Transcript کنترل خطی دانشگاه علم و صنعت ایران پاییز

‫بسم ا‪ ...‬الرحمن الرحيم‬
‫سیستمهای کنترل خطی‬
‫پاییز ‪1389‬‬
‫دکتر حسین بلندي‪ -‬دکتر سید مجید اسما عیل زاده‬
Introduction
Control
• The word control is usually taken to mean :
- regulate, ‫تنظيم کردن‬
- direct, ‫هدايت کردن‬
- command ‫ فرمان دادن‬.
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Control system
• A control system is an arrangement of
physical components connected or related
in such a manner as to command, direct, or
regulate itself or another system.
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Input
• The input is the excitation or command
applied to a control system.
• Typically from external energy source,
usually in order to produce a specified
response from the control system.
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Output
• The output is the actual response obtained
from a control system.
• It may or may not be equal to specified
response implied by the input.
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In Summary
• Input - Excitation applied to a control system
from an external source.
• Output - The response obtained from a system
• Feedback - The output of a system that is
returned to modify the input.
• Error - The difference between the reference
input and the output.
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Disturbance in a feedback control
system
• Disturbance signal is an unwanted extraneous
input signal that affects the system’s output
signal.
• Feedback control can completely or partially
eliminate the effect of disturbance signal.
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Negative Feedback Control System
+
CONTROLLER
+
+
CONTROLLED
DEVICE
-
FEEDBACK
ELEMENT
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Terms and Concepts
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Control system
• A control system is an interconnection of
components forming a system configuration that
will provide a desired system response.
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Two Types of Control Systems
• Open Loop
– No feedback
– Difficult to control
output with accuracy
• Closed Loop
– Must have feedback
– Must have sensor on output
– Almost always negative
feedback
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Open-loop control
An open-loop control system utilizes an actuating
device to control the process directly without using
feedback.
Must be closely monitored.
A common example of an open-loop control system
is an electric toaster in the kitchen.
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Closed-loop control
A closed-loop control system uses a measurement of
the output and feedback of this signal to compare it
with the desired output.
Continually adjusts the process.
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A person steering an automobile by
looking at the auto’s location on the
road and making the appropriate
adjustments.
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Manual control system
Goal: Regulate the level of fluid by adjusting the output valve.
The input is a reference level of fluid and is memorized by operator.
The sensor is visual.
Operator compares the actual level with the desired level and opens or
closes the valve ( actuator).
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The level of fluid in a tank control.
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The roles of feedback
Benefits:
• Reduce error (eliminating the error)
• Reduce sensitivity or Enhance robustness
• Disturbance rejection or elimination
• Improve dynamic performance or adjust the
transient response (such as reduce time
constant)
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Major Types of Feedback Used
Position Feedback
– Used when the output is a linear distance or
angular measurement.
Rate & Acceleration Feedback
– Feeds back rate of motion or rate of change of
motion (acceleration)
– Motion smoothing
– Uses a electrical/mechanical device call an
accelerometer
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Control systems are divided into two
classes:
a) If the aim is to maintain a physical variable at some fixed value
when there are disturbances, this is a regulator.
Example: speed-control system
b) The second class is the servomechanism. This is a control
system in which a physical variable is required to follow (track)
some desired time function.
Example: an automatic aircraft landing system, or a robot arm
designed to follow a required path in space.
Multivariable control system
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A robot is a computer-controlled
machine.
Industrial robotics is a particular
field of automation in which the
robot is designed to substitute
for human labor.
The Honda P3 humanoid robot.
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• Automation - The control of a process by automatic
means.
• Closed-loop feedback control system A system that uses a measurement of the output and
compares it with the desired output.
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Design-The process of conceiving or inventing the
forms, parts, and details of a system to achieve a
specified purpose.
Feedback signal - A measure of the output of the
system used for feedback to control the system.
Multivariable control system - A system with more
than one input variable or more than one output
variable.
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Negative feedback -The output signal is fed back so
that it subtracts from the input signal. Negative
feedback initiates to maintain or regulate physiological functions
within a set and narrow range.
Open-loop control system - A system that utilizes a
device to control the process without using
feedback.
Optimization -The adjustment of the parameters to
achieve the most favorable or advantageous design.
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Positive feedback -The output signal is fed back so that
it adds to the input signal. Positive feedback mechanisms are
designed to accelerate or enhance the output created by a stimulus that
has already been activated. In positive feedback systems the presence of a
product (or signal) results in an increase in the production (amplification)
of that product (or signal).
Process -The device, plant, or system under control.
Productivity -The ratio of physical output to physical
input of an industrial process.
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Synthesis - The combining of separate elements or
devices to form a coherent whole.
System - An interconnection of elements and devices
for a desired purpose.
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The Control System Design Process
Engineering design
• Design is the process of conceiving or inventing
the forms, parts, and details of a system to
achieve a specified purpose.
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Engineering design
Trade-off
The result of making a judgment about how to
compromise between conflicting criteria.
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Control system engineers are concerned with
understanding and controlling segments of their
environment, often called systems, to provide
useful economic products.
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Goals
Twin goals of understanding and controlling are
complementary because effective systems
control requires that the systems be
understood and modeled.
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Control engineering
Control engineering is based on the
foundations of feedback theory and linear
system analysis, and it integrates the
concepts of network theory and
communication theory.
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Given a process, how to design a feedback
control system?
Three steps:
• Modeling. Obtain mathematical description of the systems.
• Analysis. Analyze the properties of the system.
• Design. Given a plant, design a controller based on performance
specifications.
The course spans each of these steps in that sequence.
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The basis for analysis of a system is the
foundation provided by linear system theory,
which assumes a cause-effect relationship for
the components of a system.
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The design of control systems is a specific example of
engineering design.
The goal of control engineering design is to obtain the
configuration, specifications, and identification of the key
parameters of a proposed system to meet an actual need.
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The design process consists of seven main building blocks, which
are arrange into three groups:
1. Establishment of goals and variables to be controlled, and
definition of specifications against which to measure performance
2. System definition and modeling
3. Control system design and integrated system simulation and
analysis
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Design 1
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Design 2
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Design 3
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Design examples
Rotating disk speed control
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Step 1. Control goal
• Design a system that will held a rotating disk at a
constant speed. Ensure that the actual speed of
rotation is within a specified percentage of
desired speed.
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Step 2. Variable to be controlled
• Speed of rotation disc
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Step 3. Control design specification
• Design a system that will ensure that
the actual speed of rotation is within a
specified percentage of desired speed.
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Step 4 Preliminary system configuration
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Step 4 Preliminary system configuration
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With precision components, we could expect
to reduce the error of the feedback system to
one-hundredth of error of the open-loop system.
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Insulin delivery system
The blood glucose and insulin concentrations for a healthy person.
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Step 1. Control goal
• Design a system to regulate the blood sugar
concentration of a diabetic by controlled
dispensing of insulin.
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Step 2. Variable to be controlled
• Blood glucose concentration
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Step 3. Control design specification
• Provide a blood glucose level for the diabetic
that closely approximates the glucose level of
a healthy person.
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Step 4 Preliminary system configurations
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A drug-delivery system implanted in the body
uses an open-loop system, since miniaturized
glucose sensors are not yet available.
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E 1: Controlling the position of a
missile launcher from a remote
location
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Controlling the position of a missile launcher from a
remote location
The input is the desired angular position of the
missile launcher,
The control system consists:
of potentiometer,
power amplifier,
motor,
gearing between the motor and the missile launcher,
missile launcher.
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A position open loop control
The input is the desired angular position of the missile launcher,
and the control system consists of potentiometer, power amplifier,
motor, gearing between the motor and missile launcher, and missile
launcher.
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A position closed loop control
Should an error exists, it is amplified and applied to a
motor drive which adjusts the output-shaft position until it
agrees with the input-shaft position, and the error is zero.
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Applications
Applications
Control engineering is not limited to any engineering
discipline but is equally applicable to:
aeronautical,
chemical,
mechanical,
computer science and engineering ,
civil engineering,
electrical engineering.
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Prerequisite by topics
• Knowledge and proficiency in Matlab
• Concept and solution of linear ordinary
differential equations
• Laplace transform and its applications
• Poles, zeros, transfer functions, frequency
response, Bode plots
• Vectors and matrices
• Complex numbers
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