Curriculum: MechEng, UC Berkeley
|
|
- Alan Ryan
- 5 years ago
- Views:
Transcription
1 Curriculum: MechEng, UC Berkele ME 132, 3-units, required, 2 nd or 3 rd ear students Prerequisites: Programming and Scientific computing (E7); Linear Algebra and ODEs (Math 54) Emphasis: mathematics of feedback sstems, at elementar level No lab No formal text Subsequent slides discuss Extensive use of computation/simulation first 8 hours of class ME 134, 3-units, elective, classical control, w/ lab Significant overlap with 132. Popular, nevertheless and repetition is OK Uses traditional text Cross-listed w/ EECS control (which has extensive signals/sstems prereqs) ME 135, 3-units, elective, microprocessors, real-time OS: hardware, software for control (project) ME 190I, 1-unit, elective, Modeling from Data ME 190L, 1-unit, elective, Loopshaping (Nquist/Bode, Glover-McFarlane, and more) ME 190M, 1-unit, elective, Model-Predictive di Control ME 190Y, 1-unit, elective, Youla-parametrization, closed-loop design optimization ME 102A, 3-units units, required, 3 rd ear, instrumentation, signals and measurement (w/ lab) ME 102B, 3-units, required, 4 th ear, mechatronics design (w/ individual project)
2 First few hours IEEE CSM, IEEE CSM, IEEE CSM, then Simulating feedback sstems Students come in knowing : Basic ODE theor for Runge-Kutta, ode45, function handles Simple conservation laws and constitutive eqs behavior described b ODEs Feedback examples, before an analsis results Motivate feedback architecture and strategies error, gain, speed-of-response, filters/smoothing, Dela-differential equations Look at families of (r,d,n,δ) (,u) responses d r Simulating delas with ode45 u G Δ (solve in chunks), ode45dela F K z u + + n F m m Experience/internalize common behaviors/objectives/tradeoffs in time domain Build appreciation for (and understanding of) graphical-based simulation tools (eg., Simulink) b writing general purpose simulation interconnection scripts Data structure: dnamical sstems (of a component) represented b 2 functions, (f,h) Interconnection-specific routines for composite (f,h)
3 Initial move to analsis (3 hours) First-order linear sstem, Response (derive as convolution integral, from integrating factor) Free response, forced response Linearit of Definition of stabilit, time-constant Stable sstems if bounded input has a limit, then response has a limit (ie., notion of stead-state gain) If input is bounded, output is bounded (deriving bound-to-bound relationship) If input is sinusoidal, output converges to sinusoidal (direct, from convolution) Frequenc-response function Dela-differential equation Observe (via ode45dela) onset (as T increases) of instabilit Make claim that at critical-value of T, a purel sinusoidal solution emerges Equation to determine T crit and ω crit
4 Analzing feedback sstems (3 hours) First-order closed-loop loop sstems 1 st order plant, proportional control Increasing speed of response Stabilizing an unstable G Unstable G is more problematic than stable G r m Influence induced b feedback: (d on u) and (Δ on u) to reduce influence on Influence of (n on u) and (n on ) through feedback 0 th order plant, 1 st order control Obtain 0-stead-state gain d with (and onl with) pure integral in controller K z u d u G Δ Simple studies, analtical, from the 1 st order theor established. Supplemented b Time responses: (r,d,n,δ) (,u) Gang-of-6 FRF Make informal, ad-hoc connections between time-responses and FRFs No genuine mention of Fourier transforms: observe patterns; anticipate and verif on new cases Margins (anwhere in loop) Dela margin Gain margin Saturation/Antiwindup ti ti i Discrete (time) implementation of K Effect of sample time + + n At this point, student has basic knowledge of all aspects of single-loop feedback sstems.
5 Remaining Topics Generalize to higher order ODEs Routh-Hurwitz (no/es: 15 minutes) Use quadratic formula to prove 2 nd order version State 3 rd and 4 th order test with examples Onl state as stable/unstable, not with number of sign changes Memorize 2 nd and 3 rd order results, use as needed Give historical account, credit to Routh and Hurwitz, and reference to work PI, PD, PID for 1 st and 2 nd order plants Elementar loopshaping, and arithmetic of feedback loops Pole-placement No Nquist (190L) No root locus (as a technique) N th order plant, (2N-1) th order desired char-pol, solve for (N-1) th order controller N th order plant, (2N) th order desired char-pol, solve for (N) th order controller w/ integral action Theoreticall interesting, relativel eas, student s like it, feels empowering GCD, coprimeness, Bezout identit, Euclid s algorithm Generalizes PI control of 1 st order sstem Less important for higher order sstems (where do ou put the poles?) Robustness margins (gain margin, time-dela margin, percentage-uncertaint margin) If robustness margins are important in chapter 8, then the are important in chapter 10 too Example, popular text: 4 th order SISO plant; pole-placement with seemingl reasonable poles; one good-looking simulation; no mention of margins (<1degree, <0.1 db) Jacobian Linearizations Linear state-space: solutions, realizations, model conversions
6 Heaviside Yes, Laplace No Starting with Heaviside, smbolic calculus had been shown to be an effective tool for linear time-invariant dnamical sstems. Under the influence of circuit theor, it had become evident that these methods allowed to analze complex sstems, b combining series, parallel, and feedback interconnections. The spirit of Heaviside s smbolic calculus was to be able to think of a differential Oliver Heaviside 1850 operator or a dela as a formal indeterminate for which a differential operator or a dela can be substituted. Unfortunatel, analsts had squeezed this marvelous idea in the mathematical rigor (mortis) of Laplace transforms, using complex functions, with domains of convergence and other cumbersome but largel irrelevant mathematical traps. Oliver Heaviside, , man remarkable accomplishments Jan Willems, In Control, Almost from the Beginning Until the Da After Tomorrow, European Journal of Control, 2007
7 Single-Loop, linear sstems Input/output ODEs are treated as the foundational mathematical framework Understand stabilit, homogeneous solutions Frequenc-response functions Described b Linear Differential Operators, Manipulation of interconnections v r v r v G G TF is simpl notation for ODE, suggestive of Substitution, Arithmetic manipulations, Decompositions, which are then verified as correct (b appealing back to ODEs) No mention of integral transform, ROCs, etc Lose out on one result: closed-loop time domain constraints (on various responses) due to RHP poles/zeros in plant
EET 3212 Control Systems. Control Systems Engineering, 6th Edition, Norman S. Nise December 2010, A. Goykadosh and M.
NEW YORK CITY COLLEGE OF TECHNOLOGY The City University of New York 300 Jay Street Brooklyn, NY 11201-2983 Department of Electrical and Telecommunications Engineering Technology TEL (718) 260-5300 - FAX:
More informationEECE 460 : Control System Design
EECE 460 : Control System Design SISO Pole Placement Guy A. Dumont UBC EECE January 2011 Guy A. Dumont (UBC EECE) EECE 460: Pole Placement January 2011 1 / 29 Contents 1 Preview 2 Polynomial Pole Placement
More informationContents. PART I METHODS AND CONCEPTS 2. Transfer Function Approach Frequency Domain Representations... 42
Contents Preface.............................................. xiii 1. Introduction......................................... 1 1.1 Continuous and Discrete Control Systems................. 4 1.2 Open-Loop
More informationSimon Fraser University School of Engineering Science ENSC Linear Systems Spring Instructor Jim Cavers ASB
Simon Fraser University School of Engineering Science ENSC 380-3 Linear Systems Spring 2000 This course covers the modeling and analysis of continuous and discrete signals and systems using linear techniques.
More informationCourse Summary. The course cannot be summarized in one lecture.
Course Summary Unit 1: Introduction Unit 2: Modeling in the Frequency Domain Unit 3: Time Response Unit 4: Block Diagram Reduction Unit 5: Stability Unit 6: Steady-State Error Unit 7: Root Locus Techniques
More informationCourse roadmap. ME451: Control Systems. What is Root Locus? (Review) Characteristic equation & root locus. Lecture 18 Root locus: Sketch of proofs
ME451: Control Systems Modeling Course roadmap Analysis Design Lecture 18 Root locus: Sketch of proofs Dr. Jongeun Choi Department of Mechanical Engineering Michigan State University Laplace transform
More informationEEE 184 Project: Option 1
EEE 184 Project: Option 1 Date: November 16th 2012 Due: December 3rd 2012 Work Alone, show your work, and comment your results. Comments, clarity, and organization are important. Same wrong result or same
More information1) Electronic Circuits & Laboratory
ENSEA COURSES TAUGHT IN ENGLISH SPRING Semester 1) Electronic Circuits & Laboratory Lecture : 45 hours Laboratory : 45 hours US Credits : 6 Analysis of integrated amplifiers with bipolar junction transistors
More informationA New Closed-loop Identification Method of a Hammerstein-type System with a Pure Time Delay
A New Closed-loop Identification Method of a Hammerstein-tpe Sstem with a Pure Time Dela Edin Drljević a, Branislava Peruničić b, Željko Jurić c, Member of IEEE Abstract A procedure for the closed-loop
More informationCHAPTER 5 ROBUSTNESS ANALYSIS OF THE CONTROLLER
114 CHAPTER 5 ROBUSTNESS ANALYSIS OF THE CONTROLLER 5.1 INTRODUCTION Robust control is a branch of control theory that explicitly deals with uncertainty in its approach to controller design. It also refers
More informationProcess Modelling, Identification, and Control
Jan Mikles Miroslav Fikar 2008 AGI-Information Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. Process Modelling, Identification, and
More informationRobust and Optimal Control, Spring A: SISO Feedback Control A.1 Internal Stability and Youla Parameterization
Robust and Optimal Control, Spring 2015 Instructor: Prof. Masayuki Fujita (S5-303B) A: SISO Feedback Control A.1 Internal Stability and Youla Parameterization A.2 Sensitivity and Feedback Performance A.3
More informationSTABILITY OF CLOSED-LOOP CONTOL SYSTEMS
CHBE320 LECTURE X STABILITY OF CLOSED-LOOP CONTOL SYSTEMS Professor Dae Ryook Yang Spring 2018 Dept. of Chemical and Biological Engineering 10-1 Road Map of the Lecture X Stability of closed-loop control
More informationCONTROL SYSTEMS ENGINEERING Sixth Edition International Student Version
CONTROL SYSTEMS ENGINEERING Sixth Edition International Student Version Norman S. Nise California State Polytechnic University, Pomona John Wiley fir Sons, Inc. Contents PREFACE, vii 1. INTRODUCTION, 1
More informationSubband Coding and Wavelets. National Chiao Tung University Chun-Jen Tsai 12/04/2014
Subband Coding and Wavelets National Chiao Tung Universit Chun-Jen Tsai /4/4 Concept of Subband Coding In transform coding, we use N (or N N) samples as the data transform unit Transform coefficients are
More informationLocal Phase Portrait of Nonlinear Systems Near Equilibria
Local Phase Portrait of Nonlinear Sstems Near Equilibria [1] Consider 1 = 6 1 1 3 1, = 3 1. ( ) (a) Find all equilibrium solutions of the sstem ( ). (b) For each equilibrium point, give the linear approimating
More informationControls Problems for Qualifying Exam - Spring 2014
Controls Problems for Qualifying Exam - Spring 2014 Problem 1 Consider the system block diagram given in Figure 1. Find the overall transfer function T(s) = C(s)/R(s). Note that this transfer function
More informationEE 380. Linear Control Systems. Lecture 10
EE 380 Linear Control Systems Lecture 10 Professor Jeffrey Schiano Department of Electrical Engineering Lecture 10. 1 Lecture 10 Topics Stability Definitions Methods for Determining Stability Lecture 10.
More informationModeling and Control Overview
Modeling and Control Overview D R. T A R E K A. T U T U N J I A D V A N C E D C O N T R O L S Y S T E M S M E C H A T R O N I C S E N G I N E E R I N G D E P A R T M E N T P H I L A D E L P H I A U N I
More informationStability of Feedback Control Systems: Absolute and Relative
Stability of Feedback Control Systems: Absolute and Relative Dr. Kevin Craig Greenheck Chair in Engineering Design & Professor of Mechanical Engineering Marquette University Stability: Absolute and Relative
More informationFeedback Control of Dynamic Systems
THIRD EDITION Feedback Control of Dynamic Systems Gene F. Franklin Stanford University J. David Powell Stanford University Abbas Emami-Naeini Integrated Systems, Inc. TT Addison-Wesley Publishing Company
More informationDynamic Systems. Modeling and Analysis. Hung V. Vu. Ramin S. Esfandiari. THE McGRAW-HILL COMPANIES, INC. California State University, Long Beach
Dynamic Systems Modeling and Analysis Hung V. Vu California State University, Long Beach Ramin S. Esfandiari California State University, Long Beach THE McGRAW-HILL COMPANIES, INC. New York St. Louis San
More informationDigital Control Engineering Analysis and Design
Digital Control Engineering Analysis and Design M. Sami Fadali Antonio Visioli AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO Academic Press is
More informationDr Ian R. Manchester Dr Ian R. Manchester AMME 3500 : Review
Week Date Content Notes 1 6 Mar Introduction 2 13 Mar Frequency Domain Modelling 3 20 Mar Transient Performance and the s-plane 4 27 Mar Block Diagrams Assign 1 Due 5 3 Apr Feedback System Characteristics
More informationProcess Modelling, Identification, and Control
Jan Mikles Miroslav Fikar Process Modelling, Identification, and Control With 187 Figures and 13 Tables 4u Springer Contents 1 Introduction 1 1.1 Topics in Process Control 1 1.2 An Example of Process Control
More informationSOUTHERN UNIVERSITY and A&M COLLEGE DEPARTMENT OF MATHEMATICS MATH 395 CALCULUS III AND DIFFERENTIAL EQUATIONS FOR JUNIOR ENGINEERING MAJORS
SOUTHERN UNIVERSITY and A&M COLLEGE DEPARTMENT OF MATHEMATICS MATH 395 CALCULUS III AND DIFFERENTIAL EQUATIONS FOR JUNIOR ENGINEERING MAJORS COURSE DESCRIPTION: This course combines selective topics normally
More informationClosed-loop system 2/1/2016. Generally MIMO case. Two-degrees-of-freedom (2 DOF) control structure. (2 DOF structure) The closed loop equations become
Closed-loop system enerally MIMO case Two-degrees-of-freedom (2 DOF) control structure (2 DOF structure) 2 The closed loop equations become solving for z gives where is the closed loop transfer function
More informationRadnor High School Course Syllabus Advanced Placement Calculus BC 0460
Radnor High School Modified April 24, 2012 Course Syllabus Advanced Placement Calculus BC 0460 Credits: 1 Grades: 11, 12 Weighted: Yes Prerequisite: Recommended by Department Length: Year Format: Meets
More informationECE 388 Automatic Control
Lead Compensator and PID Control Associate Prof. Dr. of Mechatronics Engineeering Çankaya University Compulsory Course in Electronic and Communication Engineering Credits (2/2/3) Course Webpage: http://ece388.cankaya.edu.tr
More informationOn the design of Incremental ΣΔ Converters
M. Belloni, C. Della Fiore, F. Maloberti, M. Garcia Andrade: "On the design of Incremental ΣΔ Converters"; IEEE Northeast Workshop on Circuits and Sstems, NEWCAS 27, Montreal, 5-8 August 27, pp. 376-379.
More informationAutonomous Mobile Robot Design
Autonomous Mobile Robot Design Topic: Guidance and Control Introduction and PID Loops Dr. Kostas Alexis (CSE) Autonomous Robot Challenges How do I control where to go? Autonomous Mobile Robot Design Topic:
More informationMathematics (MAT) MAT 051 Pre-Algebra. 4 Hours. Prerequisites: None. 4 hours weekly (4-0)
Mathematics (MAT) MAT 051 Pre-Algebra 4 Hours Prerequisites: None 4 hours weekly (4-0) MAT 051 is designed as a review of the basic operations of arithmetic and an introduction to algebra. The student
More informationEC CONTROL SYSTEM UNIT I- CONTROL SYSTEM MODELING
EC 2255 - CONTROL SYSTEM UNIT I- CONTROL SYSTEM MODELING 1. What is meant by a system? It is an arrangement of physical components related in such a manner as to form an entire unit. 2. List the two types
More informationORDINARY DIFFERENTIAL EQUATIONS
PREFACE i Preface If an application of mathematics has a component that varies continuously as a function of time, then it probably involves a differential equation. For this reason, ordinary differential
More information1 An Overview and Brief History of Feedback Control 1. 2 Dynamic Models 23. Contents. Preface. xiii
Contents 1 An Overview and Brief History of Feedback Control 1 A Perspective on Feedback Control 1 Chapter Overview 2 1.1 A Simple Feedback System 3 1.2 A First Analysis of Feedback 6 1.3 Feedback System
More informationAn Overview on Behavioural Theory to Systems and Control
1 An Overview on Behavioural Theory to Systems and Control Md. Haider Ali Biswas PDEEC, FEUP E-mail: mhabiswas@yahoo.com Abstract This report deals with an overview of the behavioural theory based on the
More informationCDS 101: Lecture 4.1 Linear Systems
CDS : Lecture 4. Linear Systems Richard M. Murray 8 October 4 Goals: Describe linear system models: properties, eamples, and tools Characterize stability and performance of linear systems in terms of eigenvalues
More informationControl Systems I. Lecture 9: The Nyquist condition
Control Systems I Lecture 9: The Nyquist condition adings: Guzzella, Chapter 9.4 6 Åstrom and Murray, Chapter 9.1 4 www.cds.caltech.edu/~murray/amwiki/index.php/first_edition Emilio Frazzoli Institute
More informationCYBER EXPLORATION LABORATORY EXPERIMENTS
CYBER EXPLORATION LABORATORY EXPERIMENTS 1 2 Cyber Exploration oratory Experiments Chapter 2 Experiment 1 Objectives To learn to use MATLAB to: (1) generate polynomial, (2) manipulate polynomials, (3)
More informationChemical Process Dynamics and Control. Aisha Osman Mohamed Ahmed Department of Chemical Engineering Faculty of Engineering, Red Sea University
Chemical Process Dynamics and Control Aisha Osman Mohamed Ahmed Department of Chemical Engineering Faculty of Engineering, Red Sea University 1 Chapter 4 System Stability 2 Chapter Objectives End of this
More informationLearn2Control Laboratory
Learn2Control Laboratory Version 3.2 Summer Term 2014 1 This Script is for use in the scope of the Process Control lab. It is in no way claimed to be in any scientific way complete or unique. Errors should
More informationEE 4443/5329. LAB 3: Control of Industrial Systems. Simulation and Hardware Control (PID Design) The Torsion Disks. (ECP Systems-Model: 205)
EE 4443/539 LAB 3: Control of Industrial Systems Simulation and Hardware Control (PID Design) The Torsion Disks (ECP Systems-Model: 05) Compiled by: Nitin Swamy Email: nswamy@lakeshore.uta.edu Email: okuljaca@lakeshore.uta.edu
More informationLotka Volterra Model with Time Delay
International Journal of Mathematics Research. ISSN 976-584 Volume 6, Number (4), pp. 5- International Research Publication House http://www.irphouse.com Lotka Volterra Model with Time Dela Tapas Kumar
More informationVideo 5.1 Vijay Kumar and Ani Hsieh
Video 5.1 Vijay Kumar and Ani Hsieh Robo3x-1.1 1 The Purpose of Control Input/Stimulus/ Disturbance System or Plant Output/ Response Understand the Black Box Evaluate the Performance Change the Behavior
More informationCourse Goals and Course Objectives, as of Fall Math 102: Intermediate Algebra
Course Goals and Course Objectives, as of Fall 2015 Math 102: Intermediate Algebra Interpret mathematical models such as formulas, graphs, tables, and schematics, and draw inferences from them. Represent
More informationEE 422G - Signals and Systems Laboratory
EE 4G - Signals and Systems Laboratory Lab 9 PID Control Kevin D. Donohue Department of Electrical and Computer Engineering University of Kentucky Lexington, KY 40506 April, 04 Objectives: Identify the
More information(Continued on next page)
(Continued on next page) 18.2 Roots of Stability Nyquist Criterion 87 e(s) 1 S(s) = =, r(s) 1 + P (s)c(s) where P (s) represents the plant transfer function, and C(s) the compensator. The closedloop characteristic
More informationControl Systems I. Lecture 7: Feedback and the Root Locus method. Readings: Jacopo Tani. Institute for Dynamic Systems and Control D-MAVT ETH Zürich
Control Systems I Lecture 7: Feedback and the Root Locus method Readings: Jacopo Tani Institute for Dynamic Systems and Control D-MAVT ETH Zürich November 2, 2018 J. Tani, E. Frazzoli (ETH) Lecture 7:
More informationCONTROL * ~ SYSTEMS ENGINEERING
CONTROL * ~ SYSTEMS ENGINEERING H Fourth Edition NormanS. Nise California State Polytechnic University, Pomona JOHN WILEY& SONS, INC. Contents 1. Introduction 1 1.1 Introduction, 2 1.2 A History of Control
More informationLecture 13: Internal Model Principle and Repetitive Control
ME 233, UC Berkeley, Spring 2014 Xu Chen Lecture 13: Internal Model Principle and Repetitive Control Big picture review of integral control in PID design example: 0 Es) C s) Ds) + + P s) Y s) where P s)
More informationTrinity Christian School Curriculum Guide
Course Title: Calculus Grade Taught: Twelfth Grade Credits: 1 credit Trinity Christian School Curriculum Guide A. Course Goals: 1. To provide students with a familiarity with the properties of linear,
More informationBASE VECTORS FOR SOLVING OF PARTIAL DIFFERENTIAL EQUATIONS
BASE VECTORS FOR SOLVING OF PARTIAL DIFFERENTIAL EQUATIONS J. Roubal, V. Havlena Department of Control Engineering, Facult of Electrical Engineering, Czech Technical Universit in Prague Abstract The distributed
More informationI. AP Calculus AB Major Topic: Functions, Graphs, and Limits
A.P. Calculus AB Course Description: AP Calculus AB is an extension of advanced mathematical concepts studied in Precalculus. Topics include continuity and limits, composite functions, and graphing. An
More informationLecture 6 Classical Control Overview IV. Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore
Lecture 6 Classical Control Overview IV Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore Lead Lag Compensator Design Dr. Radhakant Padhi Asst.
More informationSoftware Engineering/Mechatronics 3DX4. Slides 6: Stability
Software Engineering/Mechatronics 3DX4 Slides 6: Stability Dr. Ryan Leduc Department of Computing and Software McMaster University Material based on lecture notes by P. Taylor and M. Lawford, and Control
More informationAnalysis of SISO Control Loops
Chapter 5 Analysis of SISO Control Loops Topics to be covered For a given controller and plant connected in feedback we ask and answer the following questions: Is the loop stable? What are the sensitivities
More informationECE317 : Feedback and Control
ECE317 : Feedback and Control Lecture : Routh-Hurwitz stability criterion Examples Dr. Richard Tymerski Dept. of Electrical and Computer Engineering Portland State University 1 Course roadmap Modeling
More informationSmith Predictor Based Autotuners for Time-delay Systems
Smith Predictor Based Autotuners for Time-dela Sstems ROMAN PROKOP, JIŘÍ KORBEL, RADEK MATUŠŮ Facult of Applied Informatics Tomas Bata Universit in Zlín Nám. TGM 5555, 76 Zlín CZECH REPUBLIC prokop@fai.utb.cz
More informationResearch Article Chaotic Attractor Generation via a Simple Linear Time-Varying System
Discrete Dnamics in Nature and Societ Volume, Article ID 836, 8 pages doi:.//836 Research Article Chaotic Attractor Generation via a Simple Linear Time-Varing Sstem Baiu Ou and Desheng Liu Department of
More informationWhy This Class? James K. Peterson. August 22, Department of Biological Sciences and Department of Mathematical Sciences Clemson University
Why This Class? James K. Peterson Department of Biological Sciences and Department of Mathematical Sciences Clemson University August 22, 2013 Outline 1 Our Point of View Mathematics, Science and Computer
More informationMEM 355 Performance Enhancement of Dynamical Systems
MEM 355 Performance Enhancement of Dynamical Systems Frequency Domain Design Intro Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University /5/27 Outline Closed Loop Transfer
More informationMAS107 Control Theory Exam Solutions 2008
MAS07 CONTROL THEORY. HOVLAND: EXAM SOLUTION 2008 MAS07 Control Theory Exam Solutions 2008 Geir Hovland, Mechatronics Group, Grimstad, Norway June 30, 2008 C. Repeat question B, but plot the phase curve
More information100 (s + 10) (s + 100) e 0.5s. s 100 (s + 10) (s + 100). G(s) =
1 AME 3315; Spring 215; Midterm 2 Review (not graded) Problems: 9.3 9.8 9.9 9.12 except parts 5 and 6. 9.13 except parts 4 and 5 9.28 9.34 You are given the transfer function: G(s) = 1) Plot the bode plot
More informationIntro to Frequency Domain Design
Intro to Frequency Domain Design MEM 355 Performance Enhancement of Dynamical Systems Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University Outline Closed Loop Transfer Functions
More informationJoão P. Hespanha. January 16, 2009
LINEAR SYSTEMS THEORY João P. Hespanha January 16, 2009 Disclaimer: This is a draft and probably contains a few typos. Comments and information about typos are welcome. Please contact the author at hespanha@ece.ucsb.edu.
More informationMATHEMATICS (MATH) Calendar
MATHEMATICS (MATH) This is a list of the Mathematics (MATH) courses available at KPU. For information about transfer of credit amongst institutions in B.C. and to see how individual courses transfer, go
More informationReview for Exam #3 MATH 3200
Review for Exam #3 MATH 3 Lodwick/Kawai You will have hrs. to complete Exam #3. There will be one full problem from Laplace Transform with the unit step function. There will be linear algebra, but hopefull,
More informationRANGE CONTROL MPC APPROACH FOR TWO-DIMENSIONAL SYSTEM 1
RANGE CONTROL MPC APPROACH FOR TWO-DIMENSIONAL SYSTEM Jirka Roubal Vladimír Havlena Department of Control Engineering, Facult of Electrical Engineering, Czech Technical Universit in Prague Karlovo náměstí
More informationLinear System Theory. Wonhee Kim Lecture 1. March 7, 2018
Linear System Theory Wonhee Kim Lecture 1 March 7, 2018 1 / 22 Overview Course Information Prerequisites Course Outline What is Control Engineering? Examples of Control Systems Structure of Control Systems
More information4452 Mathematical Modeling Lecture 13: Chaos and Fractals
Math Modeling Lecture 13: Chaos and Fractals Page 1 442 Mathematical Modeling Lecture 13: Chaos and Fractals Introduction In our tetbook, the discussion on chaos and fractals covers less than 2 pages.
More informationUnit 8: Part 2: PD, PID, and Feedback Compensation
Ideal Derivative Compensation (PD) Lead Compensation PID Controller Design Feedback Compensation Physical Realization of Compensation Unit 8: Part 2: PD, PID, and Feedback Compensation Engineering 5821:
More informationCDS 101/110: Lecture 10.3 Final Exam Review
CDS 11/11: Lecture 1.3 Final Exam Review December 2, 216 Schedule: (1) Posted on the web Monday, Dec. 5 by noon. (2) Due Friday, Dec. 9, at 5: pm. (3) Determines 3% of your grade Instructions on Front
More informationMATH4406 (Control Theory) Unit 1: Introduction Prepared by Yoni Nazarathy, July 21, 2012
MATH4406 (Control Theory) Unit 1: Introduction Prepared by Yoni Nazarathy, July 21, 2012 Unit Outline Introduction to the course: Course goals, assessment, etc... What is Control Theory A bit of jargon,
More informationReview: stability; Routh Hurwitz criterion Today s topic: basic properties and benefits of feedback control
Plan of the Lecture Review: stability; Routh Hurwitz criterion Today s topic: basic properties and benefits of feedback control Goal: understand the difference between open-loop and closed-loop (feedback)
More informationDigital Control: Summary # 7
Digital Control: Summary # 7 Proportional, integral and derivative control where K i is controller parameter (gain). It defines the ratio of the control change to the control error. Note that e(k) 0 u(k)
More informationFeedback Control of Linear SISO systems. Process Dynamics and Control
Feedback Control of Linear SISO systems Process Dynamics and Control 1 Open-Loop Process The study of dynamics was limited to open-loop systems Observe process behavior as a result of specific input signals
More informationDepartment of Electrical and Telecommunications Engineering Technology TEL (718) FAX: (718) Courses Description:
NEW YORK CITY COLLEGE OF TECHNOLOGY The City University of New York 300 Jay Street Brooklyn, NY 11201-2983 Department of Electrical and Telecommunications Engineering Technology TEL (718) 260-5300 - FAX:
More informationEffect of Fractional Order in Vertical Pole Motion Sucheta Moharir 1, Narhari Patil 2
Effect of Fractional Order in Vertical Pole Motion Sucheta Moharir 1, Narhari Patil 2 1 St.Vincent Pallotti College of Engineering and Technology, Nagpur (Maharashtra), India 2 Shri Sant Gajanan Maharaj
More informationI Stable, marginally stable, & unstable linear systems. I Relationship between pole locations and stability. I Routh-Hurwitz criterion
EE C128 / ME C134 Feedback Control Systems Lecture Chapter 6 Stability Lecture abstract Alexandre Bayen Department of Electrical Engineering & Computer Science University of California Berkeley Topics
More informationControl Systems I. Lecture 2: Modeling and Linearization. Suggested Readings: Åström & Murray Ch Jacopo Tani
Control Systems I Lecture 2: Modeling and Linearization Suggested Readings: Åström & Murray Ch. 2-3 Jacopo Tani Institute for Dynamic Systems and Control D-MAVT ETH Zürich September 28, 2018 J. Tani, E.
More informationLecture 2. Introduction to Systems (Lathi )
Lecture 2 Introduction to Systems (Lathi 1.6-1.8) Pier Luigi Dragotti Department of Electrical & Electronic Engineering Imperial College London URL: www.commsp.ee.ic.ac.uk/~pld/teaching/ E-mail: p.dragotti@imperial.ac.uk
More information2 Ordinary Differential Equations: Initial Value Problems
Ordinar Differential Equations: Initial Value Problems Read sections 9., (9. for information), 9.3, 9.3., 9.3. (up to p. 396), 9.3.6. Review questions 9.3, 9.4, 9.8, 9.9, 9.4 9.6.. Two Examples.. Foxes
More informationA brief introduction to robust H control
A brief introduction to robust H control Jean-Marc Biannic System Control and Flight Dynamics Department ONERA, Toulouse. http://www.onera.fr/staff/jean-marc-biannic/ http://jm.biannic.free.fr/ European
More informationẋ n = f n (x 1,...,x n,u 1,...,u m ) (5) y 1 = g 1 (x 1,...,x n,u 1,...,u m ) (6) y p = g p (x 1,...,x n,u 1,...,u m ) (7)
EEE582 Topical Outline A.A. Rodriguez Fall 2007 GWC 352, 965-3712 The following represents a detailed topical outline of the course. It attempts to highlight most of the key concepts to be covered and
More informationPlan of the Lecture. Review: stability; Routh Hurwitz criterion Today s topic: basic properties and benefits of feedback control
Plan of the Lecture Review: stability; Routh Hurwitz criterion Today s topic: basic properties and benefits of feedback control Plan of the Lecture Review: stability; Routh Hurwitz criterion Today s topic:
More informationPolynomial and Rational Functions
Polnomial and Rational Functions 5 Figure 1 35-mm film, once the standard for capturing photographic images, has been made largel obsolete b digital photograph. (credit film : modification of work b Horia
More informationSOLVING SOME PHYSICAL PROBLEMS USING THE METHODS OF NUMERICAL MATHEMATICS WITH THE HELP OF SYSTEM MATHEMATICA
SOLVING SOME PHYSICAL PROBLEMS USING THE METHODS OF NUMERICAL MATHEMATICS WITH THE HELP OF SYSTEM MATHEMATICA Pavel Trojovský Jaroslav Seibert Antonín Slabý ABSTRACT Ever future teacher of mathematics
More informationECEN 605 LINEAR SYSTEMS. Lecture 20 Characteristics of Feedback Control Systems II Feedback and Stability 1/27
1/27 ECEN 605 LINEAR SYSTEMS Lecture 20 Characteristics of Feedback Control Systems II Feedback and Stability Feedback System Consider the feedback system u + G ol (s) y Figure 1: A unity feedback system
More informationControl Systems I. Lecture 9: The Nyquist condition
Control Systems I Lecture 9: The Nyquist condition Readings: Åstrom and Murray, Chapter 9.1 4 www.cds.caltech.edu/~murray/amwiki/index.php/first_edition Jacopo Tani Institute for Dynamic Systems and Control
More informationUnit 11 - Week 7: Quantitative feedback theory (Part 1/2)
X reviewer3@nptel.iitm.ac.in Courses» Control System Design Announcements Course Ask a Question Progress Mentor FAQ Unit 11 - Week 7: Quantitative feedback theory (Part 1/2) Course outline How to access
More informationSECTION 5: ROOT LOCUS ANALYSIS
SECTION 5: ROOT LOCUS ANALYSIS MAE 4421 Control of Aerospace & Mechanical Systems 2 Introduction Introduction 3 Consider a general feedback system: Closed loop transfer function is 1 is the forward path
More informationplease strongly consider purchasing a TI-84 Plus or N-Spire calculator to use throughout the school year
June 2009 Dear Algebra II Parents and Students, In preparation for Algebra II it is important for students to have a solid foundation in the understanding of linear functions, which is a large topic in
More informationMCE693/793: Analysis and Control of Nonlinear Systems
MCE693/793: Analysis and Control of Nonlinear Systems Introduction to Describing Functions Hanz Richter Mechanical Engineering Department Cleveland State University Introduction Frequency domain methods
More informationExperimental Uncertainty Review. Abstract. References. Measurement Uncertainties and Uncertainty Propagation
Experimental Uncertaint Review Abstract This is intended as a brief summar of the basic elements of uncertaint analsis, and a hand reference for laborator use. It provides some elementar "rules-of-thumb"
More information* τσ σκ. Supporting Text. A. Stability Analysis of System 2
Supporting Tet A. Stabilit Analsis of Sstem In this Appendi, we stud the stabilit of the equilibria of sstem. If we redefine the sstem as, T when -, then there are at most three equilibria: E,, E κ -,,
More informationUltimate State. MEM 355 Performance Enhancement of Dynamical Systems
Ultimate State MEM 355 Performance Enhancement of Dnamical Sstems Harr G. Kwatn Department of Mechanical Engineering & Mechanics Drexel Universit Outline Design Criteria two step process Ultimate state
More informationWILEY. Differential Equations with MATLAB (Third Edition) Brian R. Hunt Ronald L. Lipsman John E. Osborn Jonathan M. Rosenberg
Differential Equations with MATLAB (Third Edition) Updated for MATLAB 2011b (7.13), Simulink 7.8, and Symbolic Math Toolbox 5.7 Brian R. Hunt Ronald L. Lipsman John E. Osborn Jonathan M. Rosenberg All
More informationMA3025 Course Prerequisites
MA3025 Course Prerequisites MA 3025 (4-1) MA3025 (4-1) Logic and Discrete Mathematics: Provides a rigorous foundation in logic and elementary discrete mathematics. Topics from logic include modeling English
More informationURSULINE ACADEMY Curriculum Guide
URSULINE ACADEMY 2018-2019 Curriculum Guide MATHEMATICS MT 510 MATHEMATICAL STRATEGIES Description: This course is designed to improve the students understanding of algebraic concepts MT 511 ALGEBRA I
More informationLecture 14 - Using the MATLAB Control System Toolbox and Simulink Friday, February 8, 2013
Today s Objectives ENGR 105: Feedback Control Design Winter 2013 Lecture 14 - Using the MATLAB Control System Toolbox and Simulink Friday, February 8, 2013 1. introduce the MATLAB Control System Toolbox
More information