# AME 455

AME455: Control System Design

SCOPE: Mathematical modeling of dynamical systems, hardware and software issues; computer simulations; classical control methods including transient response, steady-state errors, bode diagrams, root locus and design of closed loop control systems; introduction to state feedback design and digital control.

COURSE OBJECTIVES: By the end of this course, the student should be able to
• Formulate a mathematical model of a given linear physical system in time and as a transfer function.
• Develop a computer model using MATLAB.
• Determine the system’s time response due to various inputs (step, ramp and harmonic) using MATLAB or inverse transforms.
• Identify the system order and type and determine its steady state error due to a given input.
• Evaluate the system stability using criterions including Routh’s criterion, root locus, and Bode 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 using Ackerman’s formula.

CLASS MATERIAL: "Feedback Control of Dynamic Systems” by G. F. Franklin, J. D. Powell, and A Emani-Naeini, Sixth Edition, Prentice Hall, 2009. Class notes will be integral part of instruction. Material presented in class will supplement and will sometimes be different from the textbooks.

PREREQUISITES and COMPUTER SKILLS: AME 320, AME321, Matlab.

EMAIL: My email will be the preferred way to communicate. Please check your email frequently for announcements. An immediate response is not guaranteed, but you should expect to get one within 24hs when your email arrives to the instructor’s email inbox Monday to Friday before class time.

HOMEWORK: Homework will be assigned typically weekly and due one week after. There is a drop box for your homework on the west end of AME 4th floor. The homework assignments and corresponding solution will be available at D2L. The grades will be also posted at d2l. The graded homework will be available at a tray by the drop box.

EXAMS: There will be three midterm exams and one final exam. There will be no make-ups for any exam. If you are unable to take a scheduled exam due to health reasons, you must notify the instructor prior to the beginning of the exam. If you will be absent to an exam due to a death (or life-threatening illness) in your family, similar advance notification and subsequent documentation will be required. Students absent from an exam for one of the above reasons will be assigned a grade reflecting performance on homework and previous/future exams. Students missing exams under conditions not discussed above will normally be awarded a zero.
Tentative Exam schedule:
February 11, 2012, 4:30pm-5:45pm: Midterm Exam #1
March 9, 2012, 4:30pm-5:45pm: Midterm Exam #2
April 20, 2012, 4:30pm-5:45pm: Midterm Exam #3
May 9, 2012, 3:30pm-5:30pm: Final Exam
Exams are closed notes and book. Only a letter size paper with notes is allowed

FINAL PROJECT: A design project incorporating most of the material covered in the course is required. The goal of the design project is to bring an element of real-world application of control theory to the class. The project consists of analysis and testing of an existing electro-mechanical system and design and implementation of closed-loop controller for it. The work on the project will be assigned similar to homework assignments. Details of the projects will be announced later in the class.

NEW PROJECT for SPRING 2012Modeling and Control the Pan/Tilt Motion Control System with Solar Panel

This purpose of this project is to develop a rigid body model of the fully actuated pan/tilt device shown in Figure 1 and to control the orientation of a solar panel attached to its moving arm. To derive the rigid model, a 6 DOF model tailored to the Pan/Tilt Motion Control System is to be developed. A practical use of the results consist of distributed solar farms in which the Pan/Tilt Motion Control System will efficiently capture energy from the sun by autonomously adjusting the angle of the Pan/Tilt Motion Control System according to the position of the sun and clouds. Slides introducing the Pan/Tilt Motion Control System are available here.

Student reports are available upon request.

The development of the Pan/Tilt Motion Control System and related curriculum material has been funded by Mathworks.

Pan/Tilt Motion Control System website:
http://www.u.arizona.edu/~sricardo/index.php?n=Main.ControlEducation

GRADING: The course grades will be posted at d2l and determined using the following percentages:

Homework 15%
Midterm exam #1 15%
Midterm exam #2 15%
Midterm exam #3 15%
Final exam 20%
Final project 20%

The “break points” dividing letter grades will be determined by the Instructor at the end of the semester, based on the overall performance of the class and other relevant factors. Class participation will be taken into consideration when determining boundary cases.

Grading exam papers is a difficult task, and errors or misjudgments occasionally occur. Any student who feels that his or her paper has not been graded properly may request that the paper be re-graded. However, all such requests must be made to the TA no later than one week after the assignment has been returned. The complete paper will be reexamined, and the student’s grade may change in either direction.

 Date Topics Events Week 101/07,01/11 L1: IntroductionL2: Feedback systems (notes and §1.1, §1.2) Week 201/14,01/18 L3: Modeling feedback control systemsL4: Time-invariant systems 01/18: HW1 posted Week 301/21,01/25 L5: Laplace transform and impulse responseL6: Properties of Laplace transforms 01/25: HW1 due Week 401/28,02/01 L7: Laplace transform and Transfer functionsL8: Block algebra and examples of Laplace transformL9: Poles and zeros 01/31: HW2 due Week 502/04,02/08 L10: Second Order systems. Design to match temporal specificationsL11: Practice partial expansion, design of second order sys.Review class 02/08: HW3 due Week 602/11,02/15 First midterm examL12: General feedback control system characteristicsL13: Matlab demo and stability in control systems 02/15: HW4 posted Week 702/18,02/22 L14: Rough test special casesL15 Eigenvalues and ExamplesL16: Design of classical control systems and Stead state 02/22: HW4 due Week 802/25,03/01 L17: System typeL18: System type examples and Matlab demoL19: Root locus method, guidelines 03/01: HW5 due Week 903/04,03/08 L20: Root locus examplesReview classSecond midterm exam 03/06: HW6 due Week 1003/11,03/15 Spring Break Week 1103/18,03/22 L18: Stability analysis (notes)L19: Stability analysis (notes) 11/04: HW4 due Week 1203/25,03/29 L20: Static analysis (notes)11/09: Project Progress Report Due and Present 11/07: HW5 posted11/09: Prog. Report due Week 1304/01,04/05 L21: Linearization and feedback control introd. (notes)L22: Linearization and feedback control introd. (notes) 11/16: HW5 due Week 1404/08,04/12 L23: Linearization and feedback control introd. (notes)11/23: Thanksgiving break Week 1504/15,04/19 Project Report Oral Presentations (all week) Week 1604/22,04/26 12/03: Final Review Finals week12/10,12/14 12/12/12: Final Exam12/14: Final Report due