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ABOUT THE BOOK

Mechatronics is a mongrel, a crossbreed of classic mechanical engineering, the relatively young pup of computer science, the energetic electrical engineering, the pedigree mathematics and the bloodhound of Control Theory.

All too many courses in control theory consist of a diet of ‘Everything you could ever need to know about the Laplace Transform’ rather than answering ‘What happens when your servomotor saturates?’ Topics in this book have been selected to answer the questions that the mechatronics student is most likely to raise. That does not mean that the mathematical aspects have been left out, far from it. The diet here includes matrices, transforms, eigenvectors, differential equations and even the dreaded z transform. But every effort has been made to relate them to practical experience, to make them digestible. They are there for what they can do, not to support pages of mathematical rigors that defines their origins.

The theme running throughout the book is simulation, with simple JavaScript applications that let you experience the dynamics for yourself. There are examples that involve balancing, such as a bicycle following a line, and a balancing trolley that is similar to a Segway. This can be constructed ‘for real’, with components purchased from the hobby market.

TABLE OF CONTENTS

Foreword

1. Why Do You Need Control Theory?

1.1 Control is Not Just about Algorithms

1.2. The Origins of Simulation

1.3. Discrete Time  

1.4. The Concept of Feedback

2. Modelling Time

2.1 Introduction

2.2. A Simple System

2.3 Simulation

2.4 Choosing a Computing Platform

3. A Simulation Environment

3.1 Jollies

3.2. More on Graphics

3.3. More Choices

3.4 Drawing Graphs

3.5. More Details of Jollies

4. Step Length Considerations

4.1 Choosing a Step Length

4.2. Discrete Time Solution of a First-Order System

5. Modelling a Second-Order System

5.1. A Servomoter Example

5.2 Real-Time Simulation

6. The Complication of Motor Drive Limits

6.1. Drive Saturation

6.2 The Effect of a Disturbance

6.3. A Different Visualisation

6.4. Meet the Phase Plane

6.5. In Summary

7. Practical Controller Design

7.1. Overview

7.2. The Velodyne Loop

7.3. Demand Limitation

7.4. Riding a Bicycle

7.5 Nested Loops and Pragmatic Control

8. Adding Dynamics to the Controller

8.1. Overview

8.2. Noise and Quantisation

8.3. Discrete time control

8.4. Position Control with a Real Motor

8.5. In Conclusion

9. Sensors and Actuators

9.1. Introduction

9.2. The Nature of Sensors

9.3 The Measurement of Position and Displacement

9.4 Velocity and Acceleration

9.5 Output Devices

10. Analogue Simulation

10.1. History

10.2. Analogue Circuitry

10.3. State Equations

11. Matrix State Equations

11.1. Introduction

11.2. Feedback

11.3. A Simpler Approach

12. Putting It into Practice

12.1. Introduction

12.2. A Balancing Trolley

12.3 Getting Mathematical

12.4 Pole Assignment

13. Observers

13.1 Introduction

13.2. Laplace and Heaviside

13.3. Filters

13.4 The Kalman Filter

13.5. The Balancing Trolley Example

13.6. Complementary Filtering

13.7. A Pragmatic Approach

14. More about the Mathematics

14.1 Introduction

14.2. How Did the Exponentials Come In?

14.3. More about Roots

14.4. Imaginary Roots

14.5. Complex Roots and Stability

15. Transfer Functions

15.1. Introduction

15.2. Phase Advance

15.3. A Transfer Function Matrix

16. Solving the State Equations

16.1. Introduction

16.2. Vectors and More

16.3. Eigenvectors

16.4. A General Approach

16.5. Equal Roots

17. Discrete Time and the z Operator

17.1. Introduction

17.2. Formal Methods

17.3. z and Code

17.4. Lessons Learned from z

17.5. Quantisation

17.6. Discrete Transfer Function

18. Root Locus

18.1. Introduction

18.2. The Complex Frequency Plane

18.3. Poles and Zeroes

18.4. A Root Locus Plotter

18.5. A Better Plot

18.6. Root Locus for Discrete Time

18.7. Moving the Controller Poles and Zeroes

19. More about the Phase Plane 

19.1. Drawing Phase-Plane Trajectories

19.2. Phase Plane for Saturating Drive

19.3. Bang-Bang Control and Sliding Mode

19.4. More Uses of the Phase-Plane

20. Optimisation and an Experiment.

20.1. Introduction

20.2. Time-Optimal Control

20.3. Predictive Control

20.4. A Tilting Plank Experiment - Nostalgia

20.5. Ball and Beam: A Modern Version

21. Problem Systems

21.1. Introduction

21.2. A System with a Time Delay

21.3. Integral Action

21.4 The Bathroom Shower Approach

22. Final Comments

22.1. Introduction.

22.2. Multi-Rate Systems

22.3. Motor Control with a Two-Phase Encoder

22.4. And Finally