Control Theory 

By on

Control theory looks at how systems work and are controlled from a mathematical view. This note gives a brief introduction to some of the concepts – more of a notepad of concepts really, which can be added to over time.

Introduction

 

controlTheory
Simple Control System

The diagram illustrates a control system at it’s simplest.  The required output of the system is the reference.  A sensor measures the system output and a controller compares this to the reference to determine the necessary actions to ensure the output moves towards the value given by the reference.

The taking of the system output back to the input of the controller and using this (in conjunction with the reference) is called feedback.  There are two types of feedback:

Negative – where the system responds in the opposite direction to the error (difference between the measured output and reference).  For example a thermostat at a set temperature will turn off when the room temperature exceeds this, thus cooling the room.

Positive – where the system responds in the same direction as the error.  An example of positive feedback would be placing a microphone near a speaker, where the sound will grow louder and louder.

Electrical Analogies

Building blocks for electrical, mechanical, fluid and thermal systems are often similar and analogous to each other.  The use of analogies is often helpful in explaining how things work and is particularly useful in control systems.

Electrical Mechanical Fluid Thermal
Voltage (V) Force (F) Pressure (p) Temperature (∆T, T1-T2)
Current (i) Velocity (v) Flow (q) Heat Flow (q)
Resistor (R) Dashpot (c) Hydraulic Resistance  (R) Thermal Resistance (R)
Capacitor Spring Hydraulic Capacitance (C) Thermal Capacitance(C)
Inductor Mass Hydraulic Inertance (I) No Equivalent

 

Describing
Equation
Energy /
Power
Analogous
Constant
Energy Dissipation

Electrical

 myElectrical Equation  myElectrical Equation  myElectrical Equation

Mechanical - Linear

 myElectrical Equation myElectrical Equation   myElectrical Equation

Mechanical - Rotational

 myElectrical Equation  myElectrical Equation  myElectrical Equation

Fluid - Hydraulic

 myElectrical Equation  myElectrical Equation  myElectrical Equation

Fluid - Pneumatic

 myElectrical Equation  myElectrical Equation  myElectrical Equation

Thermal

 myElectrical Equation  myElectrical Equation  myElectrical Equation
Energy Storage (Inductive)

Electrical

 myElectrical Equation myElectrical Equation   myElectrical Equation

Mechanical - Linear

 myElectrical Equation  myElectrical Equation  myElectrical Equation

Mechanical - Rotational

 myElectrical Equation  myElectrical Equation  myElectrical Equation

Fluid - Hydraulic

 myElectrical Equation  myElectrical Equation  myElectrical Equation

Fluid - Pneumatic

 myElectrical Equation  myElectrical Equation  myElectrical Equation

Thermal

 myElectrical Equation  myElectrical Equation  myElectrical Equation
Energy Storage (Capacitive)

Electrical

 myElectrical Equation  
myElectrical Equation
 myElectrical Equation

Mechanical - Linear

 myElectrical Equation  myElectrical Equation  myElectrical Equation

Mechanical - Rotational

 myElectrical Equation  myElectrical Equation myElectrical Equation

Fluid - Hydraulic

 myElectrical Equation  myElectrical Equation  myElectrical Equation

Fluid - Pneumatic

 myElectrical Equation  myElectrical Equation  myElectrical Equation

Thermal

- - -

More …

This is an introductory post, I put together as things were being moved across from the old Wiki.   If there is anything you would like adding to the post, please let me know below and I’ll look at adding it. 



Steven McFadyen's avatar Steven McFadyen

Steven has over twenty five years experience working on some of the largest construction projects. He has a deep technical understanding of electrical engineering and is keen to share this knowledge. About the author

myElectrical Engineering

comments powered by Disqus



Voltage Drop in Installations - Concepts

Problems on achieving maximum voltage drop within an installation come up often. Depending where you live, local regulations will have different limits...

Capacitors - Energy Storage Application

Capacitors have numerous applications in electrical and electronic applications.  This note examines the use of capacitors to store electrical energy....

How to Write an Electrical Note

Electrical notes are a collaborative collection of electrical engineering information and educational material. Any registered user can add content. ...

Back to basics - the Watt (or kW)

When thinking about watts (W) or kilowatt (kW = 1000 W) it can be useful too keep in mind the fundamental ideas behind the unit. Watt is not a pure electrical...

Multimeter

Multimeters are undoubtedly the most common item of electrical test equipment in use.  Often it is the first piece of equipment people will turn to when...

Electrical Engineering

Electrical engineering is a field that covers a wide variety of sub-fields, including electricity and electronics. It is a field that goes back to the...

How a Digital Substation Works

Traditionally substations have used circuit breakers, current transformers (CT), voltage transformers (VT) and protection relays all wired together using...

How to Size Current Transformers

The correct sizing of current transformers is required to ensure satisfactory operation of measuring instruments and protection relays. Several methods...

Thomas Edison

American inventor Thomas Alva Edison was born in Milan, Ohio on February 11, 1847. He was the youngest of seven children and received little formal schooling...

Resistors

Resistors are electronic components that oppose the flow of current.  Manufactured in various types and ranges they have a wide application to electronics...

Have some knowledge to share

If you have some expert knowledge or experience, why not consider sharing this with our community.  

By writing an electrical note, you will be educating our users and at the same time promoting your expertise within the engineering community.

To get started and understand our policy, you can read our How to Write an Electrical Note