EECS C128/ ME C134 Final Thu. May 14, pm. Closed book. One page, 2 sides of formula sheets. No calculators.

Save this PDF as:

Size: px
Start display at page:

Download "EECS C128/ ME C134 Final Thu. May 14, pm. Closed book. One page, 2 sides of formula sheets. No calculators." Transcription

1 Name: SID: EECS C28/ ME C34 Final Thu. May 4, pm Closed book. One page, 2 sides of formula sheets. No calculators. There are 8 problems worth points total. Problem Points Score Total In the real world, unethical actions by engineers can cost money, careers, and lives. The penalty for unethical actions on this exam will be a grade of F and a letter will be written for your file and to the Office of Student Conduct. tan 2 = 26.6 tan = 45 tan 3 = 8.4 tan 3 = 6 tan 4 = 4 tan 3 = 3 sin 3 = 2 cos 6 = log = db 2 log 2 = 6dB 2 log 2 = 3dB 2 log 2 = 6dB 2 log 5 = 2db 6dB = 4dB 2 log = db /e.37 /e 2.4 /e

2 Problem (4 pts) reference input r(t) + Σ error e(t) Controller D(s) control input u(t) plant G(s) output y(t) grid 8 pixels You are given the open-loop plant: G(s) = s + 5 (s + 2)(s + ) 3. For the above system, the partial root locus is shown for 5 different controller/plant combinations, G(s), D 2 (s)g(s),..., D 5 (s)g(s). (Note: the root locus shows open-loop pole locations for D(s)G(s), and closed-loop poles for are at end points of branches). DG +DG Imaginary Axis (seconds - ) Imaginary Axis (seconds - ) Imaginary Axis (seconds - ) 5-5 Root Locus G(s) Real Axis (seconds - ) Root locus D3(s)G(s) Real Axis (seconds - ) Root Locus D5(s)G(s) Real Axis (seconds - ) Imaginary Axis (seconds - ) Imaginary Axis (seconds - ) 5 Root Locus D2(s)G(s) Real Axis (seconds - ) Root Locus D4(s)G(s) Real Axis (seconds - ) [5 pts a) For each set of open-loop poles and zeros given above, choose the best corresponding open-loop Bode plot V,W,X,Y, or Z from the next page: (i) G(s): Bode Plot (ii) D 2 (s)g(s): Bode plot (iii) D 3 (s)g(s): Bode plot (iv) D 4 (s)g(s): Bode Plot (v) D 5 (s)g(s): Bode Plot 2

3 Problem, cont. The open-loop Bode plots for 5 different controller/plant combinations, D (s)g(s),..., D 5 (s)g(s) are shown below Bode Plot V Bode W Bode Plot X Bode Plot Y Bode Plot Z - 2 [4 pts b) For the listed Bode plots, estimate the phase and gain margin: (i) Bode plot V: phase margin (degrees) at ω = Bode plot V: gain margin db at ω = (ii) Bode plot Z: phase margin (degrees) at ω = Bode plot Z: gain margin db at ω = 3

4 Problem, cont. [5 pts c) For each closed loop controller/plant with root locus as given in part a), choose the best corresponding closed-loop step response (A-E) (i) G(s): step response (ii) D 2 (s)g(s): step response (iii) D 3 (s)g(s): step response (iv) D 4 (s)g(s): step response (v) D 5 (s)g(s): step response Step A Step B Amplitude.5.5 Amplitude Time (seconds) Step C Time (seconds) Step D Amplitude.5.5 Amplitude Time (seconds) Step E Time (seconds) Amplitude Time (seconds) 4

5 Problem 2 (4 pts) [4 pts a. You are given the open loop plant: G(s) = k s+6 s 6, with D(s) =. Sketch Nyquist plot for G(s) with k =, showing clearly any encirclements. Im G( j ω) Re G( j ) ω reference input r(t) + Σ error e(t) Controller D(s) control input u(t) plant G(s) output y(t) grid 8 pixels [2 pts b. Find the bounds on k for the system with unity feedback to be stable. [4 pts c. You are given the open loop plant G(s) = k (s 6)(s 4) (s+6)(s ). Sketch Nyquist plot for G(s) with k =, showing clearly any encirclements. Hint: phase of G(jω = 2) is +8. Im G( j ω) Re G( j ) ω [4 pts d. Find the bounds on k for the system with unity feedback to be stable. 5

6 Problem 3 (6 pts) The open-loop system is given by G(s) = 4 (s+) 3, and Bode plot for G(s) is here (Fig. 3.): 2 Bode Diagram A lag controller D(s) = k s+α s+β is to be designed such that the unity gain feedback system with openloop transfer function D(s)G(s) has the same steady state error as with OLTF G(s) and has a nominal (asymptotic approximation) phase margin φ m = 55 at ω = 8 rad s. Note 2 log G(jω = j8) = 3 db. [6 pts a. Determine gain, zero, and pole location for the lag network D(s): gain k = zero α = - pole β = - [4 pts b. Sketch the asymptotic Bode plot for the lag network D(s) alone on the plot below (Fig. 3.2): Bode Diagram [4 pts c. Sketch the asymptotic Bode plot for the combined lag network and plant D(s)G(s) on the plot (3.) above. [2 pts d. Mark the phase and phase margin frequency on the plot of D(s)G(s) (Fig. 3.). Explain briefly ( sentence) how does the actual phase margin compare to the asymptotic predction? 6

7 Problem 4 (8 pts) You are given the following plant ẋ = Ax + Bu, y = Cx where A is N N, u is scalar, B is N, C is N, and x is N. The system is observable and controllable. [2 pts a. Consider a controller u = r Kx where r is a reference input, and K is N. Determine the transfer function Y (s) R(s) = [2 pts b. Consider a controller u = K(r x) where r is a reference input, and K is N. Determine the transfer function Y (s) R(s) = [2 pts c. Draw a block diagram of the controlled system using integrators, summing junctions, and scaling functions. [3 pts d. If the same K is used in part a. and b. above, briefly explain any difference in transfer function or behavior: 7

8 Problem 5. (3 pts) Consider the following control system: [3 pts a. Write the state and output equations for the system, in terms of A, B, C, K, K e. [ ẋ ẋ N = [ [ x x N + [ x r(t), y = [ x N () [6 pts b. Given C = [, B = [ [, A = 2 find K and K e such that the closed loop poles are at s =, 2, 4. K = [ K e = [4 pts c. Show, with r(t) a unit step input, that e = in steady state (with the K, K e found above). (Hint: do not use matrix inverse.) 8

9 Problem 6. 3 pts Given the following system model: [3 pts a. Write the state and output equations for the system above. ẋ = Ax+Bu = [ ẋ ẋ 2 = [ [ x x 2 + u(t), y = Cx = [ [ x x 2 [2 pts b. Determine if the system A, B, C is controllable and observable. [2 pts c. Provide state equations for an observer which takes as inputs u(t), y(t), and provides an estimate of the state ˆx(t). [6 pts d. Find observer gain L such that the observer has closed loop poles at s =, s 2 =. 9

10 Problem 7 (4 pts) [3 pts a. Given G(s) = s+2. Let m(t) be the step response of g(t), i.e. M(s) = s(s+2). Let x (t) = m(t) m(t T ) where T is the sampling period. Find X (z) the Z transform of x (t). X (z) = [3 pts b. Given ẋ 2 (t) = 2x 2 (t) + u(t). Find the discrete time equivalent system using zeroorder hold for input u(t) and sampling period T : x 2 ((k + )T ) = Gx 2 (kt ) + Hu(kT ). G = H = [2 pts c. Find the X 2(z) U(z) state-space form. the discrete time transfer function from input u to state x 2 using the X 2 (z) U(z)

11 Problem 7, cont. [2 pts d. Does X 2(z) U(z) = X (z)? Why or why not? [4 pts e. With zero initial conditions (ZSR), T =.25, and a unit step input for x 2 (kt ), sketch m(t) and x 2 (kt ) on the plot below in the interval shown: x2(kt), m(t) t

12 Problem 8 Short Answers (8 pts) [4 pts a. Given the discrete time system below, find lim k x(k) for a unit step input u(k) =. x(k + ) = [ /6 /2 2/3 [ x(k) + u(k) lim k x(k) = [. [4 pts b. Given ẋ(t) = x(t) + u(t). The discrete time equivalent system using zero-order hold for input u(t) and sampling period T is of the form x((k + )T ) = Gx(kT ) + Hu(kT ). The discrete time system has a state feedback controller u(kt ) = r(kt ) 2x(kT ) applied. i. Find the eigenvalue for the closed loop system: ii. Find the largest value of T for which the system will be stable. (May be left in terms of ln.) : T < 2

13 Blank page for scratch work. 3

EECS C128/ ME C134 Final Wed. Dec. 14, am. Closed book. One page, 2 sides of formula sheets. No calculators. Name: SID: EECS C128/ ME C134 Final Wed. Dec. 14, 211 81-11 am Closed book. One page, 2 sides of formula sheets. No calculators. There are 8 problems worth 1 points total. Problem Points Score 1 16 2 12

EECS 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

Controls Problems for Qualifying Exam - Spring 2014 Controls Problems for Qualifying Exam - Spring 2014 Problem 1 Consider the system block diagram given in Figure 1. Find the overall transfer function T(s) = C(s)/R(s). Note that this transfer function

r + - FINAL June 12, 2012 MAE 143B Linear Control Prof. M. Krstic MAE 43B Linear Control Prof. M. Krstic FINAL June, One sheet of hand-written notes (two pages). Present your reasoning and calculations clearly. Inconsistent etchings will not be graded. Write answers

ECE 486 Control Systems ECE 486 Control Systems Spring 208 Midterm #2 Information Issued: April 5, 208 Updated: April 8, 208 ˆ This document is an info sheet about the second exam of ECE 486, Spring 208. ˆ Please read the following

EE C128 / ME C134 Final Exam Fall 2014 EE C128 / ME C134 Final Exam Fall 2014 December 19, 2014 Your PRINTED FULL NAME Your STUDENT ID NUMBER Number of additional sheets 1. No computers, no tablets, no connected device (phone etc.) 2. Pocket

EE 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

Homework 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

1 (s + 3)(s + 2)(s + a) G(s) = C(s) = K P + K I MAE 43B Linear Control Prof. M. Krstic FINAL June 9, Problem. ( points) Consider a plant in feedback with the PI controller G(s) = (s + 3)(s + )(s + a) C(s) = K P + K I s. (a) (4 points) For a given constant

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

Professor 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

Topic # Feedback Control. State-Space Systems Closed-loop control using estimators and regulators. Dynamics output feedback Topic #17 16.31 Feedback Control State-Space Systems Closed-loop control using estimators and regulators. Dynamics output feedback Back to reality Copyright 21 by Jonathan How. All Rights reserved 1 Fall

DESIGN USING TRANSFORMATION TECHNIQUE CLASSICAL METHOD 206 Spring Semester ELEC733 Digital Control System LECTURE 7: DESIGN USING TRANSFORMATION TECHNIQUE CLASSICAL METHOD For a unit ramp input Tz Ez ( ) 2 ( z ) D( z) G( z) Tz e( ) lim( z) z 2 ( z ) D( z)

1 (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

Transient response via gain adjustment. Consider a unity feedback system, where G(s) = 2. The closed loop transfer function is. s 2 + 2ζωs + ω 2 n Design via frequency response Transient response via gain adjustment Consider a unity feedback system, where G(s) = ωn 2. The closed loop transfer function is s(s+2ζω n ) T(s) = ω 2 n s 2 + 2ζωs + ω 2

Systems 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

INTRODUCTION 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 linear-time-invariant

EE C128 / ME C134 Midterm Fall 2014 EE C128 / ME C134 Midterm Fall 2014 October 16, 2014 Your PRINTED FULL NAME Your STUDENT ID NUMBER Number of additional sheets 1. No computers, no tablets, no connected device (phone etc.) 2. Pocket calculator

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

Outline. Classical Control. Lecture 5 Outline Outline Outline 1 What is 2 Outline What is Why use? Sketching a 1 What is Why use? Sketching a 2 Gain Controller Lead Compensation Lag Compensation What is Properties of a General System Why use?

Raktim Bhattacharya. . AERO 422: Active Controls for Aerospace Vehicles. Frequency Response-Design Method .. AERO 422: Active Controls for Aerospace Vehicles Frequency Response- Method Raktim Bhattacharya Laboratory For Uncertainty Quantification Aerospace Engineering, Texas A&M University. ... Response to

Frequency methods for the analysis of feedback systems. Lecture 6. Loop analysis of feedback systems. Nyquist approach to study stability Lecture 6. Loop analysis of feedback systems 1. Motivation 2. Graphical representation of frequency response: Bode and Nyquist curves 3. Nyquist stability theorem 4. Stability margins Frequency methods

100 (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

Topic # Feedback Control Topic #4 16.31 Feedback Control Stability in the Frequency Domain Nyquist Stability Theorem Examples Appendix (details) This is the basis of future robustness tests. Fall 2007 16.31 4 2 Frequency Stability

CHAPTER 7 : BODE PLOTS AND GAIN ADJUSTMENTS COMPENSATION CHAPTER 7 : BODE PLOTS AND GAIN ADJUSTMENTS COMPENSATION Objectives Students should be able to: Draw the bode plots for first order and second order system. Determine the stability through the bode plots.

Übersetzungshilfe / 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 -

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 Department of Electronics and Instrumentation Engineering M. E- CONTROL AND INSTRUMENTATION ENGINEERING CL7101 CONTROL SYSTEM DESIGN Unit I- BASICS AND ROOT-LOCUS DESIGN PART-A (2 marks) 1. What are the

Lecture 11. Frequency Response in Discrete Time Control Systems EE42 - Discrete Time Systems Spring 28 Lecturer: Asst. Prof. M. Mert Ankarali Lecture.. Frequency Response in Discrete Time Control Systems Let s assume u[k], y[k], and G(z) represents the input, output,

Introduction. Performance and Robustness (Chapter 1) Advanced Control Systems Spring / 31 Introduction Classical Control Robust Control u(t) y(t) G u(t) G + y(t) G : nominal model G = G + : plant uncertainty Uncertainty sources : Structured : parametric uncertainty, multimodel uncertainty Unstructured

Class 13 Frequency domain analysis Class 13 Frequency domain analysis The frequency response is the output of the system in steady state when the input of the system is sinusoidal Methods of system analysis by the frequency response, as

ME 475/591 Control Systems Final Exam Fall '99 ME 475/591 Control Systems Final Exam Fall '99 Closed book closed notes portion of exam. Answer 5 of the 6 questions below (20 points total) 1) What is a phase margin? Under ideal circumstances, what does

AMME3500: System Dynamics & Control Stefan B. Williams May, 211 AMME35: System Dynamics & Control Assignment 4 Note: This assignment contributes 15% towards your final mark. This assignment is due at 4pm on Monday, May 3 th during Week 13

MAE 143B - Homework 9 MAE 143B - Homework 9 7.1 a) We have stable first-order poles at p 1 = 1 and p 2 = 1. For small values of ω, we recover the DC gain K = lim ω G(jω) = 1 1 = 2dB. Having this finite limit, our straight-line

Richiami 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

(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

Test 2 SOLUTIONS. ENGI 5821: Control Systems I. March 15, 2010 Test 2 SOLUTIONS ENGI 5821: Control Systems I March 15, 2010 Total marks: 20 Name: Student #: Answer each question in the space provided or on the back of a page with an indication of where to find the

If you need more room, use the backs of the pages and indicate that you have done so. EE 343 Exam II Ahmad F. Taha Spring 206 Your Name: Your Signature: Exam duration: hour and 30 minutes. This exam is closed book, closed notes, closed laptops, closed phones, closed tablets, closed pretty

Automatic Control (MSc in Mechanical Engineering) Lecturer: Andrea Zanchettin Date: Student ID number... Signature... Automatic Control (MSc in Mechanical Engineering) Lecturer: Andrea Zanchettin Date: 29..23 Given and family names......................solutions...................... Student ID number..........................

Übersetzungshilfe / Translation aid (English) To be returned at the end of the exam! Prüfung Regelungstechnik I (Control Systems I) Prof. Dr. Lino Guzzella 5. 2. 2 Übersetzungshilfe / Translation aid (English) To be returned at the end of the exam! Do not mark up this translation aid -

Module 3F2: Systems and Control EXAMPLES PAPER 2 ROOT-LOCUS. Solutions Cambridge University Engineering Dept. Third Year Module 3F: Systems and Control EXAMPLES PAPER ROOT-LOCUS Solutions. (a) For the system L(s) = (s + a)(s + b) (a, b both real) show that the root-locus

EE C128 / ME C134 Fall 2014 HW 9 Solutions. HW 9 Solutions. 10(s + 3) s(s + 2)(s + 5) G(s) = 1. Pole Placement Given the following open-loop plant, HW 9 Solutions G(s) = 1(s + 3) s(s + 2)(s + 5) design the state-variable feedback controller u = Kx + r, where K = [k 1 k 2 k 3 ] is the feedback

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

State Regulator. Advanced Control. design of controllers using pole placement and LQ design rules Advanced Control State Regulator Scope design of controllers using pole placement and LQ design rules Keywords pole placement, optimal control, LQ regulator, weighting matrixes Prerequisites Contact state

ROOT LOCUS. Consider the system. Root locus presents the poles of the closed-loop system when the gain K changes from 0 to. H(s) H ( s) = ( s) C1 ROOT LOCUS Consider the system R(s) E(s) C(s) + K G(s) - H(s) C(s) R(s) = K G(s) 1 + K G(s) H(s) Root locus presents the poles of the closed-loop system when the gain K changes from 0 to 1+ K G ( s)

ELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 2010/2011 CONTROL ENGINEERING SHEET 5 Lead-Lag Compensation Techniques CAIRO UNIVERSITY FACULTY OF ENGINEERING ELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 00/0 CONTROL ENGINEERING SHEET 5 Lead-Lag Compensation Techniques [] For the following system, Design a compensator such

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

Exam. 135 minutes + 15 minutes reading time Exam January 23, 27 Control Systems I (5-59-L) Prof. Emilio Frazzoli Exam Exam Duration: 35 minutes + 5 minutes reading time Number of Problems: 45 Number of Points: 53 Permitted aids: Important: 4 pages

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

FREQUENCY-RESPONSE DESIGN ECE45/55: Feedback Control Systems. 9 FREQUENCY-RESPONSE DESIGN 9.: PD and lead compensation networks The frequency-response methods we have seen so far largely tell us about stability and stability margins

ME 132, Fall 2015, Quiz # 2 ME 132, Fall 2015, Quiz # 2 # 1 # 2 # 3 # 4 # 5 # 6 Total NAME 14 10 8 6 14 8 60 Rules: 1. 2 sheets of notes allowed, 8.5 11 inches. Both sides can be used. 2. Calculator is allowed. Keep it in plain view

EE C128 / ME C134 Fall 2014 HW 6.2 Solutions. HW 6.2 Solutions EE C28 / ME C34 Fall 24 HW 6.2 Solutions. PI Controller For the system G = K (s+)(s+3)(s+8) HW 6.2 Solutions in negative feedback operating at a damping ratio of., we are going to design a PI controller

Exam. 135 minutes, 15 minutes reading time Exam August 6, 208 Control Systems II (5-0590-00) Dr. Jacopo Tani Exam Exam Duration: 35 minutes, 5 minutes reading time Number of Problems: 35 Number of Points: 47 Permitted aids: 0 pages (5 sheets) A4.

EE 380 EXAM II 3 November 2011 Last Name (Print): First Name (Print): ID number (Last 4 digits): Section: DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO EE 380 EXAM II 3 November 2011 Last Name (Print): First Name (Print): ID number (Last 4 digits): Section: DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO Problem Weight Score 1 25 2 25 3 25 4 25 Total

1 Steady State Error (30 pts) Professor Fearing EECS C28/ME C34 Problem Set Fall 2 Steady State Error (3 pts) Given the following continuous time (CT) system ] ẋ = A x + B u = x + 2 7 ] u(t), y = ] x () a) Given error e(t) = r(t) y(t)

SAMPLE 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: Frequency-domain analysis and control design (15 pt) Given is a

Problem Weight Score Total 100 EE 350 EXAM IV 15 December 2010 Last Name (Print): First Name (Print): ID number (Last 4 digits): Section: DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO Problem Weight Score 1 25 2 25 3 25 4 25 Total

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: 30-Apr-14 COURSE: ECE 3084A (Prof. Michaels) NAME: STUDENT #: LAST, FIRST Write your name on the front page

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

VALLIAMMAI 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

Systems Analysis and Control Systems Analysis and Control Matthew M. Peet Illinois Institute of Technology Lecture 23: Drawing The Nyquist Plot Overview In this Lecture, you will learn: Review of Nyquist Drawing the Nyquist Plot Using

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..

Systems Analysis and Control Systems Analysis and Control Matthew M. Peet Illinois Institute of Technology Lecture 22: The Nyquist Criterion Overview In this Lecture, you will learn: Complex Analysis The Argument Principle The Contour

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

Exam. 135 minutes, 15 minutes reading time Exam August 15, 2017 Control Systems I (151-0591-00L) Prof Emilio Frazzoli Exam Exam Duration: 135 minutes, 15 minutes reading time Number of Problems: 44 Number of Points: 52 Permitted aids: Important:

Automatique. A. Hably 1. Commande d un robot mobile. Automatique. A.Hably. Digital implementation A. Hably 1 1 Gipsa-lab, Grenoble-INP ahmad.hably@grenoble-inp.fr Commande d un robot mobile (Gipsa-lab (DA)) ASI 1 / 25 Outline 1 2 (Gipsa-lab (DA)) ASI 2 / 25 of controllers Signals must be sampled and

Chapter 6 - Solved Problems Chapter 6 - Solved Problems Solved Problem 6.. Contributed by - James Welsh, University of Newcastle, Australia. Find suitable values for the PID parameters using the Z-N tuning strategy for the nominal

Professor Fearing EE C128 / ME C134 Problem Set 10 Solution Fall 2010 Jansen Sheng and Wenjie Chen, UC Berkeley Professor Fearing EE C28 / ME C34 Problem Set Solution Fall 2 Jansen Sheng and Wenjie Chen, UC Berkeley. (5 pts) Final Value Given the following continuous time (CT) system ẋ = Ax+Bu = 5 9 7 x+ u(t), y

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

Professor Fearing EE C128 / ME C134 Problem Set 4 Solution Fall 2010 Jansen Sheng and Wenjie Chen, UC Berkeley. control input. error Controller D(s) Professor Fearing EE C18 / ME C13 Problem Set Solution Fall 1 Jansen Sheng and Wenjie Chen, UC Berkeley reference input r(t) + Σ error e(t) Controller D(s) grid 8 pixels control input u(t) plant G(s) output

Control Systems I. Lecture 9: The Nyquist condition Control Systems I Lecture 9: The Nyquist condition adings: Guzzella, Chapter 9.4 6 Åstrom and Murray, Chapter 9.1 4 www.cds.caltech.edu/~murray/amwiki/index.php/first_edition Emilio Frazzoli Institute

Control Systems. Control Systems Design Lead-Lag Compensator. Design Lead-Lag Compensator hibum@seoulteh.a.kr Outline Lead ompensator design in frequeny domain Lead ompensator design steps. Example on lead ompensator design. Frequeny Domain Design Frequeny response

Classify a transfer function to see which order or ramp it can follow and with which expected error. Dr. J. Tani, Prof. Dr. E. Frazzoli 5-059-00 Control Systems I (Autumn 208) Exercise Set 0 Topic: Specifications for Feedback Systems Discussion: 30.. 208 Learning objectives: The student can grizzi@ethz.ch,

Übersetzungshilfe / Translation aid (English) To be returned at the end of the exam! Prüfung Regelungstechnik I (Control Systems I) Prof. Dr. Lino Guzzella 9. 8. 2 Übersetzungshilfe / Translation aid (English) To be returned at the end of the exam! Do not mark up this translation aid -

Frequency Response Techniques 4th Edition T E N Frequency Response Techniques SOLUTION TO CASE STUDY CHALLENGE Antenna Control: Stability Design and Transient Performance First find the forward transfer function, G(s). Pot: K 1 = 10

Digital Control Systems State Feedback Control Digital Control Systems State Feedback Control Illustrating the Effects of Closed-Loop Eigenvalue Location and Control Saturation for a Stable Open-Loop System Continuous-Time System Gs () Y() s 1 = =

Nyquist Criterion For Stability of Closed Loop System Nyquist Criterion For Stability of Closed Loop System Prof. N. Puri ECE Department, Rutgers University Nyquist Theorem Given a closed loop system: r(t) + KG(s) = K N(s) c(t) H(s) = KG(s) +KG(s) = KN(s)

Course roadmap. ME451: Control Systems. What is Root Locus? (Review) Characteristic equation & root locus. Lecture 18 Root locus: Sketch of proofs ME451: Control Systems Modeling Course roadmap Analysis Design Lecture 18 Root locus: Sketch of proofs Dr. Jongeun Choi Department of Mechanical Engineering Michigan State University Laplace transform

Frequency domain analysis Automatic Control 2 Frequency domain analysis Prof. Alberto Bemporad University of Trento Academic year 2010-2011 Prof. Alberto Bemporad (University of Trento) Automatic Control 2 Academic year 2010-2011

(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.

Root Locus Methods. The root locus procedure Root Locus Methods Design of a position control system using the root locus method Design of a phase lag compensator using the root locus method The root locus procedure To determine the value of the gain

16.30/31, 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

CONTROL OF DIGITAL SYSTEMS AUTOMATIC CONTROL AND SYSTEM THEORY CONTROL OF DIGITAL SYSTEMS Gianluca Palli Dipartimento di Ingegneria dell Energia Elettrica e dell Informazione (DEI) Università di Bologna Email: gianluca.palli@unibo.it

EE3CL4: Introduction to Linear Control Systems 1 / 30 EE3CL4: Introduction to Linear Control Systems Section 9: of and using Techniques McMaster University Winter 2017 2 / 30 Outline 1 2 3 4 / 30 domain analysis Analyze closed loop using open loop

Subject: Optimal Control Assignment-1 (Related to Lecture notes 1-10) Subject: Optimal Control Assignment- (Related to Lecture notes -). Design a oil mug, shown in fig., to hold as much oil possible. The height and radius of the mug should not be more than 6cm. The mug must

MAE 143B - Homework 8 Solutions MAE 43B - Homework 8 Solutions P6.4 b) With this system, the root locus simply starts at the pole and ends at the zero. Sketches by hand and matlab are in Figure. In matlab, use zpk to build the system

University of Toronto. Final Exam University of Toronto Final Exam Date - Dec 16, 013 Duration:.5 hrs ECE331 Electronic Circuits Lecturer - D. Johns ANSWER QUESTIONS ON THESE SHEETS USING BACKS IF NECESSARY 1. Equation sheet is on last

Electronics II. Final Examination f3fs_elct7.fm - The University of Toledo EECS:3400 Electronics I Section Student Name Electronics II Final Examination Problems Points.. 3 3. 5 Total 40 Was the exam fair? yes no Analog Electronics f3fs_elct7.fm

R10 JNTUWORLD B 1 M 1 K 2 M 2. f(t) Figure 1 Code No: R06 R0 SET - II B. Tech II Semester Regular Examinations April/May 03 CONTROL SYSTEMS (Com. to EEE, ECE, EIE, ECC, AE) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions carry

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering Dynamics and Control II Fall 2007 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering.4 Dynamics and Control II Fall 7 Problem Set #9 Solution Posted: Sunday, Dec., 7. The.4 Tower system. The system parameters are

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},

This homework will not be collected or graded. It is intended to help you practice for the final exam. Solutions will be posted. 6.003 Homework #14 This homework will not be collected or graded. It is intended to help you practice for the final exam. Solutions will be posted. Problems 1. Neural signals The following figure illustrates

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

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

FREQUENCY RESPONSE ANALYSIS Closed Loop Frequency Response Closed Loop Frequency Response The Bode plot is generally constructed for an open loop transfer function of a system. In order to draw the Bode plot for a closed loop system, the transfer function has

ME 375 EXAM #1 Friday, March 13, 2015 SOLUTION ME 375 EXAM #1 Friday, March 13, 2015 SOLUTION PROBLEM 1 A system is made up of a homogeneous disk (of mass m and outer radius R), particle A (of mass m) and particle B (of mass m). The disk is pinned .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 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