional Controller

• PI - Proportional Integral Controller

• PD - Proportional Derivative Controller

• PID - Proportional Integral Derivative Controller

Types of PID Controller

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• only one tuning parameter ( Kc ) 

• there is always an offset = steady state error or 

permanent deviation between the Set Point and

the Process Variable

P - Proportional Controller

OUT(t) = OUTdesign + (Kc)(e)

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• eliminates offset

•

more unstable compared to P Controller• two tuning parameters ( Kc , I

)

PI - Proportional Integral

ControllerOUT(t) = OUTdesign + (Kc)(e) + (Kc)/(I

) (e)dt

0

t

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• faster response

•

does not eliminates offset• susceptible to noise

• two tuning parameters ( Kc , D)

PD - Proportional Derivative

Controller

OUT(t) = OUTdesign + (Kc)(e) + (Kc)(D)(de/dt)

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• faster response

•

eliminates offset• susceptible to noise

• three tuning parameters ( Kc , I,

D)

PID - Proportional Integral

Derivative Controller

OUT(t) = OUTdesign + (Kc)(e) + (Kc)/(I) (e)dt + (Kc)(D

)(de/dt)

0

t

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Selection of Control ActionPROCESS PROPORTIONAL INTEGRAL DERIVATIVE

Flow & Liquid Pressure

0.2-50 Required Not Required

Gas Pressure 20 - Not Required Not Required

Liquid Level  2-20 OccasionallyRequired Not Required

Temperature 1-10 Required Required

CONSTANTAN