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



Fault Calculations - Introduction

Fault calculations are one of the most common types of calculation carried out during the design and analysis of electrical systems. These calculations...

Thermoplastic and Thermosetting Insulation

While there are a vast array of cable insulation materials, these are often divided into two general types; Thermoplastic or Thermosetting. For example...

How to Size Power Cable Duct

Some colleagues had an issue earlier in the week on sizing conduits to be cast in concrete for some power cables . It became clear that none of us had...

Introduction to Traction Substations

Following on from my post on railway electrification voltages, I thought an introduction to traction substations would be a good idea. Traction substations...

Equipment Verification (to IEC Standards)

One of the requirements to ensuring that everything works is to have equipment selected, manufactured and verified [tested] to IEC standards. Not all equipment...

Fault Calculation - Symmetrical Components

For unbalance conditions the calculation of fault currents is more complex. One method of dealing with this is symmetrical components. Using symmetrical...

Post Authorship

In 2011, with the introduction of it’s Panda search ranking algorithms, Google introduced tools for determining the original author of posts.  The intention...

Famous Scientists

Here’s list of some famous scientists. Deliberately short, with the aim to provide a quick memory jog or overview. If your looking for more detailed information...

Fault Calculations - Typical Equipment Parameters

A frequent problem in fault calculations is the obtaining of equipment parameters.  While it is always preferable to use the actual parameters of the equipment...

Gas Insulated or Air Insulated Switchgear

Various arguments exist around SF6 Gas Insulated (GIS) and Air Insulated (AIS) medium voltage switchgear. Recently we had to change a GIS design to AI...

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