DERIVATIVE FREE OUTPUT FEEDBACK ADAPTIVE CONTROL
|
|
- Marshall Lamb
- 5 years ago
- Views:
Transcription
1 DERIVATIVE FREE OUTPUT FEEDBACK ADAPTIVE CONTROL Tansel YUCELEN, * Kilsoo KIM, and Anthony J. CALISE Georgia Institute of Technology, Yucelen Atlanta, * GA 30332, USA * tansel@gatech.edu AIAA Guidance, Navigation, and Control Conference 8 11 August 2011, Portland, Oregon
2 Outline Motivation Adaptive Control Derivative-Free Adaptive Control Illustrative Scalar Example Output Feedback Adaptive Control Problem Formulation Control System Description Adaptive Control Architecture Visualization Wing Rock Dynamics Example Nonlinear Uncertainty External Disturbance Measurement Noise Concluding Remarks
3 Outline Motivation Adaptive Control Derivative-Free Adaptive Control Illustrative Scalar Example Output Feedback Adaptive Control Problem Formulation Control System Description Adaptive Control Architecture Visualization Wing Rock Dynamics Example Nonlinear Uncertainty External Disturbance Measurement Noise Concluding Remarks
4 Motivation Models that do not adequately capture the physical system Idealized assumptions and model simplifications Actual dynamics can be nonlinear and uncertain Many loops can be coupled (MIMO) Unknown disturbances (such as turbulance)
5 Motivation Models that do not adequately capture the physical system Idealized assumptions and model simplifications Actual dynamics can be nonlinear and uncertain Many loops can be coupled (MIMO) Unknown disturbances (such as turbulance) Sudden change in dynamics Reconfiguration Deployment of a payload Structural damage
6 Motivation Models that do not adequately capture the physical system Idealized assumptions and model simplifications Actual dynamics can be nonlinear and uncertain Many loops can be coupled (MIMO) Unknown disturbances (such as turbulance) Sudden change in dynamics Reconfiguration Deployment of a payload Structural damage Robust controllers? May fail to achieve a given performance criteria Under high levels of uncertainty Require more system modeling information
7 Motivation Models that do not adequately capture the physical system Idealized assumptions and model simplifications Actual dynamics can be nonlinear and uncertain Many loops can be coupled (MIMO) Unknown disturbances (such as turbulance) Sudden change in dynamics Reconfiguration Deployment of a payload Structural damage Robust controllers? May fail to achieve a given performance criteria Under high levels of uncertainty Require more system modeling information Adaptive controllers?
8 Adaptive Control Adaptive control is an attractive approach Address system uncertainties and nonlinearities Preserve stability w/o excessively reliance on models
9 Adaptive Control Adaptive control is an attractive approach Address system uncertainties and nonlinearities Preserve stability w/o excessively reliance on models Indirect/direct adaptive control architectures Indirect architecture: Prm estimation and adapting gains Direct architecture: Adapting gains in resp to sys variations
10 Adaptive Control Adaptive control is an attractive approach Address system uncertainties and nonlinearities Preserve stability w/o excessively reliance on models Indirect/direct adaptive control architectures Indirect architecture: Prm estimation and adapting gains Direct architecture: Adapting gains in resp to sys variations SYSTEM NOMINAL CONTROL COMMAND
11 Adaptive Control Adaptive control is an attractive approach Address system uncertainties and nonlinearities Preserve stability w/o excessively reliance on models Indirect/direct adaptive control architectures Indirect architecture: Prm estimation and adapting gains Direct architecture: Adapting gains in resp to sys variations UNCERTAIN SYSTEM NOMINAL CONTROL REFERENCE MODEL COMMAND
12 Adaptive Control Adaptive control is an attractive approach Address system uncertainties and nonlinearities Preserve stability w/o excessively reliance on models Indirect/direct adaptive control architectures Indirect architecture: Prm estimation and adapting gains Direct architecture: Adapting gains in resp to sys variations UNCERTAIN SYSTEM NOMINAL CONTROL REFERENCE MODEL COMMAND ADAPTIVE CONTROL
13 Derivative-Free Adaptive Control Derivative-based (standard) adaptive control Based on standard Lyapunov theory Existence of constant unknown ideal set of weights May require unrealistically high adaptation gain May fail to achieve a good perf under failure recovery Require mods in order to prevent from bursting
14 Derivative-Free Adaptive Control Derivative-based (standard) adaptive control Based on standard Lyapunov theory Existence of constant unknown ideal set of weights May require unrealistically high adaptation gain May fail to achieve a good perf under failure recovery Require mods in order to prevent from bursting Derivative-free adaptive control Based on Lyapunov-Krasovskii theory Guaranteed transient and steady state perf bounds Preserves stability and achieves desired performance Time-varying ideal weights (fast variation is allowed) Adv for sys with sudden change in dynamics Does not need mods in order to prevent from bursting
15 Derivative-Free Adaptive Control Derivative-free adaptive control Based on Lyapunov-Krasovskii theory Guaranteed transient and steady state perf bounds Preserves stability and achieves desired performance Time-varying ideal weights (fast variation is allowed) Adv for sys with sudden change in dynamics Does not need mods in order to prevent from bursting
16 Illustration: Constant Ideal Weights
17 Illustration: Constant Ideal Weights
18 Illustration: Constant Ideal Weights Low gain ( γ = 25 )
19 Illustration: Constant Ideal Weights Low gain ( γ = 25 ) Moderate gain ( γ = 125 )
20 Illustration: Time-Varying Ideal Weights
21 Illustration: Time-Varying Ideal Weights
22 Illustration: Time-Varying Ideal Weights Low gain ( γ = 25 )
23 Illustration: Time-Varying Ideal Weights Low gain ( γ = 25 ) Moderate gain ( γ = 90 )
24 Outline Motivation Adaptive Control Derivative-Free Adaptive Control Illustrative Scalar Example Output Feedback Adaptive Control Problem Formulation Control System Description Adaptive Control Architecture Visualization Wing Rock Dynamics Example Nonlinear Uncertainty External Disturbance Measurement Noise Concluding Remarks
25 Output Feedback Adaptive Control Extension of derivative-free adapt ctrl to output fdbk
26 Output Feedback Adaptive Control Extension of derivative-free adapt ctrl to output fdbk Augmentation of a fixed gain, observer based output fdbk ctrl
27 Output Feedback Adaptive Control Extension of derivative-free adapt ctrl to output fdbk Augmentation of a fixed gain, observer based output fdbk ctrl Realization of adapt ctrl does not require reference model Observer acts like a reference model
28 Output Feedback Adaptive Control Extension of derivative-free adapt ctrl to output fdbk Augmentation of a fixed gain, observer based output fdbk ctrl Realization of adapt ctrl does not require reference model Observer acts like a reference model Parameter dependent Riccati equation (PDRE) is used Rather than a Lyapunov equation
29 Output Feedback Adaptive Control Extension of derivative-free adapt ctrl to output fdbk Augmentation of a fixed gain, observer based output fdbk ctrl Realization of adapt ctrl does not require reference model Observer acts like a reference model Parameter dependent Riccati equation (PDRE) is used Rather than a Lyapunov equation Stability analysis uses a Lyapunov-Krasovskii functional That entails the solution of PDRE
30 Output Feedback Adaptive Control Extension of derivative-free adapt ctrl to output fdbk Augmentation of a fixed gain, observer based output fdbk ctrl Realization of adapt ctrl does not require reference model Observer acts like a reference model Parameter dependent Riccati equation (PDRE) is used Rather than a Lyapunov equation Stability analysis uses a Lyapunov-Krasovskii functional That entails the solution of PDRE Cost of implementation is far less than that of other methods
31 Output Feedback Adaptive Control Extension of derivative-free adapt ctrl to output fdbk Augmentation of a fixed gain, observer based output fdbk ctrl Realization of adapt ctrl does not require reference model Observer acts like a reference model Parameter dependent Riccati equation (PDRE) is used Rather than a Lyapunov equation Stability analysis uses a Lyapunov-Krasovskii functional That entails the solution of PDRE Cost of implementation is far less than that of other methods Advantageous for applications to systems with Sudden change in dynamics
32 Problem Formulation
33 Problem Formulation
34 Problem Formulation
35 Problem Formulation
36 Remarks
37 Remarks
38 Remarks
39 Control System Description
40 Control System Description
41 Control System Description
42 Adaptive Control Description
43 Adaptive Control Architecture (PDRE)
44 Remarks on PDRE
45 Remarks on PDRE v = v β 2
46 Remarks on PDRE 0 = A e T P + PA e + v C T PB C T PB T + Q 0
47 Remarks on PDRE 0 = A e T P + PA e + v C T PB C T PB T + Q 0 If PB = C T (positive-real), then PDRE reduces to Lyapunov eqn and v =
48 Remarks on PDRE 0 = A e T P + PA e + v C T PB C T PB T + Q 0 If PB = C T (positive-real), then PDRE reduces to Lyapunov eqn and v = This suggests that for the purposes of adaptive control design, when m > 1, it is advantageous to define a new meas by taking a linear combination of existing measurements y o t = My t = MCx t = C o x(t)
49 Remarks on PDRE 0 = A e T P + PA e + v C T PB C T PB T + Q 0 If PB = C T (positive-real), then PDRE reduces to Lyapunov eqn and v = This suggests that for the purposes of adaptive control design, when m > 1, it is advantageous to define a new meas by taking a linear combination of existing measurements y o t = My t = MCx t = C o x(t) M is a norm preserving transformation that minimizes a norm measure of N o = C o T P o B, 0 = A e T P o + P o A e + Q o
50 Remarks on PDRE 0 = A e T P + PA e + v C T PB C T PB T + Q 0 If PB = C T (positive-real), then PDRE reduces to Lyapunov eqn and v = This suggests that for the purposes of adaptive control design, when m > 1, it is advantageous to define a new meas by taking a linear combination of existing measurements y o t = My t = MCx t = C o x(t) M is a norm preserving transformation that minimizes a norm measure of N o = C o T P o B, 0 = A e T P o + P o A e + Q o Taking the Frobenius norm as a measure, it can be shown that the solution for M that min N o F subj to the constraint MC F = C F is given by M = C F B T P o C T CC T 1 B T P C o C T CCT 1 F
51 Visualization
52 Main Result
53 Main Result
54 Main Result
55 Main Result
56 Outline Motivation Adaptive Control Derivative-Free Adaptive Control Illustrative Scalar Example Output Feedback Adaptive Control Problem Formulation Control System Description Adaptive Control Architecture Visualization Wing Rock Dynamics Example Nonlinear Uncertainty External Disturbance Measurement Noise Concluding Remarks
57 Wing Rock Dynamics Wing rock is a nonlinear phenomenon in which an aircraft exhibits an oscillation in roll at high angles of attack
58 Wing Rock Dynamics Wing rock is a nonlinear phenomenon in which an aircraft exhibits an oscillation in roll at high angles of attack A two state model for wing rock dynamics can be given by where, f 1 t being a square wave having an amplitude of 0.5 and a period of 15 //...seconds, f 2 t = 0.5 sin(1.5t), and d(t) is an external disturbance
59 Wing Rock Dynamics Wing rock is a nonlinear phenomenon in which an aircraft exhibits an oscillation in roll at high angles of attack A two state model for wing rock dynamics can be given by where, f 1 t being a square wave having an amplitude of 0.5 and a period of 15 //...seconds, f 2 t = 0.5 sin(1.5t), and d(t) is an external disturbance x 1 (t) represents the roll angle and x 2 t represents the roll rate
60 Nominal and Adaptive Control Designs The reference model is selected to be second order with a natural frequency of 1.6 rad/sec and a damping ratio of 0.8, and to have a unity gain from r(t) to y m (t) at low frequency K 1 = 2.56, 2.56 K 2 = 2.56
61 Nominal and Adaptive Control Designs The reference model is selected to be second order with a natural frequency of 1.6 rad/sec and a damping ratio of 0.8, and to have a unity gain from r(t) to y m (t) at low frequency K 1 = 2.56, 2.56 K 2 = 2.56 We chose L = 12.8, 64.0 T State observer poles are 5 times larger than reference model poles
62 Nominal and Adaptive Control Designs The reference model is selected to be second order with a natural frequency of 1.6 rad/sec and a damping ratio of 0.8, and to have a unity gain from r(t) to y m (t) at low frequency K 1 = 2.56, 2.56 K 2 = 2.56 We chose L = 12.8, 64.0 T State observer poles are 5 times larger than reference model poles For adaptive control design 1 e Basis function β x = [0.5, x 1, 1 e x2 1+e x 1 1+e x 2 ]T β = 1.5 For μ = 0.05 and Q o = 0.25 I 2, it was determined that v = κ 2 < 35.4 We set Ω 1 = 0.95I 3, κ 2 = 35, and τ = 0.01 seconds
63 Nominal and Adaptive Control Designs The reference model is selected to be second order with a natural frequency of 1.6 rad/sec and a damping ratio of 0.8, and to have a unity gain from r(t) to y m (t) at low frequency K 1 = 2.56, 2.56 K 2 = 2.56 We chose L = 12.8, 64.0 T State observer poles are 5 times larger than reference model poles For adaptive control design 1 e Basis function β x = [0.5, x 1, 1 e x2 1+e x 1 1+e x 2 ]T β = 1.5 For μ = 0.05 and Q o = 0.25 I 2, it was determined that v = κ 2 < 35.4 We set Ω 1 = 0.95I 3, κ 2 = 35, and τ = 0.01 seconds Goal: Tracking a reference command
64 Constant Ideal Weights Nominal and adaptive control responses for the case of constant ideal weights
65 Time-Varying Ideal Weights Nominal and adaptive control responses for the case of time-varying ideal weights
66 Time-Varying Ideal Weights and Disturbances Depiction of d(t) and w(t)
67 Time-Varying Ideal Weights and Disturbances Nominal and adaptive control responses with disturbances for the case of time-varying ideal weights
68 Outline Motivation Adaptive Control Derivative-Free Adaptive Control Illustrative Scalar Example Output Feedback Adaptive Control Problem Formulation Control System Description Adaptive Control Architecture Visualization Wing Rock Dynamics Example Nonlinear Uncertainty External Disturbance Measurement Noise Concluding Remarks
69 Concluding Remarks Extension of state feedback, derivative-free adaptive controller to an output feedback form
70 Concluding Remarks Extension of state feedback, derivative-free adaptive controller to an output feedback form Particularly useful for situations in which Nature of sys uncertainty cannot be adequately represented by a set of basis functions with constant ideal weights
71 Concluding Remarks Extension of state feedback, derivative-free adaptive controller to an output feedback form Particularly useful for situations in which Nature of sys uncertainty cannot be adequately represented by a set of basis functions with constant ideal weights Level of complexity is far less than many other methods
72 Concluding Remarks Extension of state feedback, derivative-free adaptive controller to an output feedback form Particularly useful for situations in which Nature of sys uncertainty cannot be adequately represented by a set of basis functions with constant ideal weights Level of complexity is far less than many other methods Can be implemented in a form that augments an observer based linear controller architecture
73 Concluding Remarks Extension of state feedback, derivative-free adaptive controller to an output feedback form Particularly useful for situations in which Nature of sys uncertainty cannot be adequately represented by a set of basis functions with constant ideal weights Level of complexity is far less than many other methods Can be implemented in a form that augments an observer based linear controller architecture Illustrative example shows that the presented theory and the simulation results are compatible
74 Thank You
H 2 Adaptive Control. Tansel Yucelen, Anthony J. Calise, and Rajeev Chandramohan. WeA03.4
1 American Control Conference Marriott Waterfront, Baltimore, MD, USA June 3-July, 1 WeA3. H Adaptive Control Tansel Yucelen, Anthony J. Calise, and Rajeev Chandramohan Abstract Model reference adaptive
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 informationSupervisor: Dr. Youmin Zhang Amin Salar Zahra Gallehdari Narges Roofigari
Supervisor: Dr. Youmin Zhang Amin Salar 6032761 Zahra Gallehdari 1309102 Narges Roofigari 8907926 Fault Diagnosis and Fault Tolerant Control Systems Final Project December 2011 Contents Introduction Quad-Rotor
More informationMulti-Model Adaptive Regulation for a Family of Systems Containing Different Zero Structures
Preprints of the 19th World Congress The International Federation of Automatic Control Multi-Model Adaptive Regulation for a Family of Systems Containing Different Zero Structures Eric Peterson Harry G.
More informationEvery real system has uncertainties, which include system parametric uncertainties, unmodeled dynamics
Sensitivity Analysis of Disturbance Accommodating Control with Kalman Filter Estimation Jemin George and John L. Crassidis University at Buffalo, State University of New York, Amherst, NY, 14-44 The design
More informationFAULT DETECTION AND FAULT TOLERANT APPROACHES WITH AIRCRAFT APPLICATION. Andrés Marcos
FAULT DETECTION AND FAULT TOLERANT APPROACHES WITH AIRCRAFT APPLICATION 2003 Louisiana Workshop on System Safety Andrés Marcos Dept. Aerospace Engineering and Mechanics, University of Minnesota 28 Feb,
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 informationDepartment of Aerospace Engineering and Mechanics University of Minnesota Written Preliminary Examination: Control Systems Friday, April 9, 2010
Department of Aerospace Engineering and Mechanics University of Minnesota Written Preliminary Examination: Control Systems Friday, April 9, 2010 Problem 1: Control of Short Period Dynamics Consider the
More informationMTNS 06, Kyoto (July, 2006) Shinji Hara The University of Tokyo, Japan
MTNS 06, Kyoto (July, 2006) Shinji Hara The University of Tokyo, Japan Outline Motivation & Background: H2 Tracking Performance Limits: new paradigm Explicit analytical solutions with examples H2 Regulation
More informationAircraft Stability & Control
Aircraft Stability & Control Textbook Automatic control of Aircraft and missiles 2 nd Edition by John H Blakelock References Aircraft Dynamics and Automatic Control - McRuler & Ashkenas Aerodynamics, Aeronautics
More informationWeak Convergence of Nonlinear High-Gain Tracking Differentiator
1074 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 58, NO. 4, APRIL 2013 Weak Convergence of Nonlinear High-Gain Tracking Differentiator Bao-Zhu Guo and Zhi-Liang Zhao In applications, the signal may be
More informationDerivative-Free Output Feedback Adaptive Control
Derivative-Free Output Feedback Adaptive Control Tansel Yucelen, Kilsoo Kim, and Anthony J. Calise Georgia Institute of Technology, Atlanta, GA, 3332-15 USA This paper presents an output feedback adaptive
More informationDirect Adaptive Reconfigurable Control of a Tailless Fighter Aircraft
AIAA-98-48 Direct Adaptive Reconfigurable Control of a ailless Fighter Aircraft A.J. Calise, S. Lee and M. Sharma Georgia Institute of echnology School of Aerospace Engineering Atlanta, GA 333 Abstract
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 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 informationADAPTIVE NEURAL NETWORK CONTROLLER DESIGN FOR BLENDED-WING UAV WITH COMPLEX DAMAGE
ADAPTIVE NEURAL NETWORK CONTROLLER DESIGN FOR BLENDED-WING UAV WITH COMPLEX DAMAGE Kijoon Kim*, Jongmin Ahn**, Seungkeun Kim*, Jinyoung Suk* *Chungnam National University, **Agency for Defense and Development
More informationConcurrent Learning Adaptive Control of Linear Systems with Exponentially Convergent Bounds
INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING Int. J. Adapt. Control Signal Process. 211; :1 25 Published online in Wiley InterScience (www.interscience.wiley.com). Concurrent Learning
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 informationControlling Human Heart Rate Response During Treadmill Exercise
Controlling Human Heart Rate Response During Treadmill Exercise Frédéric Mazenc (INRIA-DISCO), Michael Malisoff (LSU), and Marcio de Queiroz (LSU) Special Session: Advances in Biomedical Mathematics 2011
More informationFAULT-TOLERANT CONTROL OF CHEMICAL PROCESS SYSTEMS USING COMMUNICATION NETWORKS. Nael H. El-Farra, Adiwinata Gani & Panagiotis D.
FAULT-TOLERANT CONTROL OF CHEMICAL PROCESS SYSTEMS USING COMMUNICATION NETWORKS Nael H. El-Farra, Adiwinata Gani & Panagiotis D. Christofides Department of Chemical Engineering University of California,
More informationComposite Model Reference Adaptive Control with Parameter Convergence under Finite Excitation
Composite Model Reference Adaptive Control with Parameter Convergence under Finite Excitation Namhoon Cho, Hyo-Sang Shin*, Youdan Kim, and Antonios Tsourdos Abstract A new parameter estimation method is
More informationEvent-triggering architectures for adaptive control of uncertain dynamical systems
Scholars' Mine Doctoral Dissertations Student Theses and Dissertations Fall 217 Event-triggering architectures for adaptive control of uncertain dynamical systems Ali Talib Oudah Albattat Follow this and
More informationModelling the Dynamics of Flight Control Surfaces Under Actuation Compliances and Losses
Modelling the Dynamics of Flight Control Surfaces Under Actuation Compliances and Losses Ashok Joshi Department of Aerospace Engineering Indian Institute of Technology, Bombay Powai, Mumbai, 4 76, India
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 informationAdaptive Control with a Nested Saturation Reference Model
Adaptive Control with a Nested Saturation Reference Model Suresh K Kannan and Eric N Johnson School of Aerospace Engineering Georgia Institute of Technology, Atlanta, GA 3332 This paper introduces a neural
More informationA brief introduction to robust H control
A brief introduction to robust H control Jean-Marc Biannic System Control and Flight Dynamics Department ONERA, Toulouse. http://www.onera.fr/staff/jean-marc-biannic/ http://jm.biannic.free.fr/ European
More informationInternal Model Control of A Class of Continuous Linear Underactuated Systems
Internal Model Control of A Class of Continuous Linear Underactuated Systems Asma Mezzi Tunis El Manar University, Automatic Control Research Laboratory, LA.R.A, National Engineering School of Tunis (ENIT),
More informationA Comparative Study on Automatic Flight Control for small UAV
Proceedings of the 5 th International Conference of Control, Dynamic Systems, and Robotics (CDSR'18) Niagara Falls, Canada June 7 9, 18 Paper No. 13 DOI: 1.11159/cdsr18.13 A Comparative Study on Automatic
More 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 informationState 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
More informationExam. 135 minutes, 15 minutes reading time
Exam August 6, 208 Control Systems II (5-0590-00) Dr. Jacopo Tani Exam Exam Duration: 35 minutes, 5 minutes reading time Number of Problems: 35 Number of Points: 47 Permitted aids: 0 pages (5 sheets) A4.
More informationQFT Framework for Robust Tuning of Power System Stabilizers
45-E-PSS-75 QFT Framework for Robust Tuning of Power System Stabilizers Seyyed Mohammad Mahdi Alavi, Roozbeh Izadi-Zamanabadi Department of Control Engineering, Aalborg University, Denmark Correspondence
More informationLecture 12. Upcoming labs: Final Exam on 12/21/2015 (Monday)10:30-12:30
289 Upcoming labs: Lecture 12 Lab 20: Internal model control (finish up) Lab 22: Force or Torque control experiments [Integrative] (2-3 sessions) Final Exam on 12/21/2015 (Monday)10:30-12:30 Today: Recap
More informationI. D. Landau, A. Karimi: A Course on Adaptive Control Adaptive Control. Part 9: Adaptive Control with Multiple Models and Switching
I. D. Landau, A. Karimi: A Course on Adaptive Control - 5 1 Adaptive Control Part 9: Adaptive Control with Multiple Models and Switching I. D. Landau, A. Karimi: A Course on Adaptive Control - 5 2 Outline
More informationConcurrent Learning Adaptive Control in the Presence of Uncertain Control Allocation Matrix
Concurrent Learning Adaptive Control in the Presence of Uncertain Control Allocation Matrix Ben Reish, Girish Chowdhary,, Distributed Autonomous Systems Laboratory, Oklahoma State University, Stillwater,
More informationAdaptive Predictive Observer Design for Class of Uncertain Nonlinear Systems with Bounded Disturbance
International Journal of Control Science and Engineering 2018, 8(2): 31-35 DOI: 10.5923/j.control.20180802.01 Adaptive Predictive Observer Design for Class of Saeed Kashefi *, Majid Hajatipor Faculty of
More informationStability theory is a fundamental topic in mathematics and engineering, that include every
Stability Theory Stability theory is a fundamental topic in mathematics and engineering, that include every branches of control theory. For a control system, the least requirement is that the system is
More informationANALYSIS OF MULTIPLE FLIGHT CONTROL ARCHITECTURES ON A SIX DEGREE OF FREEDOM GENERAL AVIATION AIRCRAFT. A Thesis by. John Taylor Oxford, Jr.
ANALYSIS OF MULTIPLE FLIGHT CONTROL ARCHITECTURES ON A SIX DEGREE OF FREEDOM GENERAL AVIATION AIRCRAFT A Thesis by John Taylor Oxford, Jr. Bachelor of Science, Georgia Institute of Technology, 2007 Submitted
More informationHere represents the impulse (or delta) function. is an diagonal matrix of intensities, and is an diagonal matrix of intensities.
19 KALMAN FILTER 19.1 Introduction In the previous section, we derived the linear quadratic regulator as an optimal solution for the fullstate feedback control problem. The inherent assumption was that
More informationChapter 9 Robust Stability in SISO Systems 9. Introduction There are many reasons to use feedback control. As we have seen earlier, with the help of a
Lectures on Dynamic Systems and Control Mohammed Dahleh Munther A. Dahleh George Verghese Department of Electrical Engineering and Computer Science Massachuasetts Institute of Technology c Chapter 9 Robust
More informationUnit quaternion observer based attitude stabilization of a rigid spacecraft without velocity measurement
Proceedings of the 45th IEEE Conference on Decision & Control Manchester Grand Hyatt Hotel San Diego, CA, USA, December 3-5, 6 Unit quaternion observer based attitude stabilization of a rigid spacecraft
More informationFRTN 15 Predictive Control
Department of AUTOMATIC CONTROL FRTN 5 Predictive Control Final Exam March 4, 27, 8am - 3pm General Instructions This is an open book exam. You may use any book you want, including the slides from the
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 informationProblem 1: Ship Path-Following Control System (35%)
Problem 1: Ship Path-Following Control System (35%) Consider the kinematic equations: Figure 1: NTNU s research vessel, R/V Gunnerus, and Nomoto model: T ṙ + r = Kδ (1) with T = 22.0 s and K = 0.1 s 1.
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 informationSeveral Extensions in Methods for Adaptive Output Feedback Control
Several Extensions in Methods for Adaptive Output Feedback Control Nakwan Kim Postdoctoral Fellow School of Aerospace Engineering Georgia Institute of Technology Atlanta, GA 333 5 Anthony J. Calise Professor
More informationEE363 Automatic Control: Midterm Exam (4 problems, 90 minutes)
EE363 Automatic Control: Midterm Exam (4 problems, 90 minutes) ) Block diagram simplification (0 points). Simplify the following block diagram.,i.e., find the transfer function from u to y. Your answer
More informationLecture 9: Input Disturbance A Design Example Dr.-Ing. Sudchai Boonto
Dr-Ing Sudchai Boonto Department of Control System and Instrumentation Engineering King Mongkuts Unniversity of Technology Thonburi Thailand d u g r e u K G y The sensitivity S is the transfer function
More informationsc 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
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 informationDISTURBANCES MONITORING FROM CONTROLLER STATES
DISTURBANCES MONITORING FROM CONTROLLER STATES Daniel Alazard Pierre Apkarian SUPAERO, av. Edouard Belin, 3 Toulouse, France - Email : alazard@supaero.fr Mathmatiques pour l Industrie et la Physique, Université
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 informationUNCERTAINTY MODELING VIA FREQUENCY DOMAIN MODEL VALIDATION
AIAA 99-3959 UNCERTAINTY MODELING VIA FREQUENCY DOMAIN MODEL VALIDATION Martin R. Waszak, * NASA Langley Research Center, Hampton, Virginia Dominick Andrisani II, Purdue University, West Lafayette, Indiana
More informationANALYSIS AND SYNTHESIS OF DISTURBANCE OBSERVER AS AN ADD-ON ROBUST CONTROLLER
ANALYSIS AND SYNTHESIS OF DISTURBANCE OBSERVER AS AN ADD-ON ROBUST CONTROLLER Hyungbo Shim (School of Electrical Engineering, Seoul National University, Korea) in collaboration with Juhoon Back, Nam Hoon
More informationL 1 Adaptive Controller for a Missile Longitudinal Autopilot Design
AIAA Guidance, Navigation and Control Conference and Exhibit 8-2 August 28, Honolulu, Hawaii AIAA 28-6282 L Adaptive Controller for a Missile Longitudinal Autopilot Design Jiang Wang Virginia Tech, Blacksburg,
More informationSubject: Optimal Control Assignment-1 (Related to Lecture notes 1-10)
Subject: Optimal Control Assignment- (Related to Lecture notes -). Design a oil mug, shown in fig., to hold as much oil possible. The height and radius of the mug should not be more than 6cm. The mug must
More informationL 1 Adaptive Output Feedback Controller to Systems of Unknown
Proceedings of the 27 American Control Conference Marriott Marquis Hotel at Times Square New York City, USA, July 11-13, 27 WeB1.1 L 1 Adaptive Output Feedback Controller to Systems of Unknown Dimension
More informationProportional, Integral & Derivative Control Design. Raktim Bhattacharya
AERO 422: Active Controls for Aerospace Vehicles Proportional, ntegral & Derivative Control Design Raktim Bhattacharya Laboratory For Uncertainty Quantification Aerospace Engineering, Texas A&M University
More informationIterative Learning Control Analysis and Design I
Iterative Learning Control Analysis and Design I Electronics and Computer Science University of Southampton Southampton, SO17 1BJ, UK etar@ecs.soton.ac.uk http://www.ecs.soton.ac.uk/ Contents Basics Representations
More informationPRECISION CONTROL OF LINEAR MOTOR DRIVEN HIGH-SPEED/ACCELERATION ELECTRO-MECHANICAL SYSTEMS. Bin Yao
PRECISION CONTROL OF LINEAR MOTOR DRIVEN HIGH-SPEED/ACCELERATION ELECTRO-MECHANICAL SYSTEMS Bin Yao Intelligent and Precision Control Laboratory School of Mechanical Engineering Purdue University West
More informationControl System Design
ELEC ENG 4CL4: Control System Design Notes for Lecture #11 Wednesday, January 28, 2004 Dr. Ian C. Bruce Room: CRL-229 Phone ext.: 26984 Email: ibruce@mail.ece.mcmaster.ca Relative Stability: Stability
More informationTopic # Feedback Control Systems
Topic #1 16.31 Feedback Control Systems Motivation Basic Linear System Response Fall 2007 16.31 1 1 16.31: Introduction r(t) e(t) d(t) y(t) G c (s) G(s) u(t) Goal: Design a controller G c (s) so that the
More informationRaktim Bhattacharya. . AERO 632: Design of Advance Flight Control System. Preliminaries
. AERO 632: of Advance Flight Control System. Preliminaries Raktim Bhattacharya Laboratory For Uncertainty Quantification Aerospace Engineering, Texas A&M University. Preliminaries Signals & Systems Laplace
More informationStability and Robustness 1
Lecture 2 Stability and Robustness This lecture discusses the role of stability in feedback design. The emphasis is notonyes/notestsforstability,butratheronhowtomeasurethedistanceto instability. The small
More informationAutonomous Helicopter Landing A Nonlinear Output Regulation Perspective
Autonomous Helicopter Landing A Nonlinear Output Regulation Perspective Andrea Serrani Department of Electrical and Computer Engineering Collaborative Center for Control Sciences The Ohio State University
More informationA Design, Analysis, and Verification framework for Adaptive Flight Control
A Design, Analysis, and Verification framework for Adaptive Flight Control Mario Luca Fravolini 1 University of Perugia, Perugia, Italy, 6125 ansel Yucelen 2, Daniel Wagner 3 and Benjamin Gruenwald 4 Missouri
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 informationChaos suppression of uncertain gyros in a given finite time
Chin. Phys. B Vol. 1, No. 11 1 1155 Chaos suppression of uncertain gyros in a given finite time Mohammad Pourmahmood Aghababa a and Hasan Pourmahmood Aghababa bc a Electrical Engineering Department, Urmia
More information(a) Find the transfer function of the amplifier. Ans.: G(s) =
126 INTRDUCTIN T CNTR ENGINEERING 10( s 1) (a) Find the transfer function of the amplifier. Ans.: (. 02s 1)(. 001s 1) (b) Find the expected percent overshoot for a step input for the closed-loop system
More informationChapter 7 Interconnected Systems and Feedback: Well-Posedness, Stability, and Performance 7. Introduction Feedback control is a powerful approach to o
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 7 Interconnected
More informationOutput Feedback Concurrent Learning Model Reference Adaptive Control
Output Feedback Concurrent Learning Model Reference Adaptive Control John F. Quindlen Massachusetts Institute of Technology, Cambridge, MA, 2139 Girish Chowdhary Oklahoma State University, Stillwater,
More informationDynamics and Control Preliminary Examination Topics
Dynamics and Control Preliminary Examination Topics 1. Particle and Rigid Body Dynamics Meirovitch, Leonard; Methods of Analytical Dynamics, McGraw-Hill, Inc New York, NY, 1970 Chapters 1-5 2. Atmospheric
More informationFormally Analyzing Adaptive Flight Control
Formally Analyzing Adaptive Flight Control Ashish Tiwari SRI International 333 Ravenswood Ave Menlo Park, CA 94025 Supported in part by NASA IRAC NRA grant number: NNX08AB95A Ashish Tiwari Symbolic Verification
More informationA SIMPLIFIED ANALYSIS OF NONLINEAR LONGITUDINAL DYNAMICS AND CONCEPTUAL CONTROL SYSTEM DESIGN
A SIMPLIFIED ANALYSIS OF NONLINEAR LONGITUDINAL DYNAMICS AND CONCEPTUAL CONTROL SYSTEM DESIGN ROBBIE BUNGE 1. Introduction The longitudinal dynamics of fixed-wing aircraft are a case in which classical
More informationTopic # Feedback Control Systems
Topic #20 16.31 Feedback Control Systems Closed-loop system analysis Bounded Gain Theorem Robust Stability Fall 2007 16.31 20 1 SISO Performance Objectives Basic setup: d i d o r u y G c (s) G(s) n control
More informationAdaptive Dynamic Inversion Control of a Linear Scalar Plant with Constrained Control Inputs
5 American Control Conference June 8-, 5. Portland, OR, USA ThA. Adaptive Dynamic Inversion Control of a Linear Scalar Plant with Constrained Control Inputs Monish D. Tandale and John Valasek Abstract
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 informationLONGITUDINAL STABILITY AUGMENTATION DESIGN WITH TWO DEGREE OF FREEDOM CONTROL STRUCTURE AND HANDLING QUALITIES REQUIREMENTS
LONGITUDINAL STABILITY AUGMENTATION DESIGN WITH TWO DEGREE OF FREEDOM CONTROL STRUCTURE AND HANDLING QUALITIES REQUIREMENTS Francisco J. Triveno Vargas, Fernando J. O. Moreira, Pedro Paglione *EMBRAER,
More informationConcurrent Learning for Convergence in Adaptive Control without Persistency of Excitation
Concurrent Learning for Convergence in Adaptive Control without Persistency of Excitation Girish Chowdhary and Eric Johnson Abstract We show that for an adaptive controller that uses recorded and instantaneous
More informationH inf. Loop Shaping Robust Control vs. Classical PI(D) Control: A case study on the Longitudinal Dynamics of Hezarfen UAV
Proceedings of the 2nd WSEAS International Conference on Dynamical Systems and Control, Bucharest, Romania, October 16-17, 2006 105 H inf. Loop Shaping Robust Control vs. Classical PI(D) Control: A case
More informationAdaptive Control for Nonlinear Uncertain Systems with Actuator Amplitude and Rate Saturation Constraints
Adaptive Control for Nonlinear Uncertain Systems with Actuator Amplitude and Rate Saturation Constraints Alexander Leonessa Dep. of Mechanical, Materials and Aerospace Engineering University of Central
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 informationRaktim Bhattacharya. . AERO 422: Active Controls for Aerospace Vehicles. Dynamic Response
.. AERO 422: Active Controls for Aerospace Vehicles Dynamic Response Raktim Bhattacharya Laboratory For Uncertainty Quantification Aerospace Engineering, Texas A&M University. . Previous Class...........
More informationRobust Multivariable Control
Lecture 1 Anders Helmersson anders.helmersson@liu.se ISY/Reglerteknik Linköpings universitet Addresses email: anders.helmerson@liu.se mobile: 0734278419 http://users.isy.liu.se/rt/andersh/teaching/robkurs.html
More informationControl of Chatter using Active Magnetic Bearings
Control of Chatter using Active Magnetic Bearings Carl R. Knospe University of Virginia Opportunity Chatter is a machining process instability that inhibits higher metal removal rates (MRR) and accelerates
More informationContents. 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
More informationAutomatic Control 2. Loop shaping. Prof. Alberto Bemporad. University of Trento. Academic year
Automatic Control 2 Loop shaping Prof. Alberto Bemporad University of Trento Academic year 21-211 Prof. Alberto Bemporad (University of Trento) Automatic Control 2 Academic year 21-211 1 / 39 Feedback
More informationÜbersetzungshilfe / Translation aid (English) To be returned at the end of the exam!
Prüfung Regelungstechnik I (Control Systems I) Prof. Dr. Lino Guzzella 3.. 24 Übersetzungshilfe / Translation aid (English) To be returned at the end of the exam! Do not mark up this translation aid -
More informationControl Systems Theory and Applications for Linear Repetitive Processes
Eric Rogers, Krzysztof Galkowski, David H. Owens Control Systems Theory and Applications for Linear Repetitive Processes Springer Contents 1 Examples and Representations 1 1.1 Examples and Control Problems
More informationUnifying Behavior-Based Control Design and Hybrid Stability Theory
9 American Control Conference Hyatt Regency Riverfront St. Louis MO USA June - 9 ThC.6 Unifying Behavior-Based Control Design and Hybrid Stability Theory Vladimir Djapic 3 Jay Farrell 3 and Wenjie Dong
More informationChapter 3. LQ, LQG and Control System Design. Dutch Institute of Systems and Control
Chapter 3 LQ, LQG and Control System H 2 Design Overview LQ optimization state feedback LQG optimization output feedback H 2 optimization non-stochastic version of LQG Application to feedback system design
More informationGUIDANCE AND CONTROL FOR D-SEND#2
GUIDANCE AND CONTROL FOR D-SEND#2 Jun ichiro Kawaguchi, Tetsujiro Ninomiya, Hirokazu Suzuki Japan Aerospace Exploration Agency kawaguchi.junichiroh@jaxa.jp; ninomiya.tetsujiro@jaxa.jp; suzuki.hirokazu@jaxa.jp
More informationChemical Process Dynamics and Control. Aisha Osman Mohamed Ahmed Department of Chemical Engineering Faculty of Engineering, Red Sea University
Chemical Process Dynamics and Control Aisha Osman Mohamed Ahmed Department of Chemical Engineering Faculty of Engineering, Red Sea University 1 Chapter 4 System Stability 2 Chapter Objectives End of this
More informationDr Ian R. Manchester
Week Content Notes 1 Introduction 2 Frequency Domain Modelling 3 Transient Performance and the s-plane 4 Block Diagrams 5 Feedback System Characteristics Assign 1 Due 6 Root Locus 7 Root Locus 2 Assign
More informationMech 6091 Flight Control System Course Project. Team Member: Bai, Jing Cui, Yi Wang, Xiaoli
Mech 6091 Flight Control System Course Project Team Member: Bai, Jing Cui, Yi Wang, Xiaoli Outline 1. Linearization of Nonlinear F-16 Model 2. Longitudinal SAS and Autopilot Design 3. Lateral SAS and Autopilot
More informationMechatronics Assignment # 1
Problem # 1 Consider a closed-loop, rotary, speed-control system with a proportional controller K p, as shown below. The inertia of the rotor is J. The damping coefficient B in mechanical systems is usually
More informationCopyrighted Material. 1.1 Large-Scale Interconnected Dynamical Systems
Chapter One Introduction 1.1 Large-Scale Interconnected Dynamical Systems Modern complex dynamical systems 1 are highly interconnected and mutually interdependent, both physically and through a multitude
More informationControl and Robustness for Quantum Linear Systems
CCC 2013 1 Control and Robustness for Quantum Linear Systems Ian R. Petersen School of Engineering and Information Technology, UNSW Canberra CCC 2013 2 Introduction Developments in quantum technology and
More informationOn Practical Applications of Active Disturbance Rejection Control
2010 Chinese Control Conference On Practical Applications of Active Disturbance Rejection Control Qing Zheng Gannon University Zhiqiang Gao Cleveland State University Outline Ø Introduction Ø Active Disturbance
More information-MASTER THESIS- ADVANCED ACTIVE POWER AND FREQUENCY CONTROL OF WIND POWER PLANTS
-MASTER THESIS- ADVANCED ACTIVE POWER AND FREQUENCY CONTROL OF WIND POWER PLANTS C L AU D I U I O N I TA 1, 2, A L I N G EO R G E R A D U C U 1, F LO R I N I OV 2 1 V A T T E N F A L L W I N D P O W E
More information