EECS C128/ ME C134 Final Wed. Dec. 15, am. Closed book. Two pages of formula sheets. No calculators.


 Chester Fleming
 3 years ago
 Views:
Transcription
1 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 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 = tan = 45 tan = 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 = 6dB 2 2 log 5 = 2db 6dB = 4dB 2 log = db /e.37 /e 2.4 /e
2 Problem (2 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) = 8 (s + 3)(s 2 + 2s + 4) The Bode plots for the plant G(s) and the plant with 3 different compensators are given below. Bode Plot G(s) Bode Plot D2(s)G(S) Magnitude (db) Magnitude (db) Phase (deg) Phase (deg) Frequency (rad/sec) 27 2 Frequency (rad/sec) Bode Plot D3(s)G(s) Bode Plot D4(s)G(s) 2 2 Magnitude (db) Magnitude (db) Phase (deg) 8 27 Phase (deg) Frequency (rad/sec) 27 2 Frequency (rad/sec) [4 pts] a) For each Bode plot, estimate the phase and gain margin: (i) G(s): phase margin gain margin db (ii) D 2 (s)g(s): phase margin gain margin db (iii) D 3 (s)g(s): phase margin gain margin db (iv) D 4 (s)g(s): phase margin gain margin db 2
3 Problem, cont. [4 pts] b) For each openloop Bode plot on the previous page, choose the best corresponding closedloop root locus (write in letter W,X,Y, or Z). Note: the root locus is zoomed in and does not show the openloop pole at s = 3. (Hint: the root locus shows openloop pole locations for D(s)G(s), and closedloop poles for DG +DG ). (i) G(s): root locus (ii) D 2 (s)g(s): root locus (iii) D 3 (s)g(s): root locus (iv) D 4 (s)g(s): root locus Root Locus W Root locus X Imaginary Axis 5 Imaginary Axis Real Axis Real Axis Root Locus Y Root Locus Z 5 Imaginary Axis 5 Imaginary Axis Real Axis 5 5 Real Axis 3
4 Problem, cont. [4 pts] c) For each openloop Bode plot on page 2, choose the best corresponding closedloop step response (AD) (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.5 Step A.5 Step B Amplitude Amplitude Time (sec) Time (sec).5 Step C.5 Step D Amplitude Amplitude Time (sec) Time (sec) 4
5 Problem 2 (6 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) =. The system is to be controlled using s 2 +2s+5 proportional plus integral PI control, that is D(s) = k p + k I s. [8 pts] a) Sketch the positive root locus as k I varies for fixed k p = 5, noting: (i) approximate asymptote intersection point s = (ii) approximate angle of departure for the poles: [8 pts] b) Sketch the positive root locus as k p varies for fixed k I =, noting: (i) approximate angle of departure for the poles: Given: the roots of s 3 + 2s 2 + 5s + (s +.268)(s j)(s j) 5
6 Problem 3 ( pts) You are given the following plant [ ẋ = Ax + Bu = 6 5 ] [ x + ] u(t), y = [ ] x We want to add a lead compensator to the system such that U(s) V (s) = s+ s+2 = s+2, where v(t) is the input to the compensator, and u(t) is the original input to the plant. [6 pts] a) Determine the new state space equations (that is, fill in the values) for the combined system of plant plus lead compensator by adding a new state variable z: x x 2 ż = x x 2 z + v(t) y = [ ] x x 2 z + [ ]v(t) () [4 pts] b) Prove that the compensated system is observable (hint: consider new state and output matrices Ā and C). 6
7 Problem 4 (4 pts) Given the following model of the inverted pendulum [ ] [ ẋ = Ax + Bu = x + 4 A full order observer is given ˆx = (A TC)ˆx + Bu + TCx ] u(t) y = [ ]x [3 pts] a) For combined plant and full state estimator with state feedback u = F ˆx and observer gain T, derive the combined state equations for [x e] using e = ˆx x. (Please leave equations in terms of A,B,C,T rather than numerical values.) [3 pts] b) Using a), show that the eigenvalues for the plant and the observer can be set independently (separation principle). (Hint: use property of determinants.) [3 pts] c) Find feedback gains F such that the controller has closed loop poles at 2 and 4. F = [f f 2 ] = [ ] [3 pts] d) Find observer gains T such that the observer has closed loop poles at  and 6. T = [t t 2 ] = [ ] [2 pts] e) What would the effect be on system performance if the observer poles were slower than the controller poles? 7
8 Problem 5 (6 pts) You are given the following [ 8 ẋ = Ax + Bu = 2 29 ] [ x + ] u(t), y = [3 ] x [2 pts] a) Determine if the system is controllable and observable. [4 pts] b) Find the transformation P and Ā such that Ā = P AP is in modal canonical (diagonal) form. [ ] [ ] P = Ā = [2 pts] c) Find B, C such that x = Ā x + Bu and y = C x. [ ] B = C = [ ] [4 pts] d) Find eāt and e At : [ ] eāt = [ ] e At = [4 pts] e) Draw a block diagram representation for the system in modal form with input u and output y. Note any modes which are not observable or not controllable. 8
9 Problem 6. ( pts) You are given a continuous time plant described by the following state equation. [ ] [ ] 3 ẋ = Ax = x x(t = ) = 2 Every T seconds the state of the system is measured with an A/D converter, that is x[n] = x(t = nt). [2 pts] a) For the zero input response, the sampled state can be represented by: x[n + ] = Gx[n]. What are the elements of G(T)? (Leave in terms of an exact expression.) G = [2 pts] b) If you were given G and x[], how would you find x[n]? x[n] = [2 pts] c) For what conditions will the sampled system x[n + ] = Gx[n] be stable? [4 pts] d) You are given a continuous time system ẋ(t) = Ax(t)+Bu(t) and its zeroorder hold equivalent system x[n+] = Gx[n] +Hu[n], with sample rate T. The continuous time system is controlled using full state feedback u = kx, that is ẋ = Ax + Bu = Ax + B( k)x = [A Bk]x, with k such that the system is asymptotically stable. Will the zeroorderhold equivalent sampled system with the same state feedback, that is x[n + ] = (G Hk)x[n], necessarily be asymptotically stable? Why or why not? 9
10 Problem 7 ( pts) The simplified dynamics of a magnetically suspended steel ball are given by: mÿ = mg c u2 y 2. where m is mass of ball, g is gravity, y is ball position, and u is the control input. [2 pts] a) using the states x = y and x 2 = ẏ write down a nonlinear state space description of this system. x = x 2 = [2 pts] b) What equilibrium control input must be applied to suspend the ball at position y = y o? u e = [2 pts] c) Write the linearized state space equations for state and input variables representing perturbations away from the equilibrium of part b). [ ] [ ][ ] [ ] x x = + u(t) (2) x 2 x 2 [2 pts] d) Is the linearized model stable? What can you conclude about the stability of the nonlinear system close to the equilibrium point x e? [2 pts] e) Briefly describe, using a block diagram, how to implement a controller to regulate steel ball position at y = y o, specifying u(t). You have access to only output y.
11 Problem 8. (2 pts) True/False questions. + point for correct answer,  point for incorrect answer, for blank. Write T or F in blank. (Minimum points on problem 8 is zero). [7 pts] a) In lab 3, we used a PD controller on the Quanser carts to track a reference position input. Which of the following are true about PD control? (i) PD control allows us to have both a shorter rise time and a smaller overshoot for a step input compared to just P control. (ii) (iii) (iv) (v) (vi) (vii) PD control is useful for eliminating steady state error. A PD controller can be approximated by a lag compensator. A PD controller can always be converted into an equivalent statefeedback controller. A PD controller amplifies noise. The derivative term of a PD controller is used to increase the damping. The best way of estimating velocity for PD control is to use numerical differentiation. [5 pts] b) In Lab 5a, state feedback controller for the inverted pendulum, we linearized the system around the inverted position, and get the state space model as ẋ = Ax+Bu,y = Cx. The linearized model is controllable and observable. The objective of that lab is to regulate the pendulum at the inverted position (θ = ). In the simulation, the controller is able to regulate the system with zero steady state error. However, in actual hardware response, we observe that the pendulum usually continues to oscillate about the equilibrium point. Please check the correctness of the following statements: (i) (ii) (iii) The continuous oscillation behavior is mostly because it is impossible to initialize the pendulum perfectly vertical, so the desired θ = is slightly tilted. The difference between simulation and actual hardware response is partially due to the linearization error of the system model at actual regulation position. Using a fullorder observer to estimate the system states and state feedback will eliminate the continuous oscillation behavior. (iv) The LQR control can eliminate this continuous oscillation behavior. (v) Assume we want to implement the integral control as u = vdt = K(r x)dt or u = v = K(r x), where r is the reference input. The extended system with [x;u] as the system states and v as the system input will become uncontrollable.
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 8111 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
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 informationControls Problems for Qualifying Exam  Spring 2014
Controls Problems for Qualifying Exam  Spring 2014 Problem 1 Consider the system block diagram given in Figure 1. Find the overall transfer function T(s) = C(s)/R(s). Note that this transfer function
More informationState Regulator. Advanced Control. design of controllers using pole placement and LQ design rules
Advanced Control State Regulator Scope design of controllers using pole placement and LQ design rules Keywords pole placement, optimal control, LQ regulator, weighting matrixes Prerequisites Contact state
More informationEE 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
More informationD(s) G(s) A control system design definition
R E Compensation D(s) U Plant G(s) Y Figure 7. A control system design definition x x x 2 x 2 U 2 s s 7 2 Y Figure 7.2 A block diagram representing Eq. (7.) in control form z U 2 s z Y 4 z 2 s z 2 3 Figure
More information1 (30 pts) Dominant Pole
EECS C8/ME C34 Fall Problem Set 9 Solutions (3 pts) Dominant Pole For the following transfer function: Y (s) U(s) = (s + )(s + ) a) Give state space description of the system in parallel form (ẋ = Ax +
More informationEE221A Linear System Theory Final Exam
EE221A Linear System Theory Final Exam Professor C. Tomlin Department of Electrical Engineering and Computer Sciences, UC Berkeley Fall 2016 12/16/16, 811am Your answers must be supported by analysis,
More information1 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)
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 informationPrüfung 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 informationOutline. Classical Control. Lecture 5
Outline Outline Outline 1 What is 2 Outline What is Why use? Sketching a 1 What is Why use? Sketching a 2 Gain Controller Lead Compensation Lag Compensation What is Properties of a General System Why use?
More informationÜbersetzungshilfe / Translation aid (English) To be returned at the end of the exam!
Prüfung Regelungstechnik I (Control Systems I) Prof. Dr. Lino Guzzella 3.. 24 Übersetzungshilfe / Translation aid (English) To be returned at the end of the exam! Do not mark up this translation aid 
More informationEE 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
More informationECE 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
More informationAMME3500: 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
More informationContents. PART I METHODS AND CONCEPTS 2. Transfer Function Approach Frequency Domain Representations... 42
Contents Preface.............................................. xiii 1. Introduction......................................... 1 1.1 Continuous and Discrete Control Systems................. 4 1.2 OpenLoop
More informationDepartment of Electronics and Instrumentation Engineering M. E CONTROL AND INSTRUMENTATION ENGINEERING CL7101 CONTROL SYSTEM DESIGN Unit I BASICS AND ROOTLOCUS DESIGN PARTA (2 marks) 1. What are the
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 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 informationÜbersetzungshilfe / 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 
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 informationR a) Compare open loop and closed loop control systems. b) Clearly bring out, from basics, Forcecurrent and ForceVoltage 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, Forcecurrent and ForceVoltage analogies..
More informationSystems Analysis and Control
Systems Analysis and Control Matthew M. Peet Arizona State University Lecture 21: Stability Margins and Closing the Loop Overview In this Lecture, you will learn: Closing the Loop Effect on Bode Plot Effect
More 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 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 informationCourse Outline. Higher Order Poles: Example. Higher Order Poles. Amme 3500 : System Dynamics & Control. State Space Design. 1 G(s) = s(s + 2)(s +10)
Amme 35 : System Dynamics Control State Space Design Course Outline Week Date Content Assignment Notes 1 1 Mar Introduction 2 8 Mar Frequency Domain Modelling 3 15 Mar Transient Performance and the splane
More informationECEn 483 / ME 431 Case Studies. Randal W. Beard Brigham Young University
ECEn 483 / ME 431 Case Studies Randal W. Beard Brigham Young University Updated: December 2, 2014 ii Contents 1 Single Link Robot Arm 1 2 Pendulum on a Cart 9 3 Satellite Attitude Control 17 4 UUV Roll
More informationIf 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
More informationLinear State Feedback Controller Design
Assignment For EE5101  Linear Systems Sem I AY2010/2011 Linear State Feedback Controller Design Phang Swee King A0033585A Email: king@nus.edu.sg NGS/ECE Dept. Faculty of Engineering National University
More informationÜbersetzungshilfe / 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 
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 informationEE 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
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 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 informationLecture 9. Introduction to Kalman Filtering. Linear Quadratic Gaussian Control (LQG) G. Hovland 2004
MER42 Advanced Control Lecture 9 Introduction to Kalman Filtering Linear Quadratic Gaussian Control (LQG) G. Hovland 24 Announcement No tutorials on hursday mornings 89am I will be present in all practical
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 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 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 informationOutline. 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 informationME 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
More informationControl Systems I. Lecture 4: Diagonalization, Modal Analysis, Intro to Feedback. Readings: Emilio Frazzoli
Control Systems I Lecture 4: Diagonalization, Modal Analysis, Intro to Feedback Readings: Emilio Frazzoli Institute for Dynamic Systems and Control DMAVT ETH Zürich October 13, 2017 E. Frazzoli (ETH)
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 informationCONTROL DESIGN FOR SET POINT TRACKING
Chapter 5 CONTROL DESIGN FOR SET POINT TRACKING In this chapter, we extend the pole placement, observerbased output feedback design to solve tracking problems. By tracking we mean that the output is commanded
More informationMAE143a: Signals & Systems (& Control) Final Exam (2011) solutions
MAE143a: Signals & Systems (& Control) Final Exam (2011) solutions Question 1. SIGNALS: Design of a noisecancelling headphone system. 1a. Based on the lowpass filter given, design a highpass filter,
More informationAutomatic 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..........................
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 informationEE 16B Midterm 2, March 21, Name: SID #: Discussion Section and TA: Lab Section and TA: Name of left neighbor: Name of right neighbor:
EE 16B Midterm 2, March 21, 2017 Name: SID #: Discussion Section and TA: Lab Section and TA: Name of left neighbor: Name of right neighbor: Important Instructions: Show your work. An answer without explanation
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 informationECEN 420 LINEAR CONTROL SYSTEMS. Lecture 6 Mathematical Representation of Physical Systems II 1/67
1/67 ECEN 420 LINEAR CONTROL SYSTEMS Lecture 6 Mathematical Representation of Physical Systems II State Variable Models for Dynamic Systems u 1 u 2 u ṙ. Internal Variables x 1, x 2 x n y 1 y 2. y m Figure
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 informationEC Control Engineering Quiz II IIT Madras
EC34  Control Engineering Quiz II IIT Madras Linear algebra Find the eigenvalues and eigenvectors of A, A, A and A + 4I Find the eigenvalues and eigenvectors of the following matrices: (a) cos θ sin θ
More informationControl 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 DMAVT ETH Zürich November 24, 2017 E. Frazzoli (ETH) Lecture
More informationUNIVERSITY OF BOLTON SCHOOL OF ENGINEERING. MSc SYSTEMS ENGINEERING AND ENGINEERING MANAGEMENT SEMESTER 2 EXAMINATION 2015/2016
TW2 UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING MSc SYSTEMS ENGINEERING AND ENGINEERING MANAGEMENT SEMESTER 2 EXAMINATION 2015/2016 ADVANCED CONTROL TECHNOLOGY MODULE NO: EEM7015 Date: Monday 16 May 2016
More informationExam. 135 minutes, 15 minutes reading time
Exam August 6, 208 Control Systems II (5059000) 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.
More informationCHAPTER 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.
More informationExam. 135 minutes, 15 minutes reading time
Exam August 15, 2017 Control Systems I (151059100L) Prof Emilio Frazzoli Exam Exam Duration: 135 minutes, 15 minutes reading time Number of Problems: 44 Number of Points: 52 Permitted aids: Important:
More informationSystems Analysis and Control
Systems Analysis and Control Matthew M. Peet Arizona State University Lecture 23: Drawing The Nyquist Plot Overview In this Lecture, you will learn: Review of Nyquist Drawing the Nyquist Plot Using the
More informationECE557 Systems Control
ECE557 Systems Control Bruce Francis Course notes, Version.0, September 008 Preface This is the second Engineering Science course on control. It assumes ECE56 as a prerequisite. If you didn t take ECE56,
More informationTopic # Feedback Control Systems
Topic #19 16.31 Feedback Control Systems Stengel Chapter 6 Question: how well do the large gain and phase margins discussed for LQR map over to DOFB using LQR and LQE (called LQG)? Fall 2010 16.30/31 19
More informationsc Control Systems Design Q.1, Sem.1, Ac. Yr. 2010/11
sc46  Control Systems Design Q Sem Ac Yr / Mock Exam originally given November 5 9 Notes: Please be reminded that only an A4 paper with formulas may be used during the exam no other material is to be
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 informationSystems 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
More informationDynamic Compensation using root locus method
CAIRO UNIVERSITY FACULTY OF ENGINEERING ELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 00/0 CONTROL ENGINEERING SHEET 9 Dynamic Compensation using root locus method [] (Final00)For the system shown in the
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 informationLecture 9 Nonlinear Control Design
Lecture 9 Nonlinear Control Design Exactlinearization Lyapunovbased design Lab 2 Adaptive control Sliding modes control Literature: [Khalil, ch.s 13, 14.1,14.2] and [GladLjung,ch.17] Course Outline
More informationControl 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 information5. Observerbased Controller Design
EE635  Control System Theory 5. Observerbased Controller Design Jitkomut Songsiri state feedback poleplacement design regulation and tracking state observer feedback observer design LQR and LQG 51
More informationME 132, Fall 2017, UC Berkeley, A. Packard 334 # 6 # 7 # 13 # 15 # 14
ME 132, Fall 2017, UC Berkeley, A. Packard 334 30.3 Fall 2017 Final # 1 # 2 # 3 # 4 # 5 # 6 # 7 # 8 NAME 20 15 20 15 15 18 15 20 # 9 # 10 # 11 # 12 # 13 # 14 # 15 # 16 18 12 12 15 12 20 18 15 Facts: 1.
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 informationMASSACHUSETTS 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 informationEEE582 Homework Problems
EEE582 Homework Problems HW. Write a statespace realization of the linearized model for the cruise control system around speeds v = 4 (Section.3, http://tsakalis.faculty.asu.edu/notes/models.pdf). Use
More informationExercises for lectures 13 Design using frequency methods
Exercises for lectures 13 Design using frequency methods Michael Šebek Automatic control 2016 31317 Setting of the closed loop bandwidth At the transition frequency in the open loop is (from definition)
More information6.1 Sketch the zdomain root locus and find the critical gain for the following systems K., the closedloop characteristic equation is K + z 0.
6. Sketch the zdomain 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 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 informationAutomatic Control 2. Model reduction. Prof. Alberto Bemporad. University of Trento. Academic year
Lecture: Automatic Control 2 Prof. Alberto Bemporad University of Trento Academic year 20102011 Prof. Alberto Bemporad (University of Trento) Automatic Control 2 Academic year 20102011 1 / 17 Lecture:
More informationNPTEL Online Course: Control Engineering
NPTEL Online Course: Control Engineering Ramkrishna Pasumarthy Assignment11 : s 1. Consider a system described by state space model [ ] [ 0 1 1 x + u 5 1 2] y = [ 1 2 ] x What is the transfer function
More informationMASSACHUSETTS 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
More informationa. Closedloop system; b. equivalent transfer function Then the CLTF () T is s the poles of () T are s from a contribution of a
Root Locus Simple definition Locus of points on the s plane that represents the poles of a system as one or more parameter vary. RL and its relation to poles of a closed loop system RL and its relation
More informationDepartment of Aerospace Engineering and Mechanics University of Minnesota Written Preliminary Examination: Control Systems Friday, April 9, 2010
Department of Aerospace Engineering and Mechanics University of Minnesota Written Preliminary Examination: Control Systems Friday, April 9, 2010 Problem 1: Control of Short Period Dynamics Consider the
More informationSystems 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
More information6 OUTPUT FEEDBACK DESIGN
6 OUTPUT FEEDBACK DESIGN When the whole sate vector is not available for feedback, i.e, we can measure only y = Cx. 6.1 Review of observer design Recall from the first class in linear systems that a simple
More informationGEORGIA 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: 30Apr14 COURSE: ECE 3084A (Prof. Michaels) NAME: STUDENT #: LAST, FIRST Write your name on the front page
More informationEE 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 openloop plant, HW 9 Solutions G(s) = 1(s + 3) s(s + 2)(s + 5) design the statevariable feedback controller u = Kx + r, where K = [k 1 k 2 k 3 ] is the feedback
More informationME 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
More informationECEEN 5448 Fall 2011 Homework #4 Solutions
ECEEN 5448 Fall 2 Homework #4 Solutions Professor David G. Meyer Novemeber 29, 2. The statespace realization is A = [ [ ; b = ; c = [ which describes, of course, a free mass (in normalized units) with
More informationHomework Solution # 3
ECSE 644 Optimal Control Feb, 4 Due: Feb 17, 4 (Tuesday) Homework Solution # 3 1 (5%) Consider the discrete nonlinear control system in Homework # For the optimal control and trajectory that you have found
More informationEE 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
More informationRoot 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
More informationINSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad ELECTRICAL AND ELECTRONICS ENGINEERING TUTORIAL QUESTION BANK
Course Name Course Code Class Branch INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad 500 043 ELECTRICAL AND ELECTRONICS ENGINEERING TUTORIAL QUESTION BAN : CONTROL SYSTEMS : A50 : III B. Tech
More informationCDS 101/110a: Lecture 81 Frequency Domain Design
CDS 11/11a: Lecture 81 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 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 informationProportional plus Integral (PI) Controller
Proportional plus Integral (PI) Controller 1. A pole is placed at the origin 2. This causes the system type to increase by 1 and as a result the error is reduced to zero. 3. Originally a point A is on
More informationProblem 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 informationMAE143A Signals & Systems, Final Exam  Wednesday March 16, 2005
MAE13A Signals & Systems, Final Exam  Wednesday March 16, 5 Instructions This quiz is open book. You may use whatever written materials you choose including your class notes and the textbook. You may
More informationECE317 : Feedback and Control
ECE317 : Feedback and Control Lecture : Steadystate error Dr. Richard Tymerski Dept. of Electrical and Computer Engineering Portland State University 1 Course roadmap Modeling Analysis Design Laplace
More informationModeling and System Identification for a DC Servo
Modeling and System Identification for a DC Servo Kevin M. Passino and Nicanor Quijano Dept. Electrical Engineering, The Ohio State University 5 Neil Avenue, Columbus, OH 37 March 7, Abstract First, you
More informationTopic # Feedback Control
Topic #5 6.3 Feedback Control StateSpace Systems Fullstate Feedback Control How do we change the poles of the statespace system? Or,evenifwecanchangethepolelocations. Where do we put the poles? Linear
More informationECE317 : Feedback and Control
ECE317 : Feedback and Control Lecture : RouthHurwitz stability criterion Examples Dr. Richard Tymerski Dept. of Electrical and Computer Engineering Portland State University 1 Course roadmap Modeling
More informationGEORGIA 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: 09Dec13 COURSE: ECE 3084A (Prof. Michaels) NAME: STUDENT #: LAST, FIRST Write your name on the front page
More information