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CDS 101: Lecture 1. 1 Introduction to Feedback and Control Richard M. Murray 27 September 2004 Goals: ŸGive an overview of CDS 101/110; describe course structure, administration ŸDefine feedback systems and learn how to recognize main features ŸDescribe what control systems do and the primary principles of feedback Reading (available on course web page): ŸÅström and Murray, Analysis and Design of Feedback Systems, Ch 1 (available from course web page) 27 Sep 04 R. M. Murray, Caltech CDS

Course Administration Course syllabus ŸCDS 101 vs CDS 110 ab ŸLectures, recitations ŸOffice hours ŸGrading ŸHomework policy ŸCourse text and references ŸClass homepage ŸSoftware ŸCourse outline ŸSignup sheet, mailing list ŸLecture DVDs: 102 Steele, Box G ŸCourse load: keep track of hours ŸCourse ombuds: Wednesday 27 Sep 04 R. M. Murray, Caltech CDS 2

CDS 101/110 Instructional Staff Lecturer: Richard Murray (CDS) Co-Instructors ŸAnand Asthagiri (Ch. E) ŸTim Colonius (ME) ŸAli Hajimiri (EE) ŸSteven Low (CS/EE) ŸHideo Mabuchi (Ph/CDS) Murray Asthagiri Colonius Hajimiri Low Mabuchi Head TA: Steve Waydo (CDS) TAs ŸDomitilla Del Vecchio ŸAsa Hopkins ŸHaomiao “H” Huang ŸHao Jiang ŸMorr Mehyar/Kevin Tang 27 Sep 04 Domitilla Steve Hao R. M. Murray, Caltech CDS Asa Morr H Kevin 3

Mud Cards Mud cards Ÿ 3 x 5 cards passed out at beginning of each lecture ŸDescribe “muddiest” part of the lecture (or other questions) ŸTurn in cards at end of class ŸResponses posted on FAQ list by 8 pm on the day of the lecture (make sure to look!) Class FAQ list ŸSearchable database of responses to mud cards and other frequently asked questions in the class 27 Sep 04 What does closed loop mean? You used this term without defining it. FAQ R. M. Murray, Caltech CDS 4

What is Feedback? Miriam Webster: the return to the input of a part of the output of a machine, system, or process (as for producing changes in an electronic circuit that improve performance or in an automatic control device that provide self-corrective action) [1920] Feedback = mutual interconnection of two (or more) systems ŸSystem 1 affects system 2 ŸSystem 2 affects system 1 ŸCause and effect is tricky; systems are mutually dependent Feedback is ubiquitous in natural and engineered systems 27 Sep 04 System 1 System 2 Terminology System 1 R. M. Murray, Caltech CDS System 2 Closed Loop Open Loop 5

Example #1: Flyball Governor “Flyball” Governor (1788) Ÿ Regulate speed of steam engine Ÿ Reduce effects of variations in load (disturbance rejection) Ÿ Major advance of industrial revolution Balls fly out as speed increases, Valve closes, slowing engine Steam engine Boulton-Watt steam engine 27 Sep 04 Flyball governor http: //www. heeg. de/~roland/Steam. Engine. html R. M. Murray, Caltech CDS 6

Other Examples of Feedback Biological Systems ŸPhysiological regulation (homeostasis) ŸBio-molecular regulatory networks Environmental Systems ŸMicrobial ecosystems ŸGlobal carbon cycle Financial Systems ŸMarkets and exchanges ŸSupply and service chains 27 Sep 04 ESE R. M. Murray, Caltech CDS 7

Control = Sensing + Computation + Actuation In Feedback “Loop” Actuate Sense Gas Pedal Vehicle Speed Compute Control “Law” Goals ŸStability: system maintains desired operating point (hold steady speed) ŸPerformance: system responds rapidly to changes (accelerate to 6 m/sec) ŸRobustness: system tolerates perturbations in dynamics (mass, drag, etc) 27 Sep 04 R. M. Murray, Caltech CDS 8

Two Main Principles of Feedback Robustness to Uncertainty through Feedback ŸFeedback allows high performance in the presence of uncertainty ŸExample: repeatable performance of amplifiers with 5 X component variation ŸKey idea: accurate sensing to compare actual to desired, correction through computation and actuation Design of Dynamics through Feedback ŸFeedback allows the dynamics (behavior) of a system to be modified ŸExample: stability augmentation for highly agile, unstable aircraft ŸKey idea: interconnection gives closed loop that modifies natural behavior 27 Sep 04 R. M. Murray, Caltech CDS X-29 experimental aircraft 9

Example #2: Speed Control disturbance “Bob” reference velocity ® 1 as k ®¥ ® 0 as k ®¥ time 27 Sep 04 + - Control + System Stability/performance ŸSteady state velocity approaches desired velocity as k ® ¥ ŸSmooth response; no overshoot or oscillations Disturbance rejection ŸEffect of disturbances (eg, hills) approaches zero as k ® ¥ Robustness ŸResults don’t depend on the specific values of b, m or k, for k sufficiently large R. M. Murray, Caltech CDS 10

Example #3: Insect Flight SENSING neural superposition eyes hind wing gyroscopes (halteres) specialized “power” muscles two wings (di-ptera) ACTUATION COMPUTATION ~500, 000 neurons 27 Sep 04 More information: Ÿ M. D. Dickinson, Solving the mystery of insect flight, Scientific American, June 2001 Ÿ CDS 101 seminar : Friday, 10 Oct 03 R. M. Murray, Caltech CDS 11

Control Tools MATLAB Toolboxes Modeling Ÿ SIMULINK ŸInput/output representations for subsystems + Ÿ Control System interconnection rules Ÿ Neural Network ŸSystem identification theory and algorithms ŸTheory and algorithms for reduced order modeling Ÿ Data Acquisition Ÿ Optimization + model reduction Analysis ŸStability of feedback systems, including robustness “margins” ŸPerformance of input/output systems (disturbance rejection, robustness) Synthesis ŸConstructive tools for design of feedback systems ŸConstructive tools for signal processing and estimation (Kalman filters) 27 Sep 04 R. M. Murray, Caltech CDS Ÿ Fuzzy Logic Ÿ Robust Control Ÿ Instrument Control Ÿ Signal Processing Ÿ LMI Control Ÿ Statistics Ÿ Model Predictive Control Ÿ System Identification Ÿ µ-Analysis and Synthesis 12

Overview of the Course Wk Mon/Wed Fri 1 Introduction to Feedback and Control MATLAB tutorial, Steve W. 2 System Modeling Linear algebra/ODE review, Steve W. 3 Stability and Performance Control of cavity oscillations, T. Colonius 4 Linear Systems Internet Congestion Control, S. Low 5 Controllability and Observability Midterm exam Review for midterm, Steve W. 6 Transfer Functions Piloted flight, D. Mc. Ruer (tentative) 7 Loop Analysis of Feedback Systems Stability in Electronic Circuits, A. Hajimiri 8 Frequency Domain Design Molecular Feedback Mechanisms, A. Asthagiri 9 Limits on Performance Thanksgiving holiday 10 Uncertainty Analysis and Robustness Final exam Review for final, TBD 27 Sep 04 R. M. Murray, Caltech CDS 13

Summary: Introduction to Feedback and Control Actuate Sense Control = Sensing + Computation + Actuation Feedback Principles ŸRobustness to Uncertainty ŸDesign of Dynamics Compute Many examples of feedback and control in natural & engineered systems: BIO ESE CS 27 Sep 04 R. M. Murray, Caltech CDS 14

What’s Next week: System Modeling Homework problems: due 10/6 Ÿ Define what a model is and what types Ÿ 5 examples of control systems of questions it can be used to answer ŸMATLAB cruise control example Ÿ Introduce the concepts of state, (hint: get this running now) dynamic, and inputs ŸCDS 110: steady cam example plus Ÿ Provide examples of common modeling more MATLAB techniques Ÿ Describe common modeling tradeoffs Wednesday: 1 -3 pm, 74 JRG ŸReview of linear algebra and ODEs Friday: 2 -3 pm, 74 JRG ŸMATLAB tutorial – plan on attending if you have never used MATLAB before Don’t forget to fill out MUD CARDS

Welcome to CDS 101 – Design and Analysis of Feedback Systems CDS 110 a – Introductory Control Theory Instructor: Richard M. Murray PICK UP HANDOUTSIDE OF LECTURE HALL 27 Sep 04 R. M. Murray, Caltech CDS 16