Chapter 2. Classical Control System Design. Dutch Institute of Systems and Control
|
|
- Darren Grant
- 6 years ago
- Views:
Transcription
1 Chapter 2 Classical Control System Design
2 Overview Ch Classical control system design Introduction Introduction Steady-state Steady-state errors errors Type Type k k systems systems Integral Integral control control Frequency Frequency response response plots plots Bode Bode plots plots Classical Classical design design techniques techniques Classical Classical design design specifications specifications Lead, Lead, lag, lag, lead-lag lead-lag compensation compensation Guillemin-Truxal Guillemin-Truxal method method Quantitative Quantitative Feedback Feedback Theory Theory Root Root locus locus Nyquist Nyquist plots plots M- M- and and N-circles N-circles Nichols Nichols plots plots
3 Steady-state errors-1 r + F C P y Tracking behavior: Assume n t rt () = 1() t n! rs ˆ( ) = 1 n 1 s + Response ys $( ) Ls ( ) = ( )$( ) Ls ( ) Fsrs H( s) Tracking error ε ˆ() s = rˆ() s yˆ() s = [1 H()]() s rˆ s
4 Steady-state errors-2 Steady-state tracking error ( n) ε = lim ε( t) = lim sεˆ ( s) = lim t s 0 s 0 If F(s)=1 (no prefilter) then 1 1 H( s) = 1 + Ls ( ) 1 H( s) s n ( n) ε = 1 lim 0 n [1 + ( )] s s L s
5 Type k system A feedback system is of type k if Then Lo () s Ls () =, Lo (0) 0 k s ( n) ε = 1 L s lim s 0 n [1 + ( )] s 0 for 0 n< k n s = lim = 1/ Lo (0) for n k s 0 k = s + Lo () s for n> k k
6 Steady-state errors-3
7 Integral control-1 Integral control: Design the closed-loop system such that Type k control: Ls () = L o k s () s Ls () = Lo () s s Results in good steady-state behavior Also: k 1 s k Ss () = = = O( s ) for s Ls ( ) k s + L () s o
8 Integral control-2 Type k control: Hence if k Ss () = O( s ) for s 0 n t 1 vt () = 1(), t vs ˆ( ) = n! n s + 1 then the steady-state error is zero if n < k (rejection) k = 1: Integral control: Rejection of constant disturbances k = 2: Type-2 control: Rejection of ramp disturbances Etc.
9 Integral control-3 Integral control: Lo () s Ls () = = PsCs () () k s The loop has integrating action of order k Natural integrating action is present if the plant transfer function has one or several poles at 0 If no natural integrating action exists then the compensator needs to provide it
10 Integral control-4 Pure integral control: Cs () = 1 st i PI control: Cs () = g 1+ 1 st i PID control: Cs () = g std st i Ziegler-Nichols tuning rules
11 Internal model principle Asymptotic tracking if model of disturbance is included in the compensator Francis, D.A. and Wonham, W.M., (1975) The internal model principle for linear multivariable regulators, Applied Mathematics and Optimization, vol 2, pp
12 Frequency response plots Bode plots Nichols plots Nyquist plots
13 Bode plots-1 Bode plot: doubly logarithmic plot of L(jω) versus ω semi logarithmic plot of arg L(jω) versus ω L( jω ) = 2 ωo o o j + o ( jω ) 2 ζ ω ( ω) ω
14 Bode plots-2 Helpful technique: By construction of the asymptotic Bode plots of elementary first- and second-order factors of the form The shape of the Bode plot of ( jω z1)( jω z2) L( jω zm ) L( jω ) = k ( j ω p )( j ω p ) L( j ω p ) o o jω + α and ( jω) + 2 ζ ω ( jω) + ω may be sketched m
15 Nyquist plots Nyquist plot: Locus of L(jω) in the complex plane with ω as parameter Contains less information than the Bode plot if ω is not marked along the locus L( jω ) = 2 ωo o o j + o ( jω ) 2 ζ ω ( ω) ω
16 M- and N-circles-1 r + L y Closed-loop transfer function: H L = = T 1 + L M-circle: Locus of points z in the complex plane where z = M 1+ z N-circle: Locus of points z in the complex plane where arg z 1+ z = N
17 M- and N-circles-2
18 Nichols plots Nichols plot: Locus of L(jω) with ω as parameter in the log magnitude versus argument plane 2 ωo o o j + o L( jω ) = ( jω) 2 ζ ω ( ω) ω Nichols chart: Nichols plot with M- and N-loci included
19 Classical design specifications Time Rise time, delay time, overshoot, settling time, steady-state error of the response to step reference and disturbance inputs; error constants domain domain Frequency Bandwidth, resonance peak, roll-on and roll-off of the closed-loop frequency response and sensitivity functions; stability margins
20 Classical design techniques Lead, lag, and lag-lead compensation (loopshaping) (Root locus approach) (Guillemin-Truxal design procedure) Quantitative feedback theory QFT (robust loopshaping)
21 Classical design techniques Rules for loopshaping Change open-loop L(s) to achieve certain closed-loop specs first modify phase then correct gain
22 Lead compensation Lead compensation: Add extra phase in the cross-over region to improve the stability margins Typical compensator: Phase-advance network 1+ jωt C( jω) = α, 0< α < 1 1+ jωα T
23 Lead/lag compensator C( jω) = α 1+ jωt 1+ jωα T
24 Lag compensation Lag compensation: Increase the low frequency gain without affecting the phase in the cross-over region Example: PI-control: C( jω ) = k 1+ jωt jωt
25 Lead-lag compensation Lead-lag compensation: Joint use of lag compensation at low frequencies phase lead compensation at crossover Lead, lag, and lead-lag compensation are always used in combination with gain adjustment
26 Notch compensation (inverse) Notch filters: suppression of parasitic dynamics additional gain at specific frequencies Special form of general second order filter
27 Notch compensation H = u ε = s ω s ω β + 2β 1 2 s ω s ω Notch -filter :ω 1 = ω 2
28 Notch compensation ampl. β β 1 2 fase 0
29 Root locus method-1 Important stage of many designs: Fine tuning of gain compensator pole and zero locations Helpful approach: the root locus method (use rltool!)
30 Root locus method-2 Ls () N() s ( s z1)( s z2) L( s zm ) = = k D() s ( s p )( s p ) L( s p ) 1 2 n L Closed-loop characteristic polynomial χ () s = D() s + N() s = ( s p )( s p ) L( s p ) + k( s z )( s z ) L( s z ) 1 2 n 1 2 Root locus method: Determine the loci of the roots of χ as the gain k varies m
31 Root locus method-3 χ () s = ( s p )( s p ) L( s p ) + k( s z )( s z ) L( s z ) 1 2 n 1 2 Rules: For k = 0 the roots are the open-loop poles p i For k a number m of the roots approach the open-loop zeros z i. The remaining roots approach The directions of the asymptotes of those roots that approach are given by the angles 2i + 1, i 0,1,, n m 1 n m π = L m
32 Root locus method-4 The asymptotes intersect on the real axis in the point (sum of open-loop poles) (sum of open-loop zeros) n m Those sections of the real axis located to the left of an odd total number of open-loop poles and zeros on this axis belong to a locus The loci are symmetric with respect to the real axis...
33 Root locus method-5 Ls () = k ss ( + 2) Ls () = ks ( + 2) ss ( + 1) Ls () = k ss ( + 1)( s+ 2)
34 Guillemin-Truxal method-1 r + C P y Closed-loop transfer function: PC H = 1 + PC Procedure: Specify H Solve the compensator from C 1 H = P 1 H
35 Guillemin-Truxal method-2 Example: Choose H() s = m m 1 ams + am 1s + L+ a0 n n 1 m m 1 + n 1 + L+ m + m 1 + L+ 0 s a s a s a s a This guarantees the system to be of type m + 1 How to choose the denominator polynomial? Well-known options: Butterworth polynomials Optimal ITAE polynomials
36 Butterworth and ITAE polynomials Butterworth polynomials Choose the n left-half plane poles on the unit circle so that together with their right-half plane mirror images they are uniformly distributed along the unit circle ITAE polynomials Place the poles so that () tet dt 0 is minimal, where e is the tracking error for a step input
37 Butterworth and ITAE m = 0
38 Guillemin-Truxal method-3 Disadvantages of the method: Difficult to translate the specs into an unambiguous choice of H. Often experimentation with other design methods is needed to establish what may be achieved. In any case preparatory analysis is required to determine the order of the compensator and to make sure that it is proper The method often results in undesired pole-zero cancellation between the plant and the compensator
39 Quantitative feedback theory QFT-1 Ingredients of QFT: For a number of selected frequencies, represent the uncertainty regions of the plant frequency response in the Nichols chart Specify tolerance bounds on the magnitude of T Shape the loop gain so that the tolerance bounds are never violated
40 QFT-2 Example: Plant Ps () = s 2 g (1 + sθ ) Nominal parameter values: g = 1, θ = 0 Parameter uncertainties: 0.5 g 2, 0 θ 0.2 Tentative compensator: k + std Cs () =, k= 1, Td = 1.414, To = st o
41 QFT-3 Responses of the nominal design Specs on T Frequency [rad/s] Tolerance band [db]
42 Uncertainty regions Uncertainty regions for the nominal design The specs are not satisfied Additional requirement: The critical area may not be entered
43 QFT-4 Design method: Manipulate the compensator frequency reponse so that the loop gain satisfies the tolerance bounds avoids the critical region Preparatory step 1: For each selected frequency, determine the performance boundary Preparatory step 2: For each selectedfrequency, determine the robustness boundary
44 Performance and robustness boundaries Nominal plant frequency response Robustness boundaries Performance boundaries
45 QFT-5 Design step: Modify the loop gain such that for each selected frequency the corresponding point on the loop gain plot lies above and to the right of the corresponding boundary For the case at hand this may be accomplished by a lead compensator of the form 1+ st Cs () = 1 + st Step 1: Set T 2 = 0, vary T 1 Step 2: Keep T 1 fixed, vary T 2 1 2
46 QFT-6 Eventual design: T 1 = 3 T 2 = 0.02
47 QFT-7 Responses of the redesigned system
48 Prefilter design-1 2½-degree-of-freedom configuration Closed-loop transfer function H = NF D cl F o r F o e C o F X Y X + + u P z For the present case: Dcl ( s) = 0.02 ( s ) ( s )( s ) N() s = 1
49 Prefilter design-2 Use the polynomial F to cancel the (slow) pole at , and let 2 ωo Fo ( s) =, ωo = 1, ζo = s + 2ζ ω s+ ω 2 2 Perturbed responses o o o
Automatic 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 21-211 Prof. Alberto Bemporad (University of Trento) Automatic Control 2 Academic year 21-211 1 / 39 Feedback
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 informationCDS 101/110a: Lecture 8-1 Frequency Domain Design
CDS 11/11a: Lecture 8-1 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 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 2002-2003 Schedule November 25 MSt December 2 MSt Homework # 1 December 9
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 informationRaktim Bhattacharya. . AERO 422: Active Controls for Aerospace Vehicles. Basic Feedback Analysis & Design
AERO 422: Active Controls for Aerospace Vehicles Basic Feedback Analysis & Design Raktim Bhattacharya Laboratory For Uncertainty Quantification Aerospace Engineering, Texas A&M University Routh s Stability
More informationSystems Analysis and Control
Systems Analysis and Control Matthew M. Peet Arizona State University Lecture 24: Compensation in the Frequency Domain Overview In this Lecture, you will learn: Lead Compensators Performance Specs Altering
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 5-059-00 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 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 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 D-MAVT ETH Zürich November 24, 2017 E. Frazzoli (ETH) Lecture
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 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 informationKINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING
KINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING QUESTION BANK SUB.NAME : CONTROL SYSTEMS BRANCH : ECE YEAR : II SEMESTER: IV 1. What is control system? 2. Define open
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 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 informationINTRODUCTION TO DIGITAL CONTROL
ECE4540/5540: Digital Control Systems INTRODUCTION TO DIGITAL CONTROL.: Introduction In ECE450/ECE550 Feedback Control Systems, welearnedhow to make an analog controller D(s) to control a linear-time-invariant
More informationROOT LOCUS. Consider the system. Root locus presents the poles of the closed-loop system when the gain K changes from 0 to. H(s) H ( s) = ( s)
C1 ROOT LOCUS Consider the system R(s) E(s) C(s) + K G(s) - H(s) C(s) R(s) = K G(s) 1 + K G(s) H(s) Root locus presents the poles of the closed-loop system when the gain K changes from 0 to 1+ K G ( s)
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 information9. Two-Degrees-of-Freedom Design
9. Two-Degrees-of-Freedom Design In some feedback schemes we have additional degrees-offreedom outside the feedback path. For example, feed forwarding known disturbance signals or reference signals. In
More informationELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 2010/2011 CONTROL ENGINEERING SHEET 5 Lead-Lag Compensation Techniques
CAIRO UNIVERSITY FACULTY OF ENGINEERING ELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 00/0 CONTROL ENGINEERING SHEET 5 Lead-Lag Compensation Techniques [] For the following system, Design a compensator such
More informationExercise 1 (A Non-minimum Phase System)
Prof. Dr. E. Frazzoli 5-59- Control Systems I (Autumn 27) Solution Exercise Set 2 Loop Shaping clruch@ethz.ch, 8th December 27 Exercise (A Non-minimum Phase System) To decrease the rise time of the system,
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 informationRobust fixed-order H Controller Design for Spectral Models by Convex Optimization
Robust fixed-order H Controller Design for Spectral Models by Convex Optimization Alireza Karimi, Gorka Galdos and Roland Longchamp Abstract A new approach for robust fixed-order H controller design by
More informationControl Systems Design
ELEC4410 Control Systems Design Lecture 18: State Feedback Tracking and State Estimation Julio H. Braslavsky julio@ee.newcastle.edu.au School of Electrical Engineering and Computer Science Lecture 18:
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 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 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 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 informationExercise 1 (A Non-minimum Phase System)
Prof. Dr. E. Frazzoli 5-59- Control Systems I (HS 25) Solution Exercise Set Loop Shaping Noele Norris, 9th December 26 Exercise (A Non-minimum Phase System) To increase the rise time of the system, we
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 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 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 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 informationVALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur
VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur 603 203. DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING SUBJECT QUESTION BANK : EC6405 CONTROL SYSTEM ENGINEERING SEM / YEAR: IV / II year
More informationDIGITAL CONTROLLER DESIGN
ECE4540/5540: Digital Control Systems 5 DIGITAL CONTROLLER DESIGN 5.: Direct digital design: Steady-state accuracy We have spent quite a bit of time discussing digital hybrid system analysis, and some
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 informationCDS 101/110a: Lecture 10-1 Robust Performance
CDS 11/11a: Lecture 1-1 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 information6.1 Sketch the z-domain root locus and find the critical gain for the following systems K., the closed-loop characteristic equation is K + z 0.
6. Sketch the z-domain root locus and find the critical gain for the following systems K (i) Gz () z 4. (ii) Gz K () ( z+ 9. )( z 9. ) (iii) Gz () Kz ( z. )( z ) (iv) Gz () Kz ( + 9. ) ( z. )( z 8. ) (i)
More informationAnalysis and Synthesis of Single-Input Single-Output Control Systems
Lino Guzzella Analysis and Synthesis of Single-Input Single-Output Control Systems l+kja» \Uja>)W2(ja»\ um Contents 1 Definitions and Problem Formulations 1 1.1 Introduction 1 1.2 Definitions 1 1.2.1 Systems
More informationFREQUENCY-RESPONSE DESIGN
ECE45/55: Feedback Control Systems. 9 FREQUENCY-RESPONSE DESIGN 9.: PD and lead compensation networks The frequency-response methods we have seen so far largely tell us about stability and stability margins
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 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 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 fixed-order
More information7.4 STEP BY STEP PROCEDURE TO DRAW THE ROOT LOCUS DIAGRAM
ROOT LOCUS TECHNIQUE. Values of on the root loci The value of at any point s on the root loci is determined from the following equation G( s) H( s) Product of lengths of vectors from poles of G( s)h( s)
More information(b) A unity feedback system is characterized by the transfer function. Design a suitable compensator to meet the following specifications:
1. (a) The open loop transfer function of a unity feedback control system is given by G(S) = K/S(1+0.1S)(1+S) (i) Determine the value of K so that the resonance peak M r of the system is equal to 1.4.
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 informationChapter 6 - Solved Problems
Chapter 6 - Solved Problems Solved Problem 6.. Contributed by - James Welsh, University of Newcastle, Australia. Find suitable values for the PID parameters using the Z-N tuning strategy for the nominal
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 information16.30/31, Fall 2010 Recitation # 2
16.30/31, Fall 2010 Recitation # 2 September 22, 2010 In this recitation, we will consider two problems from Chapter 8 of the Van de Vegte book. R + - E G c (s) G(s) C Figure 1: The standard block diagram
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. Root Locus & Pole Assignment. L. Lanari
Control Systems Root Locus & Pole Assignment L. Lanari Outline root-locus definition main rules for hand plotting root locus as a design tool other use of the root locus pole assignment Lanari: CS - Root
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 informationMAE 143B - Homework 9
MAE 43B - Homework 9 7.2 2 2 3.8.6.4.2.2 9 8 2 2 3 a) G(s) = (s+)(s+).4.6.8.2.2.4.6.8. Polar plot; red for negative ; no encirclements of, a.s. under unit feedback... 2 2 3. 4 9 2 2 3 h) G(s) = s+ s(s+)..2.4.6.8.2.4
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 informationRaktim Bhattacharya. . AERO 422: Active Controls for Aerospace Vehicles. Frequency Response-Design 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 informationPlan of the Lecture. Goal: wrap up lead and lag control; start looking at frequency response as an alternative methodology for control systems design.
Plan of the Lecture Review: design using Root Locus; dynamic compensation; PD and lead control Today s topic: PI and lag control; introduction to frequency-response design method Goal: wrap up lead and
More informationEE C128 / ME C134 Fall 2014 HW 6.2 Solutions. HW 6.2 Solutions
EE C28 / ME C34 Fall 24 HW 6.2 Solutions. PI Controller For the system G = K (s+)(s+3)(s+8) HW 6.2 Solutions in negative feedback operating at a damping ratio of., we are going to design a PI controller
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 information7.2 Controller tuning from specified characteristic polynomial
192 Finn Haugen: PID Control 7.2 Controller tuning from specified characteristic polynomial 7.2.1 Introduction The subsequent sections explain controller tuning based on specifications of the characteristic
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 informationIC6501 CONTROL SYSTEMS
DHANALAKSHMI COLLEGE OF ENGINEERING CHENNAI DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING YEAR/SEMESTER: II/IV IC6501 CONTROL SYSTEMS UNIT I SYSTEMS AND THEIR REPRESENTATION 1. What is the mathematical
More informationControl for. Maarten Steinbuch Dept. Mechanical Engineering Control Systems Technology Group TU/e
Control for Maarten Steinbuch Dept. Mechanical Engineering Control Systems Technology Group TU/e Motion Systems m F Introduction Timedomain tuning Frequency domain & stability Filters Feedforward Servo-oriented
More informationR10 JNTUWORLD B 1 M 1 K 2 M 2. f(t) Figure 1
Code No: R06 R0 SET - II B. Tech II Semester Regular Examinations April/May 03 CONTROL SYSTEMS (Com. to EEE, ECE, EIE, ECC, AE) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions carry
More informationModule 3F2: Systems and Control EXAMPLES PAPER 2 ROOT-LOCUS. Solutions
Cambridge University Engineering Dept. Third Year Module 3F: Systems and Control EXAMPLES PAPER ROOT-LOCUS Solutions. (a) For the system L(s) = (s + a)(s + b) (a, b both real) show that the root-locus
More informationTopic # Feedback Control Systems
Topic #19 16.31 Feedback Control Systems Stengel Chapter 6 Question: how well do the large gain and phase margins discussed for LQR map over to DOFB using LQR and LQE (called LQG)? Fall 2010 16.30/31 19
More informationReturn Difference Function and Closed-Loop Roots Single-Input/Single-Output Control Systems
Spectral Properties of Linear- Quadratic Regulators Robert Stengel Optimal Control and Estimation MAE 546 Princeton University, 2018! Stability margins of single-input/singleoutput (SISO) systems! Characterizations
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 informationNADAR SARASWATHI COLLEGE OF ENGINEERING AND TECHNOLOGY Vadapudupatti, Theni
NADAR SARASWATHI COLLEGE OF ENGINEERING AND TECHNOLOGY Vadapudupatti, Theni-625531 Question Bank for the Units I to V SE05 BR05 SU02 5 th Semester B.E. / B.Tech. Electrical & Electronics engineering IC6501
More informationLecture 5: Frequency domain analysis: Nyquist, Bode Diagrams, second order systems, system types
Lecture 5: Frequency domain analysis: Nyquist, Bode Diagrams, second order systems, system types Venkata Sonti Department of Mechanical Engineering Indian Institute of Science Bangalore, India, 562 This
More informationEE C128 / ME C134 Fall 2014 HW 8 - Solutions. HW 8 - Solutions
EE C28 / ME C34 Fall 24 HW 8 - Solutions HW 8 - Solutions. Transient Response Design via Gain Adjustment For a transfer function G(s) = in negative feedback, find the gain to yield a 5% s(s+2)(s+85) overshoot
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 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 informationPart II. Advanced PID Design Methods
Part II Advanced PID Design Methods 54 Controller transfer function C(s) = k p (1 + 1 T i s + T d s) (71) Many extensions known to the basic design methods introduced in RT I. Four advanced approaches
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 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 informationPositioning Control of One Link Arm with Parametric Uncertainty using Quantitative Feedback Theory
Memoirs of the Faculty of Engineering, Okayama University, Vol. 43, pp. 39-48, January 2009 Positioning Control of One Link Arm with Parametric Uncertainty using Quantitative Feedback Theory Takayuki KUWASHIMA,
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 closed-loop behavior what we want it to be. To review: - G c (s) G(s) H(s) you are here! plant For
More informationAdditional Closed-Loop Frequency Response Material (Second edition, Chapter 14)
Appendix J Additional Closed-Loop Frequency Response Material (Second edition, Chapter 4) APPENDIX CONTENTS J. Closed-Loop Behavior J.2 Bode Stability Criterion J.3 Nyquist Stability Criterion J.4 Gain
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 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 informationDesign and Tuning of Fractional-order PID Controllers for Time-delayed Processes
Design and Tuning of Fractional-order PID Controllers for Time-delayed Processes Emmanuel Edet Technology and Innovation Centre University of Strathclyde 99 George Street Glasgow, United Kingdom emmanuel.edet@strath.ac.uk
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 informationECEn 483 / ME 431 Case Studies. Randal W. Beard Brigham Young University
ECEn 483 / ME 431 Case Studies Randal W. Beard Brigham Young University Updated: December 2, 2014 ii Contents 1 Single Link Robot Arm 1 2 Pendulum on a Cart 9 3 Satellite Attitude Control 17 4 UUV Roll
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 informationÜbersetzungshilfe / Translation aid (English) To be returned at the end of the exam!
Prüfung Regelungstechnik I (Control Systems I) Prof. Dr. Lino Guzzella 5. 2. 2 Übersetzungshilfe / Translation aid (English) To be returned at the end of the exam! Do not mark up this translation aid -
More informationAnswers to multiple choice questions
Answers to multiple choice questions Chapter 2 M2.1 (b) M2.2 (a) M2.3 (d) M2.4 (b) M2.5 (a) M2.6 (b) M2.7 (b) M2.8 (c) M2.9 (a) M2.10 (b) Chapter 3 M3.1 (b) M3.2 (d) M3.3 (d) M3.4 (d) M3.5 (c) M3.6 (c)
More informationControl of Electromechanical Systems
Control of Electromechanical Systems November 3, 27 Exercise Consider the feedback control scheme of the motor speed ω in Fig., where the torque actuation includes a time constant τ A =. s and a disturbance
More informationEC6405 - CONTROL SYSTEM ENGINEERING Questions and Answers Unit - I Control System Modeling Two marks 1. What is control system? A system consists of a number of components connected together to perform
More informationPD, PI, PID Compensation. M. Sami Fadali Professor of Electrical Engineering University of Nevada
PD, PI, PID Compensation M. Sami Fadali Professor of Electrical Engineering University of Nevada 1 Outline PD compensation. PI compensation. PID compensation. 2 PD Control L= loop gain s cl = desired closed-loop
More informationPrüfung Regelungstechnik I (Control Systems I) Übersetzungshilfe / Translation aid (English) To be returned at the end of the exam!
Prüfung Regelungstechnik I (Control Systems I) Prof. Dr. Lino Guzzella 29. 8. 2 Übersetzungshilfe / Translation aid (English) To be returned at the end of the exam! Do not mark up this translation aid
More informationSolutions to Skill-Assessment Exercises
Solutions to Skill-Assessment Exercises To Accompany Control Systems Engineering 4 th Edition By Norman S. Nise John Wiley & Sons Copyright 2004 by John Wiley & Sons, Inc. All rights reserved. No part
More informationChapter 9: Controller design
Chapter 9. Controller Design 9.1. Introduction 9.2. Effect of negative feedback on the network transfer functions 9.2.1. Feedback reduces the transfer function from disturbances to the output 9.2.2. Feedback
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 informationDiscrete Systems. Step response and pole locations. Mark Cannon. Hilary Term Lecture
Discrete Systems Mark Cannon Hilary Term 22 - Lecture 4 Step response and pole locations 4 - Review Definition of -transform: U() = Z{u k } = u k k k= Discrete transfer function: Y () U() = G() = Z{g k},
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 informationExercises for lectures 13 Design using frequency methods
Exercises for lectures 13 Design using frequency methods Michael Šebek Automatic control 2016 31-3-17 Setting of the closed loop bandwidth At the transition frequency in the open loop is (from definition)
More informationAN INTRODUCTION TO THE CONTROL THEORY
Open-Loop controller An Open-Loop (OL) controller is characterized by no direct connection between the output of the system and its input; therefore external disturbance, non-linear dynamics and parameter
More informationME 475/591 Control Systems Final Exam Fall '99
ME 475/591 Control Systems Final Exam Fall '99 Closed book closed notes portion of exam. Answer 5 of the 6 questions below (20 points total) 1) What is a phase margin? Under ideal circumstances, what does
More information(Refer Slide Time: 2:11)
Control Engineering Prof. Madan Gopal Department of Electrical Engineering Indian institute of Technology, Delhi Lecture - 40 Feedback System Performance based on the Frequency Response (Contd.) The summary
More information