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

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

Mechanical - Linear

Mechanical - Rotational

Fluid - Hydraulic

Fluid - Pneumatic

Thermal

Energy Storage (Inductive)

Electrical

Mechanical - Linear

Mechanical - Rotational

Fluid - Hydraulic

Fluid - Pneumatic

Thermal

Energy Storage (Capacitive)

Electrical

Mechanical - Linear

Mechanical - Rotational

Fluid - Hydraulic

Fluid - Pneumatic

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.

More interesting Notes:

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

Medium Voltage Switchgear Room Design Guide

Many medium voltage (MV) indoor switchgear rooms  exist worldwide. The complexity of these rooms varies considerably depending on location, function and...

Questions - Reputation and Privilege

Our question and answer system while letting you do exactly what it says, is much more.  It is a dynamic user driven system, where our users not only ask...

Restricted Earth Fault Protection

The windings of many medium and small sized transformers are protected by restricted earth fault (REF) systems. The illustration shows the principal of...

Electromagnetic Fields - Exposure Limits

Exposure to time varying magnetic fields, from power frequencies to the gigahertz range can have harmful consequences.  A lot of research has been conducted...

Cable Sizing Tool

Our cable sizing tool is one of the more popular tools on the site.  The tool enables cables to be sized in compliance with BS 7671 (the IEE Wiring Regulations...

Cost Performance and Time

Often us engineers get so bogged down in equations, using software, producing drawings and writing specifications that this becomes the sole focus.   ...

Meeting room of the future

The IET site has a video of a visit showing of a high tech meeting room developed at Napier University in Edinburgh. It a good demonstration of innovative...

Wiki Depreciation

We have had the Wiki with us for a long time now, but at last I have decided to say bye bye – more details on why below.

Three Phase Power Simplified

A single phase system is perhaps the most common type of system most people are familiar with. This is what people have in their homes and what appliances...

Power Factor

Power factor is the ratio between the real power (P in kW) and apparent power (S in kVA) drawn by an electrical load. The reactive power (Q in kVAr)...

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