Control Theory 

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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

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Mechanical - Linear

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Mechanical - Rotational

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Fluid - Hydraulic

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Fluid - Pneumatic

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Thermal

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Energy Storage (Inductive)

Electrical

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Mechanical - Linear

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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

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Energy Storage (Capacitive)

Electrical

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Mechanical - Linear

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Mechanical - Rotational

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Fluid - Hydraulic

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Fluid - Pneumatic

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Thermal

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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

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