1 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 and disadvantages of open loop control systems. 2. Write Requirements of a good control system. Is an automatic electric iron an open loop or closed loop control system? 3. Explain concept of superposition for linear system with examples. CHAPTER 6 Hydraulic Control System 1. Compare hydraulic and pneumatic control system. State the different applications of pneumatic control system. 2. Write short note on Dashpots. 3. Attempt : (i) Essential elements of hydraulic circuit and (ii) Working of Directional Control Valve 4. State the various components of any hydraulic circuits. Name the various types of pumps commonly used for hydraulic power purposes. 5. State the different types of hydraulic pumps and explain the factors affecting selection it. Explain the construction and working of vane pump with neat sketch. 6. Describe proportional plus integral plus derivative (PID) control action type automatic industrial controller. Write down equation of the system. Write down expression for the transfer function. 7. Compare hydraulic and electrical control system. CHAPTER 7 Pneumatic Control System 1. Sketch and explain pneumatic nozzle-flapper amplifier. 2. State the various types of Industrial controllers and describe any two of them. 3. Explain the construction and working of 4 land rotary spool valve with neat sketches. 4. What is FRL unit in pneumatic system? Write about pneumatic power sources. State various components used in pneumatic circuit. 5. Describe the working of a force distance type pneumatic proportional controller and its transfer function. Control Engineering ( ) Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 1
2 Chapter 2 Mathematical modelling of systems 1 What do you mean by mathematical modeling of a control system? Explain its importance. Given as part of Tutorial 2 2 Derive transfer function of Armature controlled DC motor. Tutorial 2 3 Derive transfer function of field controlled DC motor. Tutorial 2 4 Derive transfer function of Gear train. Tutorial 3 5 Derive a transfer function for a liquid level system. Explain resistance and capacitance of any liquid level system. Also derive transfer function of interacting and non-interacting liquid level systems. Tutorial 3 6 Derive transfer function of a thermal system. Tutorial 3 7 Draw equivalent mechanical and electrical systems to relate force voltage or force current analogy 8 What does a block diagram represent? Explain it in detail. List its salient characteristics. Explain the following: Summing point, take off point. Tutorial 3 Tutorial 4 9 Enlist various rules of block diagram algebra. Tutorial 4 10 What are signal flow graphs? Write down the rules for signal flow graphs reduction? Write down Mason s gain formula for signal flow graphs. Explain Mason s gain formula with the help of one example. 11 Define node, transmittance, branch, source, sink, path, loop, and loop gain. Write down important properties of signal flow graphs. Chapter 4 Frequency response analysis Tutorial 5 Tutorial 5 1 What is the need of frequency response analysis? Explain in detail. Tutorial 10 2 Enlist various frequency domain specifications and define each. Tutorial 10 3 Derive correlation between time domain and frequency domain specifications. Tutorial 10 Control Engineering ( ) Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 2
3 Chapter 5A Stability 1 What do you mean by stability of a control system? Explain Routh s stability criterion. 2 Explain the difference between Open loop and Close loop control system with examples. Compare their merits and demerits. 2 What do you understand by Transient and steady state response and hence discuss the various types of input test signals used for time response analysis of a control system 3 Explain standard Test signals & derive equation of steady state error constant Kp, Kv, and Ka. Unit 3 Time response Given as part of Tutorial 8 Tutorial 1 Tutorial 8 Tutorial 8 1 Explain unit step response of first order linear time invariant systems. Tutorial 5 2 Define transient response specifications of second order system using neat Tutorial 5 sketch: OR Explain the performance indices second order system. 3 Derive the unit impulse response of second order system for all value of Tutorial 5 damping factor (ξ). 4 Derive the step response of second order system for all value of damping Tutorial 6 factor (ξ). 5 Explain in detail about P-I, P-D, and P-I-D control action. Tutorial 6 Unit 5B Root Locus 1 Explain Rules for construction of Root Locus. Tutorial 9 Unit 8 SSA 1 Write a short note on state space representation of a control system. Tutorial 10 2 Write definitions of state and state variables. Explain the fact that for any system, the set of state variables are non-unique. Discuss the limitations of transfer functions and advantages of analysis of control systems using state space. Tutorial 10 Control Engineering ( ) Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 3
4 CONTROL ENGINEERING EXPERIMENT NO. 01 DATE : Definition of Laplace Transform: Laplace transform F( of a function f(t) is defined as MATHEMATICAL PRELIMINARIES FOR CONTROL THEORY: LAPLACE TRANSFORMS & DIFFERENTIAL EQUATIONS 1 Where, f(t) = a function of time t such that f(t) = 0, for t <0 s = a complex variable of the form Standard Laplace Transform Pair:
5 EXPERIMENT NO. 01 DATE : MATHEMATICAL PRELIMINARIES FOR CONTROL THEORY: LAPLACE TRANSFORMS & DIFFERENTIAL EQUATIONS 2
6 EXPERIMENT NO. 01 DATE : Properties of Laplace Transform: MATHEMATICAL PRELIMINARIES FOR CONTROL THEORY: LAPLACE TRANSFORMS & DIFFERENTIAL EQUATIONS 3 Initial Value Theorem: Final Value Theorem:
7 EXPERIMENT NO. 01 DATE : MATHEMATICAL PRELIMINARIES FOR CONTROL THEORY: LAPLACE TRANSFORMS & DIFFERENTIAL EQUATIONS 4 Using Standard Laplace Transform pairs and its properties to solve following problems 1) Obtain LT of the function defined as 2) Obtain LT of the function defined as 3) Obtain LT of the function defined as Obtain the inverse LT of the function defined below: 1 2 3
8 EXPERIMENT NO. 01 DATE : MATHEMATICAL PRELIMINARIES FOR CONTROL THEORY: LAPLACE TRANSFORMS & DIFFERENTIAL EQUATIONS Obtain the solution of the differential equation defined below: NOTE: Verify all above examples using MATLAB and list the command used for the same with small description. GRADE LAB-INCHARGE H.O.D
9 CONTROL ENGINEERING EXPERIMENT NO. 02 DATE : (1) Define the following giving one suitable example. (a) Transfer function (b) Order of the system (c) Type of the system (d) Characteristic equation (e) Pole & zero of the system TO STUDY OF SYSTEM & SYSTEM TRANSFER FUNCTION 1 DOC. CODE : DIET/EC (2) Find transfer function of following system. Also find characteristic equation order and type of there system. (3) Find transfer function of the following system and identity its poles & zeros.
10 EXPERIMENT NO. 02 DATE : TO STUDY OF SYSTEM & SYSTEM TRANSFER FUNCTION 2 DOC. CODE : DIET/EC (4) Find the transfer function of the following system and verify if the transfer function is equal to the product of transfer functions giving appropriate reason. CONCLUSION: GRADE LAB-INCHARGE H.O.D.
11 CONTROL ENGINEERING EXPERIMENT NO. 03 DATE : 1. Explain Force-Voltage Analogy & Force-Current Analogy MODELLING OF MECHANICAL SYSTEMS 1 2. Draw the equivalent mechanical system of the given system. Hence write the set of equilibrium equations for it and obtain electrical analogous circuits using (i) F-V Analogy (ii) F-I Analogy (a) (b) (c) 3. Consider Rotational system shown in the following figure, Where J = Moment of inertia of disk B = Friction Constant K = Torsional Spring Constant And disk subjected to torque T(t) as shown. Draw its analogous network based on (i) F V Analogy (ii) F I Analogy
12 EXPERIMENT NO. 03 DATE : MODELLING OF MECHANICAL SYSTEMS 2 4. For the mechanical system shown, obtain the analogous electrical network based on F V Analogy 5. The figure shows F I Analogous Electrical Network for translational mechanical system. Draw the mechanical system.
13 CONTROL ENGINEERING TO STUDY BLOCK DIAGRAM REDUCTION TECHNIQUE 1 EXPERIMENT NO. 04 DATE : REV. R NO.: 3.00/JAN-2013 (1) Explain the block diagram reduction rules with the block diagram before and after the transformation. (2) Simplify the block diagram showing in the below figure. (3) Assume that linear approximations in the form of transfer functions are available for each block of the Supply and Demand System of given problem, and that the system can be represented by given figure. Determine the overall transfer functionn of the system. (4) Simplify the block diagram showing in the below figure. And obtain the transfer function relating R( and c(.
14 TO STUDY BLOCK DIAGRAM REDUCTION TECHNIQUE 2 EXPERIMENT NO. 04 DATE : (5) Simplify the block diagram showing in the below figure. (6) Simplify the block diagram showing in the below figure. (7) Simplify the block diagram showing in the below figure with unity feedback.
15 TO STUDY BLOCK DIAGRAM REDUCTION TECHNIQUE 3 EXPERIMENT NO. 04 DATE : (8) Simplify the block diagram showing in the below figure. (9) Simplify the block diagram showing in the below figure. (10) Simplify the block diagram showing in the below figure. GRADE LAB-INCHARGE H.O.D.
16 CONTROL ENGINEERING EXPERIMENT NO. 05 DATE : TIME RESPONSE ANALYSIS - I 1 1. What are Standard Test signals? Explain each of them with a sketch and its mathematical expression in both time and Laplace domain. 2. Define the following (a) Time response analysis and Frequency response analysis (b) Transient response and Steady state response. 3. (For Even roll numbers in the batch). Derive a general expression showing unit ramp response of a first order system. Sketch input and output with respect to time. Also comment on the error signal and value of steady state error. (For Odd roll numbers in the batch). Derive a general expression showing unit step response of a first order system. Sketch input and output with respect to time. Also comment on the error signal and value of steady state error. 4. (For Even roll numbers in the batch). Derive a general expression showing unit impulse response of a second order system. Sketch response for different values of damping ratio. (For Odd roll numbers in the batch). Derive a general expression showing unit impulse response of a second order system. Sketch response for different values of damping ratio. 5. Define the following terms related to step response of a second order system. (a) Delay time (b) Rise time (c) Peak time (d) Maximum peak overshoot (d) Settling time. 6. Write the expression of response of a second order system to a unit step input and derive expression of the following (For Even roll numbers in the batch). (a) Rise time (b) Maximum peak over shoot (For Odd roll numbers in the batch). (a) Peak time (b) Settling time 7. Obtain the response of a unity feedback system whose open-loop transfer function is 3 = +4 for a unit step input.
17 EXPERIMENT NO. 05 DATE : TIME RESPONSE ANALYSIS - I 2 8. Obtain the unit step response of a system whose forward path and feed back path transfer function are given as = 10 +3, = The open loop transfer function of a unity feedback system is 4 G s = s s+1 Determine the nature of response of the closed-loop system for a unit-step input. Also determine the damping ratio, natural frequency of oscillation, damped frequency of oscillation, rise time, peak time, peak overshoot and settling time. 10. A second order system is represented by a transfer function given below C s R s = 1 Js +fs+k When this system is excited with a step input of magnitude 10 units, following results were measured from the system response. (a) Peak overshoot 6% (b) Peak time = 1 s (c) Steady state value of output = 0.5 Determine the values of J, f and K
18 CONTROL ENGINEERING EXPERIMENT NO. 06 DATE : 1. Define a) Signal flow graph. b) Node c) Multiplication factor/ Transminattance. d) Branch e) Source SIGNAL FLOW GRAPH 1 g) Mixed node h) Path i) Loop and loop gain j) Nontouching loop k) Forward path and Forward path gain f) Sink 2. Mention the properties of SFG. 3. Consider the signal flow graph given in Fig and 4. Find the transfer function for the fig. using signal flow graphs.
19 EXPERIMENT NO. 06 DATE : SIGNAL FLOW GRAPH 2 5. Find the transfer function for the fig. using signal flow graphs. 6. Find the transfer function for the fig. using signal flow graphs. 7. Find the transfer function for the fig. using signal flow graphs.
20 CONTROL ENGINEERING EXPERIMENT NO. 07 DATE : TIME RESPONSE ANALYSIS - II 1 1. Study and use following MATLAB functions for time response analysis of systems. (a) tf (b) step (c) impulse (d) residue (e) tf2zpk (Self study, no need to write in file 2. Using MATLAB obtain time response of following systems for step and impulse input C( 10 (a) = ; identify the value of system time constant R ( s ) s + 2 (b) C( = R( s ;(c) 0.2s + 1 C( = R ( s ) s (d) C( = R( s 2 1 (e) + 2s + 1 C( = R( s s + 1 For (b) to (e) identify the value of ζ and ω n and comment of the damping present in the system. (write or attaché print out of the program and response plot) 3. Define steady state response and steady state error. Derive the equation of steady state error for a general closed loop system with G( as forward path transfer function, H( as feedback path transfer function, R( as input and C( as output. 4. Define static error constant. Derive the value of steady state errors for type 0, type 1 and type 2 systems. 5. For control systems with open-loop transfer functions given below, which type of input signal will give finite, non-zero steady state error. Also calculate the error for that input ( s + 4) 20 G ( H ( =, G( H ( =, G( H ( = 2 ( s + 1)( s + 4) s( s + 1)( s + 2) s ( s + 1)( s + 4) 6. Consider a unity feedback system whose closed loop transfer function is C( Ks + b = R ( s ) s 2 + as + b Find open loop transfer function. Also show that the steady-state error with unit ramp input is given by (a-k)/b. 7. The open loop transfer function of a servo system with unity feedback is 10 G ( H ( = s(0.1s + 1) Evaluate the static error co-efficient (Kp, Kv, Ka) for the system. Obtain the steady-state error of the system when subjected to following inputs (i) 2 u(t) (ii) 2t u(t) (iii) t 2 u(t) (iv) (2 + 2t + t 2 ) u(t)
21 CONTROL ENGINEERING EXPERIMENT NO. 08 DATE : STABILITY ANALYSIS USING RH CRITERION 1 1. Define stability criteria for LTI system. 2. Show location of following poles on s-plane and sketch approximate impulse response contributed by each of them giving its approximate equation. (a) s = -5 (b) s = 5 (c) s1,s2 = ±j (d) s1,s2 = -5±j (e) s1,s2 = 5±j (f) s = 0 (g) s1,s2 = 0 (h) s1,s2 =j s3,s4 = -j 3. Using Routh Criterion, determine the stability of the system represented by following characteristic equation. For system found to be unstable identify number of roots in the right half of s-plane (a) s + 2s + 8s + 15s + 20s + 16s + 16 = (b) s + 2s + s + 2s + 3s + 4s + 5 = (c) s + 3s + 5s + 9s + 8s + 6s + 4 = 0 4. System characteristic equation is given below, looking at the equation comment on system stability. Identify number of roots in right half of the s-plane. If the roots lie on jω axis identify the frequency of sustained oscillation. s s + 24s + 48s 25s 50 = 0 5. A unity feedback system has following forward path transfer function; determine the range of K system stability. Also determine the value of K when the system exhibits sustained oscillation and also find frequency of oscillation. K (a) G ( = (b) G 2 s( s + s + 1)( s + 2) K( s 2) = ( s + 1)( s + 6s + 25) ( 2 6. Using Hurwitz stability criterion, determine the range of K for system with following characteristic equation to be stable s s + (4 + K) s + 9s + 25 = 0 7. For given characteristic equation determine the range f=of values of K such that the system poles are located on left of point s=-1. s (1 + K) s + (5 + 7K) s + (4K + 7) = 0
22 CONTROL ENGINEERING EXPERIMENT NO. 09 DATE : ROOT LOCUS 1 Root locus: It is the locus of the roots of the characteristic equation of the closed loop system as a specific parameter (usually the gain K) Is varied from zero to infinity. Condition: Roots of characteristic equation: 1+ G ( H ( = 0 G( H ( = 1 Thus, a point in s-plane will lie on root locus if it satisfies following condtions. (a) Magnitude criterion: G ( H ( = 1 o (b) Angle Criterion = G( H ( = ± 180 (2l + 1); l = 0,1,2,3... KN( Consider the open loop transfer function G ( H ( = having n poles and m zeros (n>m). D( 1. Each branch of the root locus begins at an open-loop pole (K = 0) and ends at an open-loop (finite) zero or at a zero at infinity (K ). The locus will be symmetric about real axis. 2. Starting at + and moving along the real axis toward the left, the root locus lies on the real axis to the left of an odd number of real-axis open-loop poles or zeros. 3. If n > m, there will be n-m branches of the root locus going to infinity. they will follow asymptotes that meet at a common point on the real axis and make specified angles with respect to the positive real axis. The angles of asymptotes, φ A, and the center of asymptotes, σ A, are given by 4. If G(H( has a complex conjugate pole, then the root locus branch will start from the pole making θ D angle (angle of departure) with respect to the positive real axis. θ D = ±(2q+1)+ [ θ z θ P ] ; q = 0,1,2,. θ P = net angle contributed by all other poles at give complex conjugate pole. θ z = net angle contributed by all other zeros at give complex conjugate pole. 5. If G(H( has a complex conjugate zero, then the root locus branch will end at the zero making θ A angle (angle of arrival) with respect to the positive real axis. θ A = ±(2q+1)- [ θ z θ P ] ; q = 0,1,2,. θ P = net angle contributed by all other poles at give complex conjugate pole. θ z = net angle contributed by all other zeros at give complex conjugate pole. 6. If the root locus on the real axis lies in the interval between two open-loop poles, there will always be a break-away point between the poles where the root locus leaves the real axis. Similarly If the root locus on the real axis lies in the interval between two open-loop zeros,
23 EXPERIMENT NO. 09 DATE : ROOT LOCUS 2 there will always be a break-in point between the zeros where the root locus enters the real axis. All break points break-away points and break-in points can be determined from the dk roots of equation = 0. r branches of root locus meet at break point at an angle of ds 180 ±. r 7. The point of intersection of the root locus branches with the imaginary axis and the critical value of K can be determined by use of Routh criterion. Exercise 1. Draw Root Locus for a unit feedback system whose forward path transfer function is given as G ( = K. Also find the value of K at s = -1±2j. s( s + 1)( s + 4) 2. Sketch the Root Locus of unity feedback control system whose open-loop transfer function is given below. Determine the range of gain for stability and the point at which it crosses the imaginary axis. Determine the value of gain K at the breakaway point. K G ( =. 2 ( s 1)( s + 4s + 7) 3. Sketch Root Locus for the system shown in figure below. Also find the value of gain for the value of ζ= Sketch Root Locus for the system shown in figure below. (for odd roll nos.)
24 EXPERIMENT NO. 09 DATE : ROOT LOCUS 3 (For even roll nos.) 5. Sketch Root Locus for the system with following open loop transfer function. On basis of the root locus obtained comment on the system stability for various values of gain K. Also find value of gain at break points. K( s + 3) (a) G(H( = (For odd roll nos.) s( s + 2) K( s + 1) (b) G(H( = (For even roll nos.) s( s 3) 6. Sketch root locus for the following system 2 K( s + 2s + 10) G(H(= 2 s ( s + 2)
25 CONTROL ENGINEERING EXPERIMENT NO. 10 DATE : TO STUDY STATE SPACE REPRESENTATION 1 1. Define the following terms. a) State b) State variable c) State space d) State vector e) State trajectory 2. Derive expression of transfer function of the system which is represented in the following standard state space form and also define transfer matrix. 3. Derive the correlation between transfer function and state space analysis. 4. Obtain the transfer function of the system defined by following state-space equations. 5. Obtain the transfer function of the system defined by following state-space equations. 6. Obtain the transfer function of the system defined by following state-space equations. Dashing Institute of Engineering And Technology, Rajkot
26 EXPERIMENT NO. 10 DATE : TO STUDY STATE SPACE REPRESENTATION 2 7. Obtain the transfer function of the system defined by following state-space equations. 8. Obtain the transfer function of the system from the data given below.,, 9. Obtain the transfer function of the system defined by following state-space equations. 10. Obtain the state space representation of nth order systems given by the following linear differential equations. 11. Obtain the state space representation of the system given by the following linear differential equations. Dashing Institute of Engineering And Technology, Rajkot
27 EXPERIMENT NO. 10 DATE : TO STUDY STATE SPACE REPRESENTATION Obtain the state space representation of the system given by the following transfer function. 13. Obtain the state space model of the system shown in the figure. 14. Dashing Institute of Engineering And Technology, Rajkot
28 EXPERIMENT NO. 10 DATE : TO STUDY STATE SPACE REPRESENTATION Obtain the state space representation of nth order systems given by the following linear differential equations. 16. Obtain the state space representation of the system given by the following transfer function. 17. For a given LRC circuit, derive the state model of the system. 18. Obtain the state space model of the system shown in the figure. Dashing Institute of Engineering And Technology, Rajkot
ROOT LOCUS TECHNIQUE. Values of on the root loci The value of at any point s on the root loci is determined from the following equation G( s) H( s) Product of lengths of vectors from poles of G( s)h( s)
VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur 603 203 DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING QUESTION BANK V SEMESTER IC650 CONTROL SYSTEMS Regulation 203 Academic Year 207 8 Prepared
Alireza Mousavi Brunel University 1 » Control Process» Control Systems Design & Analysis 2 Open-Loop Control: Is normally a simple switch on and switch off process, for example a light in a room is switched
ME 375 Final Examination Thursday, May 7, 2015 SOLUTION POBLEM 1 (25%) negligible mass wheels negligible mass wheels v motor no slip ω r r F D O no slip e in Motor% Cart%with%motor%a,ached% The coupled
Chapter 7 : Root Locus Technique By Electrical Engineering Department College of Engineering King Saud University 1431-143 7.1. Introduction 7.. Basics on the Root Loci 7.3. Characteristics of the Loci
Root Locus ELEC304-Alper Erdogan 1 1 Lecture 1 Root Locus What is Root-Locus? : A graphical representation of closed loop poles as a system parameter varied. Based on Root-Locus graph we can choose the
Chemical Process Dynamics and Control Aisha Osman Mohamed Ahmed Department of Chemical Engineering Faculty of Engineering, Red Sea University 1 Chapter 4 System Stability 2 Chapter Objectives End of this
KINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING QUESTION BANK SUBJECT CODE & NAME: CONTROL SYSTEMS YEAR / SEM: II / IV UNIT I SYSTEMS AND THEIR REPRESENTATION PARTA [2
Root Locus Motivation Sketching Root Locus Examples ME375 Root Locus - 1 Servo Table Example DC Motor Position Control The block diagram for position control of the servo table is given by: θ D 0.09 See
NADAR SARASWATHI COLLEGE OF ENGINEERING AND TECHNOLOGY Vadapudupatti, Theni-625531 Question Bank for the Units I to V SE05 BR05 SU02 5 th Semester B.E. / B.Tech. Electrical & Electronics engineering IC6501
FEEDBAC CONTROL SYSTEMS. Control System Design. Open and Closed-Loop Control Systems 3. Why Closed-Loop Control? 4. Case Study --- Speed Control of a DC Motor 5. Steady-State Errors in Unity Feedback Control
Performance of Feedback Control Systems Design of a PID Controller Transient Response of a Closed Loop System Damping Coefficient, Natural frequency, Settling time and Steady-state Error and Type 0, Type
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
CHAPTER 5 : REDUCTION OF MULTIPLE SUBSYSTEMS Objectives Students should be able to: Reduce a block diagram of multiple subsystems to a single block representing the transfer function from input to output
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
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
BEE501- CONTROL SYSTEM UNIT 1 SYSTEMS AND THEIR REPRESENTATION Definition of Control System A control system is a system of devices or set of devices, that manages commands, directs or regulates the behavior
Transient Response of a Second-Order System ECEN 830 Spring 01 1. Introduction In connection with this experiment, you are selecting the gains in your feedback loop to obtain a well-behaved closed-loop
CHAPTER 7 STEADY-STATE RESPONSE ANALYSES 1. Introduction The steady state error is a measure of system accuracy. These errors arise from the nature of the inputs, system type and from nonlinearities of
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering. Dynamics and Control II Fall 7 Problem Set #7 Solution Posted: Friday, Nov., 7. Nise problem 5 from chapter 8, page 76. Answer:
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
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
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
Page 1 of 5 Example: Modeling DC Motor Position Physical Setup System Equations Design Requirements MATLAB Representation and Open-Loop Response Physical Setup A common actuator in control systems is the
Power System Operations and Control Prof. S.N. Singh Department of Electrical Engineering Indian Institute of Technology, Kanpur Module 3 Lecture 8 Welcome to lecture number 8 of module 3. In the previous
Laboratory 11 State Feedback Controller for Position Control of a Flexible Joint 11.1 Objective The objective of this laboratory is to design a full state feedback controller for endpoint position control
EDEXCEL NATIONALS UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES ASSIGNMENT No. 3 - ELECTRO MAGNETIC INDUCTION NAME: I agree to the assessment as contained in this assignment. I confirm that the work submitted
Dynamic Response Assoc. Prof. Enver Tatlicioglu Department of Electrical & Electronics Engineering Izmir Institute of Technology Chapter 3 Assoc. Prof. Enver Tatlicioglu (EEE@IYTE) EE362 Feedback Control
Root Locus S5-1 S O L U T I O N S Root locus 5 Note: All references to Figures and Equations whose numbers are not preceded by an "S" refer to the textbook. (a) Rule 2 is all that is required to find the
PD, PI, PID Compensation M. Sami Fadali Professor of Electrical Engineering University of Nevada 1 Outline PD compensation. PI compensation. PID compensation. 2 PD Control L= loop gain s cl = desired closed-loop
Quanser NI-ELVIS Trainer (QNET) Series: QNET Experiment #02: DC Motor Position Control DC Motor Control Trainer (DCMCT) Student Manual Table of Contents 1 Laboratory Objectives1 2 References1 3 DCMCT Plant
Root Locus Motivation Sketching Root Locus Examples ME375 Root Locus - 1 Servo Table Example DC Motor Position Control The block diagram for position control of the servo table is given by: D 0.09 Position
EE 370L Controls Laboratory Laboratory Exercise #7 Root Locus Department of Electrical an Computer Engineering University of Nevaa, at Las Vegas 1. Learning Objectives To emonstrate the concept of error
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
MAK 391 System Dynamics & Control Presentation Topic The Root Locus Method Student Number: 9901.06047 Group: I-B Name & Surname: Göksel CANSEVEN Date: December 2001 The Root-Locus Method Göksel CANSEVEN
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.
Project Lab Report Michael Hall Hao Zhu Neil Nevgi Station 6 Ta: Yan Cui Nov. 12 th 2012 Table of Contents: Executive Summary 3 Modeling Report.4-7 System Identification 7-11 Control Design..11-15 Simulation
EE C28 / ME C34 Feedback Control Systems Lecture Chapter 8 Root Locus Techniques Lecture abstract Alexandre Bayen Department of Electrical Engineering & Computer Science University of California Berkeley
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:
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)
Cleveland State University MCE441: Intr. Linear Control Lecture 7:Time Influence of Poles and Zeros Higher Order and Pole Criterion Prof. Richter 1 / 26 First-Order Specs: Step : Pole Real inputs contain
Similarly, the program for the fourth-order transfer function approximation with T = 0.1 sec is [num,denl = pade(0.1, 4); printsys(num, den, 'st) numlden = sa4-2o0sa3 + 1 80O0sA2-840000~ + 16800000 sa4
PID Control Objectives The objective of this lab is to study basic design issues for proportional-integral-derivative control laws. Emphasis is placed on transient responses and steady-state errors. The
Introduction to Feedback Control Control System Design Why Control? Open-Loop vs Closed-Loop (Feedback) Why Use Feedback Control? Closed-Loop Control System Structure Elements of a Feedback Control System
MODERN CONTROL SYSTEMS Lecture 1 Root Locu Emam Fathy Department of Electrical and Control Engineering email: email@example.com http://www.aat.edu/cv.php?dip_unit=346&er=68525 1 Introduction What i root locu?
Chapter 3 AUTOMATIC VOLTAGE CONTROL . INTRODUCTION TO EXCITATION SYSTEM The basic function of an excitation system is to provide direct current to the field winding of the synchronous generator. The excitation
MM11 Root Locus Design Method Reading material: FC pp.270-328 9/9/2011 Classical Control 1 What have we talked in lecture (MM10)? Lead and lag compensators D(s)=(s+z)/(s+p) with z < p or z > p D(s)=K(Ts+1)/(Ts+1),
INSTRUMENTAL ENGINEERING Subject Code: IN Course Structure Sections/Units Section A Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Section B Section C Section D Section E Section F Section G Section H Section
Contents Chapter Topic Page Chapter- Chapter- Chapter-3 Chapter-4 Introduction Transfer Function, Block Diagrams and Signal Flow Graphs Mathematical Modeling Control System 35 Time Response Analysis of
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
Richiami di Controlli Automatici Gianmaria De Tommasi 1 1 Università degli Studi di Napoli Federico II firstname.lastname@example.org Ottobre 2012 Corsi AnsaldoBreda G. De Tommasi (UNINA) Richiami di Controlli Automatici
Design via Root Locus I 9 Chapter Learning Outcomes J After completing this chapter the student will be able to: Use the root locus to design cascade compensators to improve the steady-state error (Sections
VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur 6 DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING QESTION BANK ME-Power Systems Engineering I st Year SEMESTER I IN55- SYSTEM THEORY Regulation
1 / 17 EE3CL4: Introduction to Linear Control Systems Section 7: McMaster University Winter 2018 2 / 17 Outline 1 4 / 17 Cascade compensation Throughout this lecture we consider the case of H(s) = 1. We
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
Second Order and Higher Order Systems 1. Second Order System In this section, we shall obtain the response of a typical second-order control system to a step input. In terms of damping ratio and natural
Feedback Control of Linear SISO systems Process Dynamics and Control 1 Open-Loop Process The study of dynamics was limited to open-loop systems Observe process behavior as a result of specific input signals
Chapter 1 Feedbac Control Feedbac control allows a system dynamic response to be modified without changing any system components. Below, we show an open-loop system (a system without feedbac) and a closed-loop
ECE382/ME482 Fall 2008 Homework 3 Solution October 20, 2008 1 Homework Assignment 3 Assigned September 30, 2008. Due in lecture October 7, 2008. Note that you must include all of your work to obtain full
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
Chapter. DYNAMIC MODELING Understanding the nature of the process to be controlled is a central issue for a control engineer. Thus the engineer must construct a model of the process with whatever information
M.Tech. [ 24 103 ] Degree Examination ndustrial Process nstrumentation First Semester COMPUTER CONTROL OF PROCESSES (Effective from the Admitted Batch of2003-2004) Time: 3 Hours Maximum marks: 100 Answer
Notes for ECE-3 Winter 4-5 by R. Throne Contents Table of Laplace Transforms 5 Laplace Transform Review 6. Poles and Zeros.................................... 6. Proper and Strictly Proper Transfer Functions...................
Overview of motors and motion control. Elements of a motion-control system Power upply High-level controller ow-level controller Driver Motor. Types of motors discussed here; Brushed, PM DC Motors Cheap,
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
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
DIGITAL CONTROL OF POWER CONVERTERS 3 Digital controller design Frequency response of discrete systems H(z) Properties: z e j T s 1 DC Gain z=1 H(1)=DC 2 Periodic nature j Ts z e jt e s cos( jt ) j sin(
Module 4 : Laplace and Z Transform Problem Set 4 Problem 1 The input x(t) and output y(t) of a causal LTI system are related to the block diagram representation shown in the figure. (a) Determine a differential
ECE382/ME482 Spring 25 Homework 6 Solution April 17, 25 1 Solution to HW6 P8.17 We are given a system with open loop transfer function G(s) = 4(s/2 + 1) s(2s + 1)[(s/8) 2 + (s/2) + 1] (1) and unity negative
Modeling a Servo Motor System Definitions Motor: A device that receives a continuous (Analog) signal and operates continuously in time. Digital Controller: Discretizes the amplitude of the signal and also
EE12 Prof. S. Boyd EE12 Homework 2, 3, and 4 Solutions 7. Some convolution systems. Consider a convolution system, y(t) = + u(t τ)h(τ) dτ, where h is a function called the kernel or impulse response of
Vehicle longitudinal speed control Prof. R.G. Longoria Department of Mechanical Engineering The University of Texas at Austin February 10, 2015 1 Introduction 2 Control concepts Open vs. Closed Loop Control
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
ENG M 54 Laboratory #7 University of Alberta ENGM 54: Modeling and Simulation of Engineering Systems Laboratory #7 M.G. Lipsett & M. Mashkournia 2 Mixed Systems Modeling with MATLAB & SIMULINK Mixed systems
Frequency Response Analysis Consider let the input be in the form Assume that the system is stable and the steady state response of the system to a sinusoidal inputdoes not depend on the initial conditions
AERO 422: Active Controls for Aerospace Vehicles Proportional, ntegral & Derivative Control Design Raktim Bhattacharya Laboratory For Uncertainty Quantification Aerospace Engineering, Texas A&M University
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.
Professor Fearing EE C128 / ME C134 Problem Set 2 Solution Fall 21 Jansen Sheng and Wenjie Chen, UC Berkeley 1. (15 pts) Partial fraction expansion (review) Find the inverse Laplace transform of the following