Inst ToolsInst ToolsInst Tools
  • Courses
  • Automation
    • PLC
    • Control System
    • Safety System
    • Communication
    • Fire & Gas System
  • Instrumentation
    • Design
    • Pressure
    • Temperature
    • Flow
    • Level
    • Vibration
    • Analyzer
    • Control Valve
    • Switch
    • Calibration
    • Erection & Commissioning
  • Interview
    • Instrumentation
    • Electrical
    • Electronics
    • Practical
  • Q&A
    • Instrumentation
    • Control System
    • Electrical
    • Electronics
    • Analog Electronics
    • Digital Electronics
    • Power Electronics
    • Microprocessor
Search
  • Books
  • Software
  • Projects
  • Process
  • Tools
  • Basics
  • Formula
  • Power Plant
  • Root Cause Analysis
  • Electrical Basics
  • Animation
  • Standards
  • 4-20 mA Course
  • Siemens PLC Course
Reading: Overview of PID Control terms
Share
Notification Show More
Font ResizerAa
Inst ToolsInst Tools
Font ResizerAa
  • Courses
  • Design
  • PLC
  • Interview
  • Control System
Search
  • Courses
  • Automation
    • PLC
    • Control System
    • Safety System
    • Communication
    • Fire & Gas System
  • Instrumentation
    • Design
    • Pressure
    • Temperature
    • Flow
    • Level
    • Vibration
    • Analyzer
    • Control Valve
    • Switch
    • Calibration
    • Erection & Commissioning
  • Interview
    • Instrumentation
    • Electrical
    • Electronics
    • Practical
  • Q&A
    • Instrumentation
    • Control System
    • Electrical
    • Electronics
    • Analog Electronics
    • Digital Electronics
    • Power Electronics
    • Microprocessor
Follow US
All rights reserved. Reproduction in whole or in part without written permission is prohibited.
Inst Tools > Blog > Control Systems > Overview of PID Control terms

Overview of PID Control terms

Last updated: October 24, 2019 7:36 am
Editorial Staff
Control Systems
2 Comments
Share
7 Min Read
SHARE

PID control can be a confusing concept to understand. Here, a brief summary of each term within PID (P. I, and D) is presented for your learning benefit.

Contents
Proportional control mode (P)Integral control mode (I)Derivative control mode (D)

Proportional control mode (P)

Proportional – sometimes called gain or sensitivity – is a control action reproducing changes in input as changes in output. Proportional controller action responds to present changes in input by generating immediate and commensurate changes in output. When you think of “proportional action” (P), think prompt : this control action works immediately (never too soon or too late) to match changes in the input signal.

Mathematically defined, proportional action is the ratio of output change to input change. This may be expressed as a quotient of differences, or as a derivative (a rate of change, using calculus notation):

Proportional control mode

For example, if the PV input of a proportional-only process controller with a gain of 2 suddenly changes (“steps”) by 5 percent, and the output will immediately jump by 10 percent (∆Output = Gain × ∆Input). The direction of this output jump in relation to the direction of the input jump depends on whether the controller is configured for direct or reverse action.

A legacy term used to express this same concept is proportional band: the mathematical reciprocal of gain. “Proportional band” is defined as the amount of input change necessary to evoke fullscale (100%) output change in a proportional controller. Incidentally, it is always expressed as a percentage, never as fraction or as a per unit value:

Proportional band equation

Using the same example of a proportional controller exhibiting an output “step” of 10% in response to a PV “step” of 5%, the proportional band would be 50%: the reciprocal of its gain ( 1/2 = 50%).

Another way of saying this is that a 50% input “step” would be required to change the output of this controller by a full 100%, since its gain is set to a value of 2.

Integral control mode (I)

Integral – sometimes called reset or floating control – is a control action causing the output signal to change over time at a rate proportional to the amount of error (the difference between PV and SP values).

Integral controller action responds to error accumulated over time, ramping the output signal are far as it needs to go to completely eliminate error. If proportional (P) action tells the output how far to move when an error appears, integral (I) action tells the output how fast to move when an error appears.

If proportional (P) action acts on the present, integral (I) action acts on the past. Thus, how far the output signal gets driven by integral action depends on the history of the error over time: how much error existed, and for how long. When you think of “integral action” (I), think impatience: this control action drives the output further and further the longer PV fails to match SP.

Mathematically defined, integral action is the ratio of output velocity to input error:

Integral Controller Value

An alternate way to express integral action is to use the reciprocal unit of “minutes per repeat.” If we define integral action in these terms, the defining equations must be reciprocated:

minutes per repeat

For example, if an error of 5% appears between PV and SP on an integral-only process controller with an integral value of 3 repeats per minute (i.e. an integral time constant of 0.333 minutes per repeat), the output will begin ramping at a rate of 15% per minute ( dm/dt = Integral value × e, or dm/dt = e/Ti).

In most PI and PID controllers, integral response is also multiplied by proportional gain, so the same conditions applied to a PI controller that happened to also have a gain of 2 would result in an output ramping rate of 30% per minute ( dm/dt = Gain value × Integral value x e, or  dm/dt = Gain value × e/Ti ).

The direction of this ramping in relation to the direction (sign) of the error depends on whether the controller is configured for direct or reverse action.

Derivative control mode (D)

Derivative – sometimes called rate or pre-act – is a control action causing the output signal to be offset by an amount proportional to the rate at which the input is changing. Derivative controller action responds to how quickly the input changes over time, biasing the output signal commensurate with that rate of input change.

If proportional (P) action tells the output how far to move when an error appears, derivative (D) action tells the output how far to move when the input ramps. If proportional (P) action acts on the present and integral (I) action acts on the past, derivative (D) action acts on the future:

it effectively “anticipates” overshoot by tempering the output response according to how fast the process variable is rising or falling. When you think of “derivative action” (D), think discretion: this control action is cautious and prudent, working against change.

Mathematically defined, derivative action is the ratio of output offset to input velocity:

Derivative control mode (D)

For example, if the PV signal begins to ramp at a rate of 5% per minute on a process controller with a derivative time constant of 4 minutes, the output will immediately become offset by 20% (∆Output = Derivative value × de/dt ).

In most PD and PID controllers, derivative response is also multiplied by proportional gain, so the same conditions applied to a PD controller that happened to also have a gain of 2 would result in an immediate offset of 40% (∆Output = Gain value × Derivative value × de/dt ).

The direction (sign) of this offset in relation to the direction of the input ramping depends on whether the controller is configured for direct or reverse action.

Don't Miss Our Updates
Be the first to get exclusive content straight to your email.
We promise not to spam you. You can unsubscribe at any time.
Invalid email address
You've successfully subscribed !

Continue Reading

Interactions With Process Control Systems Philosophy
Package Control and Safety Systems Implementation Methods
What is Loop Checking?
Alarm and Trip Systems
How does a Redundant Controller comes in line when the Main Controller fails?
Liquid Level Switch Control Pump and Lamp
Share This Article
Facebook Whatsapp Whatsapp LinkedIn Copy Link
Share
2 Comments
  • Aditya says:
    January 17, 2018 at 6:58 am

    Very brief and well studies explanation. Thank you so much!!!

    Reply
  • Feeroz says:
    March 5, 2018 at 1:54 pm

    Information

    Reply

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Stay Connected

128.3kFollowersLike
69.1kFollowersFollow
208kSubscribersSubscribe
38kFollowersFollow

Categories

Explore More

2-wire Transmitters Current Loops
What is a Network Connector? – Types of Connectors
Cyber Security Multiple Choice Questions and Answers
Key Facts About RS485 Industrial Network
Feedback Control Principle
What is a Annunciator Panel?
Direct Digital Control (DDC) Systems
Vendor View of Supplying Industrial Process Control & Safety Systems

Keep Learning

Control Loop

What is a Control Loop ?

Ziegler-Nichols closed-loop Tuning - 1

Heuristic PID Tuning Method

Stripping tower unit

Process Control High Level Alarm Fault Analysis

EcoStruxure Machine Expert - HVAC - Programming Software

How to Write a Program in Ecostruxure Machine Expert HVAC Software?

BACNet Protocol

What is the BACNet Protocol? BACNet IP vs. BACNet MS/TP

Fixed Type Motor control center (MCC)

Motor Control Center (MCC) Signal Interface Termination (SIT)

Wellhead Control Panel

Basics of Wellhead Control Panel (WHCP)

PID Controllers with output high select Logic

PID Controllers with Output High Select Logic

Learn More

Burst Transformers Root Cause Analysis

Burst Transformer – Electrical Problem Solved

What is PID Controller

What is PID Controller?

4-20ma-formulas-and-examples

4-20mA Formulas and Examples

Electrification in Mining Industry

Electrification in Mining Industry

Open-Tank-DP-Level-Transmitter-with-Zero-Suppression-Calibration

DP Level Transmitter with Zero Suppression Calibration

Digital Electronics Objective Questions

Digital Electronics Objective Questions – Set 1

Electric Circuits Objective Questions

Electric Circuits Objective Questions – Set 13

Ion Spectrometers Questions & Answers

Ion Spectroscopy Questions & Answers

Follow US
All rights reserved. Reproduction in whole or in part without written permission is prohibited.
Welcome Back!

Sign in to your account

Username or Email Address
Password

Lost your password?