Robust and Optimal Control, Spring A: SISO Feedback Control A.1 Internal Stability and Youla Parameterization


 Grant Summers
 2 years ago
 Views:
Transcription
1 Robust and Optimal Control, Spring 2015 Instructor: Prof. Masayuki Fujita (S5303B) A: SISO Feedback Control A.1 Internal Stability and Youla Parameterization A.2 Sensitivity and Feedback Performance A.3 Loop Shaping [SP05, Sec. 3.2, 4.1.5, 4.7, 4.8] [SP05, Sec. 2.2, 5.2] [SP05, Sec. 2.4, 2.6] Reference: [SP05] S. Skogestad and I. Postlethwaite, Multivariable Feedback Control; Analysis and Design, Second Edition, Wiley, 2005.
2 Internal Stability Gang of Four [AM08, p. 317] Sensitivity Complementary Sensitivity Load Sensitivity Noise Sensitivity [AM08] K.J. Astrom and R.M. Murray, Feedback Systems, Princeton University Press,
3 Internal Stability [SP05, Ex. 4.16] (p. 144) Sensitivity Load Sensitivity Comp. Sensitivity Noise Sensitivity Stable? Step Response Unstable Time [s] Time [s] Time [s] Time [s] 3
4 Internal Stability [SP05, Theorem 4.6] (p. 145) The feedback system in the above figure is internally stable if and only if all Gang of Four ( ) are stable Wellposedness: (Gang of Four: welldefined and proper) C. Desoer C.A. Desoer and W.S. Chan, Journal of the Franklin Institute, 300 (56) ,
5 Youla Parameterization ( Parameterization) Case 1: Stable Plant [SP05, p. 148] All Stabilizing Controllers: Internal Model Control (IMC) Structure parameter Gang of Four : Proper Stable Transfer Function 5
6 Youla Parameterization Case 2: Unstable Plant Coprime Factorization [SP05, p. 122] [SP05, p. 149] Coprime: No common righthalf plane(rhp) zeros : Proper Stable Transfer Functions [SP05, Ex. 4.1] (*) Bezout Identity : Coprime : Proper Stable Transfer Functions [SP05, Ex.] : (*) [Ex.] : Integer : Integer 6
7 Youla Parameterization Case 2: Unstable Plants [SP05, p. 149] A Stabilizing Controller [SP05, Ex.] All Stabilizing Controllers Gang of Four Affine Functions of 7
8 Sensitivity and Feedback Performance Disturbance Attenuation Openloop Closedloop : Sensitivity small: good Feedback Performance 8
9 Insensitivity to Plant Variations [SP05, p. 23] small : good Feedback Performance 9
10 Benefits of Feedback Disturbance Attenuation Insensitivity to Plant Variations Stabilization (Unstable Plant) Linearizing Effects Reference Tracking : small Twodegreesoffreedom Control Feedback + Feedforward 10
11 Waterbed Effects [SP05, p. 167] There exists a frequency range over which the magnitude of the sensitivity function exceeds 1 if it is to be kept below 1 at the other frequency range. [db] [SP05, Ex., p. 170] Frequency [rad/s] (unstable) 11
12 Maximum Peaks of Sensitivity and [SP05, p. 36] Complementary Sensitivity : Maximum Peak Magnitude of : Maximum Peak Magnitude of : Bandwidth Frequency of : Bandwidth Frequency of 12
13 Loop Shaping Loop Transfer Function Sensitivity: Comp. Sensitivity: + Constraint large Loop Shaping small Closedloop Open Loop small small Stability, Performance, Robustness 13
14 Loop Transfer Function [SP05, Ex. 2.4] (p. 34) Gain Crossover Frequency Stability Margins [SP05, p. 32] Gain Margin Phase Margin Time Delay Margin Stability Margin [SP05, Ex. 2.4] (p. 34) 14
15 Frequency Domain Performance [SP05, Ex. 2.4] (p. 34) Maximum Peak Criteria [SP05, p. 36] [Ex.] [Ex.] 15
16 Bode Gainphase Relationship [SP05, p. 18] (minimum phase systems) Slope of the Gain Curve at Steep Slope: Small Phase Margin [SP05, Ex., p. 20]
17 Fundamental Limitations Bound on the Crossover Frequency [SP05, pp. 183] RHP (Right halfplane) Zero Fast RHP Zeros ( large): Loose Restrictions Slow RHP Zeros ( small): Tight Restrictions Im worse better Time Delay 0 z Unstable zero Step Response Re Frequency [rad/s] Time [s]
18 Fundamental Limitations Bound on the Crossover Frequency RHP (Right halfplane) Pole [SP05, pp. 192, 194] Slow RHP Poles ( small): Loose Restrictions Fast RHP Poles ( large): Tight Restrictions Frequency [rad/s] Poles on imaginary axis Im better worse 0 p Re Unstable pole
19 SISO Loop Shaping [SP05, pp. 41, 42, 343] Performance Robust Stability (+ Rolloff) Loop Shaping Specifications Gain Crossover Frequency Shape of System Type, Defined as the Number of Pure Integrators in Rolloff at Higher Frequencies 19
20 Step response analysis/performance criteria Rise time Settling time Peak time Overshoot Error tolerance Firstorder System Secondorder System Rise time Settling time Rise time Settling time Overshoot Overshoot Peak Time [QZ07] L. Qiu and K. Zhou (2007) Introduction to Feedback Control, Prentice Hall. 20
21 Design Relations Maximum Peak Magnitude of Complementary Sensitivity Phase Margin Bandwidth if if if : Maximum Peak Magnitude of : Bandwidth Frequency of [FPN09] G.F. Franklin, J.D. Powell and A. E.Naeini (2009) Feedback Control of Dynamic Systems, Sixth Edition, Prentice Hall. 21
22 Controllability analysis with SISO feedback control [SP05, pp ] Margin to stay within constraints Margin for performance Margin because of RHPpole Margin because of RHPzero Margin because of frequency where plant has phase lag Margin because of delay Typically, the closedloop bandwidth of the spacecraft is an order of magnitude less than the lowest mode frequency, and as long as the controller does not excite any of the flexible modes, the sampling period may be selected solely based on the closedloop bandwidth. [Le10] W.S. Levine (Eds.) (2010) The Control Handbook, Second Edition: Control System Fundamentals, Second Edition, CRC Press. 22
23 RHP Poles/Zeros, Time Delays and Sensitivity p z M S For systems with a RHP pole and RHP zero (or a time delay τ ), any stabilizing controller gives sensitivity functions with the property = sup S( jω) ω p p + z z M T = supt ( jω) ω e pτ RHP pole and zero and time delay significantly limit the achievable performance of a system S( jω) M S p p + z z M T T ( jω) pτ e 9
24 RHP Poles/Zeros, Time Delays and Sensitivity Allpass system( p =1, z = b, τ ) sτ b s e P ap ( s) = P ( ) = s ap s 1 s 1 z or 6 < z / p pτ < 0. 3 / p <1/ RHP pole/zero pair 6 The zero and the pole must be sufficiently far apart P allowable phase lag of at : ap ω RHP pole and time delay The product of RHP pole and time delay must be sufficiently small gc ϕ l = 90 10
Robust Control. 2nd class. Spring, 2018 Instructor: Prof. Masayuki Fujita (S5303B) Tue., 17th April, 2018, 10:45~12:15, S423 Lecture Room
Robust Control Spring, 2018 Instructor: Prof. Masayuki Fujita (S5303B) 2nd class Tue., 17th April, 2018, 10:45~12:15, S423 Lecture Room 2. Nominal Performance 2.1 Weighted Sensitivity [SP05, Sec. 2.8,
More informationRobust Control. 1st class. Spring, 2017 Instructor: Prof. Masayuki Fujita (S5303B) Tue., 11th April, 2017, 10:45~12:15, S423 Lecture Room
Robust Control Spring, 2017 Instructor: Prof. Masayuki Fujita (S5303B) 1st class Tue., 11th April, 2017, 10:45~12:15, S423 Lecture Room Reference: [H95] R.A. Hyde, Aerospace Control Design: A VSTOL Flight
More informationLet the plant and controller be described as:
Summary of Fundamental Limitations in Feedback Design (LTI SISO Systems) From Chapter 6 of A FIRST GRADUATE COURSE IN FEEDBACK CONTROL By J. S. Freudenberg (Winter 2008) Prepared by: Hammad Munawar (Institute
More informationChapter Eleven. Frequency Domain Design Sensitivity Functions
Feedback Systems by Astrom and Murray, v2.11b http://www.cds.caltech.edu/~murray/fbswiki Chapter Eleven Frequency Domain Design Sensitivity improvements in one frequency range must be paid for with sensitivity
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 informationMEM 355 Performance Enhancement of Dynamical Systems
MEM 355 Performance Enhancement of Dynamical Systems Frequency Domain Design Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University 5/8/25 Outline Closed Loop Transfer Functions
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 informationThe loop shaping paradigm. Lecture 7. Loop analysis of feedback systems (2) Essential specifications (2)
Lecture 7. Loop analysis of feedback systems (2). Loop shaping 2. Performance limitations The loop shaping paradigm. Estimate performance and robustness of the feedback system from the loop transfer L(jω)
More informationAutomatic Control 2. Loop shaping. Prof. Alberto Bemporad. University of Trento. Academic year
Automatic Control 2 Loop shaping Prof. Alberto Bemporad University of Trento Academic year 21211 Prof. Alberto Bemporad (University of Trento) Automatic Control 2 Academic year 21211 1 / 39 Feedback
More informationControl Systems 2. Lecture 4: Sensitivity function limits. Roy Smith
Control Systems 2 Lecture 4: Sensitivity function limits Roy Smith 2017314 4.1 Inputoutput controllability Control design questions: 1. How well can the plant be controlled? 2. What control structure
More informationRobust Control 3 The Closed Loop
Robust Control 3 The Closed Loop Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University /2/2002 Outline Closed Loop Transfer Functions Traditional Performance Measures Time
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 informationRobust Performance Example #1
Robust Performance Example # The transfer function for a nominal system (plant) is given, along with the transfer function for one extreme system. These two transfer functions define a family of plants
More informationCDS 101/110a: Lecture 81 Frequency Domain Design
CDS 11/11a: Lecture 81 Frequency Domain Design Richard M. Murray 17 November 28 Goals: Describe canonical control design problem and standard performance measures Show how to use loop shaping to achieve
More informationOutline. Classical Control. Lecture 1
Outline Outline Outline 1 Introduction 2 Prerequisites Block diagram for system modeling Modeling Mechanical Electrical Outline Introduction Background Basic Systems Models/Transfers functions 1 Introduction
More informationClosedloop system 2/1/2016. Generally MIMO case. Twodegreesoffreedom (2 DOF) control structure. (2 DOF structure) The closed loop equations become
Closedloop system enerally MIMO case Twodegreesoffreedom (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 informationReturn Difference Function and ClosedLoop Roots SingleInput/SingleOutput Control Systems
Spectral Properties of Linear Quadratic Regulators Robert Stengel Optimal Control and Estimation MAE 546 Princeton University, 2018! Stability margins of singleinput/singleoutput (SISO) systems! Characterizations
More informationControl System Design
ELEC ENG 4CL4: Control System Design Notes for Lecture #11 Wednesday, January 28, 2004 Dr. Ian C. Bruce Room: CRL229 Phone ext.: 26984 Email: ibruce@mail.ece.mcmaster.ca Relative Stability: Stability
More informationHomework 7  Solutions
Homework 7  Solutions Note: This homework is worth a total of 48 points. 1. Compensators (9 points) For a unity feedback system given below, with G(s) = K s(s + 5)(s + 11) do the following: (c) Find the
More informationControl Systems I Lecture 10: System Specifications
Control Systems I Lecture 10: System Specifications Readings: Guzzella, Chapter 10 Emilio Frazzoli Institute for Dynamic Systems and Control DMAVT ETH Zürich November 24, 2017 E. Frazzoli (ETH) Lecture
More informationIntroduction. Performance and Robustness (Chapter 1) Advanced Control Systems Spring / 31
Introduction Classical Control Robust Control u(t) y(t) G u(t) G + y(t) G : nominal model G = G + : plant uncertainty Uncertainty sources : Structured : parametric uncertainty, multimodel uncertainty Unstructured
More informationRobust Control. 8th class. Spring, 2018 Instructor: Prof. Masayuki Fujita (S5303B) Tue., 29th May, 2018, 10:45~11:30, S423 Lecture Room
Robust Control Spring, 2018 Instructor: Prof. Masayuki Fujita (S5303B) 8th class Tue., 29th May, 2018, 10:45~11:30, S423 Lecture Room 1 8. Design Example 8.1 HiMAT: Control (Highly Maneuverable Aircraft
More informationStability of CL System
Stability of CL System Consider an open loop stable system that becomes unstable with large gain: At the point of instability, K( j) G( j) = 1 0dB K( j) G( j) K( j) G( j) K( j) G( j) =± 180 o 180 o Closed
More informationUse of Monte Carlo Techniques in Robustness Evaluation of Different Temperature Control Methods of Heated Plates. SC Solutions
Use of Monte Carlo Techniques in Robustness Evaluation of Different Temperature Control Methods of Heated Plates Dick de Roover, A. EmamiNaeini, J. L. Ebert, G.W. van der Linden, L. L. Porter and R. L.
More informationFrequency methods for the analysis of feedback systems. Lecture 6. Loop analysis of feedback systems. Nyquist approach to study stability
Lecture 6. Loop analysis of feedback systems 1. Motivation 2. Graphical representation of frequency response: Bode and Nyquist curves 3. Nyquist stability theorem 4. Stability margins Frequency methods
More informationChapter 15  Solved Problems
Chapter 5  Solved Problems Solved Problem 5.. Contributed by  Alvaro Liendo, Universidad Tecnica Federico Santa Maria, Consider a plant having a nominal model given by G o (s) = s + 2 The aim of the
More informationRichiami di Controlli Automatici
Richiami di Controlli Automatici Gianmaria De Tommasi 1 1 Università degli Studi di Napoli Federico II detommas@unina.it Ottobre 2012 Corsi AnsaldoBreda G. De Tommasi (UNINA) Richiami di Controlli Automatici
More informationAdditional ClosedLoop Frequency Response Material (Second edition, Chapter 14)
Appendix J Additional ClosedLoop Frequency Response Material (Second edition, Chapter 4) APPENDIX CONTENTS J. ClosedLoop Behavior J.2 Bode Stability Criterion J.3 Nyquist Stability Criterion J.4 Gain
More informationCDS 101/110a: Lecture 101 Robust Performance
CDS 11/11a: Lecture 11 Robust Performance Richard M. Murray 1 December 28 Goals: Describe how to represent uncertainty in process dynamics Describe how to analyze a system in the presence of uncertainty
More informationRobust Loop Shaping Controller Design for Spectral Models by Quadratic Programming
Robust Loop Shaping Controller Design for Spectral Models by Quadratic Programming Gorka Galdos, Alireza Karimi and Roland Longchamp Abstract A quadratic programming approach is proposed to tune fixedorder
More informationChapter 2. Classical Control System Design. Dutch Institute of Systems and Control
Chapter 2 Classical Control System Design Overview Ch. 2. 2. Classical control system design Introduction Introduction Steadystate Steadystate errors errors Type Type k k systems systems Integral Integral
More information1 Loop Control. 1.1 Openloop. ISS0065 Control Instrumentation
Lecture 4 ISS0065 Control Instrumentation 1 Loop Control System has a continuous signal (analog) basic notions: openloop control, closeloop control. 1.1 Openloop Openloop / avatud süsteem / открытая
More informationEE3CL4: Introduction to Linear Control Systems
1 / 30 EE3CL4: Introduction to Linear Control Systems Section 9: of and using Techniques McMaster University Winter 2017 2 / 30 Outline 1 2 3 4 / 30 domain analysis Analyze closed loop using open loop
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 informationExercise 1 (A Nonminimum Phase System)
Prof. Dr. E. Frazzoli 559 Control Systems I (Autumn 27) Solution Exercise Set 2 Loop Shaping clruch@ethz.ch, 8th December 27 Exercise (A Nonminimum Phase System) To decrease the rise time of the system,
More informationToday (10/23/01) Today. Reading Assignment: 6.3. Gain/phase margin lead/lag compensator Ref. 6.4, 6.7, 6.10
Today Today (10/23/01) Gain/phase margin lead/lag compensator Ref. 6.4, 6.7, 6.10 Reading Assignment: 6.3 Last Time In the last lecture, we discussed control design through shaping of the loop gain GK:
More information6.302 Feedback Systems Recitation 16: Compensation Prof. Joel L. Dawson
Bode Obstacle Course is one technique for doing compensation, or designing a feedback system to make the closedloop behavior what we want it to be. To review:  G c (s) G(s) H(s) you are here! plant For
More informationControl System Design
ELEC ENG 4CL4: Control System Design Notes for Lecture #22 Dr. Ian C. Bruce Room: CRL229 Phone ext.: 26984 Email: ibruce@mail.ece.mcmaster.ca Friday, March 5, 24 More General Effects of Open Loop Poles
More informationDesign and Tuning of Fractionalorder PID Controllers for Timedelayed Processes
Design and Tuning of Fractionalorder PID Controllers for Timedelayed Processes Emmanuel Edet Technology and Innovation Centre University of Strathclyde 99 George Street Glasgow, United Kingdom emmanuel.edet@strath.ac.uk
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 informationFEL3210 Multivariable Feedback Control
FEL3210 Multivariable Feedback Control Lecture 5: Uncertainty and Robustness in SISO Systems [Ch.7(8)] Elling W. Jacobsen, Automatic Control Lab, KTH Lecture 5:Uncertainty and Robustness () FEL3210 MIMO
More informationShould we forget the Smith Predictor?
FrBT3. Should we forget the Smith Predictor? Chriss Grimholt Sigurd Skogestad* Abstract: The / controller is the most used controller in industry. However, for processes with large time delays, the common
More informationELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 2010/2011 CONTROL ENGINEERING SHEET 5 LeadLag Compensation Techniques
CAIRO UNIVERSITY FACULTY OF ENGINEERING ELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 00/0 CONTROL ENGINEERING SHEET 5 LeadLag Compensation Techniques [] For the following system, Design a compensator such
More informationECSE 4962 Control Systems Design. A Brief Tutorial on Control Design
ECSE 4962 Control Systems Design A Brief Tutorial on Control Design Instructor: Professor John T. Wen TA: Ben Potsaid http://www.cat.rpi.edu/~wen/ecse4962s04/ Don t Wait Until The Last Minute! You got
More informationECE 486 Control Systems
ECE 486 Control Systems Spring 208 Midterm #2 Information Issued: April 5, 208 Updated: April 8, 208 ˆ This document is an info sheet about the second exam of ECE 486, Spring 208. ˆ Please read the following
More informationDESIGN USING TRANSFORMATION TECHNIQUE CLASSICAL METHOD
206 Spring Semester ELEC733 Digital Control System LECTURE 7: DESIGN USING TRANSFORMATION TECHNIQUE CLASSICAL METHOD For a unit ramp input Tz Ez ( ) 2 ( z ) D( z) G( z) Tz e( ) lim( z) z 2 ( z ) D( z)
More informationTopic # Feedback Control Systems
Topic #20 16.31 Feedback Control Systems Closedloop system analysis Bounded Gain Theorem Robust Stability Fall 2007 16.31 20 1 SISO Performance Objectives Basic setup: d i d o r u y G c (s) G(s) n control
More informationExercise 1 (A Nonminimum Phase System)
Prof. Dr. E. Frazzoli 559 Control Systems I (HS 25) Solution Exercise Set Loop Shaping Noele Norris, 9th December 26 Exercise (A Nonminimum Phase System) To increase the rise time of the system, we
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 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 informationThe parameterization of all. of all twodegreeoffreedom strongly stabilizing controllers
The parameterization stabilizing controllers 89 The parameterization of all twodegreeoffreedom strongly stabilizing controllers Tatsuya Hoshikawa, Kou Yamada 2, Yuko Tatsumi 3, Nonmembers ABSTRACT
More informationChapter 7  Solved Problems
Chapter 7  Solved Problems Solved Problem 7.1. A continuous time system has transfer function G o (s) given by G o (s) = B o(s) A o (s) = 2 (s 1)(s + 2) = 2 s 2 + s 2 (1) Find a controller of minimal
More informationInputoutput Controllability Analysis
Inputoutput Controllability Analysis Idea: Find out how well the process can be controlled  without having to design a specific controller Note: Some processes are impossible to control Reference: S.
More informationRaktim Bhattacharya. . AERO 422: Active Controls for Aerospace Vehicles. Frequency ResponseDesign Method
.. AERO 422: Active Controls for Aerospace Vehicles Frequency Response Method Raktim Bhattacharya Laboratory For Uncertainty Quantification Aerospace Engineering, Texas A&M University. ... Response to
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 informationEngraving Machine Example
Engraving Machine Example MCE44  Fall 8 Dr. Richter November 24, 28 Basic Design The Xaxis of the engraving machine has the transfer function G(s) = s(s + )(s + 2) In this basic example, we use a proportional
More informationMethods for analysis and control of dynamical systems Lecture 4: The root locus design method
Methods for analysis and control of Lecture 4: The root locus design method O. Sename 1 1 Gipsalab, CNRSINPG, FRANCE Olivier.Sename@gipsalab.inpg.fr www.gipsalab.fr/ o.sename 5th February 2015 Outline
More informationIan G. Horn, Jeffery R. Arulandu, Christopher J. Gombas, Jeremy G. VanAntwerp, and Richard D. Braatz*
Ind. Eng. Chem. Res. 996, 35, 3437344 3437 PROCESS DESIGN AND CONTROL Improved Filter Design in Internal Model Control Ian G. Horn, Jeffery R. Arulandu, Christopher J. Gombas, Jeremy G. VanAntwerp, and
More informationKars Heinen. Frequency analysis of reset systems containing a Clegg integrator. An introduction to higher order sinusoidal input describing functions
Frequency analysis of reset systems containing a Clegg integrator An introduction to higher order sinusoidal input describing functions Delft Center for Systems and Control Frequency analysis of reset
More informationTable of Laplacetransform
Appendix Table of Laplacetransform pairs 1(t) f(s) oct), unit impulse at t = 0 a, a constant or step of magnitude a at t = 0 a s t, a ramp function e at, an exponential function s + a sin wt, a sine fun
More informationTradeoffs and Limits of Performance
Chapter 9 Tradeoffs and Limits of Performance 9. Introduction Fundamental limits of feedback systems will be investigated in this chapter. We begin in Section 9.2 by discussing the basic feedback loop
More information9. TwoDegreesofFreedom Design
9. TwoDegreesofFreedom Design In some feedback schemes we have additional degreesoffreedom outside the feedback path. For example, feed forwarding known disturbance signals or reference signals. In
More informationClassify a transfer function to see which order or ramp it can follow and with which expected error.
Dr. J. Tani, Prof. Dr. E. Frazzoli 505900 Control Systems I (Autumn 208) Exercise Set 0 Topic: Specifications for Feedback Systems Discussion: 30.. 208 Learning objectives: The student can grizzi@ethz.ch,
More informationMethods for analysis and control of. Lecture 4: The root locus design method
Methods for analysis and control of Lecture 4: The root locus design method O. Sename 1 1 Gipsalab, CNRSINPG, FRANCE Olivier.Sename@gipsalab.inpg.fr www.lag.ensieg.inpg.fr/sename Lead Lag 17th March
More informationDesign Methods for Control Systems
Design Methods for Control Systems Maarten Steinbuch TU/e Gjerrit Meinsma UT Dutch Institute of Systems and Control Winter term 20022003 Schedule November 25 MSt December 2 MSt Homework # 1 December 9
More informationFeedback Control of Linear SISO systems. Process Dynamics and Control
Feedback Control of Linear SISO systems Process Dynamics and Control 1 OpenLoop Process The study of dynamics was limited to openloop systems Observe process behavior as a result of specific input signals
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 informationA Comparative Study on Automatic Flight Control for small UAV
Proceedings of the 5 th International Conference of Control, Dynamic Systems, and Robotics (CDSR'18) Niagara Falls, Canada June 7 9, 18 Paper No. 13 DOI: 1.11159/cdsr18.13 A Comparative Study on Automatic
More informationAnalysis and Design of Analog Integrated Circuits Lecture 12. Feedback
Analysis and Design of Analog Integrated Circuits Lecture 12 Feedback Michael H. Perrott March 11, 2012 Copyright 2012 by Michael H. Perrott All rights reserved. Open Loop Versus Closed Loop Amplifier
More informationAchievable performance of multivariable systems with unstable zeros and poles
Achievable performance of multivariable systems with unstable zeros and poles K. Havre Λ and S. Skogestad y Chemical Engineering, Norwegian University of Science and Technology, N7491 Trondheim, Norway.
More informationMAE 142 Homework #5 Due Friday, March 13, 2009
MAE 142 Homework #5 Due Friday, March 13, 2009 Please read through the entire homework set before beginning. Also, please label clearly your answers and summarize your findings as concisely as possible.
More informationSystems Analysis and Control
Systems Analysis and Control Matthew M. Peet Arizona State University Lecture 21: Stability Margins and Closing the Loop Overview In this Lecture, you will learn: Closing the Loop Effect on Bode Plot Effect
More informationCHAPTER 7 : BODE PLOTS AND GAIN ADJUSTMENTS COMPENSATION
CHAPTER 7 : BODE PLOTS AND GAIN ADJUSTMENTS COMPENSATION Objectives Students should be able to: Draw the bode plots for first order and second order system. Determine the stability through the bode plots.
More informationUniversity of Science and Technology, Sudan Department of Chemical Engineering.
ISO 91:28 Certified Volume 3, Issue 6, November 214 Design and Decoupling of Control System for a Continuous Stirred Tank Reactor (CSTR) Georgeous, N.B *1 and Gasmalseed, G.A, Abdalla, B.K (12) University
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 informationCHBE320 LECTURE XI CONTROLLER DESIGN AND PID CONTOLLER TUNING. Professor Dae Ryook Yang
CHBE320 LECTURE XI CONTROLLER DESIGN AND PID CONTOLLER TUNING Professor Dae Ryook Yang Spring 2018 Dept. of Chemical and Biological Engineering 111 Road Map of the Lecture XI Controller Design and PID
More informationA Design Method for Smith Predictors for MinimumPhase TimeDelay Plants
00 ECTI TRANSACTIONS ON COMPUTER AND INFORMATION TECHNOLOGY VOL., NO.2 NOVEMBER 2005 A Design Method for Smith Predictors for MinimumPhase TimeDelay Plants Kou Yamada Nobuaki Matsushima, Nonmembers
More information] [ 200. ] 3 [ 10 4 s. [ ] s + 10 [ P = s [ 10 8 ] 3. s s (s 1)(s 2) series compensator ] 2. s command prefilter [ 0.
EEE480 Exam 2, Spring 204 A.A. Rodriguez Rules: Calculators permitted, One 8.5 sheet, closed notes/books, open minds GWC 352, 965372 Problem (Analysis of a Feedback System) Consider the feedback system
More informationRoot Locus Design Example #4
Root Locus Design Example #4 A. Introduction The plant model represents a linearization of the heading dynamics of a 25, ton tanker ship under empty load conditions. The reference input signal R(s) is
More informationFall 線性系統 Linear Systems. Chapter 08 State Feedback & State Estimators (SISO) FengLi Lian. NTUEE Sep07 Jan08
Fall 2007 線性系統 Linear Systems Chapter 08 State Feedback & State Estimators (SISO) FengLi Lian NTUEE Sep07 Jan08 Materials used in these lecture notes are adopted from Linear System Theory & Design, 3rd.
More informationFrequency Response Techniques
4th Edition T E N Frequency Response Techniques SOLUTION TO CASE STUDY CHALLENGE Antenna Control: Stability Design and Transient Performance First find the forward transfer function, G(s). Pot: K 1 = 10
More informationLecture 1: Feedback Control Loop
Lecture : Feedback Control Loop Loop Transfer function The standard feedback control system structure is depicted in Figure. This represend(t) n(t) r(t) e(t) u(t) v(t) η(t) y(t) F (s) C(s) P (s) Figure
More informationA unified doubleloop multiscale control strategy for NMP integratingunstable systems
Home Search Collections Journals About Contact us My IOPscience A unified doubleloop multiscale control strategy for NMP integratingunstable systems This content has been downloaded from IOPscience.
More informationChapter 9 Robust Stability in SISO Systems 9. Introduction There are many reasons to use feedback control. As we have seen earlier, with the help of a
Lectures on Dynamic Systems and Control Mohammed Dahleh Munther A. Dahleh George Verghese Department of Electrical Engineering and Computer Science Massachuasetts Institute of Technology c Chapter 9 Robust
More informationVibration and motion control design and tradeoff for highperformance mechatronic systems
Proceedings of the 2006 IEEE International Conference on Control Applications Munich, Germany, October 46, 2006 WeC11.5 Vibration and motion control design and tradeoff for highperformance mechatronic
More informationControl Systems. Root Locus & Pole Assignment. L. Lanari
Control Systems Root Locus & Pole Assignment L. Lanari Outline rootlocus definition main rules for hand plotting root locus as a design tool other use of the root locus pole assignment Lanari: CS  Root
More informationLoop shaping exercise
Loop shaping exercise Excerpt 1 from Controlli Automatici  Esercizi di Sintesi, L. Lanari, G. Oriolo, EUROMA  La Goliardica, 1997. It s a generic book with some typical problems in control, not a collection
More informationAndrea Zanchettin Automatic Control AUTOMATIC CONTROL. Andrea M. Zanchettin, PhD Spring Semester, Linear systems (frequency domain)
1 AUTOMATIC CONTROL Andrea M. Zanchettin, PhD Spring Semester, 2018 Linear systems (frequency domain) 2 Motivations Consider an LTI system Thanks to the Lagrange s formula we can compute the motion of
More informationChapter 5 The SIMC Method for Smooth PID Controller Tuning
Chapter 5 The SIMC Method for Smooth PID Controller Tuning Sigurd Skogestad and Chriss Grimholt 5.1 Introduction Although the proportionalintegralderivative (PID) controller has only three parameters,
More informationMULTILOOP CONTROL APPLIED TO INTEGRATOR MIMO. PROCESSES. A Preliminary Study
MULTILOOP CONTROL APPLIED TO INTEGRATOR MIMO PROCESSES. A Preliminary Study Eduardo J. Adam 1,2*, Carlos J. Valsecchi 2 1 Instituto de Desarrollo Tecnológico para la Industria Química (INTEC) (Universidad
More informationControl System Design
ELEC ENG 4CL4: Control System Design Notes for Lecture #15 Friday, February 6, 2004 Dr. Ian C. Bruce Room: CRL229 Phone ext.: 26984 Email: ibruce@mail.ece.mcmaster.ca (3) CohenCoon Reaction Curve Method
More informationProblem Set 4 Solution 1
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.245: MULTIVARIABLE CONTROL SYSTEMS by A. Megretski Problem Set 4 Solution Problem 4. For the SISO feedback
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 informationWind Turbine Control
Wind Turbine Control W. E. Leithead University of Strathclyde, Glasgow Supergen Student Workshop 1 Outline 1. Introduction 2. Control Basics 3. General Control Objectives 4. Constant Speed Pitch Regulated
More informationRELAY CONTROL WITH PARALLEL COMPENSATOR FOR NONMINIMUM PHASE PLANTS. Ryszard Gessing
RELAY CONTROL WITH PARALLEL COMPENSATOR FOR NONMINIMUM PHASE PLANTS Ryszard Gessing Politechnika Śl aska Instytut Automatyki, ul. Akademicka 16, 44101 Gliwice, Poland, fax: +4832 372127, email: gessing@ia.gliwice.edu.pl
More informationSTABILITY OF CLOSEDLOOP CONTOL SYSTEMS
CHBE320 LECTURE X STABILITY OF CLOSEDLOOP CONTOL SYSTEMS Professor Dae Ryook Yang Spring 2018 Dept. of Chemical and Biological Engineering 101 Road Map of the Lecture X Stability of closedloop control
More informationRobust stability and Performance
122 c Perry Y.Li Chapter 5 Robust stability and Performance Topics: ([ author ] is supplementary source) Sensitivities and internal stability (Goodwin 5.15.4) Modeling Error and Model Uncertainty (Goodwin
More informationAutomatic Control (MSc in Mechanical Engineering) Lecturer: Andrea Zanchettin Date: Student ID number... Signature...
Automatic Control (MSc in Mechanical Engineering) Lecturer: Andrea Zanchettin Date: 29..23 Given and family names......................solutions...................... Student ID number..........................
More informationNyquist Stability Criteria
Nyquist Stability Criteria Dr. Bishakh Bhattacharya h Professor, Department of Mechanical Engineering IIT Kanpur Joint Initiative of IITs and IISc  Funded by MHRD This Lecture Contains Introduction to
More informationTransient Response of a SecondOrder System
Transient Response of a SecondOrder System ECEN 830 Spring 01 1. Introduction In connection with this experiment, you are selecting the gains in your feedback loop to obtain a wellbehaved closedloop
More information