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. 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
Biography
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.
