1st Edition

Control Basics for Mechatronics

By John Billingsley Copyright 2024
    174 Pages 71 B/W Illustrations
    by CRC Press

    174 Pages 71 B/W Illustrations
    by CRC Press

    174 Pages 71 B/W Illustrations
    by CRC Press

    Also available as eBook on:

    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 rigour 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.


    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





    As a Cambridge Mathematics Scholar, John completed the mathematics tripos in two years, then spent his third year studying electronics. Following a Graduate Apprenticeship, he designed algorithms and electronics for aircraft control systems. He then returned to Cambridge to complete his doctoral research on Predictive Control.

    He remained in Cambridge as a Fellow of Sidney Sussex College. Eight years later he moved to a Readership at Portsmouth Polytechnic, now Portsmouth University and later became Professor of Robotics. He led groups researching the ‘Craftsman Robot’ and walking robots. He helped found companies designing embedded electronics for domestic appliances and nuclear test equipment.

    In1992 John moved to Toowoomba, Australia, where he applied machine vision to precision tractor guidance. He co-founded the National Centre for Engineering in Agriculture of the University of Southern Queensland.

    This year he was joint organiser of the twenty-sixth annual conference on Mechatronics and Machine Vision in Practice, a series which he inaugurated in 1994.