Chap 8. State Feedback and State Estimators
|
|
|
- Cory Robbins
- 6 years ago
- Views:
Transcription
1 Chap 8. State Feedback and State Estimators
2 Outlines Introduction State feedback Regulation and tracking State estimator Feedback from estimated states State feedback-multivariable case State estimators-multivariable case Feedback from estimated states-multivariable case 2
3 1. Introduction Use controllability and observability Control design
4 2. State Feedback Single-variable system Input with negative state feedback Closed-loop
5 2. State Feedback Theorem 8.1
6 2. State Feedback Remark
7 2. State Feedback
8 2. State Feedback
9 2. State Feedback The power of state feedback
10 2. State Feedback Theorem 8.2
11 2. State Feedback
12 2. State Feedback Theorem 8.3
13 2. State Feedback
14 2. State Feedback Feedback transfer function Plant (A, b, c) With negative feedback bk Numerators are the same.
15 2. State Feedback
16 2. State Feedback
17 2. State Feedback Matlab command: place How to select the desired eigenvalues According to performance criteria Rise time Settling time Overshoot Desired regions
18 2. State Feedback: solving Lyap. Eq A different method to computing feedback gain However, new eigenvalues cannot contain any original eigenvalues of A Procedure
19 2. State Feedback: solving Lyap. Eq Justification Theorem 8.4
20 2. State Feedback: solving Lyap. Eq
21 2. State Feedback: solving Lyap. Eq
22 2. State Feedback: solving Lyap. Eq
23 2. State Feedback: solving Lyap. Eq
24 3. Regulation and Tracking Regulation Reference r is 0, and the response is caused by some nonzero initial conditions Find a state feedback gain so that the response will die out at a desired rate Tracking Reference r is a constant a (more generally, a varying signal a(t)) Find a state feedback gain so that the response will approach a when t goes to infinity
25 3. Regulation and Tracking Plant (A, b, c) Regulation u = r-kx, (A-bk, b, c) Response: Tracking u = pr-kx, p is the feedforword gain TF: p:
26 3. Regulation and Tracking: stabilization Uncontrollable system State feedback Closed-loop
27 4. State Estimator State feedback requires all states are available, which may not be the case in practice State estimator / observer, will generate the estimate of the state
28 4. State Estimator Open-loop estimator System Duplication (if A and b are known) If tow systems have the same initial state Initial state can be computed, if original system is observable Thus, if original system is observable, open-loop estimator can be used 28
29 4. State Estimator Closed-loop estimator y is used in closed-loop estimator the output difference will be used to correct the estimated state or 29
30 4. State Estimator Define 30
31 4. State Estimator 31
32 4. State Estimator Theorem 8.O3 Justification Solving Lyapunov Equation: a different design 32
33 4. State Estimator Procedure 8.O1 33
34 4. State Estimator Justification 34
35 4. State Estimator: reduced dimension Basic idea Procedure 8.R1 35
36 4. State Estimator: reduced dimension Justification Theorem
37 4. State Estimator: reduced dimension 37
38 4. State Estimator: reduced dimension 38
39 4. State Estimator: reduced dimension 39
40 5. Feedback from Estimated States System Feedback from estimated states 40
41 5. Feedback from Estimated States 3 concerns Consider the system
42 5. Feedback from Estimated States Using equivalence transformation
43 5. Feedback from Estimated States Observation
44 6. State Feedback-Multivariable Case p-input State feedback K is p-by-n Theorem 8.M1
45 6. State Feedback-Multivariable Case Theorem 8.M3 Cyclic design Change the multi-input problem into a single-input problem Cyclic matrix: if its characteristic polynomial equals its minimal polynomial A is cyclic iff the Jordan form of A has one and only one Jordan block associated with each distinct eigenvalue
46 6. State Feedback-Multivariable Case Theorem 8.7 Justification
47 6. State Feedback-Multivariable Case
48 6. State Feedback-Multivariable Case Theorem 8.8 Justification
49 6. State Feedback-Multivariable Case
50 6. State Feedback-Multivariable Case An example
51 6. State Feedback-Multivariable Case State feedback cyclic design
52 6. State Feedback-Multivariable Case Lyapunov-Equation Method: extend the Lyapunov procedure to multivariable case Procedure 8.M1 Justification
53 6. State Feedback-Multivariable Case Theorem 8.M4
54 7. State Estimators-Multivariable Case n-dimensional p-input q-output system Full dimension estimator Error and error dynamics
55 7. State Estimators-Multivariable Case Reduced-dimensional estimators Procedure 8.MR1
56 7. State Estimators-Multivariable Case Justification
57 7. State Estimators-Multivariable Case Theorem 8.M6
58 8. Feedback from Estimated States- Multivariable case System Estimator Partition the inverse of P
59 8. Feedback from Estimated States- Multivariable case
60 8. Feedback from Estimated States- Multivariable case
Fall 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.
Chap 3. Linear Algebra
Chap 3. Linear Algebra Outlines 1. Introduction 2. Basis, Representation, and Orthonormalization 3. Linear Algebraic Equations 4. Similarity Transformation 5. Diagonal Form and Jordan Form 6. Functions
EEE582 Homework Problems
EEE582 Homework Problems HW. Write a state-space realization of the linearized model for the cruise control system around speeds v = 4 (Section.3, http://tsakalis.faculty.asu.edu/notes/models.pdf). Use
Linear State Feedback Controller Design
Assignment For EE5101 - Linear Systems Sem I AY2010/2011 Linear State Feedback Controller Design Phang Swee King A0033585A Email: king@nus.edu.sg NGS/ECE Dept. Faculty of Engineering National University
Control Systems. Design of State Feedback Control.
Control Systems Design of State Feedback Control chibum@seoultech.ac.kr Outline Design of State feedback control Dominant pole design Symmetric root locus (linear quadratic regulation) 2 Selection of closed-loop
Control 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
Advanced 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
a. Closed-loop system; b. equivalent transfer function Then the CLTF () T is s the poles of () T are s from a contribution of a
Root Locus Simple definition Locus of points on the s- plane that represents the poles of a system as one or more parameter vary. RL and its relation to poles of a closed loop system RL and its relation
Control 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
EE 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
State 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 =
Separation Principle & Full-Order Observer Design
Separation Principle & Full-Order Observer Design Suppose you want to design a feedback controller. Using full-state feedback you can place the poles of the closed-loop system at will. U Plant Kx If the
CONTROL 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
Chapter 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
EEE 184: Introduction to feedback systems
EEE 84: Introduction to feedback systems Summary 6 8 8 x 7 7 6 Level() 6 5 4 4 5 5 time(s) 4 6 8 Time (seconds) Fig.. Illustration of BIBO stability: stable system (the input is a unit step) Fig.. step)
Course 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
Feedback Control part 2
Overview Feedback Control part EGR 36 April 19, 017 Concepts from EGR 0 Open- and closed-loop control Everything before chapter 7 are open-loop systems Transient response Design criteria Translate criteria
Full 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
Motor Controller. A block diagram for the motor with a feedback controller is shown below
Motor Controller A block diagram for the motor with a feedback controller is shown below A few things to note 1. In this modeling problem, there is no established method or set of criteria for selecting
João P. Hespanha. January 16, 2009
LINEAR SYSTEMS THEORY João P. Hespanha January 16, 2009 Disclaimer: This is a draft and probably contains a few typos. Comments and information about typos are welcome. Please contact the author at hespanha@ece.ucsb.edu.
Note. 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
1 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
Digital Control Engineering Analysis and Design
Digital Control Engineering Analysis and Design M. Sami Fadali Antonio Visioli AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO Academic Press is
MCE/EEC 647/747: Robot Dynamics and Control. Lecture 8: Basic Lyapunov Stability Theory
MCE/EEC 647/747: Robot Dynamics and Control Lecture 8: Basic Lyapunov Stability Theory Reading: SHV Appendix Mechanical Engineering Hanz Richter, PhD MCE503 p.1/17 Stability in the sense of Lyapunov A
Module 03 Linear Systems Theory: Necessary Background
Module 03 Linear Systems Theory: Necessary Background Ahmad F. Taha EE 5243: Introduction to Cyber-Physical Systems Email: ahmad.taha@utsa.edu Webpage: http://engineering.utsa.edu/ taha/index.html September
SECTION 5: ROOT LOCUS ANALYSIS
SECTION 5: ROOT LOCUS ANALYSIS MAE 4421 Control of Aerospace & Mechanical Systems 2 Introduction Introduction 3 Consider a general feedback system: Closed loop transfer function is 1 is the forward path
SYSTEMTEORI - ÖVNING 5: FEEDBACK, POLE ASSIGNMENT AND OBSERVER
SYSTEMTEORI - ÖVNING 5: FEEDBACK, POLE ASSIGNMENT AND OBSERVER Exercise 54 Consider the system: ẍ aẋ bx u where u is the input and x the output signal (a): Determine a state space realization (b): Is the
Time-Invariant Linear Quadratic Regulators!
Time-Invariant Linear Quadratic Regulators Robert Stengel Optimal Control and Estimation MAE 546 Princeton University, 17 Asymptotic approach from time-varying to constant gains Elimination of cross weighting
Linear Quadratic Regulator (LQR) Design II
Lecture 8 Linear Quadratic Regulator LQR) Design II Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore Outline Stability and Robustness properties
Contents. PART I METHODS AND CONCEPTS 2. Transfer Function Approach Frequency Domain Representations... 42
Contents Preface.............................................. xiii 1. Introduction......................................... 1 1.1 Continuous and Discrete Control Systems................. 4 1.2 Open-Loop
Bangladesh University of Engineering and Technology. EEE 402: Control System I Laboratory
Bangladesh University of Engineering and Technology Electrical and Electronic Engineering Department EEE 402: Control System I Laboratory Experiment No. 4 a) Effect of input waveform, loop gain, and system
7.4 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)
Control 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:
EEL2216 Control Theory CT1: PID Controller Design
EEL6 Control Theory CT: PID Controller Design. Objectives (i) To design proportional-integral-derivative (PID) controller for closed loop control. (ii) To evaluate the performance of different controllers
Controls 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
5. 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
EE 380 EXAM II 3 November 2011 Last Name (Print): First Name (Print): ID number (Last 4 digits): Section: DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO
EE 380 EXAM II 3 November 2011 Last Name (Print): First Name (Print): ID number (Last 4 digits): Section: DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO Problem Weight Score 1 25 2 25 3 25 4 25 Total
SYSTEMTEORI - ÖVNING Stability of linear systems Exercise 3.1 (LTI system). Consider the following matrix:
SYSTEMTEORI - ÖVNING 3 1. Stability of linear systems Exercise 3.1 (LTI system. Consider the following matrix: ( A = 2 1 Use the Lyapunov method to determine if A is a stability matrix: a: in continuous
Contents. 1 State-Space Linear Systems 5. 2 Linearization Causality, Time Invariance, and Linearity 31
Contents Preamble xiii Linear Systems I Basic Concepts 1 I System Representation 3 1 State-Space Linear Systems 5 1.1 State-Space Linear Systems 5 1.2 Block Diagrams 7 1.3 Exercises 11 2 Linearization
Inverted Pendulum: State-Space Methods for Controller Design
1 de 12 18/10/2015 22:45 Tips Effects TIPS ABOUT BASICS HARDWARE INDEX NEXT INTRODUCTION CRUISE CONTROL MOTOR SPEED MOTOR POSITION SYSTEM MODELING ANALYSIS Inverted Pendulum: State-Space Methods for Controller
CALIFORNIA INSTITUTE OF TECHNOLOGY Control and Dynamical Systems
CDS 101 1. For each of the following linear systems, determine whether the origin is asymptotically stable and, if so, plot the step response and frequency response for the system. If there are multiple
Example on Root Locus Sketching and Control Design
Example on Root Locus Sketching and Control Design MCE44 - Spring 5 Dr. Richter April 25, 25 The following figure represents the system used for controlling the robotic manipulator of a Mars Rover. We
MODERN CONTROL DESIGN
CHAPTER 8 MODERN CONTROL DESIGN The classical design techniques of Chapters 6 and 7 are based on the root-locus and frequency response that utilize only the plant output for feedback with a dynamic controller
Due Wednesday, February 6th EE/MFS 599 HW #5
Due Wednesday, February 6th EE/MFS 599 HW #5 You may use Matlab/Simulink wherever applicable. Consider the standard, unity-feedback closed loop control system shown below where G(s) = /[s q (s+)(s+9)]
EE 422G - Signals and Systems Laboratory
EE 4G - Signals and Systems Laboratory Lab 9 PID Control Kevin D. Donohue Department of Electrical and Computer Engineering University of Kentucky Lexington, KY 40506 April, 04 Objectives: Identify the
EEE 184 Project: Option 1
EEE 184 Project: Option 1 Date: November 16th 2012 Due: December 3rd 2012 Work Alone, show your work, and comment your results. Comments, clarity, and organization are important. Same wrong result or same
State space control for the Two degrees of freedom Helicopter
State space control for the Two degrees of freedom Helicopter AAE364L In this Lab we will use state space methods to design a controller to fly the two degrees of freedom helicopter. 1 The state space
Output Regulation of the Arneodo Chaotic System
Vol. 0, No. 05, 00, 60-608 Output Regulation of the Arneodo Chaotic System Sundarapandian Vaidyanathan R & D Centre, Vel Tech Dr. RR & Dr. SR Technical University Avadi-Alamathi Road, Avadi, Chennai-600
Suppose that we have a specific single stage dynamic system governed by the following equation:
Dynamic Optimisation Discrete Dynamic Systems A single stage example Suppose that we have a specific single stage dynamic system governed by the following equation: x 1 = ax 0 + bu 0, x 0 = x i (1) where
Autonomous Mobile Robot Design
Autonomous Mobile Robot Design Topic: Guidance and Control Introduction and PID Loops Dr. Kostas Alexis (CSE) Autonomous Robot Challenges How do I control where to go? Autonomous Mobile Robot Design Topic:
Module 06 Stability of Dynamical Systems
Module 06 Stability of Dynamical Systems Ahmad F. Taha EE 5143: Linear Systems and Control Email: ahmad.taha@utsa.edu Webpage: http://engineering.utsa.edu/ataha October 10, 2017 Ahmad F. Taha Module 06
THE DESIGN OF ACTIVE CONTROLLER FOR THE OUTPUT REGULATION OF LIU-LIU-LIU-SU CHAOTIC SYSTEM
THE DESIGN OF ACTIVE CONTROLLER FOR THE OUTPUT REGULATION OF LIU-LIU-LIU-SU CHAOTIC SYSTEM Sundarapandian Vaidyanathan 1 1 Research and Development Centre, Vel Tech Dr. RR & Dr. SR Technical University
State Regulator. Advanced Control. design of controllers using pole placement and LQ design rules
Advanced Control State Regulator Scope design of controllers using pole placement and LQ design rules Keywords pole placement, optimal control, LQ regulator, weighting matrixes Prerequisites Contact state
Alireza Mousavi Brunel University
Alireza Mousavi Brunel University 1 » Control Process» Control Systems Design & Analysis 2 Open-Loop Control: Is normally a simple switch on and switch off process, for example a light in a room is switched
Output Regulation of the Tigan System
Output Regulation of the Tigan System Dr. V. Sundarapandian Professor (Systems & Control Eng.), Research and Development Centre Vel Tech Dr. RR & Dr. SR Technical University Avadi, Chennai-6 6, Tamil Nadu,
Steady State Errors. Recall the closed-loop transfer function of the system, is
Steady State Errors Outline What is steady-state error? Steady-state error in unity feedback systems Type Number Steady-state error in non-unity feedback systems Steady-state error due to disturbance inputs
Outline. Classical Control. Lecture 5
Outline Outline Outline 1 What is 2 Outline What is Why use? Sketching a 1 What is Why use? Sketching a 2 Gain Controller Lead Compensation Lag Compensation What is Properties of a General System Why use?
Design 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
Closed-loop system 2/1/2016. Generally MIMO case. Two-degrees-of-freedom (2 DOF) control structure. (2 DOF structure) The closed loop equations become
Closed-loop system enerally MIMO case Two-degrees-of-freedom (2 DOF) control structure (2 DOF structure) 2 The closed loop equations become solving for z gives where is the closed loop transfer function
CBE507 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
Dynamics and control of mechanical systems
Dynamics and control of mechanical systems Date Day 1 (03/05) - 05/05 Day 2 (07/05) Day 3 (09/05) Day 4 (11/05) Day 5 (14/05) Day 6 (16/05) Content Review of the basics of mechanics. Kinematics of rigid
EL 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
Pole 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
9/9/2011 Classical Control 1
MM11 Root Locus Design Method Reading material: FC pp.270-328 9/9/2011 Classical Control 1 What have we talked in lecture (MM10)? Lead and lag compensators D(s)=(s+z)/(s+p) with z < p or z > p D(s)=K(Ts+1)/(Ts+1),
Simulation and Implementation of Servo Motor Control
Simulation and Implementation of Servo Motor Control with Sliding Mode Control (SMC) using Matlab and LabView Bondhan Novandy http://bono02.wordpress.com/ Outline Background Motivation AC Servo Motor Inverter
Self-tuning Control Based on Discrete Sliding Mode
Int. J. Mech. Eng. Autom. Volume 1, Number 6, 2014, pp. 367-372 Received: July 18, 2014; Published: December 25, 2014 International Journal of Mechanical Engineering and Automation Akira Ohata 1, Akihiko
Full-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,
Module 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
DESIGN OF LINEAR STATE FEEDBACK CONTROL LAWS
7 DESIGN OF LINEAR STATE FEEDBACK CONTROL LAWS Previous chapters, by introducing fundamental state-space concepts and analysis tools, have now set the stage for our initial foray into statespace methods
Chap 4. State-Space Solutions and
Chap 4. State-Space Solutions and Realizations Outlines 1. Introduction 2. Solution of LTI State Equation 3. Equivalent State Equations 4. Realizations 5. Solution of Linear Time-Varying (LTV) Equations
Control 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
Dr 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
State Space Control D R. T A R E K A. T U T U N J I
State Space Control D R. T A R E K A. T U T U N J I A D V A N C E D C O N T R O L S Y S T E M S M E C H A T R O N I C S E N G I N E E R I N G D E P A R T M E N T P H I L A D E L P H I A U N I V E R S I
Outline. 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
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.04A Systems and Controls Spring 2013
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.04A Systems and Controls Spring 2013 Problem Set #4 Posted: Thursday, Mar. 7, 13 Due: Thursday, Mar. 14, 13 1. Sketch the Root
OUTPUT REGULATION OF THE SIMPLIFIED LORENZ CHAOTIC SYSTEM
OUTPUT REGULATION OF THE SIMPLIFIED LORENZ CHAOTIC SYSTEM Sundarapandian Vaidyanathan Research and Development Centre, Vel Tech Dr. RR & Dr. SR Technical University Avadi, Chennai-600 06, Tamil Nadu, INDIA
ECE317 : Feedback and Control
ECE317 : Feedback and Control Lecture : Steady-state error Dr. Richard Tymerski Dept. of Electrical and Computer Engineering Portland State University 1 Course roadmap Modeling Analysis Design Laplace
EE221A 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,
ACTIVE CONTROLLER DESIGN FOR THE OUTPUT REGULATION OF THE WANG-CHEN-YUAN SYSTEM
ACTIVE CONTROLLER DESIGN FOR THE OUTPUT REGULATION OF THE WANG-CHEN-YUAN SYSTEM Sundarapandian Vaidyanathan Research and Development Centre, Vel Tech Dr. RR & Dr. SR Technical University Avadi, Chennai-600
An Optimization Approach to the Pole-Placement Design of Robust Linear Multivariable Control Systems
Appears in Proc. 24 American Control Conference, pp. 4298-435, Portland, OR, June 4-June 6, 24. An Optimization Approach to the Pole-Placement Design of Robust Linear Multivariable Control Systems Richard
Automatic Control Systems
Automatic Control Systems Edited by Dr. Yuri Sokolov Contributing Authors: Dr. Victor Iliushko, Dr. Emaid A. Abdul-Retha, Mr. Sönke Dierks, Dr. Pascual Marqués. Published by Marques Aviation Ltd Southport,
Chapter 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
6.1 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)
Control. CSC752: Autonomous Robotic Systems. Ubbo Visser. March 9, Department of Computer Science University of Miami
Control CSC752: Autonomous Robotic Systems Ubbo Visser Department of Computer Science University of Miami March 9, 2017 Outline 1 Control system 2 Controller Images from http://en.wikipedia.org/wiki/feed-forward
7.1 Introduction. Apago PDF Enhancer. Definition and Test Inputs. 340 Chapter 7 Steady-State Errors
340 Chapter 7 Steady-State Errors 7. Introduction In Chapter, we saw that control systems analysis and design focus on three specifications: () transient response, (2) stability, and (3) steady-state errors,
CDS 101/110a: Lecture 2.1 Dynamic Behavior
CDS 11/11a: Lecture.1 Dynamic Behavior Richard M. Murray 6 October 8 Goals: Learn to use phase portraits to visualize behavior of dynamical systems Understand different types of stability for an equilibrium
sc Control Systems Design Q.1, Sem.1, Ac. Yr. 2010/11
sc46 - Control Systems Design Q Sem Ac Yr / Mock Exam originally given November 5 9 Notes: Please be reminded that only an A4 paper with formulas may be used during the exam no other material is to be
Robust Control 2 Controllability, Observability & Transfer Functions
Robust Control 2 Controllability, Observability & Transfer Functions Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University /26/24 Outline Reachable Controllability Distinguishable
Linear Control Systems Lecture #3 - Frequency Domain Analysis. Guillaume Drion Academic year
Linear Control Systems Lecture #3 - Frequency Domain Analysis Guillaume Drion Academic year 2018-2019 1 Goal and Outline Goal: To be able to analyze the stability and robustness of a closed-loop system
HANDOUT E.22 - EXAMPLES ON STABILITY ANALYSIS
Example 1 HANDOUT E. - EXAMPLES ON STABILITY ANALYSIS Determine the stability of the system whose characteristics equation given by 6 3 = s + s + 3s + s + s + s +. The above polynomial satisfies the necessary
MAE 143B - Homework 7
MAE 143B - Homework 7 6.7 Multiplying the first ODE by m u and subtracting the product of the second ODE with m s, we get m s m u (ẍ s ẍ i ) + m u b s (ẋ s ẋ u ) + m u k s (x s x u ) + m s b s (ẋ s ẋ u
CDS 101/110a: Lecture 2.1 Dynamic Behavior
CDS 11/11a: Lecture 2.1 Dynamic Behavior Richard M. Murray 6 October 28 Goals: Learn to use phase portraits to visualize behavior of dynamical systems Understand different types of stability for an equilibrium
Ultimate State. MEM 355 Performance Enhancement of Dynamical Systems
Ultimate State MEM 355 Performance Enhancement of Dnamical Sstems Harr G. Kwatn Department of Mechanical Engineering & Mechanics Drexel Universit Outline Design Criteria two step process Ultimate state
EE451/551: Digital Control. Chapter 3: Modeling of Digital Control Systems
EE451/551: Digital Control Chapter 3: Modeling of Digital Control Systems Common Digital Control Configurations AsnotedinCh1 commondigitalcontrolconfigurations As noted in Ch 1, common digital control
Linear Quadratic Regulator (LQR) II
Optimal Control, Guidance and Estimation Lecture 11 Linear Quadratic Regulator (LQR) II Pro. Radhakant Padhi Dept. o Aerospace Engineering Indian Institute o Science - Bangalore Outline Summary o LQR design
Control Systems. LMIs in. Guang-Ren Duan. Analysis, Design and Applications. Hai-Hua Yu. CRC Press. Taylor & Francis Croup
LMIs in Control Systems Analysis, Design and Applications Guang-Ren Duan Hai-Hua Yu CRC Press Taylor & Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Croup, an
SECTION 8: ROOT-LOCUS ANALYSIS. ESE 499 Feedback Control Systems
SECTION 8: ROOT-LOCUS ANALYSIS ESE 499 Feedback Control Systems 2 Introduction Introduction 3 Consider a general feedback system: Closed-loop transfer function is KKKK ss TT ss = 1 + KKKK ss HH ss GG ss
School of Mechanical Engineering Purdue University. DC Motor Position Control The block diagram for position control of the servo table is given by:
Root Locus Motivation Sketching Root Locus Examples ME375 Root Locus - 1 Servo Table Example DC Motor Position Control The block diagram for position control of the servo table is given by: θ D 0.09 See
OUTPUT REGULATION OF RÖSSLER PROTOTYPE-4 CHAOTIC SYSTEM BY STATE FEEDBACK CONTROL
International Journal in Foundations of Computer Science & Technology (IJFCST),Vol., No., March 01 OUTPUT REGULATION OF RÖSSLER PROTOTYPE-4 CHAOTIC SYSTEM BY STATE FEEDBACK CONTROL Sundarapandian Vaidyanathan
Digital Control Systems
Digital Control Systems Lecture Summary #4 This summary discussed some graphical methods their use to determine the stability the stability margins of closed loop systems. A. Nyquist criterion Nyquist