Lecture Notes on Modeling and Control of
Mechatronic Systems
Associate Professor Jay Katupitiya
Topic 1
Introduction
1.1
What is Mechatronics?
Mechatronics is the discipline that combines the modern methodologies of mechanical design, electrical and electronic engineering, control systems and computing to develop advanced systems. In general, most large scale mechatronic systems are mechanical in nature
and are computer controlled. The purpose of the control system in such a machine is to
effect motion. Harnessing these technologies into one piece of equipment requires bonding
of computational capabilities to a mechanical system. This requires hardware interfacing as
well as software interfacing.
Before the advancement of computer technology, design of machines were primarily a mechanical design task. The drive systems such as motors were coupled to the machine through
direct and simple means such as gears and/or pulleys and belts. Power transmission across
different parts of the machine took place through gear trains or belt driven pulley systems.
In some cases hydraulic power transmission was used. As such, most motions had linear
relationships to the source of drive. That is not to say that complex mechanical machines
did not exist. Non-linear motions were realized through complex cam systems. In general,
completely mechanical, sophisticated machines provided long years of reliable service.
One of the main disadvantages suffered by these machines was their fixed nature. Once built,
alterations were seldom possible. They had set capabilities in contrast to varied capabilities
of today’s machines. Even if they had varied capabilities such as in the case of a universal
milling machine, re-configuring it for a new task was tedious. It was not possible sitting in
front of a computer. Among the other disadvantages are the cost of manufacture for having
to machine intricate parts, cost of maintenance and bulkiness.
Today, most of these limitations have been eliminated with the use of mechatronic design
approaches. Complex motions can be achieved through sophisticated control systems. Control systems are implemented in the form of control algorithms in computers. This provides
a great flexibility to adapt the control systems to suit varying system parameters and configurations. The control systems can be optimized or designed to be self tuning. They allow
the integration of a wide variety of sensors and thereby making the systems intelligent. Motions of subsystems do not have to be mechanically coupled and centralized. Instead they
can be decentralized and controlled independently, yet they can achieve synchronization.
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Distributed embedded systems in the form of small computer systems or single board computers are widely available at modest costs. Their computational power is significant. Even
designing our own small computer system is perfectly feasible. Unlike in the past, machines
can be easily reconfigured for different tasks through software means - an example is the reconfiguring of a robot for force controlled operations and pick and place operations. Another
example is the reconfiguration of a CNC milling centre for drilling and milling.
1.1.1
Definition of a Mechatronic System
A system to qualify as a mechatronic system it has to demonstrate two distinctive features.
First it has to have significant amount of power transmission between its principal mechanical elements. Next it must have a significant amount of information or data exchange
through sensors, actuators and computing equipment and a certain degree of information
processing. A system that has no information processing but a great deal of power transmission is a mechanical system. A system that has an equal degree of power transmission and
information processing is a mechatronic system. A system that has information processing
only, i.e. a system such as a calculator or a digital watch is an electronic system.
1.2
Aim of This Course
The primary aim of this course is to give you a through understanding of how to design a
control system that can be implemented using a digital computer. The purpose of a control
system is to control a certain quantity such as speed or temperature in a manner we desire.
Consider the simple example of controlling the temperature of a room. The entire control
system consists of the room with the volume of air within the room, a heating/cooling system,
some means of setting the desired temperature and most importantly some mechanism to
turn the heating/cooling system on and off to achieve the desired room temperature. A
slightly more sophisticated control system may have a means of measuring the temperature
inside the room.
When everything is well set, this system should maintain the temperature inside the room, at
the set temperature. On the other hand, if it is a badly designed system, when we expect 21◦ C
it might give us 18◦ C. Poor performance may also be indicated by a system that takes too long
to reach the desired temperature. A system that is less stable may make the temperature
oscillate around the final temperature before settling at a steady value.
For all practical purposes, almost all systems to be controlled can be viewed as continuoustime systems. These systems undergo changes continuously over time. In contrast to
continuous-time systems, digital computers are discrete-time systems. A computer that
is used to control a given system invariably involve some amount of number crunching.
Such computations require time. As such a digital computer cannot dedicate all its time to
continuously watch the system being controlled. In general, these computers attend to the
system at regular intervals. Thus the computer is blind most of the time. The computer
sees the system at regular time intervals. Therefore, the controller implemented in a digital
computer has to be a discrete-time controller.
The theory behind the discrete-time control systems are different to that behind the continuous1-2
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time control systems. Designing discrete-time control systems can be done in a number of
different ways. Broadly, they can be categorized into two groups. First, we can design the
control system entirely in continuous time domain and then convert it to a discrete-time controller so that it can be implemented in a digital computer. This is called the Indirect Design
Approach. Second approach is to carryout the entire design in the discrete-time domain.
This is called the Direct Design Approach.
1.3
What will be studied in this course?
The sections that will be covered are listed below. This course has a significant revision
of continuous-time systems that are supposed to be completed in four hours of lectures.
Therefore, your earlier knowledge of continuous systems is very valuable. The topics to be
covered are listed below
1. Continuous-time Systems
• Continuous time signals - continuous and quantized amplitudes
• Basic control block diagram
• Different types of control approaches.
– open loop control
– feedback control
– adaptive control
– robust control
– optimal control
• Feedback control systems
– P. PI, PD, PID controllers
• Qualitative analysis of a control system
2. Mathematical Representation of a Continuous-time System
• Laws of Physics and differential equations
• Laplace transforms
– Complex plane
– Meaning of the Laplace variable s.
• Transfer function
3. The Use of Continuous-time Transfer Functions
• Characteristic equation
• Time response of a system
• Relationship of the roots of characteristic equation to time response
• First order system example
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• Second order system example
• Higher order systems
• Dominant poles and pole attenuation
4. Features of a Continuous-time Transfer Function
• DC gain
• Instantaneous gain
• Properness
• Effects of poles and zeros
5. Root Locus
• What is root locus?
• How to use it.
• How to interpret a root locus.
6. Discrete-time Systems
• Anatomy
• Discrete-time signals
• Discrete-time and continuous-time interface
• Samplers
• Zero order and higher order holds
7. z-Transforms
• Starred Laplace transforms
• z - transforms
• Discrete-time transfer functions
8. The Use of Discrete-time Transfer Function
• Characteristic equation
• Time response of a discrete-time system
• Relationship of the roots of characteristic equation to time response.
9. Inverse z-transforms
• Direct table reference
• partial fractions + table reference
• direct division
• computational
• Inverse residue formulae
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10. Discretization of Continuous-time Systems
• s-z approximations
• Discretizing transfer functions
• Discretizing state space models
11. Design of Discrete-time Controllers
• Direct Design
– Root locus method
– Ragazzini’s method
• Indirect Design
– Root locus
– Bode method
• LQR and LQG designs
12. Frequency Response Methods
• Nyquist plot
• Bode plot
• Phase and gain margin
• Aliasing
13. Controllability and Observability
• Observer design
• Current observers
• Predictive observers
1.4
Recommended Text Books
1. Continuous and Discrete Control Systems by John Dorsey, McGraw Hill
2. Control System Design and Simulation by Jack Golten and Andy Verwer, McGraw Hill
3. Digital Control Systems Analysis and Design by Charles L. Phillips and H. Troy Nagle,
Prentice Hall
4. Discrete-time Control Systems by K. Ogata, Prentice Hall
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Halifax
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