NPTEL >> Mechanical Engineering >> Modeling and Control of Dynamic electro-mechanical System Module 4- Lecture 31. Observer Design
|
|
- Miranda Pope
- 6 years ago
- Views:
Transcription
1 Observer Design Dr. Bishakh Bhattacharya h Professor, Department of Mechanical Engineering IIT Kanpur Joint Initiative of IITs and IISc - Funded by MHRD
2 This Lecture Contains Full State Feedback Control for System in Non canonical form Ackermann s algorithm Bass Gura formulation Numerical Example Joint Initiative of IITs and IISc - Funded by MHRD
3 Introduction o to Observer e Design The design of full-state feedback control assumes the accessibility (possibility of sensing) of the complete state vector. However, in reality one may have only a subset of them available for direct sensing while the other states are to be estimated via simulation. Accepting that there will be finite error in this process, the focus is whether the error could be driven to zero at a faster rate than the plant-dynamics. Obviously, such a strategy is feasible only if the states are observable.
4 Observer e in a block-diagram daga reference u Plant Output (y) u B + + A Observer + Controller Estimated States () C - + Y L
5 Design of an Observer The governing equation for a dynamic system (Plant) in state- space representation may be written as: X AX Bu, Y CX The governing equation for the Observer based on the block diagram is shown below. The superscript ^ refers to estimation. Xˆ AXˆ Bu L(Y Yˆ CX ˆ Y) ˆ Define the error in estimation of state vector as e X (X X) ˆ Joint Initiative of IITs and IISc Funded by MHRD 5
6 Observer e Design based on Error Dynamics The error dynamics could be derived now from the observer governing equation and state t space equations for the system as: e Y (A LC) X e X Yˆ Ce X. The corresponding characteristic equation may be written as: si (A LC) You need to design the observer gains such that the desired error dynamics is obtained.
7 Case A: Observer design for canonical system Case Obse e des g o ca o ca syste Suppose, the system [A, C] is available in observer canonical form: a n l ˆ, ˆ, ˆ 2 C L A l l n a a
8 Observer Design for Case A The first thing you need to check is whether the system is fully observable or not. This can be done by checking whether the rank of the observability matrix equals the order of the system as stated earlier. Once the answer is affirmative you may proceed for the observer design. Whenever, the desired eigen-values related to the error-dynamics are specified, one can construct the desired characteristic equation identical to controller design. The observer gain matrix for such cases may be obtained from the simple relationship l d a i i ni ni Here d and a refer to the vector coefficients of the desired and the open-loop characteristic polynomial. n Joint Initiative of IITs and IISc Funded by MHRD 8
9 Observer design for system in non- canonical form If a system is not in observer canonical form, then one needs to transform the system matrices first into the particular canonical form. The transformation matrix required for such cases has been derived as T O O ˆ Here, O and Oˆ are the observability matrices related to the non-canonical and canonical forms respectively. After obtaining the observer gains in observer canonical form, one can transform the gain vector to the original non-canonical form as: L TLˆ O Joint Initiative of IITs and IISc Funded by MHRD 9
10 Assignment: The system matrices for a plant (A, B and C) are as follows: 4 A 2, B and C Design an observer for the plant, where the desired characteristic polynomial is given by: s 3 2 s 2 25s 5 Joint Initiative of IITs and IISc Funded by MHRD
11 Special References for this lecture Control System Design, Bernard Friedland, Dover Control Systems Engineering Norman S Nise, John Wiley & Sons Design of Feedback Control Systems Stefani, Shahian, Savant, Hostetter Oxford Joint Initiative of IITs and IISc Funded by MHRD
Reduced Order Observer Design
NPTEL >> Mechanical Engineering >> Modeling and Control of Dynamic electro-mechanical System Module 4- Lecture 3 Reduced Order Observer Design Dr Bishakh Bhattacharya h Professor, Department of Mechanical
More informationDesign of a Lead Compensator
Design of a Lead Compensator Dr. Bishakh Bhattacharya Professor, Department of Mechanical Engineering IIT Kanpur Joint Initiative of IITs and IISc - Funded by MHRD The Lecture Contains Standard Forms of
More informationProfessor, Department of Mechanical Engineering
State Space Approach in Modelling Dr Bishakh Bhattacharya Professor, Departent of Mechanical Engineering IIT Kanpur Joint Initiative of IITs and IISc - Funded by MHRD Answer of the Last Assignent Following
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 informationModeling of Electrical Elements
Modeling of Electrical Elements Dr. Bishakh Bhattacharya Professor, Department of Mechanical Engineering IIT Kanpur Joint Initiative of IITs and IISc - Funded by MHRD This Lecture Contains Modeling of
More informationState Feedback and State Estimators Linear System Theory and Design, Chapter 8.
1 Linear System Theory and Design, http://zitompul.wordpress.com 2 0 1 4 State Estimator In previous section, we have discussed the state feedback, based on the assumption that all state variables are
More informationNote. Design via State Space
Note Design via State Space Reference: Norman S. Nise, Sections 3.5, 3.6, 7.8, 12.1, 12.2, and 12.8 of Control Systems Engineering, 7 th Edition, John Wiley & Sons, INC., 2014 Department of Mechanical
More informationState Space: Observer Design Lecture 11
State Space: Oberver Deign Lecture Advanced Control Sytem Dr Eyad Radwan Dr Eyad Radwan/ACS/ State Space-L Controller deign relie upon acce to the tate variable for feedback through adjutable gain. Thi
More informationDynamic Modelling of Mechanical Systems
Dynamic Modelling of Mechanical Systems Dr. Bishakh Bhattacharya Professor, Department of Mechanical Engineering g IIT Kanpur Joint Initiative of IITs and IISc - Funded by MHRD Hints of the Last Assignment
More informationState Feedback and State Estimators Linear System Theory and Design, Chapter 8.
1 Linear System Theory and Design, http://zitompul.wordpress.com 2 0 1 4 2 Homework 7: State Estimators (a) For the same system as discussed in previous slides, design another closed-loop state estimator,
More informationMEM 355 Performance Enhancement of Dynamical Systems
MEM 355 Performance Enhancement of Dynamical Systems State Space Design Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University 11/8/2016 Outline State space techniques emerged
More informationState Space Design. MEM 355 Performance Enhancement of Dynamical Systems
State Space Design MEM 355 Performance Enhancement of Dynamical Systems Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University Outline State space techniques emerged around
More informationPower Systems Control Prof. Wonhee Kim. Ch.3. Controller Design in Time Domain
Power Systems Control Prof. Wonhee Kim Ch.3. Controller Design in Time Domain Stability in State Space Equation: State Feeback t A t B t t C t D t x x u y x u u t Kx t t A t BK t A BK x t x x x K shoul
More informationLecture 18 : State Space Design
UCSI University Kuala Lumpur, Malaysia Faculty of Engineering Department of Mechatronics Lecture 18 State Space Design Mohd Sulhi bin Azman Lecturer Department of Mechatronics UCSI University sulhi@ucsi.edu.my
More informationEL 625 Lecture 10. Pole Placement and Observer Design. ẋ = Ax (1)
EL 625 Lecture 0 EL 625 Lecture 0 Pole Placement and Observer Design Pole Placement Consider the system ẋ Ax () The solution to this system is x(t) e At x(0) (2) If the eigenvalues of A all lie in the
More informationU.C. Berkeley Better-than-Worst-Case Analysis Handout 3 Luca Trevisan May 24, 2018
U.C. Berkeley Better-than-Worst-Case Analysis Handout 3 Luca Trevisan May 24, 2018 Lecture 3 In which we show how to find a planted clique in a random graph. 1 Finding a Planted Clique We will analyze
More informationFull State Feedback for State Space Approach
Full State Feedback for State Space Approach State Space Equations Using Cramer s rule it can be shown that the characteristic equation of the system is : det[ si A] 0 Roots (for s) of the resulting polynomial
More informationOmm Al-Qura University Dr. Abdulsalam Ai LECTURE OUTLINE CHAPTER 3. Vectors in Physics
LECTURE OUTLINE CHAPTER 3 Vectors in Physics 3-1 Scalars Versus Vectors Scalar a numerical value (number with units). May be positive or negative. Examples: temperature, speed, height, and mass. Vector
More informationPole Placement (Bass Gura)
Definition: Open-Loop System: System dynamics with U =. sx = AX Closed-Loop System: System dynamics with U = -Kx X sx = (A BK x )X Characteristic Polynomial: Pole Placement (Bass Gura) a) The polynomial
More informationModel predictive control of industrial processes. Vitali Vansovitš
Model predictive control of industrial processes Vitali Vansovitš Contents Industrial process (Iru Power Plant) Neural networ identification Process identification linear model Model predictive controller
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 informationCBE507 LECTURE III Controller Design Using State-space Methods. Professor Dae Ryook Yang
CBE507 LECTURE III Controller Design Using State-space Methods Professor Dae Ryook Yang Fall 2013 Dept. of Chemical and Biological Engineering Korea University Korea University III -1 Overview States What
More informationMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science : MULTIVARIABLE CONTROL SYSTEMS by A.
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.245: MULTIVARIABLE CONTROL SYSTEMS by A. Megretski Q-Parameterization 1 This lecture introduces the so-called
More informationControl Design. Lecture 9: State Feedback and Observers. Two Classes of Control Problems. State Feedback: Problem Formulation
Lecture 9: State Feedback and s [IFAC PB Ch 9] State Feedback s Disturbance Estimation & Integral Action Control Design Many factors to consider, for example: Attenuation of load disturbances Reduction
More informationLecture 9. Introduction to Kalman Filtering. Linear Quadratic Gaussian Control (LQG) G. Hovland 2004
MER42 Advanced Control Lecture 9 Introduction to Kalman Filtering Linear Quadratic Gaussian Control (LQG) G. Hovland 24 Announcement No tutorials on hursday mornings 8-9am I will be present in all practical
More informationAdvanced Control Theory
State Feedback Control Design chibum@seoultech.ac.kr Outline State feedback control design Benefits of CCF 2 Conceptual steps in controller design We begin by considering the regulation problem the task
More information1 (30 pts) Dominant Pole
EECS C8/ME C34 Fall Problem Set 9 Solutions (3 pts) Dominant Pole For the following transfer function: Y (s) U(s) = (s + )(s + ) a) Give state space description of the system in parallel form (ẋ = Ax +
More informationIntro. Computer Control Systems: F8
Intro. Computer Control Systems: F8 Properties of state-space descriptions and feedback Dave Zachariah Dept. Information Technology, Div. Systems and Control 1 / 22 dave.zachariah@it.uu.se F7: Quiz! 2
More informationStrain Transformation equations
Strain Transformation equations R. Chandramouli Associate Dean-Research SASTRA University, Thanjavur-613 401 Joint Initiative of IITs and IISc Funded by MHRD Page 1 of 8 Table of Contents 1. Stress transformation
More informationPusan National University
Chapter 12. DESIGN VIA STATE SPACE Puan National Univerity oratory Table of Content v v v v v v v v Introduction Controller Deign Controllability Alternative Approache to Controller Deign Oberver Deign
More informationEE221A Linear System Theory Final Exam
EE221A Linear System Theory Final Exam Professor C. Tomlin Department of Electrical Engineering and Computer Sciences, UC Berkeley Fall 2016 12/16/16, 8-11am Your answers must be supported by analysis,
More informationDesign constraints Maximum clad temperature, linear power rating
Design constraints Maximum clad temperature, linear power rating K.S. Rajan Professor, School of Chemical & Biotechnology SASTRA University Joint Initiative of IITs and IISc Funded by MHRD Page 1 of 7
More informationCourse Outline. Higher Order Poles: Example. Higher Order Poles. Amme 3500 : System Dynamics & Control. State Space Design. 1 G(s) = s(s + 2)(s +10)
Amme 35 : System Dynamics Control State Space Design Course Outline Week Date Content Assignment Notes 1 1 Mar Introduction 2 8 Mar Frequency Domain Modelling 3 15 Mar Transient Performance and the s-plane
More information1. LQR formulation 2. Selection of weighting matrices 3. Matlab implementation. Regulator Problem mm3,4. u=-kx
MM8.. LQR Reglator 1. LQR formlation 2. Selection of weighting matrices 3. Matlab implementation Reading Material: DC: p.364-382, 400-403, Matlab fnctions: lqr, lqry, dlqr, lqrd, care, dare 3/26/2008 Introdction
More informationNECESSARY AND SUFFICIENT CONDITIONS FOR STATE-SPACE NETWORK REALIZATION. Philip E. Paré Masters Thesis Defense
NECESSARY AND SUFFICIENT CONDITIONS FOR STATE-SPACE NETWORK REALIZATION Philip E. Paré Masters Thesis Defense INTRODUCTION MATHEMATICAL MODELING DYNAMIC MODELS A dynamic model has memory DYNAMIC MODELS
More informationAnalysis of forming- Slipline Field Method
Analysis of forming- Slipline Field Method R. Chandramouli Associate Dean-Research SASTRA University, Thanjavur-613 401 Joint Initiative of IITs and IISc Funded by MHRD Page 1 of 7 Table of Contents 1.
More informationFull-Order Observers
Full-Order Observers Problem: The previous design requires measurements of all of the system's states. Sometimes you only have access to a few states. Can you estimate the states based upon the inputs,
More informationAnalysis of forming - Slab Method
Analysis of forming - Slab Method Forming of materials is a complex process, involving either biaxial or triaxial state of stress on the material being formed. Analysis of the forming process, therefore
More informationLecture If two operators A, B commute then they have same set of eigenkets.
Lecture 14 Matrix representing of Operators While representing operators in terms of matrices, we use the basis kets to compute the matrix elements of the operator as shown below < Φ 1 x Φ 1 >< Φ 1 x Φ
More informationControllability, Observability, Full State Feedback, Observer Based Control
Multivariable Control Lecture 4 Controllability, Observability, Full State Feedback, Observer Based Control John T. Wen September 13, 24 Ref: 3.2-3.4 of Text Controllability ẋ = Ax + Bu; x() = x. At time
More informationSAMPLE SOLUTION TO EXAM in MAS501 Control Systems 2 Autumn 2015
FACULTY OF ENGINEERING AND SCIENCE SAMPLE SOLUTION TO EXAM in MAS501 Control Systems 2 Autumn 2015 Lecturer: Michael Ruderman Problem 1: Frequency-domain analysis and control design (15 pt) Given is a
More informationControl Systems Design, SC4026. SC4026 Fall 2010, dr. A. Abate, DCSC, TU Delft
Control Systems Design, SC426 SC426 Fall 2, dr A Abate, DCSC, TU Delft Lecture 5 Controllable Canonical and Observable Canonical Forms Stabilization by State Feedback State Estimation, Observer Design
More informationChapter 9 Observers, Model-based Controllers 9. Introduction In here we deal with the general case where only a subset of the states, or linear combin
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 Observers,
More informationMultiple Choice Questions
Multiple Choice Questions There is no penalty for guessing. Three points per question, so a total of 48 points for this section.. What is the complete relationship between homogeneous linear systems of
More informationCONTROL DESIGN FOR SET POINT TRACKING
Chapter 5 CONTROL DESIGN FOR SET POINT TRACKING In this chapter, we extend the pole placement, observer-based output feedback design to solve tracking problems. By tracking we mean that the output is commanded
More information1 The Dirac notation for vectors in Quantum Mechanics
This module aims at developing the mathematical foundation of Quantum Mechanics, starting from linear vector space and covering topics such as inner product space, Hilbert space, operators in Quantum Mechanics
More informationTopic # /31 Feedback Control Systems
Topic #17 16.30/31 Feedback Control Systems Improving the transient performance of the LQ Servo Feedforward Control Architecture Design DOFB Servo Handling saturations in DOFB Fall 2010 16.30/31 17 1 LQ
More informationTopic # Feedback Control. State-Space Systems Closed-loop control using estimators and regulators. Dynamics output feedback
Topic #17 16.31 Feedback Control State-Space Systems Closed-loop control using estimators and regulators. Dynamics output feedback Back to reality Copyright 21 by Jonathan How. All Rights reserved 1 Fall
More informationControl engineering sample exam paper - Model answers
Question Control engineering sample exam paper - Model answers a) By a direct computation we obtain x() =, x(2) =, x(3) =, x(4) = = x(). This trajectory is sketched in Figure (left). Note that A 2 = I
More informationFall 線性系統 Linear Systems. Chapter 08 State Feedback & State Estimators (SISO) Feng-Li Lian. NTU-EE Sep07 Jan08
Fall 2007 線性系統 Linear Systems Chapter 08 State Feedback & State Estimators (SISO) Feng-Li Lian NTU-EE Sep07 Jan08 Materials used in these lecture notes are adopted from Linear System Theory & Design, 3rd.
More informationACM/CMS 107 Linear Analysis & Applications Fall 2016 Assignment 4: Linear ODEs and Control Theory Due: 5th December 2016
ACM/CMS 17 Linear Analysis & Applications Fall 216 Assignment 4: Linear ODEs and Control Theory Due: 5th December 216 Introduction Systems of ordinary differential equations (ODEs) can be used to describe
More informationLecture 3: DESIGN CONSIDERATION OF DRIERS
Lecture 3: DESIGN CONSIDERATION OF DRIERS 8. DESIGN OF DRYER Design of a rotary dryer only on the basis of fundamental principle is very difficult. Few of correlations that are available for design may
More informationStress transformation and Mohr s circle for stresses
Stress transformation and Mohr s circle for stresses 1.1 General State of stress Consider a certain body, subjected to external force. The force F is acting on the surface over an area da of the surface.
More informationControl System Design
ELEC4410 Control System Design Lecture 19: Feedback from Estimated States and Discrete-Time Control Design Julio H. Braslavsky julio@ee.newcastle.edu.au School of Electrical Engineering and Computer Science
More informationMODULE 4: ABSORPTION
MODULE 4: ABSORPTION LECTURE NO. 3 4.4. Deign of packed tower baed on overall ma tranfer coefficient * From overall ma tranfer equation, N K ( y y ) one can write for packed tower a N A K y (y-y*) Then,
More information6.241 Dynamic Systems and Control
6.241 Dynamic Systems and Control Lecture 24: H2 Synthesis Emilio Frazzoli Aeronautics and Astronautics Massachusetts Institute of Technology May 4, 2011 E. Frazzoli (MIT) Lecture 24: H 2 Synthesis May
More informationAustralian Journal of Basic and Applied Sciences, 3(4): , 2009 ISSN Modern Control Design of Power System
Australian Journal of Basic and Applied Sciences, 3(4): 4267-4273, 29 ISSN 99-878 Modern Control Design of Power System Atef Saleh Othman Al-Mashakbeh Tafila Technical University, Electrical Engineering
More informationNPTEL. Chemical Reaction Engineering 1 (Homogeneous Reactors) - Video course. Chemical Engineering.
NPTEL Syllabus Chemical Reaction Engineering 1 (Homogeneous Reactors) - Video course COURSE OUTLINE In simple terms, Chemical Engineering deals with the production of a variety of chemicals on large scale.
More informationUniqueness theorems, Separation of variables for Poisson's equation
NPTEL Syllabus Electrodynamics - Web course COURSE OUTLINE The course is a one semester advanced course on Electrodynamics at the M.Sc. Level. It will start by revising the behaviour of electric and magnetic
More informationNPTEL. Chemical Reaction Engineering 2 (Heterogeneous Reactors) - Video course. Chemical Engineering.
NPTEL Syllabus Chemical Reaction Engineering 2 (Heterogeneous Reactors) - Video course COURSE OUTLINE In simple terms, Chemical Engineering deals with the production of a variety of chemicals on large
More informationCONTROL SYSTEMS, ROBOTICS AND AUTOMATION - Vol. XIII - Nonlinear Observers - A. J. Krener
NONLINEAR OBSERVERS A. J. Krener University of California, Davis, CA, USA Keywords: nonlinear observer, state estimation, nonlinear filtering, observability, high gain observers, minimum energy estimation,
More informationCONTROL SYSTEMS, ROBOTICS, AND AUTOMATION Vol. III Estimation and Compensation of Nonlinear Perturbations by Disturbance Observers - Peter C.
ESTIMATION AND COMPENSATION OF NONLINEAR PERTURBATIONS BY DISTURBANCE OBSERVERS Peter C. Müller University of Wuppertal, Germany Keywords: Closed-loop control system, Compensation of nonlinearities, Disturbance
More informationPARAMETERIZATION OF STATE FEEDBACK GAINS FOR POLE PLACEMENT
PARAMETERIZATION OF STATE FEEDBACK GAINS FOR POLE PLACEMENT Hans Norlander Systems and Control, Department of Information Technology Uppsala University P O Box 337 SE 75105 UPPSALA, Sweden HansNorlander@ituuse
More information(Refer Slide Time: 00:01:30 min)
Control Engineering Prof. M. Gopal Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 3 Introduction to Control Problem (Contd.) Well friends, I have been giving you various
More informationState Observers and the Kalman filter
Modelling and Control of Dynamic Systems State Observers and the Kalman filter Prof. Oreste S. Bursi University of Trento Page 1 Feedback System State variable feedback system: Control feedback law:u =
More informationLinear algebra and differential equations (Math 54): Lecture 10
Linear algebra and differential equations (Math 54): Lecture 10 Vivek Shende February 24, 2016 Hello and welcome to class! As you may have observed, your usual professor isn t here today. He ll be back
More informationMichaelis Menten Kinetics- Identical Independent Binding Sites
Michaelis Menten Kinetics- Identical Independent Binding Sites Dr. M. Vijayalakshmi School of Chemical and Biotechnology SASTRA University Joint Initiative of IITs and IISc Funded by MHRD Page 1 of 8 Table
More informationReactivity Balance & Reactor Control System
Reactivity Balance & Reactor Control System K.S. Rajan Professor, School of Chemical & Biotechnology SASTRA University Joint Initiative of IITs and IISc Funded by MHRD Page 1 of 6 Table of Contents 1 MULTIPLICATION
More informationModule 9: State Feedback Control Design Lecture Note 1
Module 9: State Feedback Control Design Lecture Note 1 The design techniques described in the preceding lectures are based on the transfer function of a system. In this lecture we would discuss the state
More informationChapter 3. State Feedback - Pole Placement. Motivation
Chapter 3 State Feedback - Pole Placement Motivation Whereas classical control theory is based on output feedback, this course mainly deals with control system design by state feedback. This model-based
More informationMATH 304 Linear Algebra Lecture 20: Review for Test 1.
MATH 304 Linear Algebra Lecture 20: Review for Test 1. Topics for Test 1 Part I: Elementary linear algebra (Leon 1.1 1.4, 2.1 2.2) Systems of linear equations: elementary operations, Gaussian elimination,
More informationMATH 304 Linear Algebra Lecture 10: Linear independence. Wronskian.
MATH 304 Linear Algebra Lecture 10: Linear independence. Wronskian. Spanning set Let S be a subset of a vector space V. Definition. The span of the set S is the smallest subspace W V that contains S. If
More informationFundamental of Control Systems Steady State Error Lecturer: Dr. Wahidin Wahab M.Sc. Aries Subiantoro, ST. MSc.
Fundamental of Control Systems Steady State Error Lecturer: Dr. Wahidin Wahab M.Sc. Aries Subiantoro, ST. MSc. Electrical Engineering Department University of Indonesia 2 Steady State Error How well can
More information5. Observer-based Controller Design
EE635 - Control System Theory 5. Observer-based Controller Design Jitkomut Songsiri state feedback pole-placement design regulation and tracking state observer feedback observer design LQR and LQG 5-1
More information1 Continuous-time Systems
Observability Completely controllable systems can be restructured by means of state feedback to have many desirable properties. But what if the state is not available for feedback? What if only the output
More informationEC Control Engineering Quiz II IIT Madras
EC34 - Control Engineering Quiz II IIT Madras Linear algebra Find the eigenvalues and eigenvectors of A, A, A and A + 4I Find the eigenvalues and eigenvectors of the following matrices: (a) cos θ sin θ
More informationMultivariate Statistical Analysis
Multivariate Statistical Analysis Fall 2011 C. L. Williams, Ph.D. Lecture 4 for Applied Multivariate Analysis Outline 1 Eigen values and eigen vectors Characteristic equation Some properties of eigendecompositions
More informationControl Systems. State Estimation.
State Estimation chibum@seoultech.ac.kr Outline Dominant pole design Symmetric root locus State estimation We are able to place the CLPs arbitrarily by feeding back all the states: u = Kx. But these may
More informationTRACKING AND DISTURBANCE REJECTION
TRACKING AND DISTURBANCE REJECTION Sadegh Bolouki Lecture slides for ECE 515 University of Illinois, Urbana-Champaign Fall 2016 S. Bolouki (UIUC) 1 / 13 General objective: The output to track a reference
More informationVariable Structure Control ~ Disturbance Rejection. Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University
Variable Structure Control ~ Disturbance Rejection Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University Outline Linear Tracking & Disturbance Rejection Variable Structure
More informationPOLE PLACEMENT. Sadegh Bolouki. Lecture slides for ECE 515. University of Illinois, Urbana-Champaign. Fall S. Bolouki (UIUC) 1 / 19
POLE PLACEMENT Sadegh Bolouki Lecture slides for ECE 515 University of Illinois, Urbana-Champaign Fall 2016 S. Bolouki (UIUC) 1 / 19 Outline 1 State Feedback 2 Observer 3 Observer Feedback 4 Reduced Order
More informationStability, Pole Placement, Observers and Stabilization
Stability, Pole Placement, Observers and Stabilization 1 1, The Netherlands DISC Course Mathematical Models of Systems Outline 1 Stability of autonomous systems 2 The pole placement problem 3 Stabilization
More information3.2 Subspace. Definition: If S is a non-empty subset of a vector space V, and S satisfies the following conditions: (i).
. ubspace Given a vector spacev, it is possible to form another vector space by taking a subset of V and using the same operations (addition and multiplication) of V. For a set to be a vector space, it
More informationDO NOT DO HOMEWORK UNTIL IT IS ASSIGNED. THE ASSIGNMENTS MAY CHANGE UNTIL ANNOUNCED.
EE 537 Homewors Friedland Text Updated: Wednesday November 8 Some homewor assignments refer to Friedland s text For full credit show all wor. Some problems require hand calculations. In those cases do
More informationRobust Control 5 Nominal Controller Design Continued
Robust Control 5 Nominal Controller Design Continued Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University 4/14/2003 Outline he LQR Problem A Generalization to LQR Min-Max
More informationControl Systems, Lecture 05
Control Systems, Lecture 05 İbrahim Beklan Küçükdemiral Yıldız Teknik Üniversitesi 2015 1 / 33 Laplace Transform Solution of State Equations In previous sections, systems were modeled in state space, where
More informationEE C128 / ME C134 Fall 2014 HW 9 Solutions. HW 9 Solutions. 10(s + 3) s(s + 2)(s + 5) G(s) =
1. Pole Placement Given the following open-loop plant, HW 9 Solutions G(s) = 1(s + 3) s(s + 2)(s + 5) design the state-variable feedback controller u = Kx + r, where K = [k 1 k 2 k 3 ] is the feedback
More informationMath 24 Spring 2012 Questions (mostly) from the Textbook
Math 24 Spring 2012 Questions (mostly) from the Textbook 1. TRUE OR FALSE? (a) The zero vector space has no basis. (F) (b) Every vector space that is generated by a finite set has a basis. (c) Every vector
More informationD(s) G(s) A control system design definition
R E Compensation D(s) U Plant G(s) Y Figure 7. A control system design definition x x x 2 x 2 U 2 s s 7 2 Y Figure 7.2 A block diagram representing Eq. (7.) in control form z U 2 s z Y 4 z 2 s z 2 3 Figure
More informationKeywords - Integral control State feedback controller, Ackermann s formula, Coupled two tank liquid level system, Pole Placement technique.
ISSN: 39-5967 ISO 9:8 Certified Volume 3, Issue, January 4 Design and Analysis of State Feedback Using Pole Placement Technique S.JANANI, C.YASOTHA Abstract - This paper presents the design of State Feedback
More informationOptimal Polynomial Control for Discrete-Time Systems
1 Optimal Polynomial Control for Discrete-Time Systems Prof Guy Beale Electrical and Computer Engineering Department George Mason University Fairfax, Virginia Correspondence concerning this paper should
More informationLaboratory 11 Control Systems Laboratory ECE3557. State Feedback Controller for Position Control of a Flexible Joint
Laboratory 11 State Feedback Controller for Position Control of a Flexible Joint 11.1 Objective The objective of this laboratory is to design a full state feedback controller for endpoint position control
More information3. Vector spaces 3.1 Linear dependence and independence 3.2 Basis and dimension. 5. Extreme points and basic feasible solutions
A. LINEAR ALGEBRA. CONVEX SETS 1. Matrices and vectors 1.1 Matrix operations 1.2 The rank of a matrix 2. Systems of linear equations 2.1 Basic solutions 3. Vector spaces 3.1 Linear dependence and independence
More informationDecentralized control with input saturation
Decentralized control with input saturation Ciprian Deliu Faculty of Mathematics and Computer Science Technical University Eindhoven Eindhoven, The Netherlands November 2006 Decentralized control with
More informationCALIFORNIA INSTITUTE OF TECHNOLOGY Control and Dynamical Systems. CDS 110b
CALIFORNIA INSTITUTE OF TECHNOLOGY Control and Dynamical Systems CDS 110b R. M. Murray Kalman Filters 14 January 2007 Reading: This set of lectures provides a brief introduction to Kalman filtering, following
More informationComparison of four state observer design algorithms for MIMO system
Archives of Control Sciences Volume 23(LIX), 2013 No. 2, pages 131 144 Comparison of four state observer design algorithms for MIMO system VINODH KUMAR. E, JOVITHA JEROME and S. AYYAPPAN A state observer
More informationPlasticity R. Chandramouli Associate Dean-Research SASTRA University, Thanjavur
Plasticity R. Chandramouli Associate Dean-Research SASTRA University, Thanjavur-613 401 Joint Initiative of IITs and IISc Funded by MHRD Page 1 of 9 Table of Contents 1. Plasticity:... 3 1.1 Plastic Deformation,
More informationLMIs for Observability and Observer Design
LMIs for Observability and Observer Design Matthew M. Peet Arizona State University Lecture 06: LMIs for Observability and Observer Design Observability Consider a system with no input: ẋ(t) = Ax(t), x(0)
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 informationELEC E7210: Communication Theory. Lecture 10: MIMO systems
ELEC E7210: Communication Theory Lecture 10: MIMO systems Matrix Definitions, Operations, and Properties (1) NxM matrix a rectangular array of elements a A. an 11 1....... a a 1M. NM B D C E ermitian transpose
More information