Introduction to Systems Theory and Control Systems


 Leon Franklin Johnston
 10 months ago
 Views:
Transcription
1 Introduction to Systems Theory and Control Systems Paula Raica Department of Automation Dorobantilor Str., room C21, tel: Baritiu Str., room C14, tel: Technical University of ClujNapoca
2 Course organization Lectures: 2h/week, room D21 (Baritiu) Lab exercises: 4h / 2 weeks, Dorobatilor Str., yellow building on the right. Lab C01: ground floor Taught by: Paula Raica (lectures) Lab: Group When Where Who Friday C01 Paula Raica Thursday C01 Iulia Clitan Tuesday C01 Iulia Clitan Thursday 812 C01 Alexandru Codrean (odd) Zoltan Nagy (even) Tuesday C01 Paula Raica (odd) Zoltan Nagy (even)
3 Systems Theory. Grading Point accumulation Exams (see Course calendar and grading ): lab tests  including homework assignments (optional) midterm exam (optional) final exam Control Challenge Lab work policy Prerequisites: Differential equations, Linear algebra, Laplace transform, Complex numbers
4 Course objective The general objective of the course is to introduce the fundamental principles of linear system modeling, analysis and feedback control and to evaluate feedback control systems with desired behavior.
5 Systems Theory System : A set or arrangement of entities so related or connected so as to form a unity or organic whole. (Iberall) Systems theory: interdisciplinary field which studies systems. Founded by Ludwig von Bertalanffy, William Ross Ashby and others between the 1940s and the 1970s on principles from physics, biology and engineering Grew into numerous fields including philosophy, sociology, organizational theory, management and economics among others. Cybernetics is a related field, sometimes considered as a part of systems theory.
6 Control Systems Engineering Understanding systems Control of systems Modeling and control of modern, complex, interrelated systems traffic control systems, chemical processes, robotic systems industrial automation systems. Control Systems Engineering is based on the foundations of feedback theory and linear systems analysis.
7 Historical Background 300 B.C, Greece : development of the float regulator mechanisms, mid 1860s, J.C.Maxwell: the first formal study of the Theory of Control, mid 1890s, E.J. Routh and A.M. Lyapunov: Routh Stability Test and the Lyapunov Stability Criteria 1930s, H. Nyquist (Bell Telephone Laboratories): applied frequency analysis to control systems design 1930, H.W.Bode: designed electronic amplifiers using the concepts of feedback control 1950s onwards: control theory evolved with new mathematical techniques applied and computer technology.
8 Discipline of Control Systems Multidisciplinary field. Covers Mechanical Engineering, Chemical Engineering, Electrical and Electronic Engineering, Environmental, Civil, Physics, Economics and Finance, Artificial Intelligence and Computer Science Taught in the main stream Engineering and Physics courses ComputerControlled Systems: complex field in control engineering. Concepts overlap with the branch of Physics and Electrical Engineering known as Digital Signal Processing (DSP) and Communication Systems
9 Dynamical system A dynamical system is a system whose behavior changes over time, often in response to external stimulation or forcing. Inputs (cause) = quantities that are acting on the system from the environment Outputs (effect) = the results of the input acting on the system. Inputs, outputs = signals
10 Example: Helicopter Figure: Helicopter Inputs: the power produced by the engines the pilot control inputs the wind = disturbance Outputs the actual position (coordinates x, y, z) orientation (roll, pitch, yaw) velocity
11 Terminology Control of an inverted pendulum Figure: Elements in a control system Block diagram. Input. Output. Plant (Process). Measurement. Signals. Setpoint (Reference value). Comparator. Compensator. Actuator. Disturbance. Openloop. Closedloop. Negative Feedback.
12 Closedloop control system for HDD Figure: A hard disk control system
13 Examples Oven temperature control (closedloop) Washing machine: (openloop) Central heating: (closedloop) vs. radiator( openloop) Automobile steering control system Desired course of travel Error Driver Steering mechanism Automobile Actual course of travel Actual direction of travel Desired direction of travel Measurement, visual and tactile
14 Applications Figure: Maglev Figure: Traffic control
15 Applications
16 Applications Figure: Chemical industry, energy
17 Applications
18 Course contents Mathematical models of linear time invariant systems systems. Transfer functions, statespace models, block diagram models Analysis of linear continuous systems. Characteristics and performance. Stability of linear continuous systems. System analysis using root locus. Frequency response. Bode diagrams. Controller design. Leadlag compensation. PID control. State feedback Sampleddata systems. Digital control systems.
19 Bibliography R.C.Dorf, R.Bishop, Modern Control Systems, AddisonWesley, 2011; K.Ogata, Modern Control Engineering, Prentice Hall, K.Dutton, S. Thompson, B. Barraclough, The Art of Control Engineering, AddisonWesley, 1997 M. Hăngănuţ, Teoria sistemelor, UTCluj, 1996 T. Coloşi, Elemente de teoria sistemelor si reglaj automat, UTCluj, 1981
20 Introduction to Control System Modeling Paula Raica Department of Automation Dorobantilor Str., room C21, tel: Baritiu Str., room C14, tel: Technical University of ClujNapoca Introduction to Control System Modeling
21 Introduction A mathematical model is an equation or set of equations which adequately describes the behavior of a system. Two approaches to finding the model: Lumpedparameter modeling: for each element a mathematical description is established from the physical laws. System identification: an experiment can be carried out and a mathematical model can be found from the results. The important relationship is that between the manipulated inputs and measurable outputs. u(t) input Dynamic System y(t) output Introduction to Control System Modeling
22 Lumpedparameter models The systems studied in this course are: Examples. Linear  must obey the principle of superposition Stationary (or time invariant)  the parameters inside the element must not vary with time. Deterministic  The outputs of the system at any time can be determined from a knowledge of the system s inputs up to that time. The resistor: i(t) = 1 R v(t) The inductor: i(t) = 1 L v(t)dt or v(t) = L di(t) dt The capacitor: i(t) = C dv(t) dt Introduction to Control System Modeling
23 Examples Springmassdamper system Friction f Mass M k displacement y(t) Force r(t) M d2 y(t) dt 2 +f dy(t) +ky(t) = r(t) dt where: f is the friction coefficient, M  the mass, k  the stiffness of the linear spring. Introduction to Control System Modeling
24 Principle of superposition A system is defined as linear in terms of the system excitation and response. Additivity x 1 (t) y 1 (t) x 2 (t) y 2 (t) x 1 (t)+x 2 (t) y 1 (t)+y 2 (t) Homogeneity x(t) y(t) mx(t) my(t) Introduction to Control System Modeling
25 Linear Approximation Nonlinear system Nonlinear system y = x 2 y = mx +b Linear about an operating point x 0,y 0 for small changes x and y. When x = x 0 + x and y = y 0 + y: y 0 + y = mx 0 +m x +b and therefore y = m x Introduction to Control System Modeling
26 Linear Approximation If the dependent variable y depends upon several excitation variables x 1,x 2,...,x n : y = g(x 1,x 2,...,x n ). The Taylor series expansion about the operating point x 10,x 20,...,x n0 (the higherorder terms are neglected): y = g(x 10,x 20,...,x n0 )+ g x 1 x=x0 (x 1 x 10 )+ + g x 2 x=x0 (x 2 x 20 )+...+ g x n x=x0 (x n x n0 ) where x 0 is the operating point. Introduction to Control System Modeling
27 Example  Pendulum oscillator The torque on the mass is: T = MgLsin(x) The equilibrium condition for the mass is x 0 = 0 o. T T 0 = MgL sinx x x=x 0 (x x 0 ), where T 0 = 0. T = MgL(cos0 o )(x 0 o ) = MgLx The approximation is reasonably accurate for π/4 x π/4. Introduction to Control System Modeling
28 Linear Approximation Input x(t) and a response y(t): y(t) = g(x(t)) Taylor series expansion about the operating point x 0 : y = g(x) = g(x 0 )+ dg dx x x 0 x=x 0 + higher order terms 1! The slope at the operating point, m = dg dx x=x 0, y = g(x 0 )+ dg dx x=x 0 (x x 0 ) = y 0 +m(x x 0 ), Finally, this equation can be rewritten as the linear equation (y y 0 ) = m(x x 0 ) or y = m x Introduction to Control System Modeling
29 Example. Magnetic levitation The system: an ironcore electromagnet and the steel ball levitated by the electromagnet. Electromagnetic force F m : F m = C i2 (t) z 2 (t) Introduction to Control System Modeling
30 Example. Magnetic levitation Input: the current through the coils of the electromagnet i(t) Output: the displacement of the ball z(t) The equation of motion for the ball: Nonlinear model!! m z(t) = mg C i2 (t) z 2 (t) Introduction to Control System Modeling
31 Example. Magnetic levitation  linearization Rewrite the equation: g( z(t),z(t),i(t)) = m z(t) mg +C i2 (t) z 2 (t) = 0 Choose an operating point: ( z 0, z 0, i 0 ) such that m z 0 = mg C i2 0 z 2 0 Write the truncated Taylor series around the operating point: 0 = g( z(t),z(t),i(t)) g( z 0,z 0,i 0 )+ g z ( z 0, z 0, i 0 )( z(t) z 0 )+ + g z ( z 0, z 0, i 0 )(z(t) z 0 )+ + g i ( z 0, z 0, i 0 )(i(t) i 0 ) Introduction to Control System Modeling
32 Example. Magnetic levitation  linearization Compute the partial derivatives and evaluate them at the operating point. The Taylor series expansion is: 0 0+m ( z(t) z 0 ) 2C i2 0 z0 3 (z(t) z 0 )+2C i 0 z0 2 (i(t) i 0 ) Denote the variations around the operating point by: z(t) = z(t) z 0, z(t) = z(t) z 0 and i(t) = i(t) i 0 Linear differential equation in terms of z(t), z(t), i(t): m z(t) = 2C i2 0 z0 3 z(t) 2C i 0 z0 2 i(t) Introduction to Control System Modeling
33 To do Review: Differential equations Linear algebra Laplace transform Check the course webpage: Download the exercises (ControlEngineering.pdf) and detailed lecture notes Introduction to Control System Modeling
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 splane 4 27 Mar Block Diagrams Assign 1 Due 5 3 Apr Feedback System Characteristics
More informationAnalog Signals and Systems and their properties
Analog Signals and Systems and their properties Main Course Objective: Recall course objectives Understand the fundamentals of systems/signals interaction (know how systems can transform or filter signals)
More informationI Laplace transform. I Transfer function. I Conversion between systems in time, frequencydomain, and transfer
EE C128 / ME C134 Feedback Control Systems Lecture Chapter 2 Modeling in the Frequency Domain Alexandre Bayen Department of Electrical Engineering & Computer Science University of California Berkeley Lecture
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 informationDr. Ian R. Manchester
Dr Ian R. Manchester Week Content Notes 1 Introduction 2 Frequency Domain Modelling 3 Transient Performance and the splane 4 Block Diagrams 5 Feedback System Characteristics Assign 1 Due 6 Root Locus
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 informationControl Systems I. Lecture 2: Modeling. Suggested Readings: Åström & Murray Ch. 23, Guzzella Ch Emilio Frazzoli
Control Systems I Lecture 2: Modeling Suggested Readings: Åström & Murray Ch. 23, Guzzella Ch. 23 Emilio Frazzoli Institute for Dynamic Systems and Control DMAVT ETH Zürich September 29, 2017 E. Frazzoli
More informationCHAPTER 1 Basic Concepts of Control System. CHAPTER 6 Hydraulic Control System
CHAPTER 1 Basic Concepts of Control System 1. What is open loop control systems and closed loop control systems? Compare open loop control system with closed loop control system. Write down major advantages
More informationAutonomous 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:
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 informationFUZZY CONTROL CONVENTIONAL CONTROL CONVENTIONAL CONTROL CONVENTIONAL CONTROL CONVENTIONAL CONTROL CONVENTIONAL CONTROL
Eample: design a cruise control system After gaining an intuitive understanding of the plant s dynamics and establishing the design objectives, the control engineer typically solves the cruise control
More informationME 132, Dynamic Systems and Feedback. Class Notes. Spring Instructor: Prof. A Packard
ME 132, Dynamic Systems and Feedback Class Notes by Andrew Packard, Kameshwar Poolla & Roberto Horowitz Spring 2005 Instructor: Prof. A Packard Department of Mechanical Engineering University of California
More informationINSTRUMENTAL ENGINEERING
INSTRUMENTAL ENGINEERING Subject Code: IN Course Structure Sections/Units Section A Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Section B Section C Section D Section E Section F Section G Section H Section
More informationCHEE 319 Process Dynamics and Control
CHEE 319 Process Dynamics and Control Winter 2012 Instructor: M.Guay TAs: S. Dougherty, D. Park and E. Moshksar 1 Organization Instructor: Dr. Martin Guay Office: Dupuis 406 Phone: 5332788 Email: guaym@chee.queensu.ca
More informationLinear Control Systems Solution to Assignment #1
Linear Control Systems Solution to Assignment # Instructor: H. Karimi Issued: Mehr 0, 389 Due: Mehr 8, 389 Solution to Exercise. a) Using the superposition property of linear systems we can compute the
More informationNonlinear System Analysis
Nonlinear System Analysis Lyapunov Based Approach Lecture 4 Module 1 Dr. Laxmidhar Behera Department of Electrical Engineering, Indian Institute of Technology, Kanpur. January 4, 2003 Intelligent Control
More informationControl Systems! Copyright 2017 by Robert Stengel. All rights reserved. For educational use only.
Control Systems Robert Stengel Robotics and Intelligent Systems MAE 345, Princeton University, 2017 Analog vs. digital systems Continuous and Discretetime Dynamic Models Frequency Response Transfer Functions
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. 8. 24 Übersetzungshilfe / Translation aid (English) To be returned at the end of the exam! Do not mark up this translation aid
More informationAutomatic Control (TSRT15): Lecture 1
Automatic Control (TSRT15): Lecture 1 Tianshi Chen* Division of Automatic Control Dept. of Electrical Engineering Email: tschen@isy.liu.se Phone: 13282226 Office: Bhouse extrance 2527 * All lecture
More informationDepartment of Electrical and Telecommunications Engineering Technology TEL (718) FAX: (718) Courses Description:
NEW YORK CITY COLLEGE OF TECHNOLOGY The City University of New York 300 Jay Street Brooklyn, NY 112012983 Department of Electrical and Telecommunications Engineering Technology TEL (718) 2605300  FAX:
More informationTeaching State Variable Feedback to Technology Students Using MATLAB and SIMULINK
Teaching State Variable Feedback to Technology Students Using MATLAB and SIMULINK Kathleen A.K. Ossman, Ph.D. University of Cincinnati Session 448 I. Introduction This paper describes a course and laboratory
More informationFeedback Basics. David M. Auslander Mechanical Engineering University of California at Berkeley. copyright 1998, D.M. Auslander
Feedback Basics David M. Auslander Mechanical Engineering University of California at Berkeley copyright 1998, D.M. Auslander 1 I. Feedback Control Context 2 What is Feedback Control? Measure desired behavior
More informationECE 516: System Control Engineering
ECE 516: System Control Engineering This course focuses on the analysis and design of systems control. This course will introduce timedomain systems dynamic control fundamentals and their design issues
More informationCONTROL SYSTEMS, ROBOTICS, AND AUTOMATION Vol. III Controller Design  Boris Lohmann
CONROL SYSEMS, ROBOICS, AND AUOMAION Vol. III Controller Design  Boris Lohmann CONROLLER DESIGN Boris Lohmann Institut für Automatisierungstechnik, Universität Bremen, Germany Keywords: State Feedback
More informationSAMPLE SOLUTION TO EXAM in MAS501 Control Systems 2 Autumn 2015
FACULTY OF ENGINEERING AND SCIENCE SAMPLE SOLUTION TO EXAM in MAS501 Control Systems 2 Autumn 2015 Lecturer: Michael Ruderman Problem 1: Frequencydomain analysis and control design (15 pt) Given is a
More informationRELAY CONTROL WITH PARALLEL COMPENSATOR FOR NONMINIMUM PHASE PLANTS. Ryszard Gessing
RELAY CONTROL WITH PARALLEL COMPENSATOR FOR NONMINIMUM PHASE PLANTS Ryszard Gessing Politechnika Śl aska Instytut Automatyki, ul. Akademicka 16, 44101 Gliwice, Poland, fax: +4832 372127, email: gessing@ia.gliwice.edu.pl
More informationContents. Dynamics and control of mechanical systems. Focus on
Dynamics and control of mechanical systems Date Day 1 (01/08) Day 2 (03/08) Day 3 (05/08) Day 4 (07/08) Day 5 (09/08) Day 6 (11/08) Content Review of the basics of mechanics. Kinematics of rigid bodies
More informationMathematical Description of Light
Mathematical Description of Light Thursday, 8/24/2006 Physics 158 Peter Beyersdorf Document info 1 Class Outline Introductions/Announcements Properties of light Mathematical description of transverse waves
More informationLecture Notes for PHY 405 Classical Mechanics
Lecture Notes for PHY 405 Classical Mechanics From Thorton & Marion s Classical Mechanics Prepared by Dr. Joseph M. Hahn Saint Mary s University Department of Astronomy & Physics September 1, 2005 Chapter
More informationControl System. Contents
Contents Chapter Topic Page Chapter Chapter Chapter3 Chapter4 Introduction Transfer Function, Block Diagrams and Signal Flow Graphs Mathematical Modeling Control System 35 Time Response Analysis of
More informationLecture 2. Introduction to Systems (Lathi )
Lecture 2 Introduction to Systems (Lathi 1.61.8) Pier Luigi Dragotti Department of Electrical & Electronic Engineering Imperial College London URL: www.commsp.ee.ic.ac.uk/~pld/teaching/ Email: p.dragotti@imperial.ac.uk
More informationLecture 1. EE70 Fall 2007
Lecture 1 EE70 Fall 2007 Instructor Joel Kubby (that would be me) Office: BE249 Office Hours: M,W,F 23 PM or by appointment Phone: (831) 4591073 Email: jkubby@soe.ucsc.edu Teaching Assistant Drew Lohn
More informationINTRODUCTION TO DIGITAL CONTROL
ECE4540/5540: Digital Control Systems INTRODUCTION TO DIGITAL CONTROL.: Introduction In ECE450/ECE550 Feedback Control Systems, welearnedhow to make an analog controller D(s) to control a lineartimeinvariant
More informationModeling and Experimentation: Compound Pendulum
Modeling and Experimentation: Compound Pendulum Prof. R.G. Longoria Department of Mechanical Engineering The University of Texas at Austin Fall 2014 Overview This lab focuses on developing a mathematical
More informationGeneral Information Mechanical Vibrations Lesson 1 Grade Breakdown: Midterm Exam 45% Final Exam 55% Homework and Quiz 5% (Extra)
General Information Instructor: Name: Withit Chatlatanagulchai Office: 9/, 9th floor of Engineering Building Office Phone: 948555 ext 858 Mobile Phone: 839 Email: fengwtc@ku.ac.th Website: http://pirun.ku.ac.th/~fengwtc/
More informationName: Fall 2014 CLOSED BOOK
Name: Fall 2014 1. Rod AB with weight W = 40 lb is pinned at A to a vertical axle which rotates with constant angular velocity ω =15 rad/s. The rod position is maintained by a horizontal wire BC. Determine
More informationAP Physics B Syllabus
AP Physics B Syllabus Course Overview Advanced Placement Physics B is a rigorous course designed to be the equivalent of a college introductory Physics course. The focus is to provide students with a broad
More informationExam. 135 minutes + 15 minutes reading time
Exam January 23, 27 Control Systems I (559L) 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 informationDigital Pendulum Control Experiments
EE341L CONTROL SYSTEMS LAB 2013 Digital Pendulum Control Experiments Ahmed Zia Sheikh 2010030 M. Salman Khalid 2010235 Suleman Belal Kazi 2010341 TABLE OF CONTENTS ABSTRACT...2 PENDULUM OVERVIEW...3 EXERCISE
More informationLecture «Robot Dynamics»: Dynamics 2
Lecture «Robot Dynamics»: Dynamics 2 151085100 V lecture: CAB G11 Tuesday 10:15 12:00, every week exercise: HG E1.2 Wednesday 8:15 10:00, according to schedule (about every 2nd week) office hour: LEE
More informationDifferential Equations and Linear Algebra Supplementary Notes. Simon J.A. Malham. Department of Mathematics, HeriotWatt University
Differential Equations and Linear Algebra Supplementary Notes Simon J.A. Malham Department of Mathematics, HeriotWatt University Contents Chapter 1. Linear algebraic equations 5 1.1. Gaussian elimination
More informationVibrations Qualifying Exam Study Material
Vibrations Qualifying Exam Study Material The candidate is expected to have a thorough understanding of engineering vibrations topics. These topics are listed below for clarification. Not all instructors
More informationMechatronics Engineering. Li Wen
Mechatronics Engineering Li Wen Bioinspired robotdc motor drive Unstable system Mirko Kovac,EPFL Modeling and simulation of the control system Problems 1. Why we establish mathematical model of the control
More informationAP PHYSICS (B) SYLLABUS. Text: Physics, Sixth Edition by Cutnell and Johnson ISBN , Wiley and Sons, 2004 COURSE OVERVIEW
AP PHYSICS (B) SYLLABUS Text: Physics, Sixth Edition by Cutnell and Johnson ISBN 0471151831, Wiley and Sons, 2004 COURSE OVERVIEW Advanced Placement Physics is an intensive and rigorous college level
More informationControl System Design
ELEC ENG 4CL4: Control System Design Notes for Lecture #1 Monday, January 6, 2003 Instructor: Dr. Ian C. Bruce Room CRL229, Ext. 26984 ibruce@mail.ece.mcmaster.ca Office Hours: TBA Teaching Assistants:
More informationUsing Lyapunov Theory I
Lecture 33 Stability Analysis of Nonlinear Systems Using Lyapunov heory I Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science  Bangalore Outline Motivation Definitions
More informationPhysics Lecture 01: MON 25 AUG
Physics 2113 Jonathan Dowling Isaac Newton (1642 1727) Physics 2113 Lecture 01: MON 25 AUG CH13: Gravitation I Version: 8/24/14 Michael Faraday (1791 1867) Who am I & Why am I Here? Office hours: Nicholson
More informationLab 5a: Magnetic Levitation (Week 1)
ME C134 / EE C128 Fall 2017 Lab 5a Lab 5a: Magnetic Levitation (Week 1) Magnetism, as you recall from physics class, is a powerful force that causes certain items to be attracted to refrigerators. Dave
More informationInductance, RL and RLC Circuits
Inductance, RL and RLC Circuits Inductance Temporarily storage of energy by the magnetic field When the switch is closed, the current does not immediately reach its maximum value. Faraday s law of electromagnetic
More informationEE C128 / ME C134 Feedback Control Systems
EE C128 / ME C134 Feedback Control Systems Lecture Additional Material Introduction to Model Predictive Control Maximilian Balandat Department of Electrical Engineering & Computer Science University of
More information4.2 Homogeneous Linear Equations
4.2 Homogeneous Linear Equations Homogeneous Linear Equations with Constant Coefficients Consider the firstorder linear differential equation with constant coefficients a 0 and b. If f(t) = 0 then this
More informationControl System Design
ELEC ENG 4CL4: Control System Design Notes for Lecture #24 Wednesday, March 10, 2004 Dr. Ian C. Bruce Room: CRL229 Phone ext.: 26984 Email: ibruce@mail.ece.mcmaster.ca Remedies We next turn to the question
More informationLecture IV: LTI models of physical systems
BME 171: Signals and Systems Duke University September 5, 2008 This lecture Plan for the lecture: 1 Interconnections of linear systems 2 Differential equation models of LTI systems 3 eview of linear circuit
More informationExamination paper for TMA4195 Mathematical Modeling
Department of Mathematical Sciences Examination paper for TMA4195 Mathematical Modeling Academic contact during examination: Elena Celledoni Phone: 48238584, 73593541 Examination date: 11th of December
More informationEE 410/510: Electromechanical Systems Chapter 4
EE 410/510: Electromechanical Systems Chapter 4 Chapter 4. Direct Current Electric Machines and Motion Devices Permanent Magnet DC Electric Machines Radial Topology Simulation and Experimental Studies
More informationMechanics. In the Science Program, Mechanics contributes to the following program goals described in the Exit Profile:
Mechanics Objectives: 00UR Discipline: Physics Ponderation: 323 Course Code: 203NYA05 Prerequisite: Sec. V Physics 534, Mathematics 536 (or equivalent) Course Credit: 2 2/3 Corequisite: 00UP (Calculus
More informationA. F. J. Levi 1 EE539: Engineering Quantum Mechanics. Fall 2017.
A. F. J. Levi 1 Engineering Quantum Mechanics. Fall 2017. TTh 9.00 a.m. 10.50 a.m., VHE 210. Web site: http://alevi.usc.edu Web site: http://classes.usc.edu/term20173/classes/ee EE539: Abstract and Prerequisites
More informationRichiami di Controlli Automatici
Richiami di Controlli Automatici Gianmaria De Tommasi 1 1 Università degli Studi di Napoli Federico II detommas@unina.it Ottobre 2012 Corsi AnsaldoBreda G. De Tommasi (UNINA) Richiami di Controlli Automatici
More informationASTATISM IN NONLINEAR CONTROL SYSTEMS WITH APPLICATION TO ROBOTICS
dx dt DIFFERENTIAL EQUATIONS AND CONTROL PROCESSES N 1, 1997 Electronic Journal, reg. N P23275 at 07.03.97 http://www.neva.ru/journal email: diff@osipenko.stu.neva.ru Control problems in nonlinear systems
More informationLinearization problem. The simplest example
Linear Systems Lecture 3 1 problem Consider a nonlinear timeinvariant system of the form ( ẋ(t f x(t u(t y(t g ( x(t u(t (1 such that x R n u R m y R p and Slide 1 A: f(xu f(xu g(xu and g(xu exist and
More informationAP Physics C: Mechanics and Electricity & Magnetism
AP Physics C: Mechanics and Electricity & Magnetism Textbook: Giancoli, D. (2000). Physics for Scientists & Engineers Third Edition. Prentice Hall: Upper Saddle River, NJ. AP Physics C is a second year
More informationDynamic Modeling of Rotary Double Inverted Pendulum Using Classical Mechanics
ISBN 9789384468 Proceedings of 5 International Conference on Future Computational echnologies (ICFC'5) Singapore, March 93, 5, pp. 963 Dynamic Modeling of Rotary Double Inverted Pendulum Using Classical
More informationInverted Pendulum. Objectives
Inverted Pendulum Objectives The objective of this lab is to experiment with the stabilization of an unstable system. The inverted pendulum problem is taken as an example and the animation program gives
More informationPhysics 610: Electricity & Magnetism I
Physics 610: Electricity & Magnetism I [i.e. relativistic EM, electro/magnetostatics] [lin12.triumph.ca] [Jlab accelerator] [ixnovi.people.wm.edu] [Thywissen group, U. of Toronto] [nanotechetc.com] [wikipedia.org]
More informationINC 341 Feedback Control Systems: Lecture 2 Transfer Function of Dynamic Systems I Asst. Prof. Dr.Ing. Sudchai Boonto
INC 341 Feedback Control Systems: Lecture 2 Transfer Function of Dynamic Systems I Asst. Prof. Dr.Ing. Sudchai Boonto Department of Control Systems and Instrumentation Engineering King Mongkut s University
More informationExperiment 4 Oscillations
Experiment 4 Oscillations "Physics is experience, arranged in economical order." E. Mach OBJECTIVES To study some simple oscillatory systems. THEORY Typical dictionary definitions of the verb "oscillate"
More informationFeedback Control of Linear SISO systems. Process Dynamics and Control
Feedback Control of Linear SISO systems Process Dynamics and Control 1 OpenLoop Process The study of dynamics was limited to openloop systems Observe process behavior as a result of specific input signals
More informationFEEDBACK CONTROL SYSTEMS
FEEDBAC CONTROL SYSTEMS. Control System Design. Open and ClosedLoop Control Systems 3. Why ClosedLoop Control? 4. Case Study  Speed Control of a DC Motor 5. SteadyState Errors in Unity Feedback Control
More informationDesign and Stability Analysis of SingleInput Fuzzy Logic Controller
IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS PART B: CYBERNETICS, VOL. 30, NO. 2, APRIL 2000 303 Design and Stability Analysis of SingleInput Fuzzy Logic Controller ByungJae Choi, SeongWoo Kwak,
More informationStudy Material. CONTROL SYSTEM ENGINEERING (As per SCTE&VT,Odisha new syllabus) 4th Semester Electronics & Telecom Engineering
Study Material CONTROL SYSTEM ENGINEERING (As per SCTE&VT,Odisha new syllabus) 4th Semester Electronics & Telecom Engineering By Sri Asit Kumar Acharya, Lecturer ETC, Govt. Polytechnic Dhenkanal & Sri
More information(b) A unity feedback system is characterized by the transfer function. Design a suitable compensator to meet the following specifications:
1. (a) The open loop transfer function of a unity feedback control system is given by G(S) = K/S(1+0.1S)(1+S) (i) Determine the value of K so that the resonance peak M r of the system is equal to 1.4.
More informationIntroduction to Feedback Control
Introduction to Feedback Control Control System Design Why Control? OpenLoop vs ClosedLoop (Feedback) Why Use Feedback Control? ClosedLoop Control System Structure Elements of a Feedback Control System
More informationFirstOrder LowPass Filter!
Filters, Cost Functions, and Controller Structures! Robert Stengel! Optimal Control and Estimation MAE 546! Princeton University, 217!! Dynamic systems as lowpass filters!! Frequency response of dynamic
More informationDynamic Systems. Simulation of. with MATLAB and Simulink. Harold Klee. Randal Allen SECOND EDITION. CRC Press. Taylor & Francis Group
SECOND EDITION Simulation of Dynamic Systems with MATLAB and Simulink Harold Klee Randal Allen CRC Press Taylor & Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis
More informationGeneral Physics I. Lecture 14: Sinusoidal Waves. Prof. WAN, Xin ( 万歆 )
General Physics I Lecture 14: Sinusoidal Waves Prof. WAN, Xin ( 万歆 ) xinwan@zju.edu.cn http://zimp.zju.edu.cn/~xinwan/ Motivation When analyzing a linear medium that is, one in which the restoring force
More informationRoot Locus Design Example #4
Root Locus Design Example #4 A. Introduction The plant model represents a linearization of the heading dynamics of a 25, ton tanker ship under empty load conditions. The reference input signal R(s) is
More informationLecture 6 Classical Control Overview IV. Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science  Bangalore
Lecture 6 Classical Control Overview IV Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science  Bangalore Lead Lag Compensator Design Dr. Radhakant Padhi Asst.
More information6.003: Signals and Systems
6.003: Signals and Systems CT Feedback and Control October 20, 2011 1 Midterm Examination #2 Wednesday, October 26, 7:309:30pm, No recitations on the day of the exam. Coverage: Lectures 1 12 Recitations
More informationVALLIAMMAI ENGINEERING COLLEGE
VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur 603 203 DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING QUESTION BANK V SEMESTER IC650 CONTROL SYSTEMS Regulation 203 Academic Year 207 8 Prepared
More informationClassical DualInvertedPendulum Control
PRESENTED AT THE 23 IEEE CONFERENCE ON DECISION AND CONTROL 4399 Classical DualInvertedPendulum Control Kent H. Lundberg James K. Roberge Department of Electrical Engineering and Computer Science Massachusetts
More informationPower System Operations and Control Prof. S.N. Singh Department of Electrical Engineering Indian Institute of Technology, Kanpur. Module 3 Lecture 8
Power System Operations and Control Prof. S.N. Singh Department of Electrical Engineering Indian Institute of Technology, Kanpur Module 3 Lecture 8 Welcome to lecture number 8 of module 3. In the previous
More informationTime Response of Systems
Chapter 0 Time Response of Systems 0. Some Standard Time Responses Let us try to get some impulse time responses just by inspection: Poles F (s) f(t) splane Time response p =0 s p =0,p 2 =0 s 2 t p =
More informationNonlinear Control Lecture 1: Introduction
Nonlinear Control Lecture 1: Introduction Farzaneh Abdollahi Department of Electrical Engineering Amirkabir University of Technology Fall 2011 Farzaneh Abdollahi Nonlinear Control Lecture 1 1/15 Motivation
More informationState Space Representation
ME Homework #6 State Space Representation Last Updated September 6 6. From the homework problems on the following pages 5. 5. 5.6 5.7. 5.6 Chapter 5 Homework Problems 5.6. Simulation of Linear and Nonlinear
More informationCE 59700: Digital Photogrammetric Systems
CE 59700: Digital Photogrammetric Systems Fall 2016 1 Instructor: Contact Information Office: HAMP 4108 Tel: (765) 4960173 Email: ahabib@purdue.edu Lectures (HAMP 2102): Monday, Wednesday & Friday (12:30
More informationAPPLICATIONS FOR ROBOTICS
Version: 1 CONTROL APPLICATIONS FOR ROBOTICS TEX d: Feb. 17, 214 PREVIEW We show that the transfer function and conditions of stability for linear systems can be studied using Laplace transforms. Table
More informationPhysics 121, April 3, Equilibrium and Simple Harmonic Motion. Physics 121. April 3, Physics 121. April 3, Course Information
Physics 121, April 3, 2008. Equilibrium and Simple Harmonic Motion. Physics 121. April 3, 2008. Course Information Topics to be discussed today: Requirements for Equilibrium (a brief review) Stress and
More informationAnalysis and Control of MultiRobot Systems. Elements of PortHamiltonian Modeling
Elective in Robotics 2014/2015 Analysis and Control of MultiRobot Systems Elements of PortHamiltonian Modeling Dr. Paolo Robuffo Giordano CNRS, Irisa/Inria! Rennes, France Introduction to PortHamiltonian
More informationSchool of Mechanical Engineering Purdue University. ME375 Feedback Control  1
Introduction to Feedback Control Control System Design Why Control? OpenLoop vs ClosedLoop (Feedback) Why Use Feedback Control? ClosedLoop Control System Structure Elements of a Feedback Control System
More informationModeling and Experimentation: MassSpringDamper System Dynamics
Modeling and Experimentation: MassSpringDamper System Dynamics Prof. R.G. Longoria Department of Mechanical Engineering The University of Texas at Austin July 20, 2014 Overview 1 This lab is meant to
More informationCollege Physics (PHY 1301)
College Physics (PHY 1301) Lecture 1. Introduction Syllabus and teaching strategy Newtonian Mechanics, Fluid Mechanics and Thermodynamics Physical Quantities, Measurements, Units and Vectors 1 6/1/2015
More informationProfessor Fearing EE C128 / ME C134 Problem Set 7 Solution Fall 2010 Jansen Sheng and Wenjie Chen, UC Berkeley
Professor Fearing EE C8 / ME C34 Problem Set 7 Solution Fall Jansen Sheng and Wenjie Chen, UC Berkeley. 35 pts Lag compensation. For open loop plant Gs ss+5s+8 a Find compensator gain Ds k such that the
More informationWith Modern Physics For Scientists and Engineers
With Modern Physics For Scientists and Engineers Third Edition Richard Wolfson Middlebury College Jay M. Pasachoff Williams College ^ADDISONWESLEY An imprint of Addison Wesley Longman, Inc. Reading, Massachusetts
More informationMost General Definition: Trust is good, control is better.
GOALS: To provide advanced students in mechanical engineering with a solid background in dynamic system modeling and analysis and to enable them to analyze and design linear control systems. FORMAT: Lecture:
More information10 Measurement of Acceleration, Vibration and Shock Transducers
Chapter 10: Acceleration, Vibration and Shock Measurement Dr. Lufti AlSharif (Revision 1.0, 25/5/2008) 1. Introduction This chapter examines the measurement of acceleration, vibration and shock. It starts
More information10 Transfer Matrix Models
MIT EECS 6.241 (FALL 26) LECTURE NOTES BY A. MEGRETSKI 1 Transfer Matrix Models So far, transfer matrices were introduced for finite order state space LTI models, in which case they serve as an important
More informationObjective: To study P, PI, and PID temperature controller for an oven and compare their performance. Name of the apparatus Range Quantity
Objective: To study P, PI, and PID temperature controller for an oven and compare their. Apparatus Used: Name of the apparatus Range Quantity 1. Temperature Controller System 1 PID Kp (010) Kd(020) Ki(00.02)
More information1 POTENTIAL FLOW THEORY Formulation of the seakeeping problem
1 POTENTIAL FLOW THEORY Formulation of the seakeeping problem Objective of the Chapter: Formulation of the potential flow around the hull of a ship advancing and oscillationg in waves Results of the Chapter:
More informationOptimal Control and Estimation MAE 546, Princeton University Robert Stengel, Preliminaries!
Optimal Control and Estimation MAE 546, Princeton University Robert Stengel, 2017 Copyright 2017 by Robert Stengel. All rights reserved. For educational use only. http://www.princeton.edu/~stengel/mae546.html
More informationSimulation Study on Pressure Control using Nonlinear Input/Output Linearization Method and Classical PID Approach
Simulation Study on Pressure Control using Nonlinear Input/Output Linearization Method and Classical PID Approach Ufuk Bakirdogen*, Matthias Liermann** *Institute for Fluid Power Drives and Controls (IFAS),
More information