The University of Texas at Austin
Deptartment of Electrical and Computer Engineering

## EE362K: Introduction to Automatic Control

### Some Basic Information

Instructor: Constantine Caramanis

Email: caramanis AT mail DOT utexas DOT edu
Phone: (512) 471-9269
Office: ENS 427
Office Hours: Tuesday 4 - 5 pm

TA: Xinyang Yi

Email: yixy@utexas.edu
Office: ENS 137
Office Hours: Wednesday, 3:00 pm - 5:00 pm.

Lectures:

Time: Tuesday and Thursday, 5:00 - 6:30 PM,
Location: CPE 2.204

### Course Overview

The concept of feedback is central in the study of systems and control. Feedback loops naturally appear in the most basic biological phenomena, including macroscopic scale (population evolution, extinction, etc.) but also physiological function, for example, regulation of glucose level in the blood. In Engineering, feedback has long played an important role in mechanical, electronic, and now also digital systems. More generally, systems theory and feedback are central to understanding, analyzing, and designing systems with interconnected components.

The purpose of this class will be to gain a basic intuition for and understanding of, linear feedback systems, and also to develop the mathematical tools to understand the basics of design and analysis of single-input single-output feedback control systems.

### Official Course Description

Analysis of linear automatic control systems in time and frequency domains; stability analysis; state variable analysis of continuous-time and discrete-time systems; root locus; Nyquist diagrams; Bode plots; sensitivity; lead and lag compensation.Important topics we will cover include:

Course Outline (tentative):

• What is a dynamical system, control, and feedback?
• Concepts from state space design.
• Linear algebra review and some new concepts.
• State-space solution to linear systems.
• Controllability. Observability.
• Review of basics in Laplace transforms.
• System diagrams. Significance of pole and zero locations. System stability test.
• Basic equations of feedback. Performance measures, such as stability, disturbance rejection, noise attenuation, and tracking.
• Proportional-Integral-Derivative (PID) controller.
• Frequency response design. Bode and Nyquist plots, and the Nyquist criterion.
• Stability, and stability margins. Robustness.
• Time permitting: nonlinear systems, digital control.

There will be a big effort to draw interesting examples illustrating the basic concepts from a wide area, in order to give an idea of the applicability and impact ideas from Systems Theory have had, and are currently continuing to have.

### Course Prerequisites

The prerequisites for this class are: Electrical Engineering 438, as well as Mathematics 340L, with a grade of at least C in each. Much of what we cover in this class is cumulative. Thus these prerequisites are strict. Indeed, this class draws heavily on previous work in: linear algebra, transforms, and differential equations. In addition to these, part of the assignments will require use of Matlab. You do not need to have prior exposure to Matlab, but knowledge of basic programming will be helpful.

General Note: If you are concerned about the prerequisites or your background, or what the course will cover, please don't hesitate to contact me by e-mail, or come by my office hours.

### Homework and Exams

In this class there will be roughly weekly homeworks; there will be three mid-term exams in class, and then a final exam. The weighting will be as follows:
• Homework: 15%
• Midterm Exams: 45%
• Final Exam: 35%
• Class participation: 5%

Policy on Collaboration: Discussion of homework questions is encouraged. Please be sure to submit your own independent homework solution. This includes any matlab code required for the assignments. Late homework assignments will not be accepted.

### Text and References

The course will be taught from the book: Feedback Systems: An Introduction for Scientists and Engineers, by Karl J. Astrom and Richard M. Murray. This book is available (for free) from Richard Murray's web page. Please note that this is a different book than what is used in past years and other sections.

Additional References (Optional)

• Feedback Control of Dynamic Systems by G.F. Franklin, J.D. Powell, and A. Emami-Naeini.
• Control Systems: Principles and Design by M. Gopal.
Other helpful references
• Linear Algebra Done Right by Sheldon Axler.
• Advanced Calculus for Applications by F.B. Hildebrand.

### Lecture schedule (tentative)

 Lecture No. Date Problem Sets Problem Set Solutions Assigned Reading Exam 1 Thu August 30 --- --- Chapter 1 --- 2 Tue September 4 --- --- Chapter 1 --- 3 Thu September 6 Chapter 2 --- 4 Tue September 11 --- --- Chapters 2,3 --- 5 Thu September 13 Chapters 3,5 --- 6 Tue September 18 --- --- Chapter 5 --- 7 Thu September 20 Chapter 5 --- 8 Tue September 25 --- --- Chapters 6 --- 9 Thu September 27 Chapter 6 --- 10 Tue October 2 --- --- Chapter 5 --- MIDTERM 1 Thu October 4 --- --- Chapter 6 MIDTERM 1 11 Tue October 9 --- --- Chapter 6 --- 12 Thu October 11 Chapter 6 (6.1,6.2) --- 13 Tue October 16 --- --- Chapter 6 (6.1-6.3) --- 14 Thu October 18 Chapters 6,7 (6.4,7.1) --- 15 Tue October 23 --- --- --- --- 16 Thu October 25 --- --- 17 Tue October 30 --- --- --- --- MIDTERM 2 Thu November 1 --- --- Chapter 7 (7.1-7.3) MIDTERM 2 18 Tue November 6 --- --- Chapter 7 --- 19 Thu November 8 Chapter 8 (8.1) --- 20 Tue November 13 --- --- --- --- 21 Thu November 15 --- --- Chapter 8 (8.1-8.3) --- 22 Tue November 20 --- Chapter 8 (8.1-8.3) --- THANKSGIVING Thu November 22 --- --- --- --- 23 Tue November 27 --- --- Chapter 8 --- MIDTERM 3 Thu November 29 --- --- Chapter 9 MIDTERM 3 24 Tue December 4 --- --- Chapter 9 --- 25 Thu December 6 --- Chapter 9 --- Final Exam Thu December 13 7-10 pm, ETC 2.136 --- --- --- Final

### Homeworks

Homeworks are to be turned in at the beginning of the class when they are due, otherwise are counted as late. You are allowed to drop two (2) homeworks.

• problem set 1. This problem set gets us started on linear systems, stability, and also providing some linear algebra review.
• problem set 2. This problem set continues our work on linear algebra, eigenvalues and eigenvectors and matlab, as well as stability for discrete time and continuous time LTI systems.
• problem set 3. This problem set focuses on stability for CT and DT LTI systems, including practice using Jordan Canonical Form.
• problem set 4. This problem set is a good review for the midterm.
• problem set 5. This problem set focuses on reachable canonical form, and linear state feedback.
• problem set 6. This problem set gives more on reachable canonical form, and linear state feedback, and also introduces observability.
• problem set 7. This problem set focuses on observability.
• problem set 8. This problem set turns our attention to frequency domain: Laplace Transforms and partial fraction expansion.
• problem set 9. This problem set builds on the previous one, and focuses on transfer functions, block diagrams, and designing PID controllers.
• problem set 10. This problem set focuses on Nyquist plots and Nyquist stability.

### Solutions

• solution set 1
• solution set 2
• solution set 3
• solution set 4
• solution set 5
• solution set 6
• solution set 7
• solution set 8