MODERN CONTROL THEORYLecturer:鲍其莲 Bao Qilian
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Reference books :
• C.-T. Chen, Linear System Theory and Design,
3rd Ed., Oxford University Press, 1999.
• Norman S. Nice, Control System Engineering, 6th Ed.
• Richard C. Dorf, Modern Control Systems, 12th Ed. Prentice hall
Press,2011
• 现代控制理论基础(第2版)王孝武主编,机械工业出版社
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Grading policy:
• Attendance, homework, quiz: 30%
• Lab projects and reports: 30%
• Final project report: 40%
• Goals: To achieve a thorough understanding about
modern control theory and multivariable system design.
• Prerequisites: Classical control theory & Linear algebra
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chapter contents hours
1 An Introduction 2
2 Mathematic description of dynamic system 4
3 Linear algebra 4
4 Space state solutions and realization 4
5 Stability Analysis 2
6 Controllability and Observability 4
Lab Project1 2
7 State feedback and state estimator 4
8 Fundamentals of optimal control (optional: time permitted) 2
Lab Project2 4
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Chapter 1 Introduction
Objectives:
• Development of control theory
• Comparison of classic control theory and modern control theory
• History of control theory
• Classic control theory
• Modern control theory
• Basic concepts of control systems
• Design goals and structures of control systems
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History
18th Century James Watt’s centrifugal governor for the speed control of a
steam engine.
1920s Minorsky worked on automatic controllers for steering ships.
1930s Nyquist developed a method for analyzing the stability of controlled
systems
1940s Frequency response methods made it possible to design linear closed-
loop control systems
1950s Root-locus method due to Evans was fully developed
1960s State space methods, optimal control, adaptive control and
1980s Learning controls are begun to investigated and developed.
Present and on-going research fields. Recent application of modern control
theory includes such non-engineering systems such as biological, biomedical,
economic and socio-economic systems.
History 6
“Flyball” Governor (1788)
– Regulate speed of steam engine
– Reduce effects of variations in
load (disturbance rejection)
– Major advance of industrial
revolution
Balls fly out
as speed
increases,
Valve closes,
slowing engine
http://www.heeg.de/~roland/SteamEngine.html
Flyball
governor
Steam
engine
Boulton-Watt steam engine
Flyball Governor
History 7
Stage 1:Classical Control Theory
(1930~1960)
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Wiener: Mechanism of Feedback in General Systems 1948
(Control Theory: the science about control and
communication in animals or machines)
钱学森:Engineering Control Theory 1954
Main Features:
Having no need of accurate mathematical model of controlled
object. Setting controller parameters according to frequency
characteristic curve. (Satisfying design targets with onsite regulation.)
Unable to give an accurate analytical method for controller
design.
History
Stage 2: Linear system theory and optimal control
(1950~1980)
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Kalman: Controllability, Observability 1960
Bellman: Dynamic planning, Optimality Principle 1958
庞特里亚金: Maximum Value Principle 1957
Main Features:
Accurate mathematical models, specific design targets, and
perfect analytical design methods.
1.The mathematical models must be accurate descriptions of the
dynamics of objects. Neither measurement errors nor disturbances
in actual engineering have been taken into consideration.
2. Linear conditions, such as Superposition Principle, etc.
C xy
BuAxx
History
System – An interconnection of elements and devices for a
desired purpose.
Control System – An interconnection of components forming
a system configuration that will provide a desired response.
Process – The device, plant,
or system under control. The
input and output relationship
represents the cause-and-
effect relationship of the
process.
Introduction 10
Multivariable Control System
Open-Loop Control Systems
utilize a controller or control
actuator to obtain the desired
response.
Closed-Loop Control
Systems utilizes feedback to
compare the actual output to
the desired output response.
Introduction 11
Classical Control
• Design based on Input-Output models
• transfer functions and block diagrams
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Plant
Sensor
Compensator+
–
Introduction
Control = Sensing + Computation + Actuation
Sense
Vehicle Speed
Compute
Control “Law”
Actuate
Gas Pedal
In Feedback “Loop”
• Goals
– Stability: system maintains desired operating point (hold steady speed)
– Performance: system responds rapidly to changes (accelerate to 65 mph)
– Robustness: system tolerates perturbations in dynamics (mass, drag, etc)
Introduction 13
Summary
• History and development of control theory
• Comparison of classic control theory and modern control theory
• Basic concepts of control systems
• Design goals and structures of control systems
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