Feedback Control Systems

Size: px
Start display at page:

Download "Feedback Control Systems"

Transcription

1 ME Homework #0 Feedback Control Systems Last Updated November 06 Text problem 67 (Revised Chapter 6 Homework Problems- attached)

2 65 Chapter 6 Homework Problems 65 Transient Response of a Second Order Model (Section 6) For problems 6-5: a Compute the natural frequency n and damping ratio b Compute the eigenvalues and c State whether the system is underdamped or overdamped d Compute the time constant for each mode e If there is one mode and it is oscillatory compute the damped frequency of oscillation d and the damped natural period Td f Confirm by simulation that the time constant and frequency of oscillation accurately predict the response Use initial conditions of (0)= for your simulation In your simulation code set the time range from t=0 to five times the longest time constant ( 0) 0 75

3 65 Concepts of Feedback Control (Section 6) 66 Consider a DC electric motor connected to an rotational inertial load I shown at the right A voltage V(t) is applied to the electric motor and the armature possesses a rotational inertia of Ia a Derive a model for the electric V(t) motor and rotational inertia load I I Assume that rotational damping with coefficient ct is used to model frictional torque applied to the armature In your model use the symbols Kt Kb R and L to represent the torque coefficient back-emf coefficient armature resistance and armature inductance respectively and (t) to represent the angular displacement of the armature b It is desired to develop a feedback control system for the motor and inertial load A sensor is used to measure the angular velocity of the armature The measurement of the angular velocity is used by a controller and amplifier that implements integral control to supply the voltage V(t) to the motor of V ( t) Ki ( t) dt where Ki is the integral gain and (t) is the intended speed of the motor Neglecting the armature inductance L show that the model for the motor inertial load and controller with amplifier reduces to KiKt KiKt KtKb ( t) c I I T a R R R c Using the model for part b above show that the damping ratio and natural frequency can be computed from the following formulas ct KtKb R KiKt I I K K R RI n I a d Design a controller ie choose an integral gain Ki that will achieve a damping ratio of =04 As will be the case in part e the desired speed will be (t)=0 for t<0 and then switch to a constant value (t)==50 deg/sec for t0 Assuming that R=5 Kt=075 Nm/A Kb=075 Vs Ia=005 kgm I=6 kg/m ct=05nms compute the anticipated natural frequency n percent overshoot Mp settling time ts and rise time tr that will characterie the response of the motor as it transitions from (0)=0 to (t)= at steady state e With the controller designed in part d above simulate the system over the time range 0t0 sec using a value of =50 deg/sec as the desired speed You may assume that the initial conditions for the simulation are ( 0) 0 i t P 66 Ia a 76

4 ( 0) 0 rad/sec and rad/sec Plot the motor speed versus time t Using this plot verify that the percent overshoot Mp rise time tr and settling time ts computed in part d reasonably characterie the response of the motor 67 Consider a DC electric motor coupled to a rack of mass m by a pinion gear of radius r A voltage V(t) is applied to the electric motor and the armature possesses a rotational inertia of Ia The purpose of the system is to control the position of the rack P 67 V(t) c Ia I r m a Derive a model for the electric motor and the rack In your model use the symbols Kt Kb R and L to represent the torque coefficient back-emf coefficient armature resistance and armature inductance respectively and (t) to represent the angular displacement of the armature and x(t) to measure the displacement of the rack b It is desired to develop a feedback control system to control the position x(t) of the rack A sensor is used to measure the instantaneous position x(t) of the rack The measurement of the position of the rackis used by a controller and amplifier that implements proportional control to supply the voltage V(t) to the motor of V ( t) k px ( t) x where kp is the proportional gain and X(t) is the intended position of the rack Neglecting the armature inductance L the armature rotational inertia Ia and the pinion inertia I show that the model for the motor rack and controller with amplifier reduces to k pkt k pkt KtKb X ( t) x c x m x rr rr r R c Using the model for part b above show that the damping ratio and natural frequency can be computed from the following formulas c k K T KtKb r R p t n m K k rr rrm d Design a controller ie choose a proportional gain kp that will achieve a damping ratio of =04 As will be the case in part e the desired speed will be X(t)=0 for t<0 and then switch to a constant value X(t)=X for t0 Assuming that R=5 Kt=05 Nm/A Kb=05 Vs c= Ns/m m=0 kg compute the anticipated natural frequency n percent overshoot Mp settling time ts and rise time tr that will characterie the response of the t p 77

5 motor as it transitions from x(0)=0 to x(t)=x at steady state e With the controller designed in part d above simulate the system over the time range 0t0 sec using a value of X=50 cm as the desired speed Use intial conditions of m and m/sec Plot the rack displacement x(t) versus time t Using this plot verify that the percent overshoot Mp rise time tr and settling time ts computed in part d reasonably characterie the response of the motor x( 0) 0 x( 0) 0 65 Solution of Linear Homogeneous Model for Systems of Arbitary Order (Section 64) For the following problems 68-7: a Compute the eigenvalues and eigenvectors b How many exponential and oscillatory modes are there (ie what are Nr and Nc)? c Assess the stability of the system d Compute the time constants for stable exponential and oscillatory modes For all oscillatory modes (stable or unstable) compute the frequency of oscillation and the period of oscillation e Assemble the matrix [(t)] using the eigenvalues For the complex eigenvalues make sure and use the Euler formula to convert the complex exponential to sines and cosines in [(t)] as described in Section 6 f Compute the matrix [E] - g Compute the solution {q(t)}=[e][(t)][e] - {q(0)} 68 Initial conditions q(0)=- q(0)= q 56q 69 Initial conditions q(0)=0 q(0)= 0895q 687q 60 Initial conditions q(0)=0 q(0)=- 6 Initial conditions q(0)=0 q(0)= 085q 0q 0059q q 474q 095q 0q 07q 78

6 08q 458q 6 Initial conditions q(0)= q(0)= 85q 0q 098q 048q 566q 4q 6 Initial conditions q(0)=- q(0)= and q(0)=0 78q 59q 7q 89q 077q 0q 64 Initial conditions q(0)=- q(0)= and q(0)=5 5q 0075q 05q 558q 08q 79q 65 Initial conditions q(0)=0 q(0)= and q(0)=0 5q 644q 686q 706q 967q 97q 66 After completing parts a and b of Problem 54 9q 577q 54q q 6q 08q 75q 07q 08q a Compute the eigenvalues and eigenvectors b How many exponential and oscillatory modes are there (ie what is Nr and Nc)? c Assess the stability of the system d Compute the time constants for stable exponential and oscillatory modes For all oscillatory modes (stable or unstable) compute the frequency of oscillation and the period of oscillation 67 After completing part a of Problem 5 and using parameters specified in part b a Compute the eigenvalues and eigenvectors b How many exponential and oscillatory modes are there (ie what is Nr and 79

7 Nc)? c Assess the stability of the system d Compute the time constants for stable exponential and oscillatory modes For all oscillatory modes (stable or unstable) compute the frequency of oscillation and the period of oscillation 80

State Space Representation

State Space Representation ME Homework #6 State Space Representation Last Updated September 6 6. From the homework problems on the following pages 5. 5. 5.6 5.7. 5.6 Chapter 5 Homework Problems 5.6. Simulation of Linear and Nonlinear

More information

The basic principle to be used in mechanical systems to derive a mathematical model is Newton s law,

The basic principle to be used in mechanical systems to derive a mathematical model is Newton s law, 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

More information

Rotational Systems, Gears, and DC Servo Motors

Rotational Systems, Gears, and DC Servo Motors Rotational Systems Rotational Systems, Gears, and DC Servo Motors Rotational systems behave exactly like translational systems, except that The state (angle) is denoted with rather than x (position) Inertia

More information

Texas A & M University Department of Mechanical Engineering MEEN 364 Dynamic Systems and Controls Dr. Alexander G. Parlos

Texas A & M University Department of Mechanical Engineering MEEN 364 Dynamic Systems and Controls Dr. Alexander G. Parlos Texas A & M University Department of Mechanical Engineering MEEN 364 Dynamic Systems and Controls Dr. Alexander G. Parlos Lecture 6: Modeling of Electromechanical Systems Principles of Motor Operation

More information

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

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

More information

FEEDBACK CONTROL SYSTEMS

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

More information

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

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

More information

A FORCE BALANCE TECHNIQUE FOR MEASUREMENT OF YOUNG'S MODULUS. 1 Introduction

A FORCE BALANCE TECHNIQUE FOR MEASUREMENT OF YOUNG'S MODULUS. 1 Introduction A FORCE BALANCE TECHNIQUE FOR MEASUREMENT OF YOUNG'S MODULUS Abhinav A. Kalamdani Dept. of Instrumentation Engineering, R. V. College of Engineering, Bangalore, India. kalamdani@ieee.org Abstract: A new

More information

Manufacturing Equipment Control

Manufacturing Equipment Control QUESTION 1 An electric drive spindle has the following parameters: J m = 2 1 3 kg m 2, R a = 8 Ω, K t =.5 N m/a, K v =.5 V/(rad/s), K a = 2, J s = 4 1 2 kg m 2, and K s =.3. Ignore electrical dynamics

More information

Performance of Feedback Control Systems

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

More information

Quanser NI-ELVIS Trainer (QNET) Series: QNET Experiment #02: DC Motor Position Control. DC Motor Control Trainer (DCMCT) Student Manual

Quanser NI-ELVIS Trainer (QNET) Series: QNET Experiment #02: DC Motor Position Control. DC Motor Control Trainer (DCMCT) Student Manual 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

More information

INC 341 Feedback Control Systems: Lecture 3 Transfer Function of Dynamic Systems II

INC 341 Feedback Control Systems: Lecture 3 Transfer Function of Dynamic Systems II INC 341 Feedback Control Systems: Lecture 3 Transfer Function of Dynamic Systems II Asst. Prof. Dr.-Ing. Sudchai Boonto Department of Control Systems and Instrumentation Engineering King Mongkut s University

More information

Tutorial 1 - Drive fundamentals and DC motor characteristics

Tutorial 1 - Drive fundamentals and DC motor characteristics University of New South Wales School of Electrical Engineering & elecommunications ELEC4613 ELECRIC DRIVE SYSEMS utorial 1 - Drive fundamentals and DC motor characteristics 1. In the hoist drive system

More information

Overview of motors and motion control

Overview of motors and motion control 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,

More information

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

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

More information

School of Mechanical Engineering Purdue University. ME375 ElectroMechanical - 1

School of Mechanical Engineering Purdue University. ME375 ElectroMechanical - 1 Electro-Mechanical Systems DC Motors Principles of Operation Modeling (Derivation of fg Governing Equations (EOM)) Block Diagram Representations Using Block Diagrams to Represent Equations in s - Domain

More information

Chapter 4 Transients. Chapter 4 Transients

Chapter 4 Transients. Chapter 4 Transients Chapter 4 Transients Chapter 4 Transients 1. Solve first-order RC or RL circuits. 2. Understand the concepts of transient response and steady-state response. 1 3. Relate the transient response of first-order

More information

Mechatronic System Case Study: Rotary Inverted Pendulum Dynamic System Investigation

Mechatronic System Case Study: Rotary Inverted Pendulum Dynamic System Investigation Mechatronic System Case Study: Rotary Inverted Pendulum Dynamic System Investigation Dr. Kevin Craig Greenheck Chair in Engineering Design & Professor of Mechanical Engineering Marquette University K.

More information

Video 5.1 Vijay Kumar and Ani Hsieh

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

More information

R10 JNTUWORLD B 1 M 1 K 2 M 2. f(t) Figure 1

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

More information

Appendix A: Exercise Problems on Classical Feedback Control Theory (Chaps. 1 and 2)

Appendix A: Exercise Problems on Classical Feedback Control Theory (Chaps. 1 and 2) Appendix A: Exercise Problems on Classical Feedback Control Theory (Chaps. 1 and 2) For all calculations in this book, you can use the MathCad software or any other mathematical software that you are familiar

More information

3 Lab 3: DC Motor Transfer Function Estimation by Explicit Measurement

3 Lab 3: DC Motor Transfer Function Estimation by Explicit Measurement 3 Lab 3: DC Motor Transfer Function Estimation by Explicit Measurement 3.1 Introduction There are two common methods for determining a plant s transfer function. They are: 1. Measure all the physical parameters

More information

Mechatronics Engineering. Li Wen

Mechatronics Engineering. Li Wen Mechatronics Engineering Li Wen Bio-inspired robot-dc motor drive Unstable system Mirko Kovac,EPFL Modeling and simulation of the control system Problems 1. Why we establish mathematical model of the control

More information

ME 3210 Mechatronics II Laboratory Lab 4: DC Motor Characteristics

ME 3210 Mechatronics II Laboratory Lab 4: DC Motor Characteristics ME 3210 Mechatronics II Laboratory Lab 4: DC Motor Characteristics Introduction Often, due to budget constraints or convenience, engineers must use whatever tools are available to create new or improved

More information

Section 4.9; Section 5.6. June 30, Free Mechanical Vibrations/Couple Mass-Spring System

Section 4.9; Section 5.6. June 30, Free Mechanical Vibrations/Couple Mass-Spring System Section 4.9; Section 5.6 Free Mechanical Vibrations/Couple Mass-Spring System June 30, 2009 Today s Session Today s Session A Summary of This Session: Today s Session A Summary of This Session: (1) Free

More information

Handout 10: Inductance. Self-Inductance and inductors

Handout 10: Inductance. Self-Inductance and inductors 1 Handout 10: Inductance Self-Inductance and inductors In Fig. 1, electric current is present in an isolate circuit, setting up magnetic field that causes a magnetic flux through the circuit itself. This

More information

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

(b) A unity feedback system is characterized by the transfer function. Design a suitable compensator to meet the following specifications: 1. (a) The open loop transfer function of a unity feedback control system is given by G(S) = K/S(1+0.1S)(1+S) (i) Determine the value of K so that the resonance peak M r of the system is equal to 1.4.

More information

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

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

More information

(a) Torsional spring-mass system. (b) Spring element.

(a) Torsional spring-mass system. (b) Spring element. m v s T s v a (a) T a (b) T a FIGURE 2.1 (a) Torsional spring-mass system. (b) Spring element. by ky Wall friction, b Mass M k y M y r(t) Force r(t) (a) (b) FIGURE 2.2 (a) Spring-mass-damper system. (b)

More information

MECHATRONICS ENGINEERING TECHNOLOGY. Modeling a Servo Motor System

MECHATRONICS ENGINEERING TECHNOLOGY. Modeling a Servo Motor System 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

More information

System Modeling: Motor position, θ The physical parameters for the dc motor are:

System Modeling: Motor position, θ The physical parameters for the dc motor are: Dept. of EEE, KUET, Sessional on EE 3202: Expt. # 2 2k15 Batch Experiment No. 02 Name of the experiment: Modeling of Physical systems and study of their closed loop response Objective: (i) (ii) (iii) (iv)

More information

DC Motor Position: System Modeling

DC Motor Position: System Modeling 1 of 7 01/03/2014 22:07 Tips Effects TIPS ABOUT BASICS INDEX NEXT INTRODUCTION CRUISE CONTROL MOTOR SPEED MOTOR POSITION SUSPENSION INVERTED PENDULUM SYSTEM MODELING ANALYSIS DC Motor Position: System

More information

APPPHYS 217 Tuesday 6 April 2010

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

More information

Lab 3: Quanser Hardware and Proportional Control

Lab 3: Quanser Hardware and Proportional Control Lab 3: Quanser Hardware and Proportional Control The worst wheel of the cart makes the most noise. Benjamin Franklin 1 Objectives The goal of this lab is to: 1. familiarize you with Quanser s QuaRC tools

More information

Lab 5a: Pole Placement for the Inverted Pendulum

Lab 5a: Pole Placement for the Inverted Pendulum Lab 5a: Pole Placement for the Inverted Pendulum November 1, 2011 1 Purpose The objective of this lab is to achieve simultaneous control of both the angular position of the pendulum and horizontal position

More information

Applications of Second-Order Linear Differential Equations

Applications of Second-Order Linear Differential Equations CHAPTER 14 Applications of Second-Order Linear Differential Equations SPRING PROBLEMS The simple spring system shown in Fig. 14-! consists of a mass m attached lo the lower end of a spring that is itself

More information

Electric Circuit Theory

Electric Circuit Theory Electric Circuit Theory Nam Ki Min nkmin@korea.ac.kr 010-9419-2320 Chapter 8 Natural and Step Responses of RLC Circuits Nam Ki Min nkmin@korea.ac.kr 010-9419-2320 8.1 Introduction to the Natural Response

More information

King Saud University

King Saud University motor speed (rad/sec) Closed Loop Step Response ing Saud University College of Engineering, Electrical Engineering Department Labwork Manual EE 356 Control and Instrumentation Laboratory (كهر 356 معمل

More information

Rotary Motion Servo Plant: SRV02. Rotary Experiment #11: 1-DOF Torsion. 1-DOF Torsion Position Control using QuaRC. Student Manual

Rotary Motion Servo Plant: SRV02. Rotary Experiment #11: 1-DOF Torsion. 1-DOF Torsion Position Control using QuaRC. Student Manual Rotary Motion Servo Plant: SRV02 Rotary Experiment #11: 1-DOF Torsion 1-DOF Torsion Position Control using QuaRC Student Manual Table of Contents 1. INTRODUCTION...1 2. PREREQUISITES...1 3. OVERVIEW OF

More information

E11 Lecture 13: Motors. Professor Lape Fall 2010

E11 Lecture 13: Motors. Professor Lape Fall 2010 E11 Lecture 13: Motors Professor Lape Fall 2010 Overview How do electric motors work? Electric motor types and general principles of operation How well does your motor perform? Torque and power output

More information

Example: DC Motor Speed Modeling

Example: DC Motor Speed Modeling Page 1 of 5 Example: DC Motor Speed Modeling Physical setup and system equations Design requirements MATLAB representation and open-loop response Physical setup and system equations A common actuator in

More information

CHAPTER 5 : REDUCTION OF MULTIPLE SUBSYSTEMS

CHAPTER 5 : REDUCTION OF MULTIPLE SUBSYSTEMS 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

More information

Laboratory 11 Control Systems Laboratory ECE3557. State Feedback Controller for Position Control of a Flexible Joint

Laboratory 11 Control Systems Laboratory ECE3557. State Feedback Controller for Position Control of a Flexible Joint 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

More information

Lab # 4 Time Response Analysis

Lab # 4 Time Response Analysis Islamic University of Gaza Faculty of Engineering Computer Engineering Dep. Feedback Control Systems Lab Eng. Tareq Abu Aisha Lab # 4 Lab # 4 Time Response Analysis What is the Time Response? It is an

More information

Spontaneous Speed Reversals in Stepper Motors

Spontaneous Speed Reversals in Stepper Motors Spontaneous Speed Reversals in Stepper Motors Marc Bodson University of Utah Electrical & Computer Engineering 50 S Central Campus Dr Rm 3280 Salt Lake City, UT 84112, U.S.A. Jeffrey S. Sato & Stephen

More information

Dynamic Response. Assoc. Prof. Enver Tatlicioglu. Department of Electrical & Electronics Engineering Izmir Institute of Technology.

Dynamic Response. Assoc. Prof. Enver Tatlicioglu. Department of Electrical & Electronics Engineering Izmir Institute of Technology. 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

More information

DcMotor_ Model Help File

DcMotor_ Model Help File Name of Model: DcMotor_021708 Author: Vladimir L. Chervyakov Date: 2002-10-26 Executable file name DcMotor_021708.vtm Version number: 1.0 Description This model represents a Nonlinear model of a permanent

More information

Applications of Second-Order Differential Equations

Applications of Second-Order Differential Equations Applications of Second-Order Differential Equations ymy/013 Building Intuition Even though there are an infinite number of differential equations, they all share common characteristics that allow intuition

More information

Real-Time Implementation of a LQR-Based Controller for the Stabilization of a Double Inverted Pendulum

Real-Time Implementation of a LQR-Based Controller for the Stabilization of a Double Inverted Pendulum Proceedings of the International MultiConference of Engineers and Computer Scientists 017 Vol I,, March 15-17, 017, Hong Kong Real-Time Implementation of a LQR-Based Controller for the Stabilization of

More information

Introduction to Feedback Control

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

More information

LIAPUNOV S STABILITY THEORY-BASED MODEL REFERENCE ADAPTIVE CONTROL FOR DC MOTOR

LIAPUNOV S STABILITY THEORY-BASED MODEL REFERENCE ADAPTIVE CONTROL FOR DC MOTOR LIAPUNOV S STABILITY THEORY-BASED MODEL REFERENCE ADAPTIVE CONTROL FOR DC MOTOR *Ganta Ramesh, # R. Hanumanth Nayak *#Assistant Professor in EEE, Gudlavalleru Engg College, JNTU, Kakinada University, Gudlavalleru

More information

Rotary Motion Servo Plant: SRV02. Rotary Experiment #01: Modeling. SRV02 Modeling using QuaRC. Student Manual

Rotary Motion Servo Plant: SRV02. Rotary Experiment #01: Modeling. SRV02 Modeling using QuaRC. Student Manual Rotary Motion Servo Plant: SRV02 Rotary Experiment #01: Modeling SRV02 Modeling using QuaRC Student Manual SRV02 Modeling Laboratory Student Manual Table of Contents 1. INTRODUCTION...1 2. PREREQUISITES...1

More information

Mechatronics Modeling and Analysis of Dynamic Systems Case-Study Exercise

Mechatronics Modeling and Analysis of Dynamic Systems Case-Study Exercise Mechatronics Modeling and Analysis of Dynamic Systems Case-Study Exercise Goal: This exercise is designed to take a real-world problem and apply the modeling and analysis concepts discussed in class. As

More information

Robot Manipulator Control. Hesheng Wang Dept. of Automation

Robot Manipulator Control. Hesheng Wang Dept. of Automation Robot Manipulator Control Hesheng Wang Dept. of Automation Introduction Industrial robots work based on the teaching/playback scheme Operators teach the task procedure to a robot he robot plays back eecute

More information

8. Introduction and Chapter Objectives

8. Introduction and Chapter Objectives Real Analog - Circuits Chapter 8: Second Order Circuits 8. Introduction and Chapter Objectives Second order systems are, by definition, systems whose input-output relationship is a second order differential

More information

ENGG4420 LECTURE 7. CHAPTER 1 BY RADU MURESAN Page 1. September :29 PM

ENGG4420 LECTURE 7. CHAPTER 1 BY RADU MURESAN Page 1. September :29 PM CHAPTER 1 BY RADU MURESAN Page 1 ENGG4420 LECTURE 7 September 21 10 2:29 PM MODELS OF ELECTRIC CIRCUITS Electric circuits contain sources of electric voltage and current and other electronic elements such

More information

Mechatronics. MANE 4490 Fall 2002 Assignment # 1

Mechatronics. MANE 4490 Fall 2002 Assignment # 1 Mechatronics MANE 4490 Fall 2002 Assignment # 1 1. For each of the physical models shown in Figure 1, derive the mathematical model (equation of motion). All displacements are measured from the static

More information

AC Circuits Homework Set

AC Circuits Homework Set Problem 1. In an oscillating LC circuit in which C=4.0 μf, the maximum potential difference across the capacitor during the oscillations is 1.50 V and the maximum current through the inductor is 50.0 ma.

More information

Lab 3: Model based Position Control of a Cart

Lab 3: Model based Position Control of a Cart I. Objective Lab 3: Model based Position Control of a Cart The goal of this lab is to help understand the methodology to design a controller using the given plant dynamics. Specifically, we would do position

More information

Physics 116A Notes Fall 2004

Physics 116A Notes Fall 2004 Physics 116A Notes Fall 2004 David E. Pellett Draft v.0.9 Notes Copyright 2004 David E. Pellett unless stated otherwise. References: Text for course: Fundamentals of Electrical Engineering, second edition,

More information

sc Control Systems Design Q.1, Sem.1, Ac. Yr. 2010/11

sc 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 information

Noise - irrelevant data; variability in a quantity that has no meaning or significance. In most cases this is modeled as a random variable.

Noise - irrelevant data; variability in a quantity that has no meaning or significance. In most cases this is modeled as a random variable. 1.1 Signals and Systems Signals convey information. Systems respond to (or process) information. Engineers desire mathematical models for signals and systems in order to solve design problems efficiently

More information

2. Determine whether the following pair of functions are linearly dependent, or linearly independent:

2. Determine whether the following pair of functions are linearly dependent, or linearly independent: Topics to be covered on the exam include: Recognizing, and verifying solutions to homogeneous second-order linear differential equations, and their corresponding Initial Value Problems Recognizing and

More information

FUZZY LOGIC CONTROL Vs. CONVENTIONAL PID CONTROL OF AN INVERTED PENDULUM ROBOT

FUZZY LOGIC CONTROL Vs. CONVENTIONAL PID CONTROL OF AN INVERTED PENDULUM ROBOT http:// FUZZY LOGIC CONTROL Vs. CONVENTIONAL PID CONTROL OF AN INVERTED PENDULUM ROBOT 1 Ms.Mukesh Beniwal, 2 Mr. Davender Kumar 1 M.Tech Student, 2 Asst.Prof, Department of Electronics and Communication

More information

Analysis and Design of Control Systems in the Time Domain

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

More information

Math 240: Spring/Mass Systems II

Math 240: Spring/Mass Systems II Math 240: Spring/Mass Systems II Ryan Blair University of Pennsylvania Monday, March 26, 2012 Ryan Blair (U Penn) Math 240: Spring/Mass Systems II Monday, March 26, 2012 1 / 12 Outline 1 Today s Goals

More information

The Control of an Inverted Pendulum

The Control of an Inverted Pendulum The Control of an Inverted Pendulum AAE 364L This experiment is devoted to the inverted pendulum. Clearly, the inverted pendulum will fall without any control. We will design a controller to balance the

More information

1 x(k +1)=(Φ LH) x(k) = T 1 x 2 (k) x1 (0) 1 T x 2(0) T x 1 (0) x 2 (0) x(1) = x(2) = x(3) =

1 x(k +1)=(Φ LH) x(k) = T 1 x 2 (k) x1 (0) 1 T x 2(0) T x 1 (0) x 2 (0) x(1) = x(2) = x(3) = 567 This is often referred to as Þnite settling time or deadbeat design because the dynamics will settle in a Þnite number of sample periods. This estimator always drives the error to zero in time 2T or

More information

Time Response Analysis (Part II)

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

More information

Project Lab Report. Michael Hall. Hao Zhu. Neil Nevgi. Station 6. Ta: Yan Cui

Project Lab Report. Michael Hall. Hao Zhu. Neil Nevgi. Station 6. Ta: Yan Cui 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

More information

SRV02-Series Rotary Experiment # 1. Position Control. Student Handout

SRV02-Series Rotary Experiment # 1. Position Control. Student Handout SRV02-Series Rotary Experiment # 1 Position Control Student Handout SRV02-Series Rotary Experiment # 1 Position Control Student Handout 1. Objectives The objective in this experiment is to introduce the

More information

Michigan State University College of Engineering East Lansing, MI

Michigan State University College of Engineering East Lansing, MI Michigan State niversity College of Engineering East Lansing, MI 488241226 MEMO NMBER: PPBS0001 DATE: 2Sept97 TO: FROM: Distribution E. LaBudde SBJECT: PPBS Preliminary Math Model ABSTRACT: This memo contains

More information

Solved Problems. Electric Circuits & Components. 1-1 Write the KVL equation for the circuit shown.

Solved Problems. Electric Circuits & Components. 1-1 Write the KVL equation for the circuit shown. Solved Problems Electric Circuits & Components 1-1 Write the KVL equation for the circuit shown. 1-2 Write the KCL equation for the principal node shown. 1-2A In the DC circuit given in Fig. 1, find (i)

More information

PHYSICS 110A : CLASSICAL MECHANICS HW 2 SOLUTIONS. Here is a sketch of the potential with A = 1, R = 1, and S = 1. From the plot we can see

PHYSICS 110A : CLASSICAL MECHANICS HW 2 SOLUTIONS. Here is a sketch of the potential with A = 1, R = 1, and S = 1. From the plot we can see PHYSICS 11A : CLASSICAL MECHANICS HW SOLUTIONS (1) Taylor 5. Here is a sketch of the potential with A = 1, R = 1, and S = 1. From the plot we can see 1.5 1 U(r).5.5 1 4 6 8 1 r Figure 1: Plot for problem

More information

Control Systems. University Questions

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

More information

Trajectory Planning, Setpoint Generation and Feedforward for Motion Systems

Trajectory Planning, Setpoint Generation and Feedforward for Motion Systems 2 Trajectory Planning, Setpoint Generation and Feedforward for Motion Systems Paul Lambrechts Digital Motion Control (4K4), 23 Faculty of Mechanical Engineering, Control Systems Technology Group /42 2

More information

WHAT A SINGLE JOINT IS MADE OF RA

WHAT A SINGLE JOINT IS MADE OF RA Anthropomorphic robotics WHAT A SINGLE JOINT IS MADE OF Notation d F ( mv) mx Since links are physical objects with mass dt J J f i i J = moment of inertia F r F r Moment of inertia Around an axis m3 m1

More information

Math 240: Spring-mass Systems

Math 240: Spring-mass Systems Math 240: Spring-mass Systems Ryan Blair University of Pennsylvania Tuesday March 1, 2011 Ryan Blair (U Penn) Math 240: Spring-mass Systems Tuesday March 1, 2011 1 / 15 Outline 1 Review 2 Today s Goals

More information

OSCILLATIONS ABOUT EQUILIBRIUM

OSCILLATIONS ABOUT EQUILIBRIUM OSCILLATIONS ABOUT EQUILIBRIUM Chapter 13 Units of Chapter 13 Periodic Motion Simple Harmonic Motion Connections between Uniform Circular Motion and Simple Harmonic Motion The Period of a Mass on a Spring

More information

Inductance, Inductors, RL Circuits & RC Circuits, LC, and RLC Circuits

Inductance, Inductors, RL Circuits & RC Circuits, LC, and RLC Circuits Inductance, Inductors, RL Circuits & RC Circuits, LC, and RLC Circuits Self-inductance A time-varying current in a circuit produces an induced emf opposing the emf that initially set up the timevarying

More information

The Control of an Inverted Pendulum

The Control of an Inverted Pendulum The Control of an Inverted Pendulum AAE 364L This experiment is devoted to the inverted pendulum. Clearly, the inverted pendulum will fall without any control. We will design a controller to balance the

More information

Analysis of Linear State Space Models

Analysis of Linear State Space Models Max f (lb) Max y (in) 1 ME313 Homework #7 Analysis of Linear State Space Models Last Updated November 6, 213 Repeat the car-crash problem from HW#6. Use the Matlab function lsim to perform the simulation.

More information

EE 242 EXPERIMENT 8: CHARACTERISTIC OF PARALLEL RLC CIRCUIT BY USING PULSE EXCITATION 1

EE 242 EXPERIMENT 8: CHARACTERISTIC OF PARALLEL RLC CIRCUIT BY USING PULSE EXCITATION 1 EE 242 EXPERIMENT 8: CHARACTERISTIC OF PARALLEL RLC CIRCUIT BY USING PULSE EXCITATION 1 PURPOSE: To experimentally study the behavior of a parallel RLC circuit by using pulse excitation and to verify that

More information

PID Control. Objectives

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

More information

ENGR 2405 Chapter 8. Second Order Circuits

ENGR 2405 Chapter 8. Second Order Circuits ENGR 2405 Chapter 8 Second Order Circuits Overview The previous chapter introduced the concept of first order circuits. This chapter will expand on that with second order circuits: those that need a second

More information

Electrical Machine & Automatic Control (EEE-409) (ME-II Yr) UNIT-3 Content: Signals u(t) = 1 when t 0 = 0 when t <0

Electrical Machine & Automatic Control (EEE-409) (ME-II Yr) UNIT-3 Content: Signals u(t) = 1 when t 0 = 0 when t <0 Electrical Machine & Automatic Control (EEE-409) (ME-II Yr) UNIT-3 Content: Modeling of Mechanical : linear mechanical elements, force-voltage and force current analogy, and electrical analog of simple

More information

Final Exam April 30, 2013

Final Exam April 30, 2013 Final Exam Instructions: You have 120 minutes to complete this exam. This is a closed-book, closed-notes exam. You are allowed to use a calculator during the exam. Usage of mobile phones and other electronic

More information

Introduction to Controls

Introduction to Controls EE 474 Review Exam 1 Name Answer each of the questions. Show your work. Note were essay-type answers are requested. Answer with complete sentences. Incomplete sentences will count heavily against the grade.

More information

Oscillations. Simple Harmonic Motion of a Mass on a Spring The equation of motion for a mass m is attached to a spring of constant k is

Oscillations. Simple Harmonic Motion of a Mass on a Spring The equation of motion for a mass m is attached to a spring of constant k is Dr. Alain Brizard College Physics I (PY 10) Oscillations Textbook Reference: Chapter 14 sections 1-8. Simple Harmonic Motion of a Mass on a Spring The equation of motion for a mass m is attached to a spring

More information

Math Ordinary Differential Equations Sample Test 3 Solutions

Math Ordinary Differential Equations Sample Test 3 Solutions Solve the following Math - Ordinary Differential Equations Sample Test Solutions (i x 2 y xy + 8y y(2 2 y (2 (ii x 2 y + xy + 4y y( 2 y ( (iii x 2 y xy + y y( 2 y ( (i The characteristic equation is m(m

More information

(Refer Slide Time: 00:01:30 min)

(Refer Slide Time: 00:01:30 min) Control Engineering Prof. M. Gopal Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 3 Introduction to Control Problem (Contd.) Well friends, I have been giving you various

More information

Stepping Motors. Chapter 11 L E L F L D

Stepping Motors. Chapter 11 L E L F L D Chapter 11 Stepping Motors In the synchronous motor, the combination of sinusoidally distributed windings and sinusoidally time varying current produces a smoothly rotating magnetic field. We can eliminate

More information

Response of Second-Order Systems

Response of Second-Order Systems Unit 3 Response of SecondOrder Systems In this unit, we consider the natural and step responses of simple series and parallel circuits containing inductors, capacitors and resistors. The equations which

More information

Introduction to Control (034040) lecture no. 2

Introduction to Control (034040) lecture no. 2 Introduction to Control (034040) lecture no. 2 Leonid Mirkin Faculty of Mechanical Engineering Technion IIT Setup: Abstract control problem to begin with y P(s) u where P is a plant u is a control signal

More information

Lesson 17: Synchronous Machines

Lesson 17: Synchronous Machines Lesson 17: Synchronous Machines ET 332b Ac Motors, Generators and Power Systems Lesson 17_et332b.pptx 1 Learning Objectives After this presentation you will be able to: Explain how synchronous machines

More information

ME 375 Final Examination Thursday, May 7, 2015 SOLUTION

ME 375 Final Examination Thursday, May 7, 2015 SOLUTION 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

More information

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

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

More information

Lab #2: Digital Simulation of Torsional Disk Systems in LabVIEW

Lab #2: Digital Simulation of Torsional Disk Systems in LabVIEW Lab #2: Digital Simulation of Torsional Disk Systems in LabVIEW Objective The purpose of this lab is to increase your familiarity with LabVIEW, increase your mechanical modeling prowess, and give you simulation

More information

The control of a gantry

The control of a gantry The control of a gantry AAE 364L In this experiment we will design a controller for a gantry or crane. Without a controller the pendulum of crane will swing for a long time. The idea is to use control

More information

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

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

More information