Modern Control System Theory and Design...– Linear Control-System Compensation and Design –...
Transcript of Modern Control System Theory and Design...– Linear Control-System Compensation and Design –...
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Modern Control System Theory and Design
Dr. Huang, MinChemical Engineering Program
Tongji University
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Syllabus• Instructor: Dr. Huang, Min • Time and Place to meet• Office Hours: • Text Book and References
– Modern Control System Theory and Design, 2nd Ed., (1998) Stanley M. Shinners
– Lecture Notes
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Syllabus– Supplementary MATLAB Software
(http:\\ftp.hacettepe.edu.tr\pub\mirrors\MathLab\)
• Assignments– Weekly assignments are to be given and are
due at the following week regular lecture time
– Late assignments will be accepted with 50% credit
• Examinations ( Tentative Schedule )– Quiz, every time we meet– Midterm I, (close notes close book)
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Syllabus– Midterm II, (open notes open book) – Final, to be announced
• Policy– Homework 25%, Quizzes 25%, Midterm I/II
25%, Final 25% (You are allowed to drop one Midterm), Term paper, translations are encouraged for extra credits.
– Average exceeds• 90% A 80% B• 70% C 60% D
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Syllabus• Tentative Schedule
– General Concept of Control-System Design
– Fourier and Laplace Transform – Transfer Function– Signal-Flow Graphs and Mason’s Theorem– State-Variable– Matrix Form– Midterm I
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Syllabus– Mathematical Modeling of Chemical
Processes– Transfer-Function Representation of
Control-System Elements– Time-Domain Response– Development of Empirical Dynamic Models
from Step Response Data– Midterm II
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Syllabus– Performance Criteria– Nyquist-Diagram– Bode-Diagram– Nichols Chart– Root-Locus Method– Linear Control-System Compensation and
Design– Final
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General Concept of Control-System Design
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Heat Exchanger
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Typical Chemical Plant
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Stirred-tank Blending System
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Stirred-tank Blending System
• Notation:– w1, w2 and w are mass flow rates– x1, x2 and x are mass fractions of
component A• Control Objective:
– Keep x at a desired value (or “set point”) xsp, despite variations in x1(t). Flow rate w2can be adjusted for this purpose.
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Stirred-tank Blending System
• Terminology:– Controlled variable (or “output variable”):
x– Manipulated variable (or “input variable”):
w2
– Disturbance variable (or “load variable”): x1
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Control Terminology• Controlled Variables - these are the
variables which quantify the performance or quality of the final product, which are also called output variables.
• Manipulated Variables - these input variables are adjusted dynamically to keep the controlled variables at their set-points.
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Control Terminology
• Disturbance Variables - these are also called "load" variables and represent input variables that can cause the controlled variables to deviate from their respective set points.
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Control Terminology
• Set-point change - Implementing a change in the operating conditions. The set-point signal is changed and the manipulated variable is adjusted appropriately to achieve the new operating conditions. Also called servomechanism (or "servo") control.
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Control Terminology
• Disturbance change - the process transient behavior when a disturbance enters, also called regulatory control or load change. A control system should be able to return each controlled variable back to its set-point.
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What value of w2 is required to have x = xsp
1 20 (1-1)w w w= + −
1 1 2 2 0 (1-2)w x w x wx+ − =
12 1 (1-3)
1SP
SP
x xw wx−
=−
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Some Possible Control Strategies
• Control Objective:Keep x at a desired value (or “set point”) xsp, despite variations in x1(t).– Method 1. Measure x and adjust w2
– Method 2. Measure x1 and adjust w2
– Method 3. Measure x1 and x, adjust w2
This approach is a combination of Methods 1 and 2
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Measure x and adjust w2
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Feed-back Control
Measure the controlled variable
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Feed-back Control
• Advantages– Corrective action is taken regardless
of the source of the disturbance.– Reduces sensitivity of the controlled
variable to disturbances and changes in the process (shown later)
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Feed-back Control
• Disadvantages– No corrective action occurs until
after the disturbance has upset the process, that is, until after x differs from xSP.
– Very oscillatory responses (close-loop system + time delay), or even unstable
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Measure x1 and adjust w2
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Feed-forward Control
• Advantage – Correct for disturbance before it
upsets the process• Disadvantage
– Must be able to measure the disturbance
– No corrective action for unmeasured disturbances
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Feed-forward Control
• Measure a disturbance variable
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Typical Chemical Plant
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Block Diagram
• Signal-flow representation of a physical system
Input, R(s) Output, C(s)SystemG(s)
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Steering of an Automobile
• Pre adjustment of the steering wheel when the alignment is poor
• Stop the automobile in front of the stop sign or traffic light
• Negotiate a turn at the cross-section• Adjust the steering wheel to negotiate
the curvatures of the road
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Steering of an Automobile
+−
Driver’s Control(muscular action)
Automobile (power amplification)
Error
Desired position on road
Actual position on road
Sensors(visual and tactile)
Error detector(Brain)