An introduction to nonlinearity in control systems Notes | EduRev

: An introduction to nonlinearity in control systems Notes | EduRev

 Page 1


Derek Atherton
An Introduction to Nonlinearity in Control
Systems
Download free books at
Page 2


Derek Atherton
An Introduction to Nonlinearity in Control
Systems
Download free books at
Download free eBooks at bookboon.com
2 
 
Derek Atherton
An Introduction to Nonlinearity in Control 
Systems
Page 3


Derek Atherton
An Introduction to Nonlinearity in Control
Systems
Download free books at
Download free eBooks at bookboon.com
2 
 
Derek Atherton
An Introduction to Nonlinearity in Control 
Systems
Download free eBooks at bookboon.com
3 
 
An Introduction to Nonlinearity in Control Systems
© 2011 Derek Atherton & bookboon.com
ISBN 978-87-7681-790-9
Page 4


Derek Atherton
An Introduction to Nonlinearity in Control
Systems
Download free books at
Download free eBooks at bookboon.com
2 
 
Derek Atherton
An Introduction to Nonlinearity in Control 
Systems
Download free eBooks at bookboon.com
3 
 
An Introduction to Nonlinearity in Control Systems
© 2011 Derek Atherton & bookboon.com
ISBN 978-87-7681-790-9
Download free eBooks at bookboon.com
Click on the ad to read more
An Introduction to Nonlinearity in Control Systems
4 
Contents
Contents
 Preface 10
1 Introduction 12
1.1 What is nonlinearity? 12
1.2 Forms of nonlinearity 13
1.3 Structure and Behaviour 16
1.4 Overview of contents 17
1.5 References 18
2 The Phase Plane Method 19
2.1 Introduction  19
2.2 Basic Principles 19
2.2.1 The Linear Case 20
2.2.2 The Nonlinear Case 23
2.2.3 An Example  24
2.3 The Phase Plane for Systems with Linear Segmented Nonlinearities 26
2.3.1 Example 1 – Nonlinear Output Derivative Feedback 27
2.3.2 Example 2 – Relay Position Control 28
2.3.3 Example 3 – Position Control with Torque Saturation 34
© Deloitte & Touche LLP and affiliated entities.
360°
thinking.
Discover the truth at www.deloitte.ca/careers 
© Deloitte & Touche LLP and affiliated entities.
360°
thinking.
Discover the truth at www.deloitte.ca/careers 
© Deloitte & Touche LLP and affiliated entities.
360°
thinking.
Discover the truth at www.deloitte.ca/careers 
© Deloitte & Touche LLP and affiliated entities.
360°
thinking.
Discover the truth at www.deloitte.ca/careers 
Page 5


Derek Atherton
An Introduction to Nonlinearity in Control
Systems
Download free books at
Download free eBooks at bookboon.com
2 
 
Derek Atherton
An Introduction to Nonlinearity in Control 
Systems
Download free eBooks at bookboon.com
3 
 
An Introduction to Nonlinearity in Control Systems
© 2011 Derek Atherton & bookboon.com
ISBN 978-87-7681-790-9
Download free eBooks at bookboon.com
Click on the ad to read more
An Introduction to Nonlinearity in Control Systems
4 
Contents
Contents
 Preface 10
1 Introduction 12
1.1 What is nonlinearity? 12
1.2 Forms of nonlinearity 13
1.3 Structure and Behaviour 16
1.4 Overview of contents 17
1.5 References 18
2 The Phase Plane Method 19
2.1 Introduction  19
2.2 Basic Principles 19
2.2.1 The Linear Case 20
2.2.2 The Nonlinear Case 23
2.2.3 An Example  24
2.3 The Phase Plane for Systems with Linear Segmented Nonlinearities 26
2.3.1 Example 1 – Nonlinear Output Derivative Feedback 27
2.3.2 Example 2 – Relay Position Control 28
2.3.3 Example 3 – Position Control with Torque Saturation 34
© Deloitte & Touche LLP and affiliated entities.
360°
thinking.
Discover the truth at www.deloitte.ca/careers 
© Deloitte & Touche LLP and affiliated entities.
360°
thinking.
Discover the truth at www.deloitte.ca/careers 
© Deloitte & Touche LLP and affiliated entities.
360°
thinking.
Discover the truth at www.deloitte.ca/careers 
© Deloitte & Touche LLP and affiliated entities.
360°
thinking.
Discover the truth at www.deloitte.ca/careers 
Download free eBooks at bookboon.com
Click on the ad to read more
An Introduction to Nonlinearity in Control Systems
5 
Contents
2. 4 Conclusions 35
2.5 References 35
2.6 Bibliography 36
3 The Describing Function 37
3.1 Introduction 37
3.2 The Sinusoidal Describing Function 37
3.3 Some Properties of the DF 39
3.4 The Evaluation of some DFs 41
3.4.1 Cubic Nonlinearity  41
3.4.2 Saturation Nonlinearity  41
3.4.3 Relay with Dead Zone and Hysteresis 42
3.5 Nonlinear Models and DFs 44
3.6 Harmonic Outputs 45
3.7 Sine plus Bias DF and the IDF 46
3.8 Conclusions 47
3.9 References 47
3.10 Bibliography 47
3.11 Appendix -Tables of Describing Functions 47
4  Stability and Limit Cycles using the DF 51
4.1 Introduction 51
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