Control Systems Syllabus
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Beginning-of-Course Assessment Memo ECE 4850 – Linear Control Systems (Fall 2012) Course Description: This course is to explore the modeling of linear dynamic systems via differential equations and transfer functions utilizing state-space and input-output representations; analysis of control systems in the time and frequency domains and using transfer function and state-space methods; study of the classical stability tests, such as the Routh-Hurwitz and Nyquist criterions, and design methods using root-locus plots and Bode plots; and the development of control techniques based on PID, lead and lag networks, using linear state or output feedback (3 credits). (Elective for Electrical and Computer Engineering) Prerequisites: ECE 3750 – Signals and Systems (I), or equivalent. Objectives: Study the principles of system modeling, system analysis and feedback control, and use them to design and evaluate feedback control systems with desired performance; specifically, to acquire the related knowledge and techniques to meet the following course objectives: 1. Control system modeling: modeling of electric, mechanical and electromechanical systems, using differential equations, transfer functions, block diagrams, and state variables; 2. Control system analysis: analysis of properties of control systems, such as sensitivity, stability, controllability, tracking, in time and frequency domains; and 3. Control system design: design of feedback controllers, such as PID, lead and lag compen- sators, pole placement designs, to meet desired system performance specifications. Course Objectives and Program Outcomes Map: Objective 1: program outcomes 1.a (in depth); 1.b, 1.d (familiarity); 3.d (exposure) Objective 2: program outcomes 2.b, 2.f (in depth); 1.b, 1.d, 2.c (familiarity); 3.a, 3.d (exposure) Objective 3: program outcomes 2.d, 2.f (in depth); 1.b, 1.d (familiarity); 3.a, 3.d (exposure). Textbook: G. F. Franklin, J. D. Powell and A. Emami-Naeini, Feedback Control of Dynamic Systems, 6th ed., Pear- son Prentice Hall, Upper Saddle River, NJ, 2009 (ISBN-13: 978-0-13-601969-5) Topics: 1. Mathematical models of control systems (2 lectures) 2. Transfer functions and block diagrams (2 lectures) 3. Time-domain responses (2 lectures) 4. The Routh-Hurwitz stability criterion (2 lectures) 5. Feedback control systems (2 lectures) 6. Root-locus techniques (5 lectures) 7. Bode plot techniques (2 lectures) 8. The Nyquist stability criterion (2 lectures) 9. Dynamic compensation in frequency-domain (3 lectures) 10. State space analysis and design (4 lectures). 1
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course syllabus
Transcript of Control Systems Syllabus
Beginning-of-CourseAssessmentMemo
ECE 4850– Linear Control Systems (Fall 2012)
CourseDescription:This courseis to explore the modelingof linear dynamicsystemsvia differentialequationsandtransferfunctionsutilizing state-spaceand input-outputrepresentations;analysisof control systemsin the timeandfrequency domainsandusingtransferfunctionandstate-spacemethods;studyof theclassicalstabilitytests,suchasthe Routh-HurwitzandNyquist criterions,anddesignmethodsusingroot-locusplots andBodeplots;andthedevelopmentof control techniquesbasedon PID, leadandlag networks,usinglinearstateor outputfeedback(3 credits).(Elective for ElectricalandComputerEngineering)
Prerequisites:ECE3750– SignalsandSystems(I), or equivalent.
Objectives:Studytheprinciplesof systemmodeling,systemanalysisandfeedbackcontrol,andusethemto designandevaluatefeedbackcontrolsystemswith desiredperformance;specifically, to acquiretherelatedknowledgeandtechniquesto meetthefollowing courseobjectives:
1. Control system modeling: modelingof electric,mechanicalandelectromechanicalsystems,usingdifferentialequations,transferfunctions,blockdiagrams,andstatevariables;
2. Control system analysis: analysisof propertiesof control systems,suchas sensitivity,stability, controllability, tracking,in time andfrequency domains;and
3. Control system design: designof feedbackcontrollers,suchasPID, leadandlag compen-sators,poleplacementdesigns,to meetdesiredsystemperformancespecifications.
CourseObjectivesand Program OutcomesMap:Objective1: programoutcomes1.a(in depth);1.b,1.d(familiarity); 3.d(exposure)Objective2: programoutcomes2.b,2.f (in depth);1.b,1.d,2.c(familiarity); 3.a,3.d(exposure)Objective3: programoutcomes2.d,2.f (in depth);1.b,1.d(familiarity); 3.a,3.d(exposure).
Textbook:G. F. Franklin,J.D. Powell andA. Emami-Naeini,FeedbackControlof DynamicSystems,6th ed.,Pear-sonPrenticeHall, UpperSaddleRiver, NJ,2009(ISBN-13: 978-0-13-601969-5)
Topics:1. Mathematicalmodelsof controlsystems(2 lectures)2. Transferfunctionsandblockdiagrams(2 lectures)3. Time-domainresponses(2 lectures)4. TheRouth-Hurwitzstability criterion(2 lectures)5. Feedbackcontrolsystems(2 lectures)6. Root-locustechniques(5 lectures)7. Bodeplot techniques(2 lectures)8. TheNyquiststability criterion(2 lectures)9. Dynamiccompensationin frequency-domain(3 lectures)10. Statespaceanalysisanddesign(4 lectures).
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Instructor :Dr� . GangTao,ThorntonHall, RoomE311,924-4586,[email protected].
LectureHours:11:00- 12:15,TuesdaysandThursdays,RiceHall, Room032
AssessmentScheme:Therearetotally 10homeworks,1 projectand2 testsfor this course.
1.a: Applicationof calculus,differentialequations,physicallaws,complex variabletheoryinmodelingof controlsystems(assignmentsin 4 homeworks,2 tests,1 project)
1.b: Procedureof technicaldevelopmentsin homeworks,testsandproject
1.d: Standardof technicalpresentationin homeworks,testsandproject
2.b: Useof matrixdifferentialequations,Fouriertransform,Laplacetransform,matrix theory,andcomplex variabletheory(assignmentsin 8 homeworks,two testsand1 project)
2.c: Useof Matlabin controlsystemanalysisthroughouthomeworks
2.d: Studyof systemstability, sensitivity, transientandtrackingperformance,anddesignofcontrol systemswith desiredperformancespecifications(assignmentsin 7 homeworks, twotestsand1 project)
2.f: Studyof controlsystemknowledgethroughhomeworks,testsandproject
3.a: Understandingof theneedof learningmoreadvancedtopicsin controlsystems,suchasissueswith nonlinearityanduncertainty
3.d: Practiceof theUVahonorcodein completinghomeworks,testsandproject.
Program Outcomes:Programoutcomesaretheeffectivenessmeasuresof acourse,whicharegroupedinto threecategories:1. fundamentals,2. specialists,and3. citizenship.
Outcome1.a: knowledgeof mathematics(includingdifferentialequations),science,anden-gineeringfundamentals.
Outcome1.b: ability to identify, formulate,andsolveengineeringproblems.
Outcome1.d: ability to effectively communicatetechnicalmaterial.
Outcome2.b: knowledgeof advancedtopicsin mathematicsincludingvectorcalculus,trans-form calculus,complex variablesandprobabilityandstatistics.
Outcome2.c: designof systemscontainingbothhardwareandsoftwareelements.Outcome2.d: ability to specify, design,analyzeandtestanelectrical/electronicsystemto meeta setofdesiredgoals,within thecontext of abroadersystemapplication.
Outcome2.f: specializedknowledgein oneor moreof thetopicalareasof electricalengineer-ing: controls,communications,electrophysics,digital systems,or microelectronics.
Outcome3.a:recognizationof theneedfor andbeingcapableof engagingin lifelong learning.
Outcome3.d: understandingof theethicalandprofessionalresponsibilitiesof anengineeringpractitioneror researcher.
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ECE4850– Linear Control Systems (Fall 2012;3 credits)
Scheduleof Office Hours, Homeworks, and Tests
Instructor’ sofficehours: 1:00- 2:30,Wednesday;9:30- 10:45,Thursday
Solution policy: No old/new solutioncanbeconsulteduntil ahomework, projector testis handedin.
Grading policy: 1. Homeworks: 20%; 2. Test1: 30%; 3. Project:20%;4. Test2: 30%.
Homework 1 (Topic1): 1.1(c),(d), 1.5,2.9(a),2.15(b),(c), 2.20.DueonSeptember6, Thursday.
Homework 2 (Topic2): 3.3(c),3.7(d),(i), 2.9(b),3.15(theinput is va), 3.20.DueonSeptember13,Thursday.
Homework 3 (Topic 3): 3.25,3.26,3.28(hint: usingtheregion ω1� ωn
� ω2, θ1� θ � θ2 containing
thegivencircle),3.35.DueonSeptember20,Thursday
Homework 4 (Topic4): 3.42(hint: KG � s � is anopenloop transferfunction),3.43,3.45.DueonSeptember27,Thursday
Homework 5 (Topic 5): 4.2, 4.31(hint: for (c), (e) and(g), only evaluatethesteady-statevalueof θ � t �for w � t ��� w0 andθr � t ��� 0, anddo not determinesystemtypeanderrorconstant;for (a), (b), (d), (f), setw � t ��� 0; for all parts,checksystemstability),4.19,4.24(a),(b), (c).
DueonOctober 4, Thursday.
Test1 (Topics1 - 5): October 16, Tuesday;6:00 - 7:30pm (in a classroom,closed-book,two pagesofnotesallowed).
Homework 6 (Topic6a): 5.4(c),5.6(d),5.7(a),5.8(b),5.41(for 5.7(a),5.8(b)).DueonOctober 18,Thursday.
Homework 7 (Topic 6b): 5.25,5.26,5.30(hint: for (a), considera positive K for positive feedbackanduseroot locustechniquein Matlab).
DueonOctober 25,Thursday.
Homework 8 (Topics7 and8): 6.3(c),(d), (e), (h) (hint: obtaintheBodeplotsby Matlab),6.17(b),6.19(b), (d) (hint: draw Nyquistplot by handandverify it by Matlab). For 6.3(c)and(e), alsofigureout thegain margin andphasemargin of eachcaseat K � 1, for theclosed-loopunity negative feedbacksystemwith open-looptransferfunctionKL � s � . Also, for eachcase,examinetheclosed-loopstability for K � 1.
You mayusethe “grid” commandon theBodeplots to make it easyto figureout thenumbers;notethat the amplitudeBodeplots from Matlab aregiven in db: 20log � L � jω ��� , e.g.,20log � 1��� 0, andyouneedto figureout theoriginal � L � jω ��� .
DueonNovember1, Thursday.
Project: November6 - 13,Tuesday- Thuesday(takehome,open-book).
Homework 9 (Topic9): 6.49,6.50.DueonNovember27,Tuesday.
Homework 10 (Topic10): 7.17(b),7.20,7.21,7.30(a),7.48(a),(b), (c).DueonDecember6, Thursday.
Test2 (Topics7 - 10): December7, Friday (in aclassroom,6:00- 7:30,open-book).
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