Lecture 7: Anti-windup and friction compensation
|
|
- Stewart Tate
- 6 years ago
- Views:
Transcription
1 Lecture 7: Anti-windup and friction compensation Compensation for saturations (anti-windup) Friction models Friction compensation Material Lecture slides
2 Course Outline Lecture 1-3 Lecture 2-6 Lecture 7-8 Lecture 9-13 Lecture 14 Modelling and basic phenomena (linearization, phase plane, limit cycles) Analysis methods (Lyapunov, circle criterion, describing functions) Common nonlinearities (Saturation, friction, backlash, quantization) Design methods (Lyapunov methods, Backstepping, Optimal control) Summary
3 Last lecture: Stable periodic solution r e u y G(s) G(iω) 1/N(A) G(s)= (s+10)2 (s+1) 3 with feedback u= sgny gives one stable and one unstable limit cycle. The left most intersection corresponds to the stable one.
4 Periodic Solutions in Relay System The relay gainn(a) is higher for smalla: Big amplitudes Small relay gain No encirclement Shrinking amplitudes Growing relay gain One encirclement Growing amplitudes Shrinking relay gain Small amplitudes High relay gain No encirclement Shrinking amplitudes Growing relay gain Stable periodic orbit Unstable periodic orbit
5 Today s Goal To be able to design and analyze antiwindup schemes for PID state-space systems and Kalman filters (observers) To understand common models of friction To design and analyze friction compensation schemes
6 Windup The Problem v u G(s) C(s) The feedback path is broken when u saturates The controller C(s) is a dynamic system Problems when controller is unstable (or stable but not AS) Example: I-part in PID-controller
7 Example-Windup in PID Controller 2 1 Output Input Time Dashed line: ordinary PID-controller Solid line: PID-controller with anti-windup
8 Anti-windup for PID-Controller ( Tracking ) Anti-windup (a) with actuator output available and (b) without (a) y KT d s Actuator e K v u K T i 1 s + 1 e s T t )b( y KT d s Actuatormodel Actuator e K v u K T i 1 s + 1 e s T t
9 Choice of Tracking TimeT t y set-point T t =3 T t =2 T t =0.1,T t =1 T t =0.1 T t =1 T t =3 T t =2 With very smallt t (large gain1/t t ), spurious errors can saturate the output, which leads to accidental reset of the integrator. Too larget t gives too slow reaction (little effect). The tracking timet t is the design parameter of the anti-windup. Common choices:t t =T i ort t = T i T d.
10 State feedback with Observer x m y Observer State feedback Actuator x ˆ Σ L sat(v) ˆx = Aˆx+Bsat(v)+K(y Cˆx) v = L(x m ˆx) ˆx is estimate of process state,x m desired (model) state. Need model of saturation if sat(v) is not measurable
11 Antiwindup General State-Space Controller State-space controller: ẋ c (t) = Fx c (t)+gy(t) u(t) = Cx c (t)+dy(t) Windup possible if F is unstable and u saturates. (a) y S A u (b) y S B u Idea: Rewrite representation of control law from (a) to (b) such that: (a) and (b) have same input-output relation (b) behaves better when feedback loop is broken, ifs B stable
12 Antiwindup General State-Space Controller Mimic the observer-based controller: ẋ c = Fx c +Gy+K(u Cx c Dy) }{{} =0 = (F KC)x c +(G KD)y+Ku = F 0 x c +G 0 y+ku Design so thatf 0 =F KC has desired stable eigenvalues Then use controller ẋ c = F 0 x c +G 0 y+ku u = sat(cx c +Dy)
13 State-space controller without and with anti-windup: D F y G s 1 x c C u D F KC y G KD s 1 x c C v sat u K
14 5 Minute Exercise How would you do antiwindup for the following state-feedback controller with observer and integral action? y ref 1 s L i u Process y L x Estimator
15 Saturation Optimal control theory (later) Multi-loop Anti-windup (Cascaded systems): Difficult problem, several suggested solutions Turn off integrator in outer loop when inner loop saturates
16 Friction Present almost everywhere Often bad Friction in valves and mechanical constructions Sometimes good Friction in brakes Sometimes too small Earthquakes Problems How to model friction How to compensate for friction
17 Stick-slip Motion k(y x) F x y Time Time Time
18 DIP Position Control of Servo with Friction Hunting F Friction x r u Σ 1 ms v 1 s x Time Time Time
19 3 Minute Exercise What are the signals in the previous plots? What model of friction has been used in the simulation?
20 Friction N N F F F
21 Lubrication Regimes Friction Sticking Boundary lubrication Mixed lubrication Full fluid lubrication Velocity Hard to get good model atv=0
22 Stribeck Effect For low velocity: friction increases with decreasing velocity Stribeck (1902) Steady state friction: Joint Friction [Nm] Velocity [rad/sec]
23 Frictional Lag Dynamics are important also outside sticking regime Hess and Soom (1990) Experiment with unidirectional motionv(t)=v 0 +asin(ωt) Hysteresis effect! Friction Velocity
24 Classical Friction Models a) b) F F v v c) d) F F v v c) F(t) = { Fc signv(t)+f v v(t) v(t) =0 max(min(f e (t),f s ), F s ) v(t)=0 F e (t)= external applied force,f c,f v,f s constants
25 Advanced Friction Models See PhD-thesis by Henrik Olsson Karnopp model Armstrong s seven parameter model Dahl model Bristle model Reset integrator model Bliman and Sorine Wit-Olsson-Åström
26 Demands on a model To be useful for control the model should be sufficiently accurate, suitable for simulation, simple, few parameters to determine. physical interpretations, insight Pick the simplest model that does the job! If no stiction occurs the v = 0-models are not needed.
27 Friction Compensation Lubrication Integral action (beware!) Dither Non-model based control Model based friction compensation Adaptive friction compensation
28 Integral Action The integral action compensates for any external disturbance Good if friction force changes slowly (v constant). To get fast action when friction changes one must use much integral action (smallt i ) Gives phase lag, may cause stability problems etc
29 Deadzone - Modified Integral Action Modify integral part toi= K t T 0ê(t)dτ i e(t) η e(t)> η where input to integrator ê = 0 e(t) < η e(t)+ η e(t)< η ê(t) η e(t) Advantage: Avoid that small static error introduces limit cycle Disadvantage: Must accept small error (will not go to zero)
30 Mechanical Vibrator Dither Avoids sticking atv=0where there usually is high friction by adding high-frequency mechanical vibration (dither ) x r + F Friction + + PID 1 u ms v 1 s x Cf., mechanical maze puzzle (labyrintspel)
31 Adaptive Friction Compensation Coulomb Friction F = a sgn(v) F friction Friction u PID ms v 1 s x F friction Friction estimator Assumption: v measurable. Friction estimator: F friction ż = ku PID sgn(v) â = z km v = âsgn(v)
32 Result:e=a â 0ast, since de dt = dâ dt = dz dt +kmd dt v = ku PID sgn(v)+km vsgn(v) = ksgn(v)(u PID m v) = ksgn(v)(f ˆF) = k(a â) = ke Remark: Careful with d dt v atv=0.
33 The Knocker Combines Coulomb compensation and square wave dither Tore Hägglund, Innovation Cup winner + patent 1997
34 Example Friction Compensation Velocity control with a) P-controller b) PI-controller c) P + Coulomb estimation
35 Results 1 P-controller 1 PI-controller v v ref u P-controller with Coulomb estimation
36 Next Lecture Backlash Quantization
Lecture 6 Describing function analysis
Lecture 6 Describing function analysis Today s Goal: To be able to Derive describing functions for static nonlinearities Predict stability and existence of periodic solutions through describing function
More informationLecture 6 Describing function analysis
Lecture 6 Describing function analysis Today s Goal: To be able to Derive describing functions for static nonlinearities Predict stability and existence of periodic solutions through describing function
More informationMODELING AND SIMULATION OF HYDRAULIC ACTUATOR WITH VISCOUS FRICTION
MODELING AND SIMULATION OF HYDRAULIC ACTUATOR WITH VISCOUS FRICTION Jitendra Yadav 1, Dr. Geeta Agnihotri 1 Assistant professor, Mechanical Engineering Department, University of petroleum and energy studies,
More informationCM 3310 Process Control, Spring Lecture 21
CM 331 Process Control, Spring 217 Instructor: Dr. om Co Lecture 21 (Back to Process Control opics ) General Control Configurations and Schemes. a) Basic Single-Input/Single-Output (SISO) Feedback Figure
More informationSystem Identification and Adaptive Compensation of Friction in Manufacturing Automation Systems
System Identification and Adaptive Compensation of Friction in Manufacturing Automation Systems by Mustafa Hakan Turhan A thesis presented to the University of Waterloo in fulfillment of the thesis requirement
More informationLecture 9 Nonlinear Control Design
Lecture 9 Nonlinear Control Design Exact-linearization Lyapunov-based design Lab 2 Adaptive control Sliding modes control Literature: [Khalil, ch.s 13, 14.1,14.2] and [Glad-Ljung,ch.17] Course Outline
More informationObserver Based Friction Cancellation in Mechanical Systems
2014 14th International Conference on Control, Automation and Systems (ICCAS 2014) Oct. 22 25, 2014 in KINTEX, Gyeonggi-do, Korea Observer Based Friction Cancellation in Mechanical Systems Caner Odabaş
More informationGoodwin, Graebe, Salgado, Prentice Hall Chapter 11. Chapter 11. Dealing with Constraints
Chapter 11 Dealing with Constraints Topics to be covered An ubiquitous problem in control is that all real actuators have limited authority. This implies that they are constrained in amplitude and/or rate
More informationLecture 9 Nonlinear Control Design. Course Outline. Exact linearization: example [one-link robot] Exact Feedback Linearization
Lecture 9 Nonlinear Control Design Course Outline Eact-linearization Lyapunov-based design Lab Adaptive control Sliding modes control Literature: [Khalil, ch.s 13, 14.1,14.] and [Glad-Ljung,ch.17] Lecture
More informationDistributed Real-Time Control Systems
Distributed Real-Time Control Systems Chapter 9 Discrete PID Control 1 Computer Control 2 Approximation of Continuous Time Controllers Design Strategy: Design a continuous time controller C c (s) and then
More informationLecture 5 Input output stability
Lecture 5 Input output stability or How to make a circle out of the point 1+0i, and different ways to stay away from it... k 2 yf(y) r G(s) y k 1 y y 1 k 1 1 k 2 f( ) G(iω) Course Outline Lecture 1-3 Lecture
More informationExercises in Nonlinear Control Systems
Exercises in Nonlinear Control Systems Mikael Johansson Bo Bernhardsson Karl Henrik Johansson Created: 998 Latest update: November 9, 26 Introduction The exercises are divided into problem areas that roughly
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 informationOutput Feedback and State Feedback. EL2620 Nonlinear Control. Nonlinear Observers. Nonlinear Controllers. ẋ = f(x,u), y = h(x)
Output Feedback and State Feedback EL2620 Nonlinear Control Lecture 10 Exact feedback linearization Input-output linearization Lyapunov-based control design methods ẋ = f(x,u) y = h(x) Output feedback:
More informationEnhanced Single-Loop Control Strategies Chapter 16
Enhanced Single-Loop Control Strategies Chapter 16 1. Cascade control 2. Time-delay compensation 3. Inferential control 4. Selective and override control 5. Nonlinear control 6. Adaptive control 1 Chapter
More informationControl Systems with Friction
Control Systems with Friction Olsson, Henrik 1996 Document Version: Publisher's PDF, also known as Version of record Link to publication Citation for published version (APA): Olsson, H. (1996). Control
More informationModification of the Leuven Integrated Friction Model Structure
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 47, NO. 4, APRIL 2002 683 Modification of the Leuven Integrated Friction Model Structure Vincent Lampaert, Jan Swevers, and Farid Al-Bender Abstract This note
More informationLecture 5 Classical Control Overview III. Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore
Lecture 5 Classical Control Overview III Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore A Fundamental Problem in Control Systems Poles of open
More informationIDENTIFICATION OF GMS FRICTION MODEL WITHOUT FRICTION FORCE MEASUREMENT
11 8th International Multi-Conference on Systems, Signals & Devices IDENTIFICATION OF GMS FRICTION MODEL WITHOUT FRICTION FORCE MEASUREMENT Said Grami, École de Technologie Supérieure UniversitéduQuébec
More informationFriction identification in mechatronic systems
ISA Transactions 43 2004 205 216 ISA TRANSACTIONS Friction identification in mechatronic systems Bashir M. Y. Nouri* Department of Mechatronics Engineering, Faculty of Engineering, The Hashemite University,
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 informationCHBE320 LECTURE XI CONTROLLER DESIGN AND PID CONTOLLER TUNING. Professor Dae Ryook Yang
CHBE320 LECTURE XI CONTROLLER DESIGN AND PID CONTOLLER TUNING Professor Dae Ryook Yang Spring 2018 Dept. of Chemical and Biological Engineering 11-1 Road Map of the Lecture XI Controller Design and PID
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 informationFRICTION MODELLING OF A LINEAR HIGH-PRECISION ACTUATOR. P.O. Box , D Ilmenau, Germany 2
FRICTION MODELLING OF A LINEAR HIGH-PRECISION ACTUATOR J. Zimmermann, O. Sawodny, T. Hausotte 2, G. Jäger 2 Technische Universität Ilmenau, Institute for Automation and Systems Engineering, P.O. Box 565,
More informationOutline of this presentation Introduction Friction models Static models 1. Models with time delay 2. Dynamic models 3. Friction compensation Non-model
of Engineering Cybernetics Department University of Science and Technology Norwegian Problems in Servomechanisms: Friction and Compensation Techniques Modeling Jan Tommy Gravdahl, Trondheim Outline of
More informationRobotics & Automation. Lecture 25. Dynamics of Constrained Systems, Dynamic Control. John T. Wen. April 26, 2007
Robotics & Automation Lecture 25 Dynamics of Constrained Systems, Dynamic Control John T. Wen April 26, 2007 Last Time Order N Forward Dynamics (3-sweep algorithm) Factorization perspective: causal-anticausal
More informationAdaptive NN Control of Dynamic Systems with Unknown Dynamic Friction
Adaptive NN Control of Dynamic Systems with Unknown Dynamic Friction S. S. Ge 1,T.H.LeeandJ.Wang Department of Electrical and Computer Engineering National University of Singapore Singapore 117576 Abstract
More informationIntegrator Windup
3.5.2. Integrator Windup 3.5.2.1. Definition So far we have mainly been concerned with linear behaviour, as is often the case with analysis and design of control systems. There is, however, one nonlinear
More informationFriction Modeling and Compensation for Haptic Interfaces
Friction Modeling and Compensation for Haptic Interfaces Nicholas L. Bernstein * Dale A. Lawrence * Lucy Y. Pao (*) University of Colorado, Aerospace Engineering, USA ( ) University of Colorado, Electrical
More informationControl System Design
ELEC ENG 4CL4: Control System Design Notes for Lecture #36 Dr. Ian C. Bruce Room: CRL-229 Phone ext.: 26984 Email: ibruce@mail.ece.mcmaster.ca Friday, April 4, 2003 3. Cascade Control Next we turn to an
More informationROBUST FRICTION COMPENSATOR FOR HARMONIC DRIVE TRANSMISSION
Proceedings of the 1998 IEEE International Conference on Control Applications Trieste, Italy 1-4 September 1998 TAO1 12:lO ROBUST FRICTION COMPENSATOR FOR HARMONIC DRIVE TRANSMISSION H.D. Taghirad K. N.
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 informationHIL SIMULATION TECHNIQUE FOR NON-MODEL-BASED CONTROL OF DC SERVO-DRIVE WITH FRICTION. Teodor Dumitriu, Mihai Culea, Traian Munteanu, Emil Ceangă
HIL IMULTION TECHNIQUE FOR NON-MODEL-BED CONTROL OF DC ERVO-DRIVE WITH FRICTION Teodor Dumitriu, Mihai Culea, Traian Munteanu, Emil Ceangă Dunărea de os University of Galaţi, Faculty of Electrical Engineering
More information4~ ~ri. Compensation of Friction in the Flight Simulator Stick using an Adaptive Friction Compensator. University of Twente
4~ ~ri University of Twente Compensation of Friction in the Flight Simulator Stick using an Adaptive Friction Compensator Nathan van Seters M.Sc. Thesis Author: Supervisors: N. van Seters Prof. dr. if.
More informationRegular and chaotic oscillations of friction force
Regular and chaotic oscillations of friction force A Stefański 1, J Wojewoda 1, M Wiercigroch 2, and T Kapitaniak 1 1 Division of Dynamics, Technical University of Łódź, Łódź, Poland 2 Centre for Applied
More informationControl System Design
ELEC ENG 4CL4: Control System Design Notes for Lecture #24 Wednesday, March 10, 2004 Dr. Ian C. Bruce Room: CRL-229 Phone ext.: 26984 Email: ibruce@mail.ece.mcmaster.ca Remedies We next turn to the question
More informationChapter 8. Feedback Controllers. Figure 8.1 Schematic diagram for a stirred-tank blending system.
Feedback Controllers Figure 8.1 Schematic diagram for a stirred-tank blending system. 1 Basic Control Modes Next we consider the three basic control modes starting with the simplest mode, proportional
More informationCascade Controller Including Backstepping for Hydraulic-Mechanical Systems
Proceedings of the 22 IFAC Workshop on Automatic Control in Offshore Oil and Gas Production, Norwegian University of Science and Technology, Trondheim, Norway, ay 3 - June, 22 FrBT2.3 Cascade Controller
More informationLaboratory Exercise 1 DC servo
Laboratory Exercise DC servo Per-Olof Källén ø 0,8 POWER SAT. OVL.RESET POS.RESET Moment Reference ø 0,5 ø 0,5 ø 0,5 ø 0,65 ø 0,65 Int ø 0,8 ø 0,8 Σ k Js + d ø 0,8 s ø 0 8 Off Off ø 0,8 Ext. Int. + x0,
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 informationAnalyzing Control Problems and Improving Control Loop Performance
OptiControls Inc. Houston, TX Ph: 713-459-6291 www.opticontrols.com info@opticontrols.com Analyzing Control s and Improving Control Loop Performance -by Jacques F. Smuts Page: 1 Presenter Principal Consultant
More informationEL2520 Control Theory and Practice
EL2520 Control Theory and Practice Lecture 8: Linear quadratic control Mikael Johansson School of Electrical Engineering KTH, Stockholm, Sweden Linear quadratic control Allows to compute the controller
More informationFriction Compensation by the use of Friction Observer
ISSN 28-5316 ISRN LUTFD2/TFRT--5729--SE Friction Compensation by the use of Friction Observer Mikael Janiec Department of Automatic Control Lund Institute of Technology October 24 Department of Automatic
More information2.72 Elements of Mechanical Design
MIT OpenCourseWare http://ocw.mit.edu 2.72 Elements of Mechanical Design Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 2.72 Elements of
More informationFriction. Modeling, Identification, & Analysis
Friction Modeling, Identification, & Analysis Objectives Understand the friction phenomenon as it relates to motion systems. Develop a control-oriented model with appropriate simplifying assumptions for
More informationEE3CL4: Introduction to Linear Control Systems
1 / 17 EE3CL4: Introduction to Linear Control Systems Section 7: McMaster University Winter 2018 2 / 17 Outline 1 4 / 17 Cascade compensation Throughout this lecture we consider the case of H(s) = 1. We
More informationFRICTION AND FRICTION COMPENSATION IN THE FURUTA PENDULUM
FRICTION AND FRICTION COMPENSATION IN THE FURUTA PENDULUM M. Gäfvert, J. Svensson and K. J. Åström Department of Automatic Control Lund Institute of Technology, Box 8, S- Lund, Sweden Fax:+4646388,E-mail:{magnus,kja}@control.lth.se
More information6 OUTPUT FEEDBACK DESIGN
6 OUTPUT FEEDBACK DESIGN When the whole sate vector is not available for feedback, i.e, we can measure only y = Cx. 6.1 Review of observer design Recall from the first class in linear systems that a simple
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 informationEvent-triggered PI control: Saturating actuators and anti-windup compensation
Event-triggered PI control: Saturating actuators and anti-windup compensation Daniel Lehmann, Georg Aleander Kiener and Karl Henrik Johansson Abstract Event-triggered control aims at reducing the communication
More informationIDENTIFICATION AND COMPENSATION OF FRICTION FOR A DUAL STAGE POSITIONING SYSTEM. A Thesis SATISH THIMMALAPURA
IDENTIFICATION AND COMPENSATION OF FRICTION FOR A DUAL STAGE POSITIONING SYSTEM A Thesis by SATISH THIMMALAPURA Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment
More informationEvent-triggered control subject to actuator saturation
Event-triggered control subject to actuator saturation GEORG A. KIENER Degree project in Automatic Control Master's thesis Stockholm, Sweden 212 XR-EE-RT 212:9 Diploma Thesis Event-triggered control subject
More informationLecture 6: Control Problems and Solutions. CS 344R: Robotics Benjamin Kuipers
Lecture 6: Control Problems and Solutions CS 344R: Robotics Benjamin Kuipers But First, Assignment 1: Followers A follower is a control law where the robot moves forward while keeping some error term small.
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 informationEXPERIMENTAL COMPARISON OF SATURATED VELOCITY CONTROLLERS FOR DC MOTORS
Journal of ELECTRICAL ENGINEERING, VOL. 59, NO. 5, 2008, 254 259 EXPERIMENTAL COMPARISON OF SATURATED VELOCITY CONTROLLERS FOR DC MOTORS Javier Moreno Valenzuela This paper concerns the velocity control
More informationLimit Cycles in High-Resolution Quantized Feedback Systems
Limit Cycles in High-Resolution Quantized Feedback Systems Li Hong Idris Lim School of Engineering University of Glasgow Glasgow, United Kingdom LiHonIdris.Lim@glasgow.ac.uk Ai Poh Loh Department of Electrical
More informationReview of course Nonlinear control Lecture 5. Lyapunov based design Torkel Glad Lyapunov design Control Lyapunov functions Control Lyapunov function
Review of corse Nonlinear control Lectre 5 Lyapnov based design Reglerteknik, ISY, Linköpings Universitet Geometric control theory inpt-otpt linearization controller canonical form observer canonical form
More informationSystem Types in Feedback Control with Saturating Actuators
System Types in Feedback Control with Saturating Actuators Yongsoon Eun, Pierre T. Kabamba, and Semyon M. Meerkov Department of Electrical Engineering and Computer Science, University of Michigan, Ann
More informationCDS 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
More informationIterative Controller Tuning Using Bode s Integrals
Iterative Controller Tuning Using Bode s Integrals A. Karimi, D. Garcia and R. Longchamp Laboratoire d automatique, École Polytechnique Fédérale de Lausanne (EPFL), 05 Lausanne, Switzerland. email: alireza.karimi@epfl.ch
More informationOutline. 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?
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 informationControls Problems for Qualifying Exam - Spring 2014
Controls Problems for Qualifying Exam - Spring 2014 Problem 1 Consider the system block diagram given in Figure 1. Find the overall transfer function T(s) = C(s)/R(s). Note that this transfer function
More informationCDS 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
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 informationFeedback Control of Linear SISO systems. Process Dynamics and Control
Feedback Control of Linear SISO systems Process Dynamics and Control 1 Open-Loop Process The study of dynamics was limited to open-loop systems Observe process behavior as a result of specific input signals
More 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 informationModeling and Control Overview
Modeling and Control Overview 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
More informationThe Feedforward Friction Compensation of Linear Motor Using Genetic Learning Algorithm
Proceedings of the 7th World Congress The International Federation of Automatic Control Seoul, Korea, July 6-, 8 The Feedforward Friction Compensation of Linear Motor Using Genetic Learning Algorithm Chin-Sheng
More informationExam. 135 minutes + 15 minutes reading time
Exam January 23, 27 Control Systems I (5-59-L) Prof. Emilio Frazzoli Exam Exam Duration: 35 minutes + 5 minutes reading time Number of Problems: 45 Number of Points: 53 Permitted aids: Important: 4 pages
More informationValve Stiction - Definition, Modeling, Detection, Quantification and Compensation
Valve Stiction - Definition, Modeling, Detection, Quantification and Compensation Dr. M. A. A. Shoukat Choudhury Department of Chemical Engineering Bangladesh University of Engineering & Technology ()
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 Control of Mass-Spring Systems with Unknown Hysteretic Contact Friction
26 American Control Conference (ACC) Boston arriott Copley Place July 6-8, 26. Boston, A, USA Adaptive Control of ass-spring Systems with Unknown Hysteretic Contact Friction ohammad Al Janaideh and Dennis
More informationIMC based automatic tuning method for PID controllers in a Smith predictor configuration
Computers and Chemical Engineering 28 (2004) 281 290 IMC based automatic tuning method for PID controllers in a Smith predictor configuration Ibrahim Kaya Department of Electrical and Electronics Engineering,
More informationSystems Analysis and Control
Systems Analysis and Control Matthew M. Peet Arizona State University Lecture 6: Generalized and Controller Design Overview In this Lecture, you will learn: Generalized? What about changing OTHER parameters
More informationContents lecture 5. Automatic Control III. Summary of lecture 4 (II/II) Summary of lecture 4 (I/II) u y F r. Lecture 5 H 2 and H loop shaping
Contents lecture 5 Automatic Control III Lecture 5 H 2 and H loop shaping Thomas Schön Division of Systems and Control Department of Information Technology Uppsala University. Email: thomas.schon@it.uu.se,
More informationHigh-Gain Observers in Nonlinear Feedback Control. Lecture # 3 Regulation
High-Gain Observers in Nonlinear Feedback Control Lecture # 3 Regulation High-Gain ObserversinNonlinear Feedback ControlLecture # 3Regulation p. 1/5 Internal Model Principle d r Servo- Stabilizing u y
More informationPractical control method for ultra-precision positioning using a ballscrew mechanism
Available online at www.sciencedirect.com Precision Engineering 32 (2008) 309 318 Practical control method for ultra-precision positioning using a ballscrew mechanism Guilherme Jorge Maeda, Kaiji Sato
More information1 An Overview and Brief History of Feedback Control 1. 2 Dynamic Models 23. Contents. Preface. xiii
Contents 1 An Overview and Brief History of Feedback Control 1 A Perspective on Feedback Control 1 Chapter Overview 2 1.1 A Simple Feedback System 3 1.2 A First Analysis of Feedback 6 1.3 Feedback System
More informationTTK4150 Nonlinear Control Systems Solution 6 Part 2
TTK4150 Nonlinear Control Systems Solution 6 Part 2 Department of Engineering Cybernetics Norwegian University of Science and Technology Fall 2003 Solution 1 Thesystemisgivenby φ = R (φ) ω and J 1 ω 1
More informationEECS C128/ ME C134 Final Wed. Dec. 15, am. Closed book. Two pages of formula sheets. No calculators.
Name: SID: EECS C28/ ME C34 Final Wed. Dec. 5, 2 8- am Closed book. Two pages of formula sheets. No calculators. There are 8 problems worth points total. Problem Points Score 2 2 6 3 4 4 5 6 6 7 8 2 Total
More informationTrajectory Planning, Setpoint Generation and Feedforward for Motion Systems
2 Trajectory Planning, Setpoint Generation and Feedforward for Motion Systems Paul Lambrechts Digital Motion Control (4K4), 23 Faculty of Mechanical Engineering, Control Systems Technology Group /42 2
More informationFrequency Domain Identification of Dynamic Friction Model Parameters
IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 10, NO. 2, MARCH 2002 191 Frequency Domain Identification of Dynamic Friction Model Parameters Ron H. A. Hensen, Marinus (René) J. G. van de Molengraft,
More informationControl Lab. Thermal Plant. Chriss Grimholt
Control Lab Thermal Plant Chriss Grimholt Process System Engineering Department of Chemical Engineering Norwegian University of Science and Technology October 3, 23 C. Grimholt (NTNU) Thermal Plant October
More informationExam. 135 minutes, 15 minutes reading time
Exam August 15, 2017 Control Systems I (151-0591-00L) Prof Emilio Frazzoli Exam Exam Duration: 135 minutes, 15 minutes reading time Number of Problems: 44 Number of Points: 52 Permitted aids: Important:
More informationRobust Anti-Windup Compensation for PID Controllers
Robust Anti-Windup Compensation for PID Controllers ADDISON RIOS-BOLIVAR Universidad de Los Andes Av. Tulio Febres, Mérida 511 VENEZUELA FRANCKLIN RIVAS-ECHEVERRIA Universidad de Los Andes Av. Tulio Febres,
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 informationIntroduction to Nonlinear Control Lecture # 4 Passivity
p. 1/6 Introduction to Nonlinear Control Lecture # 4 Passivity È p. 2/6 Memoryless Functions ¹ y È Ý Ù È È È È u (b) µ power inflow = uy Resistor is passive if uy 0 p. 3/6 y y y u u u (a) (b) (c) Passive
More informationMechatronics Modeling and Analysis of Dynamic Systems Case-Study Exercise
Mechatronics Modeling and Analysis of Dynamic Systems Case-Study Exercise Goal: This exercise is designed to take a real-world problem and apply the modeling and analysis concepts discussed in class. As
More informationDigital 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
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 informationREPETITIVE LEARNING OF BACKSTEPPING CONTROLLED NONLINEAR ELECTROHYDRAULIC MATERIAL TESTING SYSTEM 1. Seunghyeokk James Lee 2, Tsu-Chin Tsao
REPETITIVE LEARNING OF BACKSTEPPING CONTROLLED NONLINEAR ELECTROHYDRAULIC MATERIAL TESTING SYSTEM Seunghyeokk James Lee, Tsu-Chin Tsao Mechanical and Aerospace Engineering Department University of California
More informationMCE693/793: Analysis and Control of Nonlinear Systems
MCE693/793: Analysis and Control of Nonlinear Systems Introduction to Describing Functions Hanz Richter Mechanical Engineering Department Cleveland State University Introduction Frequency domain methods
More informationVehicle longitudinal speed control
Vehicle longitudinal speed control Prof. R.G. Longoria Department of Mechanical Engineering The University of Texas at Austin February 10, 2015 1 Introduction 2 Control concepts Open vs. Closed Loop Control
More informationSystems Analysis and Control
Systems Analysis and Control Matthew M. Peet Arizona State University Lecture 21: Stability Margins and Closing the Loop Overview In this Lecture, you will learn: Closing the Loop Effect on Bode Plot Effect
More informationMS-E2133 Systems Analysis Laboratory II Assignment 2 Control of thermal power plant
MS-E2133 Systems Analysis Laboratory II Assignment 2 Control of thermal power plant How to control the thermal power plant in order to ensure the stable operation of the plant? In the assignment Production
More informationCarlos Canudas de Wit. ENSIEG-INPG, BP 46, 38402, ST. Martin d'heres, France. ultrasonic motor. more sophisticated friction model of the form:
CONTROL OF FRICTION-DRIVEN SYSTEMS Carlos Canudas de Wit Laboratoire d'automatique de Grenoble, UMR CNRS 558 ENSIEG-INPG, BP 46, 384, ST. Martin d'heres, France canudas@lag.ensieg.inpg.fr Abstract There
More information1 Loop Control. 1.1 Open-loop. ISS0065 Control Instrumentation
Lecture 4 ISS0065 Control Instrumentation 1 Loop Control System has a continuous signal (analog) basic notions: open-loop control, close-loop control. 1.1 Open-loop Open-loop / avatud süsteem / открытая
More informationModeling and Simulation of the Nonlinear Computed Torque Control in Simulink/MATLAB for an Industrial Robot
Copyright 2013 Tech Science Press SL, vol.10, no.2, pp.95-106, 2013 Modeling and Simulation of the Nonlinear Computed Torque Control in Simulink/MATLAB for an Industrial Robot Dǎnuţ Receanu 1 Abstract:
More informationFriction Compensation for a Force-Feedback Teleoperator with Compliant Transmission
Friction Compensation for a Force-Feedback Teleoperator with Compliant Transmission Mohsen Mahvash and Allison M. Okamura Department of Mechanical Engineering Engineering Research Center for Computer-Integrated
More information