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


 Robyn Stafford
 1 years ago
 Views:
Transcription
1 Prüfung Regelungstechnik I (Control Systems I) Prof. Dr. Lino Guzzella Übersetzungshilfe / Translation aid (English) To be returned at the end of the exam! Do not mark up this translation aid  The German exam is the only valid version! All answers must be written on the regular exam sheets (which are in German).
2
3 Question (Modelling, Linearization) 8 Points Figure shows a system consisting of a balloon and a pressure cylinder with a moving piston. Your task is to derive a linearized model of this system. The balloon and the volume of the cylinder that is not taken up by the piston are completely filled with oil. The oil is assumed to be incompressible. The total oil volume is V tot ; the oil volume in the balloon is V b (t). The cylinder and the balloon are connected through a large opening, i.e., the oil pressure is equal in both chambers. This pressure is determined by the filling of the balloon and it is computed by p(t) = e a V b(t) + b, where a and b are known parameters. The piston has a mass m and a frontal area F and it moves axially inside the cylinder. The position of the piston is described by r(t). Only two forces act on the piston, namely the pressure force of the oil and the external force K(t) = v(t), which is the input of the system. Friction is neglected. The output of the system is volume of the balloon w(t) = V b (t). Figure : Balloon and pressure cylinder. a) (3 Points) The state vector is defined as z(t) = [ r(t) ṙ(t) ] T. Derive the nonlinear statespace description of the form dz(t) dt = f ( z(t), v(t) ) w(t) = g ( z(t), v(t) ). Use the variable names z (t), z 2 (t), v(t), and w(t). b) (3 Points) Calculate the force v e that is necessary to keep the system in an equilibrium at z,e =. c) (2 Points) Linearize the system around this equilibrium and calculate the system matrices A, b, c, and d. /
4 Question 2 (Frequency domain, time domain) 8 Points The openloop transfer functions (loop gain) L (s), L 2 (s), L 3 (s), L 4 (s) of 4 control systems are given (see below and on the solution page of this question). Furthermore, the Nyquist plots (see below the diagrams A, B, C and D; plotted for positive frequencies only) of these transfer functions, and the resulting step responses (see below the step responses to 4) of the corresponding closed loop systems are given. Assign the correct Nyquist plot and the correct step response to each of the open loop transfer functions. Use the table provided on the solution page of this question for your solution. You do not need to justify your answers. Credits: Per correct assignment: + point Per incorrect assignment: point Minimum amount of credits for the whole question: points Table for solution L (s) = L 2 (s) = L 3 (s) = L 4 (s) = Transfer functions ( ) +. s.2 s+ ( ) (.2 s+) + 2. s (.2 s+) 2 (.2 s+) Nyquist plot (open loop) Step response (closed loop) Nyquist plot A Nyquist plot B.5.5 Im Im Re Re 2 /
5 Nyquist plot C Nyquist plot D.5.5 Im Im Re Re Step response Step response Amplitude [].5 Amplitude [] Time [s] Time [s] Step response 3 Step response Amplitude [].5 Amplitude [] Time [s] Time [s] 3 /
6 Question 3 (Controller Design) Points You are asked to design a controller for the position control of a helicopter in hover. For the sake of simplicity, you can assume that both the vertical and lateral positions are perfectly controlled. Your task is to design the remaining controller for the longitudinal position x(t). The relevant tilt angle for the longitudinal motion is the tilt angle around the lateral axis, denoted by γ(t). γ(t) x(t) Figure 2: Helicopter in hover The linearised equations of motion have already been derived: ẍ(t) = a γ(t) γ(t) = u(t) Where u(t) is the control input and a is a positive constant. The position of the helicopter is measured by GPS. The transfer function of the plant P (s) has already been derived: P (s) = a s 4 You should use a controller C(s) with the following transfer function: C(s) = k s 3 k 2 (τs + ) 4 All subquestions can be solved independently! a) (2 Points) Is it possible to control the system by a PDController? Please give reasons for your answer. b) (3 Points) In a first step, the lowpass filter is neglected, the controller is therefore given by C(s) = k s 3. i) Calculate the controller gain k such that a crossover frequency of 2 rad s ii) Calculate the resulting phase margin. is reached. c) (3 Points) In a next step, the lowpass filter of the controller F (s) should be designed. F (s) = k 2 (τs + ) 4 The phasemargin at the crossover frequency of ω c = 2 rad s should only be reduced by 3. Further on, the crossover frequency should not be changed by the filter. Calculate k 2 and τ. d) (2 Points) Your controller does not work properly in the real helicopter. Even though the controller contains a lowpass filter, the 3times differentiation causes problems. How could you augment the plant to avoid the 3times differentiation? 4 /
7 Question 4 (LaplaceTransformation) Points The following subtasks can be solved independently. a) (4 Points) Consider the system realization of the system Σ. u ẋ   ẋ s 3  s + + y 2 Figure 3: System realization of Σ. i) ( Point) Determine the associated state space description {A, b, c, d}. ii) ( Point) Determine the transfer function of Σ. iii) (2 Points) Determine the time domain system response of the system Σ( s) = 2s 2 (s+2) (s+). The system is excited by u(t) = h(t) sin(t). b) (2 Points) The following figure shows the step response of a linear, time invariant system Σ 2. y(t) [] t [s] Figure 4: Step response of Σ 2. Determine the parameters of the system under the assumption, that it is a second order system. c) (2 Point) Determine the step response of the following second order system Σ 3 in the time domain. Σ 3 (s) = 6 s 2 + 5s /
8 d) (2 Points) Your colleague claims that it is possible to connect two first order systems in series such that a second order system results that can oscillate when a step change in the reference value occurs. i) ( Point) Illustrate the system responses y (t) and y 2 (t) to a step in the reference value h(t) schematically. Assume that both systems have a static gain of. Hint: Keep in mind the tangent at the step time and the rise time. h(t) y (t) y 2 (t) Σ A Σ B Figure 5: Series connection of two first order systems Σ A and Σ B. ii) ( Point) Justify without calculation that a series connection of two first order systems cannot oscillate when a step in the reference value occurs. 6 /
9 Question 5 (Stabilization / Performance & Robustness) 9 Points You want to design a controller for a plant of which you already know the following state space description. ẋ(t) = x(t) + u(t) y(t) = ( a) x(t) + u(t) () The parameter a (physical unit rad /s) represents a characteristic of the sensor and can be selected in the range a 2. The higher the value of a is selected, the more expensive is the sensor used. The sensor is supplied with alternating current from the public electricity network. Therefore it shows distinctive noise at the network frequency of 5 Hz ( 3 rad /s). Note: The solution of the subquestion a) is a prerequisite for the subsequent subquestions b)e). The subquestions b)e) can be solved partly independently of each other. a) (2 Points) Determine the transfer function P (s) of the given plant with input u(t), output y(t) and state x(t) as a function of the sensor parameter a. Additionally, calculate the poles and zeros of this plant. b) (3 Points) In which range should the crossover frequency ω c of the control system lie, such that a reasonable controller exists? Which crossover frequency do you select, if the costs of the sensor should be minimized? Please also determine the resulting sensor parameter a which minimizes the sensor costs. Important: Due to a special offer of the sensor manufacturer you decide to buy a sensor with a = 5 rad /s. Use this value for the subquestions c) to e). c) (2 Points) You want to stabilize the plant with a Pcontroller C(s) = k p. Which values of k p are possible? d) ( Point) The absolute value of the amplification of the highfrequency sensor noise should be exactly equal to. Which value of the controller parameter k p do you have to select? e) ( Point) Use the value of k p found in d). How large is the steady state error with this value? 7 /
10 Question 6 (BodeDiagram/Nyquist Criterion) Points You want to control a plant P (s) with a transfer function P (s) = K(s2 + 3s + 7)(s 2 8s + 4) (s + 7)(s 2 s + )(s 2 + 3s + 7) where K is a constant. The plant is in a closedloop system with a controller C(s) as shown below. Due to using a wireless sensor for measuring the output, a delay of τ seconds is present in the feedback path. Also, a Nyquistdiagram of the plant P (s) is measured and shown below (the plus indicates the point + j). Nyquistdiagram of the plant P (s) 5 Block diagram of the closedloop system. Imaginary Axis 55 ω = + ω = Real Axis All subquestions can be solved independently. a) (3 Points) Assume that C(s) = and τ =. Investigate the stability of the closedloop system using the Nyquist criterion. b) (2 Points) Identify the constant K of the plant P (s), using the Bodediagram of the plant shown in Figure 6 (This Figure is given also on the solution page of this question). c) (3 Points) Assume that C(s) =. Find the maximum value of sensor delay τ (in seconds) for which the closedloop system remains asymptotically stable. Hint: Determine the phasemargin of the system and relate it to the delay τ. d) (2 Points) Assume that τ =. For a Pcontroller C(s) = k p, find the value of gain k p for which the closedloop system is asymptotically stable. Hint: Determine the gainmargin of the system and relate it to the gain k p. 8 /
11 Bodediagram of P(s) Magnitude (db) Phase (deg) Frequency (rad/s) Figure 6: Bodediagram of the plant P (s). 9 /
12 Question 7 (System Analysis) 7 Points The vehicle dynamics of a tractor semitrailer combination during forward travel can be described by.5 5 d dt x(t) = x(t) + u(t), y(t) = ( 2.5 ) x(t), 6 22 and during reverse travel by.5 5 d dt x(t) = 6 x(t) + u(t), 22 8 y(t) = ( 2.5 ) x(t). 8 The system input u(t) is the steering angle of the tractor and the system output y(t) is the articulation angle between tractor and semitrailer, as defined in Fig. 7. u(t) y(t) tractor semitrailer Figure 7: Tractor semitrailer combination a) (4 Points) During forward travel, initially moving straightahead, a step is applied to the steering angle, u(t) = k h(t), k >. i) What is the sign of the articulation angle for t? ii) In which direction (positive/negative) does the articulation angle change immediately after the step input is applied? Justify your answers mathematically. b) (3 Points) During reverse travel, initially moving straightahead, the articulation angle is steered to and maintained at a reference value y ref. Explain why the steering angle must change its sign during the maneuver. Use for your explanation one of the following system properties and show this property mathematically: asymptotically stable / unstable completely controllable / not completely controllable completely observable / not completely observable /
13 Question 8 (MultipleChoice) 8 Points Decide whether the following statements are true or false and check the corresponding check box with an X ( ) on the solution page of this question. You are not required to justify your answers. All questions are equally weighted ( Point). There will be a reduction of one point for a wrong answer. Unanswered questions will get points. The minimum sum for all questions is points. a) The differential equation δẋ = 3 δx+2 δu is the linearization of the nonlinear system ẋ = x 3 3x + u 2 around the equilibrium point {x e = 3, u e = 6}. b) A constant signal u(t) = at the input of a system with the transfer function Σ(s) = produces a constant output signal of 4 for t. s+2 s 2 4s+3 c) An unstable system with the transfer function s (s 2) can be stabilized by a Pcontroller. d) A plant with the transfer function G(s) = s 2 has to be stabilized by a controller. A s 2 s 2 cross over frequency of ω c = 6 rad/s represents a meaningful bandwidth for the specification of the control system. e) The following state space model {A, b, c, d} represents a realization for a system with the transfer function Σ(s) = s+5 [ A = 3 2 s 2 2s+3 : ], b = [ ], c = [ 5 ], D = [ ] f) The Matlab instruction tf([ 7],[ 2 5]) plots the frequency response of a system s 7 with the transfer function s 2 2s+5. g) The output of a system with the transfer function 2s+5 s+5 exceed a value of if the input is the step function h(t). (initial condition = ) will not h) The transfer function of a closed loop system from the reference signal r to the output y is T (s) = 2s+. The sensitivity of the control system is S(s) = s(s+5) s 2 +7s+ s 2 +7s+. Be aware of this fact! /
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 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 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 informationEECS C128/ ME C134 Final Thu. May 14, pm. Closed book. One page, 2 sides of formula sheets. No calculators.
Name: SID: EECS C28/ ME C34 Final Thu. May 4, 25 58 pm Closed book. One page, 2 sides of formula sheets. No calculators. There are 8 problems worth points total. Problem Points Score 4 2 4 3 6 4 8 5 3
More informationVALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur
VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur 603 203. DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING SUBJECT QUESTION BANK : EC6405 CONTROL SYSTEM ENGINEERING SEM / YEAR: IV / II year
More informationELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 2010/2011 CONTROL ENGINEERING SHEET 5 LeadLag Compensation Techniques
CAIRO UNIVERSITY FACULTY OF ENGINEERING ELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 00/0 CONTROL ENGINEERING SHEET 5 LeadLag Compensation Techniques [] For the following system, Design a compensator such
More informationDr 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 information100 (s + 10) (s + 100) e 0.5s. s 100 (s + 10) (s + 100). G(s) =
1 AME 3315; Spring 215; Midterm 2 Review (not graded) Problems: 9.3 9.8 9.9 9.12 except parts 5 and 6. 9.13 except parts 4 and 5 9.28 9.34 You are given the transfer function: G(s) = 1) Plot the bode plot
More informationAutomatic Control 2. Loop shaping. Prof. Alberto Bemporad. University of Trento. Academic year
Automatic Control 2 Loop shaping Prof. Alberto Bemporad University of Trento Academic year 21211 Prof. Alberto Bemporad (University of Trento) Automatic Control 2 Academic year 21211 1 / 39 Feedback
More informationMAS107 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 informationFrequency domain analysis
Automatic Control 2 Frequency domain analysis Prof. Alberto Bemporad University of Trento Academic year 20102011 Prof. Alberto Bemporad (University of Trento) Automatic Control 2 Academic year 20102011
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 informationAnalysis of SISO Control Loops
Chapter 5 Analysis of SISO Control Loops Topics to be covered For a given controller and plant connected in feedback we ask and answer the following questions: Is the loop stable? What are the sensitivities
More informationr +  FINAL June 12, 2012 MAE 143B Linear Control Prof. M. Krstic
MAE 43B Linear Control Prof. M. Krstic FINAL June, One sheet of handwritten notes (two pages). Present your reasoning and calculations clearly. Inconsistent etchings will not be graded. Write answers
More information1 Mathematics. 1.1 Determine the onesided Laplace transform of the following signals. + 2y = σ(t) dt 2 + 3dy dt. , where A is a constant.
Mathematics. Determine the onesided Laplace transform of the following signals. {, t < a) u(t) =, where A is a constant. A, t {, t < b) u(t) =, where A is a constant. At, t c) u(t) = e 2t for t. d) u(t)
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 information6.302 Feedback Systems Recitation 16: Compensation Prof. Joel L. Dawson
Bode Obstacle Course is one technique for doing compensation, or designing a feedback system to make the closedloop behavior what we want it to be. To review:  G c (s) G(s) H(s) you are here! plant For
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 informationCDS 101/110a: Lecture 102 Control Systems Implementation
CDS 101/110a: Lecture 102 Control Systems Implementation Richard M. Murray 5 December 2012 Goals Provide an overview of the key principles, concepts and tools from control theory  Classical control 
More informationControl Systems II. ETH, MAVT, IDSC, Lecture 4 17/03/2017. G. Ducard
Control Systems II ETH, MAVT, IDSC, Lecture 4 17/03/2017 Lecture plan: Control Systems II, IDSC, 2017 SISO Control Design 24.02 Lecture 1 Recalls, Introductory case study 03.03 Lecture 2 Cascaded Control
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 informationHomework 7  Solutions
Homework 7  Solutions Note: This homework is worth a total of 48 points. 1. Compensators (9 points) For a unity feedback system given below, with G(s) = K s(s + 5)(s + 11) do the following: (c) Find the
More informationLearn2Control Laboratory
Learn2Control Laboratory Version 3.2 Summer Term 2014 1 This Script is for use in the scope of the Process Control lab. It is in no way claimed to be in any scientific way complete or unique. Errors should
More information1. Find the solution of the following uncontrolled linear system. 2 α 1 1
Appendix B Revision Problems 1. Find the solution of the following uncontrolled linear system 0 1 1 ẋ = x, x(0) =. 2 3 1 Class test, August 1998 2. Given the linear system described by 2 α 1 1 ẋ = x +
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 informationLecture 1: Feedback Control Loop
Lecture : Feedback Control Loop Loop Transfer function The standard feedback control system structure is depicted in Figure. This represend(t) n(t) r(t) e(t) u(t) v(t) η(t) y(t) F (s) C(s) P (s) Figure
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 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 informationDistributed RealTime Control Systems
Distributed RealTime 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 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 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 informationProblem Set 5 Solutions 1
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.245: MULTIVARIABLE CONTROL SYSTEMS by A. Megretski Problem Set 5 Solutions The problem set deals with Hankel
More informationECE137B Final Exam. There are 5 problems on this exam and you have 3 hours There are pages 119 in the exam: please make sure all are there.
ECE37B Final Exam There are 5 problems on this exam and you have 3 hours There are pages 9 in the exam: please make sure all are there. Do not open this exam until told to do so Show all work: Credit
More information16.30/31, Fall 2010 Recitation # 2
16.30/31, Fall 2010 Recitation # 2 September 22, 2010 In this recitation, we will consider two problems from Chapter 8 of the Van de Vegte book. R +  E G c (s) G(s) C Figure 1: The standard block diagram
More informationECE 350 Signals and Systems Spring 2011 Final Exam  Solutions. Three 8 ½ x 11 sheets of notes, and a calculator are allowed during the exam.
ECE 35 Spring  Final Exam 9 May ECE 35 Signals and Systems Spring Final Exam  Solutions Three 8 ½ x sheets of notes, and a calculator are allowed during the exam Write all answers neatly and show your
More informationStudio Exercise Time Response & Frequency Response 1 st Order Dynamic System RC LowPass Filter
Studio Exercise Time Response & Frequency Response 1 st Order Dynamic System RC LowPass Filter i i in R out Assignment: Perform a Complete e in C e Dynamic System Investigation out of the RC LowPass
More informationRecitation 11: Time delays
Recitation : Time delays Emilio Frazzoli Laboratory for Information and Decision Systems Massachusetts Institute of Technology November, 00. Introduction and motivation. Delays are incurred when the controller
More informationCHAPTER 7 STEADYSTATE RESPONSE ANALYSES
CHAPTER 7 STEADYSTATE 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 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 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 informationEE C128 / ME C134 Fall 2014 HW 8  Solutions. HW 8  Solutions
EE C28 / ME C34 Fall 24 HW 8  Solutions HW 8  Solutions. Transient Response Design via Gain Adjustment For a transfer function G(s) = in negative feedback, find the gain to yield a 5% s(s+2)(s+85) overshoot
More informationKINGS 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 informationChapter 2. Classical Control System Design. Dutch Institute of Systems and Control
Chapter 2 Classical Control System Design Overview Ch. 2. 2. Classical control system design Introduction Introduction Steadystate Steadystate errors errors Type Type k k systems systems Integral Integral
More informationProblem 1 (Analysis of a Feedback System  Bode, Root Locus, Nyquist) Consider the feedback system defined by the open loop transfer function 1.
1 EEE480 Final Exam, Spring 2016 A.A. Rodriguez Rules: Calculators permitted, One 8.5 11 sheet, closed notes/books, open minds GWC 352, 9653712 Problem 1 (Analysis of a Feedback System  Bode, Root Locus,
More informationSystems Analysis and Control
Systems Analysis and Control Matthew M. Peet Arizona State University Lecture 24: Compensation in the Frequency Domain Overview In this Lecture, you will learn: Lead Compensators Performance Specs Altering
More informationD G 2 H + + D 2
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.302 Feedback Systems Final Exam May 21, 2007 180 minutes Johnson Ice Rink 1. This examination consists
More informationLoop shaping exercise
Loop shaping exercise Excerpt 1 from Controlli Automatici  Esercizi di Sintesi, L. Lanari, G. Oriolo, EUROMA  La Goliardica, 1997. It s a generic book with some typical problems in control, not a collection
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 informationFrequency (rad/s)
. The frequency response of the plant in a unity feedback control systems is shown in Figure. a) What is the static velocity error coefficient K v for the system? b) A lead compensator with a transfer
More informationPerformance 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 Steadystate Error and Type 0, Type
More informationAn Internal Stability Example
An Internal Stability Example Roy Smith 26 April 2015 To illustrate the concept of internal stability we will look at an example where there are several polezero cancellations between the controller and
More informationECE382/ME482 Spring 2005 Homework 7 Solution April 17, K(s + 0.2) s 2 (s + 2)(s + 5) G(s) =
ECE382/ME482 Spring 25 Homework 7 Solution April 17, 25 1 Solution to HW7 AP9.5 We are given a system with open loop transfer function G(s) = K(s +.2) s 2 (s + 2)(s + 5) (1) and unity negative feedback.
More informationLecture 7:Time Response PoleZero 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 FirstOrder Specs: Step : Pole Real inputs contain
More informationx(t) = x(t h), x(t) 2 R ), where is the time delay, the transfer function for such a e s Figure 1: Simple Time Delay Block Diagram e i! =1 \e i!t =!
1 TimeDelay Systems 1.1 Introduction Recitation Notes: Time Delays and Nyquist Plots Review In control systems a challenging area is operating in the presence of delays. Delays can be attributed to acquiring
More informationKINGS 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 STAFF NAME: Mr. P.NARASIMMAN BRANCH : ECE Mr.K.R.VENKATESAN YEAR : II SEMESTER
More informationFREQUENCYRESPONSE DESIGN
ECE45/55: Feedback Control Systems. 9 FREQUENCYRESPONSE DESIGN 9.: PD and lead compensation networks The frequencyresponse methods we have seen so far largely tell us about stability and stability margins
More informationAutomatique. A. Hably 1. Commande d un robot mobile. Automatique. A.Hably. Digital implementation
A. Hably 1 1 Gipsalab, GrenobleINP ahmad.hably@grenobleinp.fr Commande d un robot mobile (Gipsalab (DA)) ASI 1 / 25 Outline 1 2 (Gipsalab (DA)) ASI 2 / 25 of controllers Signals must be sampled and
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 informationLTI Systems (Continuous & Discrete)  Basics
LTI Systems (Continuous & Discrete)  Basics 1. A system with an input x(t) and output y(t) is described by the relation: y(t) = t. x(t). This system is (a) linear and timeinvariant (b) linear and timevarying
More informationDynamic circuits: Frequency domain analysis
Electronic Circuits 1 Dynamic circuits: Contents Free oscillation and natural frequency Transfer functions Frequency response Bode plots 1 System behaviour: overview 2 System behaviour : review solution
More information1 (20 pts) Nyquist Exercise
EE C128 / ME134 Problem Set 6 Solution Fall 2011 1 (20 pts) Nyquist Exercise Consider a close loop system with unity feedback. For each G(s), hand sketch the Nyquist diagram, determine Z = P N, algebraically
More informationAA/EE/ME 548: Problem Session Notes #5
AA/EE/ME 548: Problem Session Notes #5 Review of Nyquist and Bode Plots. Nyquist Stability Criterion. LQG/LTR Method Tuesday, March 2, 203 Outline:. A review of Bode plots. 2. A review of Nyquist plots
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 informationLaplace Transform Analysis of Signals and Systems
Laplace Transform Analysis of Signals and Systems Transfer Functions Transfer functions of CT systems can be found from analysis of Differential Equations Block Diagrams Circuit Diagrams 5/10/04 M. J.
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 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 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 informationNADAR SARASWATHI COLLEGE OF ENGINEERING AND TECHNOLOGY Vadapudupatti, Theni
NADAR SARASWATHI COLLEGE OF ENGINEERING AND TECHNOLOGY Vadapudupatti, Theni625531 Question Bank for the Units I to V SE05 BR05 SU02 5 th Semester B.E. / B.Tech. Electrical & Electronics engineering IC6501
More informationSystems 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 informationECE301 Fall, 2006 Exam 1 Soluation October 7, Name: Score: / Consider the system described by the differential equation
ECE301 Fall, 2006 Exam 1 Soluation October 7, 2006 1 Name: Score: /100 You must show all of your work for full credit. Calculators may NOT be used. 1. Consider the system described by the differential
More informationPole placement control: state space and polynomial approaches Lecture 2
: state space and polynomial approaches Lecture 2 : a state O. Sename 1 1 Gipsalab, CNRSINPG, FRANCE Olivier.Sename@gipsalab.fr www.gipsalab.fr/ o.sename based November 21, 2017 Outline : a state
More informationAndrea Zanchettin Automatic Control AUTOMATIC CONTROL. Andrea M. Zanchettin, PhD Spring Semester, Linear systems (frequency domain)
1 AUTOMATIC CONTROL Andrea M. Zanchettin, PhD Spring Semester, 2018 Linear systems (frequency domain) 2 Motivations Consider an LTI system Thanks to the Lagrange s formula we can compute the motion of
More informationH(s) = s. a 2. H eq (z) = z z. G(s) a 2. G(s) A B. s 2 s(s + a) 2 s(s a) G(s) 1 a 1 a. } = (z s 1)( z. e ) ) (z. (z 1)(z e at )(z e at )
.7 Quiz Solutions Problem : a H(s) = s a a) Calculate the zero order hold equivalent H eq (z). H eq (z) = z z G(s) Z{ } s G(s) a Z{ } = Z{ s s(s a ) } G(s) A B Z{ } = Z{ + } s s(s + a) s(s a) G(s) a a
More information6.003 (Fall 2011) Quiz #3 November 16, 2011
6.003 (Fall 2011) Quiz #3 November 16, 2011 Name: Kerberos Username: Please circle your section number: Section Time 2 11 am 3 1 pm 4 2 pm Grades will be determined by the correctness of your answers (explanations
More informationMethods for analysis and control of. Lecture 6: Introduction to digital control
Methods for analysis and of Lecture 6: to digital O. Sename 1 1 Gipsalab, CNRSINPG, FRANCE Olivier.Sename@gipsalab.inpg.fr www.lag.ensieg.inpg.fr/sename 6th May 2009 Outline Some interesting books:
More informationEC6405  CONTROL SYSTEM ENGINEERING Questions and Answers Unit  I Control System Modeling Two marks 1. What is control system? A system consists of a number of components connected together to perform
More informationReglerteknik Allmän Kurs. Del 2. Lösningar till Exempelsamling. Läsår 2015/16
Reglerteknik Allmän Kurs Del Lösningar till Exempelsamling Läsår 5/6 Avdelningen för Reglerteknik, KTH, SE 44 Stockholm, SWEDEN AUTOMATIC CONTROL COMMUNICATION SYSTEMS LINKÖPINGS UNIVERSITET Reglerteknik
More informationAnalysis 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 informationLecture: Sampling. Automatic Control 2. Sampling. Prof. Alberto Bemporad. University of Trento. Academic year
Automatic Control 2 Sampling Prof. Alberto Bemporad University of rento Academic year 20102011 Prof. Alberto Bemporad (University of rento) Automatic Control 2 Academic year 20102011 1 / 31 imediscretization
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 informationAn Introduction to Control Systems
An Introduction to Control Systems Signals and Systems: 3C1 Control Systems Handout 1 Dr. David Corrigan Electronic and Electrical Engineering corrigad@tcd.ie November 21, 2012 Recall the concept of a
More informationMath 216 Second Midterm 20 March, 2017
Math 216 Second Midterm 20 March, 2017 This sample exam is provided to serve as one component of your studying for this exam in this course. Please note that it is not guaranteed to cover the material
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 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 informationEssence of the Root Locus Technique
Essence of the Root Locus Technique In this chapter we study a method for finding locations of system poles. The method is presented for a very general setup, namely for the case when the closedloop
More informationAN INTRODUCTION TO THE CONTROL THEORY
OpenLoop controller An OpenLoop (OL) controller is characterized by no direct connection between the output of the system and its input; therefore external disturbance, nonlinear dynamics and parameter
More informationAlireza Mousavi Brunel University
Alireza Mousavi Brunel University 1 » Control Process» Control Systems Design & Analysis 2 OpenLoop Control: Is normally a simple switch on and switch off process, for example a light in a room is switched
More informationOverview of Bode Plots Transfer function review Piecewise linear approximations Firstorder terms Secondorder terms (complex poles & zeros)
Overview of Bode Plots Transfer function review Piecewise linear approximations Firstorder terms Secondorder terms (complex poles & zeros) J. McNames Portland State University ECE 222 Bode Plots Ver.
More informationChapter Eleven. Frequency Domain Design Sensitivity Functions
Feedback Systems by Astrom and Murray, v2.11b http://www.cds.caltech.edu/~murray/fbswiki Chapter Eleven Frequency Domain Design Sensitivity improvements in one frequency range must be paid for with sensitivity
More informationLecture 9 Infinite Impulse Response Filters
Lecture 9 Infinite Impulse Response Filters Outline 9 Infinite Impulse Response Filters 9 FirstOrder LowPass Filter 93 IIR Filter Design 5 93 CT Butterworth filter design 5 93 Bilinear transform 7 9
More informationTopic # Feedback Control. StateSpace Systems Closedloop control using estimators and regulators. Dynamics output feedback
Topic #17 16.31 Feedback Control StateSpace Systems Closedloop control using estimators and regulators. Dynamics output feedback Back to reality Copyright 21 by Jonathan How. All Rights reserved 1 Fall
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 informationEE202 Exam III April 6, 2017
EE202 Exam III April 6, 207 Name: (Please print clearly.) Student ID: CIRCLE YOUR DIVISION DeCarlo202 DeCarlo2022 7:30 MWF :30 TTH INSTRUCTIONS There are 3 multiple choice worth 5 points each and
More information2.010 Fall 2000 Solution of Homework Assignment 8
2.1 Fall 2 Solution of Homework Assignment 8 1. Root Locus Analysis of Hydraulic Servomechanism. The block diagram of the controlled hydraulic servomechanism is shown in Fig. 1 e r e error + i Σ C(s) P(s)
More informationSystems 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 informationSYSTEMTEORI  KALMAN FILTER VS LQ CONTROL
SYSTEMTEORI  KALMAN FILTER VS LQ CONTROL 1. Optimal regulator with noisy measurement Consider the following system: ẋ = Ax + Bu + w, x(0) = x 0 where w(t) is white noise with Ew(t) = 0, and x 0 is a stochastic
More informationSystems 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 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 informationIndex. Index. More information. in this web service Cambridge University Press
Atype elements, 4 7, 18, 31, 168, 198, 202, 219, 220, 222, 225 Atype variables. See Across variable ac current, 172, 251 ac induction motor, 251 Acceleration rotational, 30 translational, 16 Accumulator,
More information