Transcript The Principle of Automatic Control 自动控制原理 Lecturers：Prof. Jiang Bin

The Principle of Automatic
Control
自动控制原理
Lecturers：Prof. Jiang Bin
Dr. Lu Ningyun
College of Automation
Engineering
NUAA，2008. Autumn
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NUAA-The Principle of Automatic Control
Chapter 1
Introduction to control systems
控制系统简介
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The Principle of Automatic Control 2008
Course Description
• This course is concerned with the analysis and
design of control system
Analysis
System modeling, sensitivity and stability
Time-domain techniques (root-locus analysis);
Design
Simulation
Frequency-domain techniques (Bode plot,
Nyquist stability theory)
Analysis and design using MATLAB
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The Principle of Automatic Control 2008
References
• 胡寿松主编，自动控制原理，科学出版社
• K. Ogata，Modern control engineering (现代控制工程,
第四版)，有原版翻印本和中译本
• B.C.Kuo & F. Golnaraghi， Automatic control systems,
8th edition, John Wiley & Sons, 2003 （有原版翻印）
http://wwwcontrol.eng.cam.ac.uk/extras/Virtual_Library/Control_VL.html
http://www.engin.umich.edu/group/ctm/
http://csd.newcastle.edu.au/
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The Principle of Automatic Control 2008
Course Evaluation
• 64 hours, 3 credits:
– Homework: 5%
– Class participation: 5%
– Final exam: 90%
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The Principle of Automatic Control 2008
Welcome to contact us
• Prof. Jiang Bin
Email: [email protected]
Tel: 84892301-6041(O); 13611590498(M)
Office: A17-604 (明故宫校区）
• Dr. Lu Ningyun
Email: [email protected]
Tel:84892301-6063(O); 13585112514(M)
Office: A17-606 (明故宫校区）
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The Principle of Automatic Control 2008
Chapter 1. Introduction to control
systems
 WHAT a control system is?
 WHY control systems are important?
 WHAT the basic components of a control
system are?
 Examples of control system applications
 WHY feedback is incorporated into most
control systems?
 Types of control systems
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The Principle of Automatic Control 2008
Outline
1-1 Basic concepts of control systems
1-2 Control system examples
1-3 Classification of control systems
1-4 Basic requirements of a control
system
1-5 Brief introduction to MATLAB
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The Principle of Automatic Control 2008
1-1 Basic concepts
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The Principle of Automatic Control 2008
What is control?
Control：使某些物理量按指定的规律变化（e.g. keep constant, or
track a reference signal），以保证生产安全，经济及产品质量等要求
的技术手段。
Controlled variable (被控量）：指被测量(measured)并被控
制(controlled)到期望值(expected value)的变量
Manipulated variable （操纵量）:按照指定规律变化使得被
控量达到指定目标的变量(varied by controller so as to
affect the controlled variable)
e.g. Temperature control system (空调）
Speed control system （汽车）
Automatic Control：就是应用自动化仪表或控制装置代替人，
自动地对机器设备或生产过程进行控制，使之达到预期的状态
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或性能要求。
The Principle of Automatic Control 2008
What is control system?
Generally speaking, a control system is a system
that is used to realize a desired output or objective
Plant (对象）：Maybe a piece of equipment, perhaps just
a set of machine parts, functioning together, to perform a
particular operation
Process（过程）：A natural or artificial, progressively
continuing operation or development toward a particular
result
System（系统）：A combination of components that act
together and perform a certain objective
Disturbance (扰动）: A signal tends to affect the output of
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a system
The Principle of Automatic Control 2008
Open-loop control system
input
disturbance
Manipulated
var.
controller
plant
Controlled var.
Definition：
those systems in which the output has no effect on the
control action.
applications
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The Principle of Automatic Control 2008
Open-loop DC Motor speed-control system
P
u
电
压
放
r 大
器
uk
可
控
硅
功
放
电网电压
ua
M
n
负载
＋
电位器（产生给定电压
ur）假定0~10V
P
电位器
ur
电压 uk
放大器
转速0~1000转
扰动
可控硅 ua
功放
直流
电动机
n
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The Principle of Automatic Control 2008
Comments on open-loop control system
• The output is not measured and compared
with the input, no feedback
• Each input corresponds a fixed operating
condition
(电位器0-10v－－转速0-1000转)
• The accuracy of the system depends on
calibration
• In the presence of disturbance
?
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The Principle of Automatic Control 2008
Feedback control system
disturbance
Manipulated
Ref input error
Output
var.
controller
plant
sensor
A system that maintains a prescribed relationship
between the output and the reference input by
comparing and using the difference (error) as a
means of control –feedback control system
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The Principle of Automatic Control 2008
Block diagram
r
Expected
value
e
-
Controller
Actuator
Error
u
n
Disturbance
Plant
y
Controlled
variable
Sensor
comparison component
(comparison point) :
its output equals the
algebraic sum of all input
signals.
“+”: plus
“-”: minus
lead-out point:
Here, the signal is
transferred along
two separate routes.
The Block represents
the function and name of its
corresponding mode, we don’t
need to draw detailed structure,
and the line guides for the transfer route.
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The Principle of Automatic Control 2008
Feedback control systems exist
everywhere
E.g. the human body is highly advanced
feedback control system.
Body temperature and blood pressure are kept
constant by means of physiological feedback.
Feedback makes the human body relatively
insensitive to external disturbance. Thus we can
survive in a changing environment.
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The Principle of Automatic Control 2008
Closed-loop control system
• In practice, feedback control system
and closed-loop control system are used
interchangeably
• Closed-loop control always implies the
use of feedback control action in order
to reduce system error
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The Principle of Automatic Control 2008
Closed-loop DC motor speed control system
ur
u
电
压
放
大
器
uk
可
控
硅
功
放
ua
M
负载
n
＋
ub
＋
G
测速
发电
机
－
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The Principle of Automatic Control 2008
扰动
P
电位器
u
ur
ub -
电压 uk 可控硅 ua 直流
放大器
放大器
电动机
n
测速机
工作原理
引入测速发电机，这时电压放大器的输入u  ur  ub ，如果外来
的电网电压波动使电机的转速n ，则由测速发电机确定的 ub
则 u  ur  ub 则uk ，ua 则n ，消除了偏差，控制转速稳定。
——负反馈。
同开环系统相比，该系统由于干扰引起的转速
误差要小得多。
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The Principle of Automatic Control 2008
扰动
P
电位器
ur
u
ub＋
电压 uk 可控硅 ua 直流
放大器
放大器
电动机
n
测速机
如果极性接错，这时电压放大器的输入 u  ur  ub ，如果外来的
电网电压波动使电机的转速n ，则由测速发电机确定的 ub
则 u  ur  ub 则uk ，ua 则n ，则转速越来越大，电动机损坏，
失去控制。——正反馈。
正反馈不能用于控制系统
用途——振荡器（正弦信号发生器）
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The Principle of Automatic Control 2008
Comparison between open-loop
and closed-loop systems
• Open-loop control systems
Simple structure, low cost
Easy to regulate
Low accuracy and resistance of disturbance
• Closed-loop control systems
Ability to correct error
High accuracy and resistance of disturbance
Complex structure, high cost
Critical for selecting parameters (may cause
stability problem)
• Open-loop＋Closed-loop＝Composite control system22
The Principle of Automatic Control 2008
1-2 More examples of feedback
control system
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The Principle of Automatic Control 2008
Flush toilet (冲水马桶）
水
Plant: water tank
Input: water flow
Output: water level h(t )
Expected value: h0
Sensor: float
Controller: lever
Actuator: piston
h0
Controller
Level
Actuator
Piston
q1(t)
活塞
浮子
h(t)
h0
Plant
q1 (t ) Water
Tank
阀门
h(t )
q2(t)
Float
Sensor
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The Principle of Automatic Control 2008
Plane-autopilot（自动驾驶）
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The Principle of Automatic Control 2008
俯仰角控制系统方块图
扰动
θ0
给
定
装
置
放
大
器
舵
机
飞
机
θc
反馈
电位器
垂直
陀螺仪
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The Principle of Automatic Control 2008
Other examples
• 胡寿松教材pages7-9
• Ogata教材pages3-6
• Kuo教材pages2-6
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The Principle of Automatic Control 2008
Why control systems are important?
• In other words, why we (engineer) should
know control?
– Control is an essential element of almost all
engineering systems
• It happens very often that systems perform poorly
because they are designed from purely static analysis,
with no consideration of dynamics and control
– Control can give designers extra degrees of
freedom
– Control has beautiful theoretical results and really
neat devices
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The Principle of Automatic Control 2008
1-3 Classification of control
systems
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The Principle of Automatic Control 2008
According to structure
• Open-loop control systems
• Closed-loop control systems
• Composite control systems
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The Principle of Automatic Control 2008
According to type of reference input
• Constant-value control system （常值控制系统）
输入量是恒定的常值， 在各种扰动作用下都能使输出量
保持在恒定希望值附近， 如恒温、水位、恒压控制系统
• Servo/tracking(侍服/跟踪） control system
（随动控制系统）
输入量是事先不知道的任意时间函数， 使输出量迅速而
准确地跟随输入量的变化而变化， 比如：飞机和舰船的
操舵系统，雷达自动跟踪系统。
• Programming control system （程序控制系统）
输入量按照给定的程序变化， 使输出量按预先给定的程
序指令而动作， 最典型的就是数控车床和机器人控制系
统。
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The Principle of Automatic Control 2008
According to system character
• Linear system
– principle of superposition applies （齐次叠加原理）
–
described by linear differential equation（线性
微分方程）
• Nonlinear system
– described by nonlinear differential equation （非线
性微分方程）
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The Principle of Automatic Control 2008
According to system character with
respect to time
• Time-invariant system
– The parameters of a control system are stationary
with respect to time
• Time-varying system
– System contain elements that drift or vary with
time
– E.g. Guided-missile control system, time-varying
mass results in time-varying parameters of the
control system
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The Principle of Automatic Control 2008
According to form of the signals
• Continuous-data control system （连续控制系
统）
– The signals are all functions of continuous time
variable t （信号是时间的连续值）
• Discrete-data control system
– The signals are in the form of either a pulse train
or a digital code （信号是脉冲序列或数字编码）
– sample-data and digital control system
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The Principle of Automatic Control 2008
1-4 Basic requirements for control
systems
胡寿松教材，p13
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The Principle of Automatic Control 2008
The system is expected to be affected ONLY by control
input, NOT by disturbance.
Two-fold tasks:
(1) how the system responses to the external
input?
(2) how the system resists disturbances?
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The Principle of Automatic Control 2008
Typical external signals
• 为了能对不同的控制系统的性能用统一的
标准来恒量，通常需要选择几种典型的外
作用
Rules of selection
（1）Easy to generate
（2）Frequently encountered
（3）Simple mathematical expression。
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The Principle of Automatic Control 2008
r(t)
Step-function input （阶跃输入）
 R, t  0
r (t )  
0, t  0
R
0
t
在t=0时刻出现幅值为R的跳变， R=1时的阶跃函数叫
unit step function （单位阶跃函数），denoted by 1(t) 。
最不利的外作用, 常用阶跃函数作为评价系统动态性能的
典型外作用, 所以阶跃函数在自动控制系统的分析中起着
特别重要的作用。
例如飞机飞行中遇到的常值阵风扰动。
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The Principle of Automatic Control 2008
Ramp-function input （斜坡输入）
r(t)
 Rt , t  0
r (t )  
0, t  0
0
t
在t=0时刻开始，以恒定速率R随时间变化
例如雷达-高射炮防空系统，当雷达跟踪的目标以恒定
速率飞行时， 便可视为该系统工作于斜坡函数作用之
下。
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The Principle of Automatic Control 2008
Pulse/Impulse function input （脉冲输入）
 A /  ,0  t  
r (t )  
0, t  0或t  
r(t)
A
A

 0

0


t
Pulse function 脉动函数
, t  0  (t )
r (t )  
0, t  0
？  r (t )dt  A


0
t
impulse function冲激函数
Note: （1）The above impulse function does not exist in
reality, it is just mathematical definition. When A=1时，it
is called unit impulse function，denoted by δ(t);
(2)
脉冲函数很重要，任意一个外作用的输出响应可分解为
不同时刻系列脉冲输入之和
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The Principle of Automatic Control 2008
Sinusoid function input （正弦输入）
 A sin wt , t  0
r (t )  
0, t  0
A －Amplitude
w=2πf － angular frequency
r(t)
A
t
If the initial phase φis non-zero，
例如海浪对舰船的颠簸，电源
then r(t) can be described by
及机械振动的噪声可视为正弦
扰动。
 A sin( wt   ), t  0
系统在正弦函数作用下的响应，
r (t )  
即frequency characteristic，是
0, t  0
自动控制理论中研究系统性能
的重要依据。
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The Principle of Automatic Control 2008
Basic requirements for system
performance
Since step input function jumps from zero to a
constant value, it is always chosen as a typical
input signal to investigate system performance.
System performance about step input
response can be summarized as:
1. Stability －－－ 稳定性
2. Accuracy －－－ 准确性
3. Quickness－－－快速性
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The Principle of Automatic Control 2008
A control system without disturbance
输入信号
给定值
偏差
-
控制器
执行机构
被控对象
输出量
测量传感元件
当输入信号突然发生跳变时，这时输出量还处
在原有的平衡状态，这样就出现了偏差，这个
偏差控制输出量达到新的平衡，这就是一个
regulation process （调节过程）。
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The Principle of Automatic Control 2008
Output
c(t)
Input
r(t)
Response curve2
Curve 1 monotonously increases to
1
the steady-state value.
Curve 2 (decaying) oscillates to the
steady-state value.
0
t
1
Response curve1
0
t
理想的调节过程是：出现偏差后，执行机构突然动作，
使输出量立即达到新的平衡状态，调节过程瞬时完成，
实际上这是不可能的，为什么呢？
stable
物理系统均是惯性系统
系统从原平衡状态到达新的平衡状态都要经历一个过
渡过程，过渡过程的曲线形状随系统的不同而有所差
异.
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The Principle of Automatic Control 2008
Output
c(t)
Stability（稳定性）
1
Accuracy(准确性）
Quickness（快速性）
0
t
The whole regulation process can be divided into
two stages:
Transient process (瞬态过程）
reflects dynamic character
（动态特性），即输出量处于
激烈变化之中。
Steady-state process（稳
态过程） reflects steadystate character ，即输出量
稳定在新的平衡状态，并保
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持不变。
The Principle of Automatic Control 2008
Definitions
• Stability：refers to ability of a system to
recover equilibrium, i.e., convergence of
transient process (converge)
• Quickness: refers to duration of transient
process (quick)
• Accuracy：refers to the size of steadystate error when the transient process
ends.（small)
•
(Steady-state error=desired output – actual output)
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The Principle of Automatic Control 2008
Note
For a control system, the above three
performance indices (stability, quickness,
accuracy) are sometimes contradictory.
In design of a practical control system,
we always need to make compromise.
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The Principle of Automatic Control 2008
1-5 MATLAB
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The Principle of Automatic Control 2008
MATLAB
• MATLAB是具有很强数值计算、符号运算、
仿真和图形显示功能的计算分析软件。它
具有编程方便、简单易学等诸多优点，同
时提供了大量的内置函数和外置工具箱，
被广泛应用于数学计算、工程应用和社会
科学研究的诸多领域。
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The Principle of Automatic Control 2008
Simulation using MATLAB
• 1 请同学们自学MATLAB基础知识
• 2. 本课程部分章节中将给出MATLAB常用
函数以及程序实例，辅助学习课程相关内
容
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The Principle of Automatic Control 2008
1-6 Additional reading materials ——
short history of control
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The Principle of Automatic Control 2008
Short history of control
Keeping accurate track of time
– Water clock (Ktesibios, 270 BC)
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The Principle of Automatic Control 2008
Short history of control
• Industrial revolution
– Temperature regulator for furnace
(Drebbel, 1624)
– Float regulator for steam boiler (Brindley,
1758)
– Pressure regulator for steam engine (Papin,
1707)
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The Principle of Automatic Control 2008
Short history of control
• Birth of mathematical control theory
– Differential equations for telescope
pointing (Airy, 1840)
– Stability theory for Watt’s flyball governor
(Maxwell,1868)
– System theory of organic mechanism
(Whitehead, 1925)
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The Principle of Automatic Control 2008
Short history of control
• Mass communication
– Frequency domain analysis for
communication systems (1920’s, Bell
Telephone Laboratory)
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The Principle of Automatic Control 2008
Short history of control
• World Wars and classical control
– Ship control (Minorsky, 1922)
– Weapons development and gun pointing
(Hazen,1934)
– MIT radiation laboratory (1940’s)
– Stochastic analysis (Wiener, 1942)
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The Principle of Automatic Control 2008
Short history of control
• Space/computer age and modern control
–
–
–
–
Time-domain design for nonlinear systems
Optimal control and estimation theory
Nonlinear control theory
Computers in controls design and
implementation
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Short history of control
• Union of modern and classical control
• Advanced control theories
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The Principle of Automatic Control 2008
Suggestions on the course study
Pay enough attention
control theory is very interesting, very
useful, but sometimes, very difficult
Practice, practice, and practice
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End of Chapter 1
Thank you all!
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