Automatic Control Theory

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Automatic Control Theory

• School of Information Science and Engineering,CSU
  
• Teacher Yuan Yan
• auto203_at_mail.csu.edu.cn
• 8830971(O),8710510(H)
• 2014?12?2?

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• Text Book
• ??,??????(???),?????????
• Other Reference Teaching Books
• John J.DAzzo. Linear Control System Analysis
  and Design (???????????,?4?). ????????? 
• Richard C. Dorf, Robert H. Bishop. Modern
  Control Systems (Ninth Edition)(?????? ???).
  ???????
• ???. ??????(???). ???????

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• Period
• Teaching hours 80 hours
• Experiment 8 hours
• Total 88 hours
• Exams
• Closed exam.
• Grading
• Homework 15,
• Experiments 15,
• Final exam 70

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• By the end of this course, the student should
  be able to
• Formulate a mathematical model of a given
  physical system in time and Laplace domain.
• Identify the system order and type.
• Determine the systems time response due to a
  step, ramp and harmonic input.

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• Evaluate the system stability using
  Routh-Hurwitz criterion, root locus and Nyquist
  diagrams.
• Apply classical control methods such as Bode
  plots, to design closed loop control of the
  system.
• Apply state space representation of a multiple
  input multiple output (MIMO) system.
• Design a controller and observer for a MIMO
  system.

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Chapter 1 Introduction

• 1.1 Automatic Control
• 1.2 Open-loop Control System and Closed-loop
  Control System
• 1.3 Constitute of Feedback Control System
• 1.4 Classify of Control System

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1.1 Automatic Control

• 1?Automatic Control Systems permeate life in all
  advanced societies today. Technological
  developments have made it possible to
• travel to the moon
• explore outer space. And
• the successful operation of space vehicle
• the space shuttle space station
• robot
• industry control, such as the control of
  temperature, pressure, fluid, lever, and so on.

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• 2?Some Terminologies
• A control system-------- A control system is an
  interconnection of components forming a system
  configuration that will provide a desired system
  response.
• Reference input (Desired output)------Excitation
  applied to a control system from an external
  source. The reference signal produced by the
  reference selector. It is the actual signal input
  to control system.

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• Disturbance input-------A disturbance input
  signal to the system that has an unwanted effect
  on the system output.
• Output (controlled variable )--------The
  quantity that must be maintained at a prescribed
  value, i.e., it must follow the command input
  without responding to disturbance inputs.
• Feedback-----The output of a system that is
  returned to modify the input.

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• Error-----The difference between the input and
  the output.
• Open-loop control system A system in which the
  output has no effect upon the input signal. 

Feedback element The unit provides the
measurement value for feeding back the output
quantity, or a function of the output, in order
to compare it with the reference.
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• Actuating signal (error signal) The signal
  that is the difference between the reference
  input and the feedback signal. It is the input to
  the control unit that causes the output to have
  the desired value.
• Negative feedback The output signal is feed
  back so that it subtracts from the input signal.

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• Closed-loop control system A system in which
  the output has an effect upon the input quantity
  in such a manner as to maintain the desired
  output value. That is, a system that uses a
  measurement of the output and compares it with
  the desired output.

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• 3?Control systems are used to achieve
• (1) increased productivity
• (2) improved performance of a device or
  system.
• The control of an industrial process
  (manufacturing, production, and so on) by
  automatic rather than manual means is often
  called automation.
• Automation is used to improve productivity
  and obtain high-quality products.

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• 4?History of automatic control
• (1) The first automatic feedback contro-ller
  used in an industrial process is generally agreed
  to be James Walts flyball governor, developed in
  1769 for controlling the speed of a steam engine.
  Shown in Fig.1.1.

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Fig.1.1 James Watts Flyball Governor (1769)
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• The all-mechanical device, shown in Fig.1.1,
  measured the speed of the output shaft and
  utilized the movement of the flyball with speed
  to control the valve and therefore the amount of
  steam entering the engine. As the speed
  increases, the ball weights rise and move away
  from the shaft axis, thus closing the valve. The
  flyweights require power from the engine to turn
  and therefore cause the speed measurement to be
  less accurate.

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• (2) J.C.Maxwell formulated a mathema-tical
  theory related to control theory using a
  differential equation model of a governor. (1868)
  
• (3)Conventional control theory is effectively
  applied to many control design problems,
  especially to SISO systems. Its mathematical
  foundation is the Laplace transform.

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• Routh 1884 Hurwitz 1895, algebra stability
  criterion
• 1932, Nyquist, steady-state frequency-response
  techniques
• 1927, Bode and Nichols, frequency-response
  analysis
• 1948, Evans, root-locus theory
• A.M.Lyapunov, stability theory.

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• (4)Modern control theory(1960) is based on state
  variable methods, for the design of
  multiple-input multiple-output(MIMO) systems.
• Wiener(1949), Optimum design.
• Bellman(1957), Dynamic programming.
• Pontryagin(1962), Maxmum principle.
• Kalman(1960),Controllability and
  observability
• Kalman and Buey(1961), Combination of optimal
  filter and optimal controller, Linear quadratic
  Gaussian(LQG) control.

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• (5)Advanced control theory(1980)
• Robust theory.(1980s)
• Intelligent control theory
• Artificial Neural Networks(ANNS)
• Fuzzy Control(FC)
• Expert System(ES).
• GA, GP, EC, Chaos etc.

RETURN
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1.2 Open-loop Control System and
Closed-loop Control System

• 1?A control system is an interconn-ection of
  components forming a system configuration that
  will provide a desired system response.
• A component of process to be controlled can be
  represented by a block, as shown in Fig.1.2.

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(Response)
(Stimulus)
Cause (Desired response)
Effect (Actual response)
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2?An open-loop control system utilizes a
controller or control actuator to obtain the
desired response, as shown in Fig.1.3.
The control action is calculated at the initial
time t0 and then applied to the physical system
over the entire control horizon t0, tf without
modification. The output is not observed.
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• An open-loop control system utilizes an
  actuating device to control the process directly
  without using feedback.

Another open-loop control system
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3?The measure of the output is called the
feedback signal. A simple closed-loop feedback
control system is shown in Fig.1.4 or Fig.1.5.
The advantages and disadvantages of open-loop
control system and closed-loop control
system The examples of closed-loop
system Example 1 Example 2
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4.Complex control system (ideal control method)
Combine open-loop control with closed-loop
control
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1.3 Constitute of Feedback Control System

• 1?Constitute of feedback control system
• Plant Controller
• Plant(process)The device, plant or system
  under control.
• Measurement component(Sensor)
• Comparison component
• Amplifier
• Actuating device
• Compensator

Controller
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Disturb signal
Compare device
Compensator
amplifier
actuator
plant
controller
structure of general control system
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• 2?Analysis of control system

Stability the most important
Performance the transient and steady-state
response performance
Robustness.
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Stability
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Transient performance
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steady-state performance
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• 3? Control
• Control is the design and analysis of
  sensors, actuators, and computational systems
  (analog or digital) to modify the behavior of
  physical systems.

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• Typical steps
• Selection of actuators and sensors
• Development of a dynamic model of the system to
  be controlled
• Design of control systems based on the sound
  fundamental principles
• Implementation of the controller using analog or
  digital electronics

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• 4?Design of control system
• (1) Establish the system goals.
• (2) Identify the variables to control
• (3) Write the specifications for the
  variables
• (4) Establish the system configuration and
  identify the actuator
• (5) Obtain a model of the process, the
  actuator and the sensor
• (6) Describe a controller and select key
  parameters to be adjusted
• (7) Optimize the parameters and analyze the
  performance.

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RETURN
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1.4 Classify of Control System

• 1.The form of systems mathematics model
• Linear system/ Nonlinear system the dynamic
  equation of system is linear differential
  equation/nonlinear differential equation.
• A linear system satisfies the principle of
  superposition.

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• Time-varying system and time-invariant system
• Time-varying system is a system for which one or
  more of the parameters of the system may vary as
  a function of time.
• 2. Reference input
• r(t)constant
• r(t)f(t)
• can be known
• the vary rule f(t)
• cannt be known
  servo

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• 3. The transfer signal
• sequence-time system
• discrete-time system

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• Summary
• In order to design and implement a control
  system, the following essential generic elements
  are required
• 1) Knowledge of the desired value
• It is necessary to know what it is you are
  trying to control.

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2) Knowledge of the output or actual value This
must be measured by a feedback sensor ,again in a
form suitable for the controller to understand.
In additional ,the sensor must have the necessary
resolution and dynamic response ,so that the
measured value has accuracy required from the
performance specification . 3) Knowledge of the
controlling device The controller must be able to
accept measure-ments of desired and actual values
and compute a control signal in a suitable form
to drive an actuating element.
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4) Knowledge of the actuating device This unit
amplifier the control signal and provides the
effort to move the output of the plant towards
its desired value. 5) Knowledge of the
plant Most control strategies requires some
knowledge of the static and dynamic
characteristic of the plant. These can be
obtained form measurements or form the
application of Fundamental physical laws.or
combination of both.
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A general control system can be represented as
Actuating signal (error signal)
Feedback element
A closed-loop control system uses a measurement
of the output and feedback of the signal to
compare it with the desired output (reference of
command).
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Another block diagram of a generalized feedback
control system
RETURN
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The advantages and disadvantages of open-loop
control system and closed-loop control system
open-loop control system The main advantages
1) Much simple and less expansive to
construct 2) Easy to have good stability The
main disadvantages Require detailed
knowledge of each component in order to determine
the input value for a required output.
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• closed-loop control system
• The main advantages
• 1) Have higher accuracy
• 2) Not require detailed knowledge of each
  compo-nent or accurate model of the individual
  component
• 3) The ability to recover from external,
  unwanted disturbances
• 4) Reduced sensitivity to disturbance
• The main disadvantages
• 1) Complex and expensive to construct
• 2) the loss of gain
• 3) Quite easy to become unstable.

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For most cases, the advantages far outweigh the
disadvantages, and a feedback system is utilized.
Therefore it is necessary to consider the
additional complexity and the problem of
stability when designing a control system.
RETURN
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Example 1 A water temperature control system
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• Observe (through senses)
• Compute a control action (through brain) and
  apply the control
• Action (through hands, feet, etc!)

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Example 2 water temperature control system with
a automatic method
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The block diagram of the water temperature
automatic control system
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Compare manual control method to automatic
control method Brain ---- Thermostat
(Reference input or desired output)
Nervous system----
Differencing junction Hand ---- Amplifier,
Motor and Wheel drivers Eyes
and Skin sensor ---Temperature sensor Mixer
Valve ---- Mixer Valve
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• For each example try to answer these
  questions
• What is(are) the system input(s)?
• What is(are) the system output(s)?
• What is there a feedback path?

RETURN
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• The End of chapter one