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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