Control Basics for Mechatronics

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.

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. HowDid theExponentials 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 thePhase 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.