FEEDBACK CONTROL SYSTEMS
24-451 12 Units Fall 2000
Lecture: Tuesdays and Thursdays 3:00 - 4:20 pm SH 212
Lab: Fridays 2:30 - 4:20 p.m. HH B301
Matlab Tutorial URL: http://brie.library.cmu.edu/ctms/
Purpose
This course is intended to introduce students to concepts and techniques
of classical control and to briefly introduce some concepts of modern control
and discrete-time. The main goal is to enable students to analyze, design,
and synthesize linear control systems. Students will become familiar with
analytical methods and will be exposed extensively to the use of computers
for analysis and design of control systems.
Objectives
The major objectives of 24-451 are the following:
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Be familiar with the inputs, outputs, and components of a control system.
Know the difference between open-loop and closed-loop (feedback) control
systems and understand the advantages of feedback control.
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Understand the utility of Laplace transforms and transfer functions for
modeling complex interconnected systems.
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Understand the relationship of poles of a transfer function to the stability
of a system, and more generally understand the concept of poles and zeros
of a transfer function and how they affect the physical behavior of a system.
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Understand the role of integral control and generally why more than simple
proportional control is often needed in a control system.
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Know the effect of sample-rate on the stability of computer controlled
(discrete-time) systems, and more generally the fundamental differences
between continuous-time and discrete-time control systems.
In addition, by the end of the course, students should be able to do the
following:
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Derive mathematical models of a variety of electrical, mechanical, and
electro-mechanical systems.
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Understand the concept of stability of a dynamic system.
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Draw the pole-zero diagram and the root loci, which are the change in location
of the poles as parameters are of a system are varied.
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Understand the concept of frequency response and the related concepts of
bandwidth, disturbance sensitivity, and noise sensitivity. Be able to draw
Bode plots and understand their significance.
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Use frequency domain techniques to design controllers.
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Estimate time response of systems to impulse, step, ramp, and sinusoidal
inputs from the transfer function.
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Understand the meaning of proportional control, integral control, and derivative
control, lag compensation, and lead compensation, and how to use them to
achieve desired stability, steady-state error, and frequency response.
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To use Matlab® with facility to aid in the analysis and design of control
systems.
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To construct simple feedback circuits using op-amps.
Text
Control Systems Engineering, third edition, Norman S. Nise, Benjamin
Cummings, 2000.
References
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Dorf, R. and Bishop, R.Modern Control Systems
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Messner, W. and Tilbury, D. Controls Tutorials for MATLAB and Simulink
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Ogata, K., Discrete-Time Control Systems
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Strang, G., Linear Algebra
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Rough Course Plan
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The plan largely follows the order in which material is covered in the
text. Chapter numbers refer to Nise.
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Introduction to Control Systems (Chapter 1 -- 1 lecture)
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Modeling
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Laplace Transforms (Chapter 2 -- 1 lecture)
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Modeling of Op-amps and Electric Motors (1 lecture)
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State Space Representation (Chapter 3 -- 1 lecture)
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Transfer Functions and Block Diagram Algebra (Chapter 5 -- 2 lectures)
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Time Response
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Rise Time, Settle Time, Overshoot. (Chapter 4 -- 3 lectures)
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Stability (Chapter 6 -- 1 lecture)
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Steady State Error (Chapter 7 -- 1 lecture)
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Root Locus Techniques
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Definition, Properties, and Sketching Rules (Chapter 8 -- 2 lectures)
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Design via Root Locus (Chapter 9 -- 2 lectures)
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Frequency Response Techniques
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Bode Plots (Chapter 10 -- 2 lectures)
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Design via Frequency Response (Chapter 11 -- 3 lectures)
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Introduction to Discrete-Time Control (Chapter 13 -- 4 lectures)
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Components of a Computer Control System
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Difference Equations and the Z-transform
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Basic Discrete-Time Controller Design
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Tentative Lab Schedule
This course will have a laboratory component. The Lab will meet on
certain Fridays 2:30-4:30 p.m. p.m. in the Undergraduate Measurement Lab,
Hamerschlag B301.
Lab 1. Motor Identification
Lab 2. Proportional Speed Control
Lab 3. Proportional plus Integral Speed Control
Lab 4. Motor Speed Control with Lead Compensation and Integral Control
Homework Policy
Homework will be assigned every Tuesday and will be due the following
Tuesday at the beginning of class. Students are encouraged to discuss assignments,
but material submitted for grading must be the product of individual effort.
Quizzes and Exams
There will be two 30-minute quizzes (tentative dates: September 21
and November 16), a midterm exam (tentative date: October 24), and a final
exam (in the final exam week).
Grading
Combining homework (30%), quizzes (10%), midterm exam (20%), final
exam (20%) and labs (20%), grading will be given on an absolute scale:
85-100 A
75-84 B
65-74 C
55-64 D
0-54 R