Application of Dimensional Analysis in Systems Modeling and Control Design

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IET Digital Library

This title is available electronically through the IET Digital Library

  • Author:

  • Year: 2013

  • Format: Hardback

  • Product Code: PBCE0900

  • ISBN: 978-1-84919-621-5

  • Pagination: 152 pp.

  • Stock Status: In stock

£57.20 Member price

£88.00 Full price


Dimensional analysis is an engineering tool that is widely applied to numerous engineering problems, but has only recently been applied to control theory. Application of Dimensional Analysis in Systems Modeling and Control Design aims to solve control problems such as identification and model reduction, robust control, adaptive control and PID control.

This new book introduces the fundamentals of dimensional analysis to both control engineers and theorists with examples of practical applicability to industrial control problems. By adopting control theory research, the author describes how to exploit the benefits that dimensional analysis can offer to control theoretic and practical problems.  

Topics include:
• dimensional analysis and dimensional similarity
• dynamical systems dimensionless representation
• dimensionless systems identification and model order reduction
• homogeneity of PID tuning rules
• dimensionless PID tuning rules comparison
• dimensional analysis control fundamentals
• control of dimensionally similar systems
• robust control
• adaptive control in the presence of input saturation
• two time scales control.

About the Author

Pedro Balaguer is a lecturer at the Department of Industrial Systems Engineering and Design at Universitat Jaume I de Castelló, Spain. His research interests include the application of dimensional analysis to control problems, PID control, supervision of iterative and adaptive control systems, and energy cost and energy consumption optimization.

Book readership

Application of Dimensional Analysis in Systems Modeling and Control Design is an essential introduction to this powerful technique for control engineers and theorists in fields as diverse as mechanical, chemical, electrical and electronic engineering.

Book contents

1 Introduction

1.1 What is dimensional analysis?
1.2 What is dimensional similarity?
1.3 Application of dimensional analysis to science in general
1.4 Application of dimensional analysis to control problems
1.5 Book contents

2 Dimensional analysis and dimensional similarity

2.1 Physical quantities, units, and dimensions
2.2 Systems of units: dependence and independence of dimensions
2.3 Buckingham pi theorem
2.4 Matrix approach for finding the dimensionless numbers
2.5 Dimensional similarity
2.6 Exercises

3 Dynamical systems: dimensionless representation

3.1 Introduction
3.2 Transfer function dimensionless representation
3.3 State space dimensionless representation
3.4 Comparison between transfer function and state space
dimensionless representation
3.5 Discrete time models dimensionless representation
3.6 Exercises

4 Dynamical systems: dimensional similarity

4.1 Introduction
4.2 Continuous time dynamical systems similarity
4.3 Discrete time dynamical system similarity
4.4 Exercises

5 Dimensionless systems identification and model order reduction

5.1 Introduction
5.2 General procedure
5.3 Example 1: Second order inverse response model identification
5.4 Example 2: Reduced effective transfer function reduction for
PID decentralized control

6 Homogeneity of PID tuning rules

6.1 Introduction
6.2 Homogeneous PID tuning rules
6.3 Closed loop transfer functions
6.4 Optimality of homogeneous tuning rules
6.5 Homogeneous and nonhomogeneous tuning rules

7 Dimensionless PID tuning rules comparison

7.1 Introduction
7.2 Elements of the comparative framework
7.3 Dimensionless comparative framework
7.4 Dimensionless elements
7.5 Application example
7.6 PID tuning rules selection

8 Control of dimensionally similar systems

8.1 Introduction
8.2 Control of dimensionally similar systems
8.3 Complete similarity
8.4 Partial similarity
8.5 Experimental case study

9 Adaptive systems

9.1 Introduction
9.2 Actuator limitations and dimensionally similar model reference
9.3 SMRAC for first order plants
9.4 SMRAC for arbitrary order plants
9.5 Application example



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