Lecture 25: Tue Nov 27, 2018

Size: px
Start display at page:

Download "Lecture 25: Tue Nov 27, 2018"

Transcription

1 Lecture 25: Tue Nov 27, 2018 Reminder: Lab 3 moved to Tuesday Dec 4 Lecture: review time-domain characteristics of 2nd-order systems intro to control: feedback open-loop vs closed-loop control intro to PID control 0

2 Quiz 2 Results min = 66 5 mean = 91 median =

3 Q2 vs Q QUIZ QUIZ 1 2

4 Q1 + Q min = 92 mean = 166 max = 197 median =

5 Time Domain Properties of 2nd Order Systems 4

6 Underdamped LPF Step Response Can t measure n and directly, but can derive them from measurements of: steady-state value (determines H 0 ) percentage overshoot (determines ) peak time (given, determines n ) settling time (1 + )H 0 y( t ) STEP RESPONSE 1.02H 0 H H 0 0 t pk t settle t 5

7 Start with LPF: 2 H( s ) = H 0 n s n s + n Start with Impulse Response: h( t ) 8 = = = / n t -2 1/ n -4 (Later Find Step Response) 6

8 Underdamped Impulse Response? = d n 1 2 n If poles were on j axis, h( t ) = Ksin( d t)u( t ). By mod property, shifting poles to left introduces an exponential envelope: h( t ) = Ke nt sin( d t)u( t ): h( t ) ENVELOPE t 7

9 To Find the Constant K H( s ) = 2 H n s n s + n 2 H n s n = (complete the square) H 0 n n d = (use table 2 and modulation property) 1 2 s d H 0 n 1 2 n h( t ) = e nt sin( d t)u( t ). K = H n 1 2 oscillates with frequency d t 8

10 Three Different Frequencies natural frequency n damped frequency d resonant frequency r 9

11 Three Different Frequencies natural frequency n : were there no damping (no friction or resistance) + L C n = LC m y k n = k m ---- my + ky = 0 damped frequency d = n (accounts for friction or resistance) 1 2 this is the frequency of oscillations in the time domain resonant frequency r = n (where frequency response peaks) 10

12 Underdamped LPF Step Response Write Laplace transform of step response as: 2 1 Y( s ) = -- 1.H( s ) =. H n s s s n H s As + a + B d s + a d n = (where a = n ) PFE: s 2 : H 0 A = 0 A = H 0 s 1 : 2H 0 a Aa B d = 0 B = H y( t ) = H 0 u( t ) e n t u( t )[Acos( d t) + Bsin( d t)] = H 0 u( t )(1 e n t [cos( d t) sin( d t)])

13 Phasor Addition, or Trig Identity sin 1 2 cos cos( d t) sin( d t) = (sin cos( d t) + cos sin( d t)) = sin( d t + )

14 3 Equiv ways to Write Step Response Underdamped step response for a 2nd-order LPF system can be written as: y( t ) = H 0 u( t )(1 e n t [cos( d t) sin( d t)]) = H 0 u( t )( e n t sin( d t + )) 1 2 = H 0 u( t )( e n t cos( d t )): 1 2 sin 1 2 cos 13

15 y( t ) Time of Peak STEP RESPONSE 0 t t pk To find t p : Set ---- d y( t ) to zero and solve for t. dt IOW set h( t ) = 0! H 0 n 1 2 But h( t ) = e nt sin( d t)u( t ). h( t ) IMPULSE RESPONSE t pk t Zero when sin(. ) argument is equal to the time of the first step-response peak is t pk = = d n

16 Overshoot (1 + )H 0 STEP RESPONSE H 0 0 t pk t Peak overshoot can be found by evaluating step response at t p = / d : y( t p ) = H 0 (1 + e / 1 2 ) overshoot is = e / 1 2. Example: =0.707 = 0.043, or 4.3% of overshoot. 1 From measured overshoot, we can estimate via = log

17 Step response: y( t ) = H 0 u( t )(1 LPF Settling Time When does the envelope decay to 0.02? e n t = e n t sin( d t + )) 1 2 t s t s = ln n n 20 n 15 n 10 n (EXACT) (APPROX) 5 n

18 LPF Step Response (1 + )H 0 = e / = log H 0 0 t t pk = n 1 2 t s n 17

19 Relationship to Pole Locations What stays the same: d, = e / 1 2, or t s n 4 18

20 Relationship to Pole Locations What stays the same: d, = e / 1 2, or t s n 4 SAME SETTLING TIME SAME ENVELOPE SAME OSCILLATION FREQ SAME OVERSHOOT 19

21 Impact of Pole Movement 20

22 Circuit Example R L + v in ( t ) F v out ( t ) Design R and L so that its step response settles in 2 seconds (to ±2% of its steady-state value), with 20% overshoot. 21

23 Solution 1/LC 4/L H( s ) = = s 2 R s + 1/LC s 2 R s + 4/L L L % overshoot = = log L H 2-sec settling time t s = L = 2 = n R --- L = 2 n = = 4 R = 4L = t s

24 Pop Quiz A 2nd-order LPF system has the following step response: (a) Find H 0 (b) (c) Find Find n 23

25 Pop Quiz A 2nd-order LPF system has the following step response: (a) Find H 0 (b) (c) Find Find n 24

26 HPF Step Response? 1 Y( s ) = -- 1 H( s ) = s 2 s s s n s + n = = s s 2 2 n s n 2 s + n n + n s 2 2 d 1 y( t ) = e nt sin( d t + )u( t ) 1 2 s s n s + n R C + L v v in out 3 2 r = n / = sin 1 2 cos (Except for phase change, this is proportional to LPF impulse response!) n 2 n 25

27 Coming Next: Controls 26

28 Reading 27

29 Connecting Systems Series x( t ) y( t ) H 1 ( s ) H 2 ( s ) Parallel H 1 ( s ) x( t ) y( t ) + H 2 ( s ) Feedback x( t ) y( t ) H 1 ( s ) + H 2 ( s ) 28

30 Overall Transfer Functions Easy: Series H 1 ( s )H 2 ( s ) Parallel H 1 ( s ) + H 2 ( s ) Feedback: Not as easy! Chicken & egg. x( t ) e( t ) y( t ) H 1 ( s ) + H 2 ( s ) E( s ) = X( s ) Y( s )H 2 ( s ) Y( s ) = E( s )H 1 ( s ) E( s ) = Y( s )/H 1 ( s ) Ys H Equate H overall ( s ) = = ( s ) Xs 1+H 1 ( s )H 2 ( s ) 29

31 Control Components REFERENCE r( t ) CONTROLLER G c ( s ) x( t ) y( t ) ACTUATOR G p ( s ) PLANT Reference Desired output y( t ). Plant system we re trying to control. We re stuck with it. Controller Produces input to plant in attempt to produce desired output Examples: cruise control temperature control steering control robotic control rocket guidance 30

32 Two Types of Control OPEN LOOP G p ( s ) REFERENCE r( t ) CONTROLLER ACTUATOR PLANT SENSOR y( t ) G c ( s ) CLOSED LOOP G p ( s ) REFERENCE ERROR CONTROLLER x( t ) ACTUATOR PLANT SENSOR y( t ) 31

33 Two Types of Control OPEN LOOP G p ( s ) REFERENCE r( t ) CONTROLLER ACTUATOR PLANT SENSOR y( t ) G c ( s ) CLOSED LOOP G p ( s ) REFERENCE + ERROR CONTROLLER x( t ) ACTUATOR PLANT SENSOR y( t ) 32

34 Control Components: Heating a House REFERENCE 68 + ERROR CONTROLLER ACTUATOR PLANT SENSOR 33

35 Control Components: Cruise Control REFERENCE 55 MPH + ERROR CONTROLLER AMOUNT OF FUEL ACTUATOR PLANT SENSOR 34

36 Segway REFERENCE + ERROR CONTROLLER ACTUATOR PLANT SENSOR 35

37 Tracking Control Set a speed, temperature, position, angle, etc. and have plant track it. We are given or specify a reference signal r( t ), to be tracked. We want y( t ) = r( t ) How to choose x( t )? 36

38 Option 1: Open Loop Control R( s ) G c ( s ) G p ( s ) Y( s ) Y( s ) = R( s )G c ( s )G p ( s ) Example: G p ( s ) = b, how to choose open-loop controller? s + a 1 G c ( s ) = = G p s s + a b Two Problems: For a unit-step reference, differentiator yields impulse In practice we cannot know G p ( s ) exactly. 37

39 Steady-State Tracking When reference is r( t ) = r 0 u( t ): instantaneous tracking: y( t ) = r( t ) for all t, often impractical steady state tracking: y( ) = lim t y( t ) = r 0 Example: r 0 REFERENCE r( t ) y( t ) STEADY-STATE TRACKS DOESN T TRACK 0 t 38

40 Continue example... Proportional Control Does proportional controller G c ( s ) = K perfectly track in steady state? Y( s ) = R( s )G c ( s )G p ( s ) = solve for y( t ): Kbr 0 ss + a 0 t Is y( ) = r 0? What choice for controller gain K yields perfect steady-state tracking? 39

41 Pop Quiz Can an open-loop controller stabilize an unstable plant? 1 R( s ) G c ( s ) s 2 Y( s ) What open-loop controller G c ( s ) results in perfect tracking of a unit step? How robust is this controller to plant changes, e.g. if G p = 1/(s 2.1)? 40

42 Open Loop Drawbacks requires perfect knowledge of plant model not robust 41

43 Feedback: When output impacts input Advantages: robust to external disturbances robust to model knowledge can linearize system made of nonlinear components Disadvantages: can lead to oscillations can lead to instability 42

44 Closed Loop Control R( s ) E( s ) Y( s ) + G c ( s ) G p ( s ) Derive the closed-loop transfer function (relating r( t ) to y( t )): H( s ) = = Y( s ) R( s ) 43

45 Closed Loop Control R( s ) E( s ) Y( s ) + G c ( s ) G p ( s ) Derive the closed-loop transfer function (relating r( t ) to y( t )): Y( s ) H( s ) = = R( s ) G c ( s )G p ( s ) 1 + G c ( s )G p ( s ) 44

46 Examples of Controllers P PI PD PID K p G c ( s ) K p + K i /s K p + K d s K p +K i /s + K d s R( s ) E( s ) Y( s ) + G c ( s ) G p ( s ) 45

Systems Analysis and Control

Systems Analysis and Control Systems Analysis and Control Matthew M. Peet Illinois Institute of Technology Lecture 8: Response Characteristics Overview In this Lecture, you will learn: Characteristics of the Response Stability Real

More information

EE 422G - Signals and Systems Laboratory

EE 422G - Signals and Systems Laboratory EE 4G - Signals and Systems Laboratory Lab 9 PID Control Kevin D. Donohue Department of Electrical and Computer Engineering University of Kentucky Lexington, KY 40506 April, 04 Objectives: Identify the

More information

Systems Analysis and Control

Systems Analysis and Control Systems Analysis and Control Matthew M. Peet Arizona State University Lecture 8: Response Characteristics Overview In this Lecture, you will learn: Characteristics of the Response Stability Real Poles

More information

Video 5.1 Vijay Kumar and Ani Hsieh

Video 5.1 Vijay Kumar and Ani Hsieh Video 5.1 Vijay Kumar and Ani Hsieh Robo3x-1.1 1 The Purpose of Control Input/Stimulus/ Disturbance System or Plant Output/ Response Understand the Black Box Evaluate the Performance Change the Behavior

More information

FEEDBACK CONTROL SYSTEMS

FEEDBACK CONTROL SYSTEMS FEEDBAC CONTROL SYSTEMS. Control System Design. Open and Closed-Loop Control Systems 3. Why Closed-Loop Control? 4. Case Study --- Speed Control of a DC Motor 5. Steady-State Errors in Unity Feedback Control

More information

6.1 Sketch the z-domain root locus and find the critical gain for the following systems K., the closed-loop characteristic equation is K + z 0.

6.1 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 information

PID controllers. Laith Batarseh. PID controllers

PID controllers. Laith Batarseh. PID controllers Next Previous 24-Jan-15 Chapter six Laith Batarseh Home End The controller choice is an important step in the control process because this element is responsible of reducing the error (e ss ), rise time

More information

Analysis and Design of Control Systems in the Time Domain

Analysis and Design of Control Systems in the Time Domain Chapter 6 Analysis and Design of Control Systems in the Time Domain 6. Concepts of feedback control Given a system, we can classify it as an open loop or a closed loop depends on the usage of the feedback.

More information

Time Response Analysis (Part II)

Time Response Analysis (Part II) Time Response Analysis (Part II). A critically damped, continuous-time, second order system, when sampled, will have (in Z domain) (a) A simple pole (b) Double pole on real axis (c) Double pole on imaginary

More information

Problem Value Score Total 100/105

Problem Value Score Total 100/105 RULES This is a closed book, closed notes test. You are, however, allowed one piece of paper (front side only) for notes and definitions, but no sample problems. The top half is the same as from the first

More information

Dr Ian R. Manchester

Dr 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 information

AN INTRODUCTION TO THE CONTROL THEORY

AN INTRODUCTION TO THE CONTROL THEORY Open-Loop controller An Open-Loop (OL) controller is characterized by no direct connection between the output of the system and its input; therefore external disturbance, non-linear dynamics and parameter

More information

Course roadmap. Step response for 2nd-order system. Step response for 2nd-order system

Course roadmap. Step response for 2nd-order system. Step response for 2nd-order system ME45: Control Systems Lecture Time response of nd-order systems Prof. Clar Radcliffe and Prof. Jongeun Choi Department of Mechanical Engineering Michigan State University Modeling Laplace transform Transfer

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.04A Systems and Controls Spring 2013

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.04A Systems and Controls Spring 2013 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.04A Systems and Controls Spring 2013 Problem Set #4 Posted: Thursday, Mar. 7, 13 Due: Thursday, Mar. 14, 13 1. Sketch the Root

More information

(b) A unity feedback system is characterized by the transfer function. Design a suitable compensator to meet the following specifications:

(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 information

Control System (ECE411) Lectures 13 & 14

Control System (ECE411) Lectures 13 & 14 Control System (ECE411) Lectures 13 & 14, Professor Department of Electrical and Computer Engineering Colorado State University Fall 2016 Steady-State Error Analysis Remark: For a unity feedback system

More information

Feedback Control of Linear SISO systems. Process Dynamics and Control

Feedback 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 information

Lecture 12. Upcoming labs: Final Exam on 12/21/2015 (Monday)10:30-12:30

Lecture 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 information

BASIC PROPERTIES OF FEEDBACK

BASIC PROPERTIES OF FEEDBACK ECE450/550: Feedback Control Systems. 4 BASIC PROPERTIES OF FEEDBACK 4.: Setting up an example to benchmark controllers There are two basic types/categories of control systems: OPEN LOOP: Disturbance r(t)

More information

Systems Analysis and Control

Systems Analysis and Control Systems Analysis and Control Matthew M. Peet Illinois Institute of Technology Lecture : Different Types of Control Overview In this Lecture, you will learn: Limits of Proportional Feedback Performance

More information

IC6501 CONTROL SYSTEMS

IC6501 CONTROL SYSTEMS DHANALAKSHMI COLLEGE OF ENGINEERING CHENNAI DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING YEAR/SEMESTER: II/IV IC6501 CONTROL SYSTEMS UNIT I SYSTEMS AND THEIR REPRESENTATION 1. What is the mathematical

More information

C(s) R(s) 1 C(s) C(s) C(s) = s - T. Ts + 1 = 1 s - 1. s + (1 T) Taking the inverse Laplace transform of Equation (5 2), we obtain

C(s) R(s) 1 C(s) C(s) C(s) = s - T. Ts + 1 = 1 s - 1. s + (1 T) Taking the inverse Laplace transform of Equation (5 2), we obtain analyses of the step response, ramp response, and impulse response of the second-order systems are presented. Section 5 4 discusses the transient-response analysis of higherorder systems. Section 5 5 gives

More information

Review: stability; Routh Hurwitz criterion Today s topic: basic properties and benefits of feedback control

Review: stability; Routh Hurwitz criterion Today s topic: basic properties and benefits of feedback control Plan of the Lecture Review: stability; Routh Hurwitz criterion Today s topic: basic properties and benefits of feedback control Goal: understand the difference between open-loop and closed-loop (feedback)

More information

Topic # Feedback Control Systems

Topic # 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 information

Control Systems, Lecture04

Control Systems, Lecture04 Control Systems, Lecture04 İbrahim Beklan Küçükdemiral Yıldız Teknik Üniversitesi 2015 1 / 53 Transfer Functions The output response of a system is the sum of two responses: the forced response and the

More information

Professional Portfolio Selection Techniques: From Markowitz to Innovative Engineering

Professional Portfolio Selection Techniques: From Markowitz to Innovative Engineering Massachusetts Institute of Technology Sponsor: Electrical Engineering and Computer Science Cosponsor: Science Engineering and Business Club Professional Portfolio Selection Techniques: From Markowitz to

More information

Control of Manufacturing Processes

Control of Manufacturing Processes Control of Manufacturing Processes Subject 2.830 Spring 2004 Lecture #18 Basic Control Loop Analysis" April 15, 2004 Revisit Temperature Control Problem τ dy dt + y = u τ = time constant = gain y ss =

More information

Plan of the Lecture. Review: stability; Routh Hurwitz criterion Today s topic: basic properties and benefits of feedback control

Plan of the Lecture. Review: stability; Routh Hurwitz criterion Today s topic: basic properties and benefits of feedback control Plan of the Lecture Review: stability; Routh Hurwitz criterion Today s topic: basic properties and benefits of feedback control Plan of the Lecture Review: stability; Routh Hurwitz criterion Today s topic:

More information

UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING BSC (HONS) MECHATRONICS TOP-UP SEMESTER 1 EXAMINATION 2017/2018 ADVANCED MECHATRONIC SYSTEMS

UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING BSC (HONS) MECHATRONICS TOP-UP SEMESTER 1 EXAMINATION 2017/2018 ADVANCED MECHATRONIC SYSTEMS ENG08 UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING BSC (HONS) MECHATRONICS TOP-UP SEMESTER EXAMINATION 07/08 ADVANCED MECHATRONIC SYSTEMS MODULE NO: MEC600 Date: 7 January 08 Time: 0.00.00 INSTRUCTIONS TO

More information

Root Locus Design Example #4

Root 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 information

Outline. Classical Control. Lecture 2

Outline. Classical Control. Lecture 2 Outline Outline Outline Review of Material from Lecture 2 New Stuff - Outline Review of Lecture System Performance Effect of Poles Review of Material from Lecture System Performance Effect of Poles 2 New

More information

EEL2216 Control Theory CT1: PID Controller Design

EEL2216 Control Theory CT1: PID Controller Design EEL6 Control Theory CT: PID Controller Design. Objectives (i) To design proportional-integral-derivative (PID) controller for closed loop control. (ii) To evaluate the performance of different controllers

More information

KINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING

KINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING KINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING QUESTION BANK SUB.NAME : CONTROL SYSTEMS BRANCH : ECE YEAR : II SEMESTER: IV 1. What is control system? 2. Define open

More information

Index. Index. More information. in this web service Cambridge University Press

Index. Index. More information.  in this web service Cambridge University Press A-type elements, 4 7, 18, 31, 168, 198, 202, 219, 220, 222, 225 A-type variables. See Across variable ac current, 172, 251 ac induction motor, 251 Acceleration rotational, 30 translational, 16 Accumulator,

More information

Chapter 12. Feedback Control Characteristics of Feedback Systems

Chapter 12. Feedback Control Characteristics of Feedback Systems Chapter 1 Feedbac Control Feedbac control allows a system dynamic response to be modified without changing any system components. Below, we show an open-loop system (a system without feedbac) and a closed-loop

More information

Control of Manufacturing Processes

Control of Manufacturing Processes Control of Manufacturing Processes Subject 2.830 Spring 2004 Lecture #19 Position Control and Root Locus Analysis" April 22, 2004 The Position Servo Problem, reference position NC Control Robots Injection

More information

Automatic 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 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 information

Outline. Classical Control. Lecture 1

Outline. Classical Control. Lecture 1 Outline Outline Outline 1 Introduction 2 Prerequisites Block diagram for system modeling Modeling Mechanical Electrical Outline Introduction Background Basic Systems Models/Transfers functions 1 Introduction

More information

Dr Ian R. Manchester Dr Ian R. Manchester AMME 3500 : Review

Dr Ian R. Manchester Dr Ian R. Manchester AMME 3500 : Review Week Date Content Notes 1 6 Mar Introduction 2 13 Mar Frequency Domain Modelling 3 20 Mar Transient Performance and the s-plane 4 27 Mar Block Diagrams Assign 1 Due 5 3 Apr Feedback System Characteristics

More information

Performance of Feedback Control Systems

Performance of Feedback Control Systems Performance of Feedback Control Systems Design of a PID Controller Transient Response of a Closed Loop System Damping Coefficient, Natural frequency, Settling time and Steady-state Error and Type 0, Type

More information

First and Second Order Circuits. Claudio Talarico, Gonzaga University Spring 2015

First and Second Order Circuits. Claudio Talarico, Gonzaga University Spring 2015 First and Second Order Circuits Claudio Talarico, Gonzaga University Spring 2015 Capacitors and Inductors intuition: bucket of charge q = Cv i = C dv dt Resist change of voltage DC open circuit Store voltage

More information

R a) Compare open loop and closed loop control systems. b) Clearly bring out, from basics, Force-current and Force-Voltage analogies.

R a) Compare open loop and closed loop control systems. b) Clearly bring out, from basics, Force-current and Force-Voltage analogies. SET - 1 II B. Tech II Semester Supplementary Examinations Dec 01 1. a) Compare open loop and closed loop control systems. b) Clearly bring out, from basics, Force-current and Force-Voltage analogies..

More information

Acknowledgements. Control System. Tracking. CS122A: Embedded System Design 4/24/2007. A Simple Introduction to Embedded Control Systems (PID Control)

Acknowledgements. Control System. Tracking. CS122A: Embedded System Design 4/24/2007. A Simple Introduction to Embedded Control Systems (PID Control) Acknowledgements A Simple Introduction to Embedded Control Systems (PID Control) The material in this lecture is adapted from: F. Vahid and T. Givargis, Embedded System Design A Unified Hardware/Software

More information

MAS107 Control Theory Exam Solutions 2008

MAS107 Control Theory Exam Solutions 2008 MAS07 CONTROL THEORY. HOVLAND: EXAM SOLUTION 2008 MAS07 Control Theory Exam Solutions 2008 Geir Hovland, Mechatronics Group, Grimstad, Norway June 30, 2008 C. Repeat question B, but plot the phase curve

More information

Introduction to Feedback Control

Introduction to Feedback Control Introduction to Feedback Control Control System Design Why Control? Open-Loop vs Closed-Loop (Feedback) Why Use Feedback Control? Closed-Loop Control System Structure Elements of a Feedback Control System

More information

Chapter 2 SDOF Vibration Control 2.1 Transfer Function

Chapter 2 SDOF Vibration Control 2.1 Transfer Function Chapter SDOF Vibration Control.1 Transfer Function mx ɺɺ( t) + cxɺ ( t) + kx( t) = F( t) Defines the transfer function as output over input X ( s) 1 = G( s) = (1.39) F( s) ms + cs + k s is a complex number:

More information

Control Systems. University Questions

Control Systems. University Questions University Questions UNIT-1 1. Distinguish between open loop and closed loop control system. Describe two examples for each. (10 Marks), Jan 2009, June 12, Dec 11,July 08, July 2009, Dec 2010 2. Write

More information

APPPHYS 217 Tuesday 6 April 2010

APPPHYS 217 Tuesday 6 April 2010 APPPHYS 7 Tuesday 6 April Stability and input-output performance: second-order systems Here we present a detailed example to draw connections between today s topics and our prior review of linear algebra

More information

Step input, ramp input, parabolic input and impulse input signals. 2. What is the initial slope of a step response of a first order system?

Step input, ramp input, parabolic input and impulse input signals. 2. What is the initial slope of a step response of a first order system? IC6501 CONTROL SYSTEM UNIT-II TIME RESPONSE PART-A 1. What are the standard test signals employed for time domain studies?(or) List the standard test signals used in analysis of control systems? (April

More information

MEM 355 Performance Enhancement of Dynamical Systems

MEM 355 Performance Enhancement of Dynamical Systems MEM 355 Performance Enhancement of Dynamical Systems Frequency Domain Design Intro Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University /5/27 Outline Closed Loop Transfer

More information

Lecture 12. AO Control Theory

Lecture 12. AO Control Theory Lecture 12 AO Control Theory Claire Max with many thanks to Don Gavel and Don Wiberg UC Santa Cruz February 18, 2016 Page 1 What are control systems? Control is the process of making a system variable

More information

CDS 101/110a: Lecture 8-1 Frequency Domain Design

CDS 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 information

Lecture 7:Time Response Pole-Zero Maps Influence of Poles and Zeros Higher Order Systems and Pole Dominance Criterion

Lecture 7:Time Response Pole-Zero Maps Influence of Poles and Zeros Higher Order Systems and Pole Dominance Criterion Cleveland State University MCE441: Intr. Linear Control Lecture 7:Time Influence of Poles and Zeros Higher Order and Pole Criterion Prof. Richter 1 / 26 First-Order Specs: Step : Pole Real inputs contain

More information

Discrete Systems. Step response and pole locations. Mark Cannon. Hilary Term Lecture

Discrete Systems. Step response and pole locations. Mark Cannon. Hilary Term Lecture Discrete Systems Mark Cannon Hilary Term 22 - Lecture 4 Step response and pole locations 4 - Review Definition of -transform: U() = Z{u k } = u k k k= Discrete transfer function: Y () U() = G() = Z{g k},

More information

PD, PI, PID Compensation. M. Sami Fadali Professor of Electrical Engineering University of Nevada

PD, PI, PID Compensation. M. Sami Fadali Professor of Electrical Engineering University of Nevada PD, PI, PID Compensation M. Sami Fadali Professor of Electrical Engineering University of Nevada 1 Outline PD compensation. PI compensation. PID compensation. 2 PD Control L= loop gain s cl = desired closed-loop

More information

Mechatronics Engineering. Li Wen

Mechatronics Engineering. Li Wen Mechatronics Engineering Li Wen Bio-inspired robot-dc 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 information

School of Mechanical Engineering Purdue University. ME375 Feedback Control - 1

School of Mechanical Engineering Purdue University. ME375 Feedback Control - 1 Introduction to Feedback Control Control System Design Why Control? Open-Loop vs Closed-Loop (Feedback) Why Use Feedback Control? Closed-Loop Control System Structure Elements of a Feedback Control System

More information

School of Engineering Faculty of Built Environment, Engineering, Technology & Design

School of Engineering Faculty of Built Environment, Engineering, Technology & Design Module Name and Code : ENG60803 Real Time Instrumentation Semester and Year : Semester 5/6, Year 3 Lecture Number/ Week : Lecture 3, Week 3 Learning Outcome (s) : LO5 Module Co-ordinator/Tutor : Dr. Phang

More information

LABORATORY INSTRUCTION MANUAL CONTROL SYSTEM I LAB EE 593

LABORATORY INSTRUCTION MANUAL CONTROL SYSTEM I LAB EE 593 LABORATORY INSTRUCTION MANUAL CONTROL SYSTEM I LAB EE 593 ELECTRICAL ENGINEERING DEPARTMENT JIS COLLEGE OF ENGINEERING (AN AUTONOMOUS INSTITUTE) KALYANI, NADIA CONTROL SYSTEM I LAB. MANUAL EE 593 EXPERIMENT

More information

Control Systems I Lecture 10: System Specifications

Control Systems I Lecture 10: System Specifications Control Systems I Lecture 10: System Specifications Readings: Guzzella, Chapter 10 Emilio Frazzoli Institute for Dynamic Systems and Control D-MAVT ETH Zürich November 24, 2017 E. Frazzoli (ETH) Lecture

More information

Course Background. Loosely speaking, control is the process of getting something to do what you want it to do (or not do, as the case may be).

Course Background. Loosely speaking, control is the process of getting something to do what you want it to do (or not do, as the case may be). ECE4520/5520: Multivariable Control Systems I. 1 1 Course Background 1.1: From time to frequency domain Loosely speaking, control is the process of getting something to do what you want it to do (or not

More information

PID Control. Objectives

PID Control. Objectives PID Control Objectives The objective of this lab is to study basic design issues for proportional-integral-derivative control laws. Emphasis is placed on transient responses and steady-state errors. The

More information

CHAPTER 7 STEADY-STATE RESPONSE ANALYSES

CHAPTER 7 STEADY-STATE RESPONSE ANALYSES CHAPTER 7 STEADY-STATE RESPONSE ANALYSES 1. Introduction The steady state error is a measure of system accuracy. These errors arise from the nature of the inputs, system type and from nonlinearities of

More information

Lab Experiment 2: Performance of First order and second order systems

Lab Experiment 2: Performance of First order and second order systems Lab Experiment 2: Performance of First order and second order systems Objective: The objective of this exercise will be to study the performance characteristics of first and second order systems using

More information

Controller Design using Root Locus

Controller Design using Root Locus Chapter 4 Controller Design using Root Locus 4. PD Control Root locus is a useful tool to design different types of controllers. Below, we will illustrate the design of proportional derivative controllers

More information

Control Systems I. Lecture 6: Poles and Zeros. Readings: Emilio Frazzoli. Institute for Dynamic Systems and Control D-MAVT ETH Zürich

Control Systems I. Lecture 6: Poles and Zeros. Readings: Emilio Frazzoli. Institute for Dynamic Systems and Control D-MAVT ETH Zürich Control Systems I Lecture 6: Poles and Zeros Readings: Emilio Frazzoli Institute for Dynamic Systems and Control D-MAVT ETH Zürich October 27, 2017 E. Frazzoli (ETH) Lecture 6: Control Systems I 27/10/2017

More information

Control Systems Design

Control Systems Design ELEC4410 Control Systems Design Lecture 18: State Feedback Tracking and State Estimation Julio H. Braslavsky julio@ee.newcastle.edu.au School of Electrical Engineering and Computer Science Lecture 18:

More information

Time Response of Systems

Time 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) s-plane Time response p =0 s p =0,p 2 =0 s 2 t p =

More information

Process Control J.P. CORRIOU. Reaction and Process Engineering Laboratory University of Lorraine-CNRS, Nancy (France) Zhejiang University 2016

Process Control J.P. CORRIOU. Reaction and Process Engineering Laboratory University of Lorraine-CNRS, Nancy (France) Zhejiang University 2016 Process Control J.P. CORRIOU Reaction and Process Engineering Laboratory University of Lorraine-CNRS, Nancy (France) Zhejiang University 206 J.P. Corriou (LRGP) Process Control Zhejiang University 206

More information

CHBE320 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 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 information

Control System. Contents

Control System. Contents Contents Chapter Topic Page Chapter- Chapter- Chapter-3 Chapter-4 Introduction Transfer Function, Block Diagrams and Signal Flow Graphs Mathematical Modeling Control System 35 Time Response Analysis of

More information

ECEN 605 LINEAR SYSTEMS. Lecture 20 Characteristics of Feedback Control Systems II Feedback and Stability 1/27

ECEN 605 LINEAR SYSTEMS. Lecture 20 Characteristics of Feedback Control Systems II Feedback and Stability 1/27 1/27 ECEN 605 LINEAR SYSTEMS Lecture 20 Characteristics of Feedback Control Systems II Feedback and Stability Feedback System Consider the feedback system u + G ol (s) y Figure 1: A unity feedback system

More information

Intro to Frequency Domain Design

Intro to Frequency Domain Design Intro to Frequency Domain Design MEM 355 Performance Enhancement of Dynamical Systems Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University Outline Closed Loop Transfer Functions

More information

Systems Analysis and Control

Systems 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 information

MODULE I. Transient Response:

MODULE I. Transient Response: Transient Response: MODULE I The Transient Response (also known as the Natural Response) is the way the circuit responds to energies stored in storage elements, such as capacitors and inductors. If a capacitor

More information

Course Summary. The course cannot be summarized in one lecture.

Course Summary. The course cannot be summarized in one lecture. Course Summary Unit 1: Introduction Unit 2: Modeling in the Frequency Domain Unit 3: Time Response Unit 4: Block Diagram Reduction Unit 5: Stability Unit 6: Steady-State Error Unit 7: Root Locus Techniques

More information

EC CONTROL SYSTEM UNIT I- CONTROL SYSTEM MODELING

EC CONTROL SYSTEM UNIT I- CONTROL SYSTEM MODELING EC 2255 - CONTROL SYSTEM UNIT I- CONTROL SYSTEM MODELING 1. What is meant by a system? It is an arrangement of physical components related in such a manner as to form an entire unit. 2. List the two types

More information

سایت آموزش مهندسی مکانیک

سایت آموزش مهندسی مکانیک http://www.drshokuhi.com سایت آموزش مهندسی مکانیک 1 Single-degree-of-freedom Systems 1.1 INTRODUCTION In this chapter the vibration of a single-degree-of-freedom system will be analyzed and reviewed. Analysis,

More information

9. Two-Degrees-of-Freedom Design

9. 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 information

School of Mechanical Engineering Purdue University. ME375 Dynamic Response - 1

School of Mechanical Engineering Purdue University. ME375 Dynamic Response - 1 Dynamic Response of Linear Systems Linear System Response Superposition Principle Responses to Specific Inputs Dynamic Response of f1 1st to Order Systems Characteristic Equation - Free Response Stable

More information

MAE143a: Signals & Systems (& Control) Final Exam (2011) solutions

MAE143a: Signals & Systems (& Control) Final Exam (2011) solutions MAE143a: Signals & Systems (& Control) Final Exam (2011) solutions Question 1. SIGNALS: Design of a noise-cancelling headphone system. 1a. Based on the low-pass filter given, design a high-pass filter,

More information

Feedback Control part 2

Feedback Control part 2 Overview Feedback Control part EGR 36 April 19, 017 Concepts from EGR 0 Open- and closed-loop control Everything before chapter 7 are open-loop systems Transient response Design criteria Translate criteria

More information

Today s goals So far Today 2.004

Today s goals So far Today 2.004 Today s goals So far Feedback as a means for specifying the dynamic response of a system Root Locus: from the open-loop poles/zeros to the closed-loop poles Moving the closed-loop poles around Today Proportional

More information

Alireza Mousavi Brunel University

Alireza Mousavi Brunel University Alireza Mousavi Brunel University 1 » Control Process» Control Systems Design & Analysis 2 Open-Loop Control: Is normally a simple switch on and switch off process, for example a light in a room is switched

More information

Distributed Real-Time Control Systems

Distributed 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 information

Exercises for lectures 13 Design using frequency methods

Exercises for lectures 13 Design using frequency methods Exercises for lectures 13 Design using frequency methods Michael Šebek Automatic control 2016 31-3-17 Setting of the closed loop bandwidth At the transition frequency in the open loop is (from definition)

More information

D(s) G(s) A control system design definition

D(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 information

Basic Procedures for Common Problems

Basic Procedures for Common Problems Basic Procedures for Common Problems ECHE 550, Fall 2002 Steady State Multivariable Modeling and Control 1 Determine what variables are available to manipulate (inputs, u) and what variables are available

More information

Introduction to control theory

Introduction to control theory Introduction to control theory Reference These slides are freely adapted from the book Embedded Systems design - A unified Hardware/Software introduction, Frank Vahid, Tony Givargis Some figures are excerpt

More information

Part IB Paper 6: Information Engineering LINEAR SYSTEMS AND CONTROL. Glenn Vinnicombe HANDOUT 5. An Introduction to Feedback Control Systems

Part IB Paper 6: Information Engineering LINEAR SYSTEMS AND CONTROL. Glenn Vinnicombe HANDOUT 5. An Introduction to Feedback Control Systems Part IB Paper 6: Information Engineering LINEAR SYSTEMS AND CONTROL Glenn Vinnicombe HANDOUT 5 An Introduction to Feedback Control Systems ē(s) ȳ(s) Σ K(s) G(s) z(s) H(s) z(s) = H(s)G(s)K(s) L(s) ē(s)=

More information

GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL & COMPUTER ENGINEERING FINAL EXAM. COURSE: ECE 3084A (Prof. Michaels)

GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL & COMPUTER ENGINEERING FINAL EXAM. COURSE: ECE 3084A (Prof. Michaels) GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL & COMPUTER ENGINEERING FINAL EXAM DATE: 09-Dec-13 COURSE: ECE 3084A (Prof. Michaels) NAME: STUDENT #: LAST, FIRST Write your name on the front page

More information

Raktim Bhattacharya. . AERO 632: Design of Advance Flight Control System. Preliminaries

Raktim 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 information

(a) Find the transfer function of the amplifier. Ans.: G(s) =

(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 information

Systems Analysis and Control

Systems 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 information

General procedure for formulation of robot dynamics STEP 1 STEP 3. Module 9 : Robot Dynamics & controls

General procedure for formulation of robot dynamics STEP 1 STEP 3. Module 9 : Robot Dynamics & controls Module 9 : Robot Dynamics & controls Lecture 32 : General procedure for dynamics equation forming and introduction to control Objectives In this course you will learn the following Lagrangian Formulation

More information

Laboratory Exercise 1 DC servo

Laboratory 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 information

Übersetzungshilfe / Translation aid (English) To be returned at the end of the exam!

Übersetzungshilfe / 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 information

ECE317 : Feedback and Control

ECE317 : Feedback and Control ECE317 : Feedback and Control Lecture : Steady-state error Dr. Richard Tymerski Dept. of Electrical and Computer Engineering Portland State University 1 Course roadmap Modeling Analysis Design Laplace

More information

Prüfung Regelungstechnik I (Control Systems I) Übersetzungshilfe / Translation aid (English) To be returned at the end of the exam!

Prüfung Regelungstechnik I (Control Systems I) Übersetzungshilfe / Translation aid (English) To be returned at the end of the exam! Prüfung Regelungstechnik I (Control Systems I) Prof. Dr. Lino Guzzella 29. 8. 2 Übersetzungshilfe / Translation aid (English) To be returned at the end of the exam! Do not mark up this translation aid

More information

Second Order and Higher Order Systems

Second Order and Higher Order Systems Second Order and Higher Order Systems 1. Second Order System In this section, we shall obtain the response of a typical second-order control system to a step input. In terms of damping ratio and natural

More information