EE 474 Lab Part 2: Open-Loop and Closed-Loop Control (Velocity Servo)

Size: px
Start display at page:

Download "EE 474 Lab Part 2: Open-Loop and Closed-Loop Control (Velocity Servo)"

Transcription

1 Contents EE 474 Lab Part 2: Open-Loop and Closed-Loop Control (Velocity Servo) 1 Introduction Discovery learning in the Controls Teaching Laboratory A Laboratory Notebook Prelab Goals of Lab Writeup for the prelab Introducing open and closed-loop control Open-loop control Closed-loop control Determining DC gain and designing open-loop control Open-loop controller design Designing P-type closed-loop control Designing P-type closed-loop control with feed forward Introduction 1.1 Discovery learning in the Controls Teaching Laboratory The Controls Teaching Laboratory sequence of six laboratory exercises is designed to maximize discovery learning. Toward this objective, the laboratory handouts, starting with this one, become progressively more open ended. In the section below, the laboratory goals are spelled out with some detail and some guidance on carrying out the measurements, controller design and evaluation. In the succeeding Labs, the description of goals becomes successively broader and the quantity of detail will be progressively reduced, giving the student progressively more freedom in designing the details of measurement, analysis, design and testing for each lab. The fifth laboratory handout is only 3 pages long! Here are some suggestions Think through the goals and how the tools can be used to reach them. Its no crime to go down the wrong path, and start over (but good to figure it out sooner, rather than later). Ask questions! EE-474 Lab Part 2: Open-Loop and Closed-Loop Control (Revised: Sep 25, 2017) Page 2-1

2 1.2 A Laboratory Notebook In lab you will need a laboratory notebook and graph paper. In EE-474 Lab you will be doing five laboratory exercises. Each exercise builds on those previous, and you will need good notes of what you have already done. Each laboratory group will need a laboratory notebook. The notebook must be on hand for the first laboratory experiment, to record calibrations and measurements taken. The appropriate standard for a professional engineers notebook is sufficient explanation of what was done and what was used to reproduce the situation, and sufficient detail of observations and measurements to accurately reconstruct what happened. You will be surprised as you enter professional practice how often in real life things are not completely understood the first time around. Questions come up after a piece of equipment has left the shop floor, and notes which permit reconstructing something unanticipated at the time the observations were made will have a value beyond their measure. 2 Prelab 2.1 Goals of Lab 2 The goals of lab 2are to do these things: 1. Learn to use the Quanser Hardware In the Loop (HIL) tools in Simulink. Open, modify and run model EE474_Lab01_Model01.mdl Observe command voltage and sensor values with Scope blocks Utilize and save data recorded to the Matlab workspace 2. Characterize the performance of the three sensors on the SRV02 3. Calibrate each of the three sensors on the SRV02 4. Determine the linearized model of the SRV02, by measuring the steady-state velocity as a function of applied voltage, to develop data comparable to that of figure 4, setting an operating point, and determining the DC Gain K uv. 5. Design open and closed-loop controllers for the SRV02, test these with respect to square wave tracking. The materials related to goals 1, 2 and 3 are addressed in the EE 474 Lab Reference Manual. Read the reference manual and answer the prelab questions given there, before proceeding with the items here. EE-474 Lab Part 2: Open-Loop and Closed-Loop Control (Revised: Sep 25, 2017) Page 2-2

3 2.2 Writeup for the prelab 1. Answer the prelab questions found at the end of the Reference Manual, which address material in the reference manual. 2. Answer questions included in this section, in subsections 2.3 to Introducing open and closed-loop control Controllers generate and send a command signal regulates equipment or a process. Examples are industrial process controls, vehicle control, such as car cruise control or a flight autopilot, or regulation of robot motions. Controllers can be classified into two groups: open and closed-loop control Open-loop control Open-loop control is characterized by the absence of a feedback path, that is, the absence of a signaling pathway for the output signal to affect the input. An open-loop control system is illustrated in figure 1. d(t) r(t) Open-Loop Control Law u c (t) u(t) Plant y(t) u(t) = b 0 b 1 r(t) G uv (s) Figure 1: Open-loop velocity control with disturbance input. An example system that can be operated with open-loop control is the SRV02 motor servo, seen in figure 2. Considering this example, G uv (s) is the transfer function model for the motor servo from voltage input to velocity output. The signals of the system in figure 1 are listed in table 1. r(t) reference input, [radians/second] u c (t) motor command (controller output), [volts] d(t) u(t) y(t) disturbance input (shown in parallel with the motor command), [volts-equivalent] Total effective command to the motor [volts] system output, [radians/second] Table 1: Definitions of signals in figure 1. Transfer function G uv (s) is the model of the SRV02 that is the basis for controller design. Since we are considering the velocity of the output, the transfer function has units of radians per second EE-474 Lab Part 2: Open-Loop and Closed-Loop Control (Revised: Sep 25, 2017) Page 2-3

4 Figure 2: Quanser SRV02 motor servo. of rotation speed per applied volt, G uv (s) : [ ] radians/sec = volt [ ] radians. volt-second Closed-loop control A closed-loop controller is characterized by the utilization of feedback, that is, a pathway for the output signal to affect the input. An closed-loop control system is illustrated in figure 3. The additional signals of the system in figure 3 are listed in table 2. r(t) e(t) Closed-Loop Control Law u c (t) u(t) Plant y(t) G c (s) G uv (s) - P-type control: u(t) = K p e(t) n(t) y s (t) d(t) Figure 3: Closed-loop velocity control with velocity sensing and disturbance input. e(t) the error signal, it is the difference between r(t) and y(t), [radians/second] n(t) sensor noise signal, [radians/second] y s (t) sensed velocity signal, [radians/second] Table 2: Signals added for the closed-loop system. EE-474 Lab Part 2: Open-Loop and Closed-Loop Control (Revised: Sep 25, 2017) Page 2-4

5 In lab 2 you will approximate the plant model G uv (s) with a constant: G uv (s) = K uv (1) where K uv is the DC gain of the motor servo. You will identify (measure) K uv and design open-loop and closed-loop controllers to cause the motor output y(t) to track the reference input r(t). And evaluate the performance of your controllers for a step input. 2.4 Determining DC gain and designing open-loop control Velocity versus applied voltage data for one possible motor servo are seen in figure 4. These data show velocity to be a nearly linear function of voltage, except near zero volts where motor friction introduces a nonlinearity. The DC gain of the system for variations in velocity about an operating point of 12.5 [rad/sec] can be determined from the slope of the input-output function at the operating point. The slope is seen to be 7.25 [rad/sec/volt] in figure Measured Velocity [rad/sec] 10 Fit Curve Operating Point Nonlinearity Applied Voltage Figure 4: A plot of measured velocity as a function of applied voltage. The points mark the data points, the curves are lines fit through the data points. EE-474 Lab Part 2: Open-Loop and Closed-Loop Control (Revised: Sep 25, 2017) Page 2-5

6 2.5 Open-loop controller design An open-loop controller is seen in figure 1. Starting with the modeling equations y(t) y 0 K uv δu(t) (2) δu(t) = u(t) u 0 (3) and adding the control law u(t) = b 0 b 1 r(t) (4) an open-loop controller can be found according to b 1 = 1 K uv (5) b 0 = u 0 b 1 y 0 (6) Question 1. What are the units of b 0 and b 1? Show that the units in equation (4) balance. Question 2. Starting with modeling equations (2) and (3), and control law (4), show mathematically that design equations (5) and (6) would give perfect tracking (that is, y(t) = r(t)) if the model is perfect and there are no disturbances. Question 3. Determine the open-loop gains, b 0 and b 1, for the system associated with the data of figure 4 using an operating point of y 0 =12.5 [rad/sec]. Determine the applied voltage when r(t) = 10:0 [rad/sec]. 2.6 Designing P-type closed-loop control In a closed-loop controller, such as seen in figure 3, the control law is the function that computes the control signal based on an error signal. Writing in the most general form, we may write the control law as u(t) = g c (e(t)) (7) where g c ( )is a function. For what is known as proportional-type or P-type control (used in many simple applications) the control effort is given as u(t) = K p e(t) (8) where K p is the controller proportional gain constant. EE-474 Lab Part 2: Open-Loop and Closed-Loop Control (Revised: Sep 25, 2017) Page 2-6

7 The loop gain of a servo system is the product of the gains of all of the blocks in the feedback loop. Approximating the plant transfer function by its DC gain (the simplest approximation to the actual transfer function): G p (s) = K uv (9) then the loop gain is given as the product G loop (s) = G c (s) G p (s) = K p K uv. (10) where G c (s) = K p is the transfer function of a P-type controller. Turning around equation (10) gives an equation for designing P-type closed-loop control: K p = K loop K uv (11) where K loop is the DC value of the loop gain G loop (s). Question 4. For the system of figure 3 and data given in figure 4, determine K p to give a loop gain of Determine the applied voltage when r(t) = 10:0 [rad/sec] and y(t) = 9:0 [rad/sec]. 2.7 Designing P-type closed-loop control with feed forward Equation (4) is an example of a feed-forward control term; it is a calculation of the control effort based on the reference signal r(t). Equation (8) is an example of a feedback control term; it is a calculation of control effort based on the measured output of the system y(t). Feedback control is widely used in practice, because of its ability to correct for errors. In some controllers a feed-forward term is added to the control law, to reduce the errors that require correction. The control law for P-type closed-loop control with feed forward may be written: u(t) = b 0 b 1 r(t)k p e(t) (12) QuestionCap Draw the block diagram for a system with control law (12). Using the controller parameters determined in steps 3 and 4 in equation (12), calculate the applied motor voltage when r(t) = 10:0 and y(t) = 9:0 [rad/sec]. EE-474 Lab Part 2: Open-Loop and Closed-Loop Control (Revised: Sep 25, 2017) Page 2-7

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

State Feedback Controller for Position Control of a Flexible Link

State Feedback Controller for Position Control of a Flexible Link Laboratory 12 Control Systems Laboratory ECE3557 Laboratory 12 State Feedback Controller for Position Control of a Flexible Link 12.1 Objective The objective of this laboratory is to design a full state

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

Department of Electrical and Computer Engineering. EE461: Digital Control - Lab Manual

Department of Electrical and Computer Engineering. EE461: Digital Control - Lab Manual Department of Electrical and Computer Engineering EE461: Digital Control - Lab Manual Winter 2011 EE 461 Experiment #1 Digital Control of DC Servomotor 1 Objectives The objective of this lab is to introduce

More information

Teaching State Variable Feedback to Technology Students Using MATLAB and SIMULINK

Teaching State Variable Feedback to Technology Students Using MATLAB and SIMULINK Teaching State Variable Feedback to Technology Students Using MATLAB and SIMULINK Kathleen A.K. Ossman, Ph.D. University of Cincinnati Session 448 I. Introduction This paper describes a course and laboratory

More information

SRV02-Series Rotary Experiment # 7. Rotary Inverted Pendulum. Student Handout

SRV02-Series Rotary Experiment # 7. Rotary Inverted Pendulum. Student Handout SRV02-Series Rotary Experiment # 7 Rotary Inverted Pendulum Student Handout SRV02-Series Rotary Experiment # 7 Rotary Inverted Pendulum Student Handout 1. Objectives The objective in this experiment is

More information

YTÜ Mechanical Engineering Department

YTÜ Mechanical Engineering Department YTÜ Mechanical Engineering Department Lecture of Special Laboratory of Machine Theory, System Dynamics and Control Division Coupled Tank 1 Level Control with using Feedforward PI Controller Lab Date: Lab

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

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

(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

Classify a transfer function to see which order or ramp it can follow and with which expected error.

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

More information

D(s) G(s) A control system design definition

D(s) G(s) A control system design definition R E Compensation D(s) U Plant G(s) Y Figure 7. A control system design definition x x x 2 x 2 U 2 s s 7 2 Y Figure 7.2 A block diagram representing Eq. (7.) in control form z U 2 s z Y 4 z 2 s z 2 3 Figure

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

Lab 6a: Pole Placement for the Inverted Pendulum

Lab 6a: Pole Placement for the Inverted Pendulum Lab 6a: Pole Placement for the Inverted Pendulum Idiot. Above her head was the only stable place in the cosmos, the only refuge from the damnation of the Panta Rei, and she guessed it was the Pendulum

More information

DC-motor PID control

DC-motor PID control DC-motor PID control This version: November 1, 2017 REGLERTEKNIK Name: P-number: AUTOMATIC LINKÖPING CONTROL Date: Passed: Chapter 1 Introduction The purpose of this lab is to give an introduction to

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

An Introduction to Control Systems

An Introduction to Control Systems An Introduction to Control Systems Signals and Systems: 3C1 Control Systems Handout 1 Dr. David Corrigan Electronic and Electrical Engineering corrigad@tcd.ie November 21, 2012 Recall the concept of a

More information

Coordinated Tracking Control of Multiple Laboratory Helicopters: Centralized and De-Centralized Design Approaches

Coordinated Tracking Control of Multiple Laboratory Helicopters: Centralized and De-Centralized Design Approaches Coordinated Tracking Control of Multiple Laboratory Helicopters: Centralized and De-Centralized Design Approaches Hugh H. T. Liu University of Toronto, Toronto, Ontario, M3H 5T6, Canada Sebastian Nowotny

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

Lecture 12. Upcoming labs: Final Exam on 12/21/2015 (Monday)10:30-12:30

Lecture 12. Upcoming labs: Final Exam on 12/21/2015 (Monday)10:30-12:30 289 Upcoming labs: Lecture 12 Lab 20: Internal model control (finish up) Lab 22: Force or Torque control experiments [Integrative] (2-3 sessions) Final Exam on 12/21/2015 (Monday)10:30-12:30 Today: Recap

More information

Automatic Control (TSRT15): Lecture 1

Automatic Control (TSRT15): Lecture 1 Automatic Control (TSRT15): Lecture 1 Tianshi Chen* Division of Automatic Control Dept. of Electrical Engineering Email: tschen@isy.liu.se Phone: 13-282226 Office: B-house extrance 25-27 * All lecture

More information

ME 132, Dynamic Systems and Feedback. Class Notes. Spring Instructor: Prof. A Packard

ME 132, Dynamic Systems and Feedback. Class Notes. Spring Instructor: Prof. A Packard ME 132, Dynamic Systems and Feedback Class Notes by Andrew Packard, Kameshwar Poolla & Roberto Horowitz Spring 2005 Instructor: Prof. A Packard Department of Mechanical Engineering University of California

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

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

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

Double Inverted Pendulum (DBIP)

Double Inverted Pendulum (DBIP) Linear Motion Servo Plant: IP01_2 Linear Experiment #15: LQR Control Double Inverted Pendulum (DBIP) All of Quanser s systems have an inherent open architecture design. It should be noted that the following

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

7.1 Introduction. Apago PDF Enhancer. Definition and Test Inputs. 340 Chapter 7 Steady-State Errors

7.1 Introduction. Apago PDF Enhancer. Definition and Test Inputs. 340 Chapter 7 Steady-State Errors 340 Chapter 7 Steady-State Errors 7. Introduction In Chapter, we saw that control systems analysis and design focus on three specifications: () transient response, (2) stability, and (3) steady-state errors,

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

EE 476 DC Motor Control Lab

EE 476 DC Motor Control Lab EE 476 DC Motor Control Lab - Contents 1 Introduction 2 1.1 Policies................................................ 2 2 Modeling 3 2.1 Pre-Lab................................................ 3 Torque

More information

Experiment # 5 5. Coupled Water Tanks

Experiment # 5 5. Coupled Water Tanks Experiment # 5 5. Coupled Water Tanks 5.. Objectives The Coupled-Tank plant is a Two-Tank module consisting of a pump with a water basin and two tanks. The two tanks are mounted on the front plate such

More information

State space control for the Two degrees of freedom Helicopter

State space control for the Two degrees of freedom Helicopter State space control for the Two degrees of freedom Helicopter AAE364L In this Lab we will use state space methods to design a controller to fly the two degrees of freedom helicopter. 1 The state space

More information

Subject: Introduction to Process Control. Week 01, Lectures 01 02, Spring Content

Subject: Introduction to Process Control. Week 01, Lectures 01 02, Spring Content v CHEG 461 : Process Dynamics and Control Subject: Introduction to Process Control Week 01, Lectures 01 02, Spring 2014 Dr. Costas Kiparissides Content 1. Introduction to Process Dynamics and Control 2.

More information

Automatic Control II Computer exercise 3. LQG Design

Automatic Control II Computer exercise 3. LQG Design Uppsala University Information Technology Systems and Control HN,FS,KN 2000-10 Last revised by HR August 16, 2017 Automatic Control II Computer exercise 3 LQG Design Preparations: Read Chapters 5 and 9

More information

Experiment 14 It s Snow Big Deal

Experiment 14 It s Snow Big Deal Experiment 14 It s Snow Big Deal OUTCOMES After completing this experiment, the student should be able to: use computer-based data acquisition techniques to measure temperatures. draw appropriate conclusions

More information

MEAM 510 Fall 2012 Bruce D. Kothmann

MEAM 510 Fall 2012 Bruce D. Kothmann Balancing g Robot Control MEAM 510 Fall 2012 Bruce D. Kothmann Agenda Bruce s Controls Resume Simple Mechanics (Statics & Dynamics) of the Balancing Robot Basic Ideas About Feedback & Stability Effects

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

Lab-Report Control Engineering. Proportional Control of a Liquid Level System

Lab-Report Control Engineering. Proportional Control of a Liquid Level System Lab-Report Control Engineering Proportional Control of a Liquid Level System Name: Dirk Becker Course: BEng 2 Group: A Student No.: 9801351 Date: 10/April/1999 1. Contents 1. CONTENTS... 2 2. INTRODUCTION...

More information

Reglerteknik, TNG028. Lecture 1. Anna Lombardi

Reglerteknik, TNG028. Lecture 1. Anna Lombardi Reglerteknik, TNG028 Lecture 1 Anna Lombardi Today lecture We will try to answer the following questions: What is automatic control? Where can we nd automatic control? Why do we need automatic control?

More information

EE 422G - Signals and Systems Laboratory

EE 422G - Signals and Systems Laboratory EE 4G - Signals and Systems Laboratory Lab 9 PID Control Kevin D. Donohue Department of Electrical and Computer Engineering University of Kentucky Lexington, KY 40506 April, 04 Objectives: Identify the

More information

Lab 1: Dynamic Simulation Using Simulink and Matlab

Lab 1: Dynamic Simulation Using Simulink and Matlab Lab 1: Dynamic Simulation Using Simulink and Matlab Objectives In this lab you will learn how to use a program called Simulink to simulate dynamic systems. Simulink runs under Matlab and uses block diagrams

More information

Computer Aided Control Design

Computer Aided Control Design Computer Aided Control Design Project-Lab 3 Automatic Control Basic Course, EL1000/EL1100/EL1120 Revised August 18, 2008 Modified version of laboration developed by Håkan Fortell and Svante Gunnarsson

More information

EE 3CL4: Introduction to Control Systems Lab 4: Lead Compensation

EE 3CL4: Introduction to Control Systems Lab 4: Lead Compensation EE 3CL4: Introduction to Control Systems Lab 4: Lead Compensation Tim Davidson Ext. 27352 davidson@mcmaster.ca Objective To use the root locus technique to design a lead compensator for a marginally-stable

More information

Control System. Contents

Control System. Contents 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

More information

Lab 5a: Magnetic Levitation (Week 1)

Lab 5a: Magnetic Levitation (Week 1) ME C134 / EE C128 Fall 2017 Lab 5a Lab 5a: Magnetic Levitation (Week 1) Magnetism, as you recall from physics class, is a powerful force that causes certain items to be attracted to refrigerators. Dave

More information

MEAM 510 Fall 2011 Bruce D. Kothmann

MEAM 510 Fall 2011 Bruce D. Kothmann Balancing g Robot Control MEAM 510 Fall 2011 Bruce D. Kothmann Agenda Bruce s Controls Resume Simple Mechanics (Statics & Dynamics) of the Balancing Robot Basic Ideas About Feedback & Stability Effects

More information

Department of Mechanical Engineering

Department of Mechanical Engineering Department of Mechanical Engineering 2.010 CONTROL SYSTEMS PRINCIPLES Laboratory 2: Characterization of the Electro-Mechanical Plant Introduction: It is important (for future lab sessions) that we have

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

06 Feedback Control System Characteristics The role of error signals to characterize feedback control system performance.

06 Feedback Control System Characteristics The role of error signals to characterize feedback control system performance. Chapter 06 Feedback 06 Feedback Control System Characteristics The role of error signals to characterize feedback control system performance. Lesson of the Course Fondamenti di Controlli Automatici of

More information

Lecture 6: Control Problems and Solutions. CS 344R: Robotics Benjamin Kuipers

Lecture 6: Control Problems and Solutions. CS 344R: Robotics Benjamin Kuipers Lecture 6: Control Problems and Solutions CS 344R: Robotics Benjamin Kuipers But First, Assignment 1: Followers A follower is a control law where the robot moves forward while keeping some error term small.

More information

YTÜ Mechanical Engineering Department

YTÜ Mechanical Engineering Department YTÜ Mechanical Engineering Department Lecture of Special Laboratory of Machine Theory, System Dynamics and Control Division Coupled Tank 1 Level Control with using Feedforward PI Controller Lab Report

More information

Control. CSC752: Autonomous Robotic Systems. Ubbo Visser. March 9, Department of Computer Science University of Miami

Control. CSC752: Autonomous Robotic Systems. Ubbo Visser. March 9, Department of Computer Science University of Miami Control CSC752: Autonomous Robotic Systems Ubbo Visser Department of Computer Science University of Miami March 9, 2017 Outline 1 Control system 2 Controller Images from http://en.wikipedia.org/wiki/feed-forward

More information

AE2610 Introduction to Experimental Methods in Aerospace DYNAMIC RESPONSE OF A 3-DOF HELICOPTER MODEL

AE2610 Introduction to Experimental Methods in Aerospace DYNAMIC RESPONSE OF A 3-DOF HELICOPTER MODEL AE2610 Introduction to Experimental Methods in Aerospace DYNAMIC RESPONSE OF A 3-DOF HELICOPTER MODEL Objectives The primary objective of this experiment is to introduce the student to the measurement

More information

Linear Experiment #11: LQR Control. Linear Flexible Joint Cart Plus Single Inverted Pendulum (LFJC+SIP) Student Handout

Linear Experiment #11: LQR Control. Linear Flexible Joint Cart Plus Single Inverted Pendulum (LFJC+SIP) Student Handout Linear Motion Servo Plants: IP01 or IP02 Linear Experiment #11: LQR Control Linear Flexible Joint Cart Plus Single Inverted Pendulum (LFJC+SIP) Student Handout Table of Contents 1. Objectives...1 2. Prerequisites...2

More information

State Feedback MAE 433 Spring 2012 Lab 7

State Feedback MAE 433 Spring 2012 Lab 7 State Feedback MAE 433 Spring 1 Lab 7 Prof. C. Rowley and M. Littman AIs: Brandt Belson, onathan Tu Princeton University April 4-7, 1 1 Overview This lab addresses the control of an inverted pendulum balanced

More information

Steady State Errors. Recall the closed-loop transfer function of the system, is

Steady State Errors. Recall the closed-loop transfer function of the system, is Steady State Errors Outline What is steady-state error? Steady-state error in unity feedback systems Type Number Steady-state error in non-unity feedback systems Steady-state error due to disturbance inputs

More information

Dr Ian R. Manchester

Dr Ian R. Manchester Week Content Notes 1 Introduction 2 Frequency Domain Modelling 3 Transient Performance and the s-plane 4 Block Diagrams 5 Feedback System Characteristics Assign 1 Due 6 Root Locus 7 Root Locus 2 Assign

More information

University of Utah Electrical & Computer Engineering Department ECE 3510 Lab 9 Inverted Pendulum

University of Utah Electrical & Computer Engineering Department ECE 3510 Lab 9 Inverted Pendulum University of Utah Electrical & Computer Engineering Department ECE 3510 Lab 9 Inverted Pendulum p1 ECE 3510 Lab 9, Inverted Pendulum M. Bodson, A. Stolp, 4/2/13 rev, 4/9/13 Objectives The objective of

More information

LQG/LTR CONTROLLER DESIGN FOR ROTARY INVERTED PENDULUM QUANSER REAL-TIME EXPERIMENT

LQG/LTR CONTROLLER DESIGN FOR ROTARY INVERTED PENDULUM QUANSER REAL-TIME EXPERIMENT LQG/LR CONROLLER DESIGN FOR ROARY INVERED PENDULUM QUANSER REAL-IME EXPERIMEN Cosmin Ionete University of Craiova, Faculty of Automation, Computers and Electronics Department of Automation, e-mail: cosmin@automation.ucv.ro

More information

ECE 220 Laboratory 4 Volt Meter, Comparators, and Timer

ECE 220 Laboratory 4 Volt Meter, Comparators, and Timer ECE 220 Laboratory 4 Volt Meter, Comparators, and Timer Michael W. Marcellin Please follow all rules, procedures and report requirements as described at the beginning of the document entitled ECE 220 Laboratory

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

What is flight dynamics? AE540: Flight Dynamics and Control I. What is flight control? Is the study of aircraft motion and its characteristics.

What is flight dynamics? AE540: Flight Dynamics and Control I. What is flight control? Is the study of aircraft motion and its characteristics. KING FAHD UNIVERSITY Department of Aerospace Engineering AE540: Flight Dynamics and Control I Instructor Dr. Ayman Hamdy Kassem What is flight dynamics? Is the study of aircraft motion and its characteristics.

More information

GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL & COMPUTER ENGINEERING FINAL EXAM. COURSE: ECE 3084A (Prof. Michaels)

GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL & COMPUTER ENGINEERING FINAL EXAM. COURSE: ECE 3084A (Prof. Michaels) GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL & COMPUTER ENGINEERING FINAL EXAM DATE: 30-Apr-14 COURSE: ECE 3084A (Prof. Michaels) NAME: STUDENT #: LAST, FIRST Write your name on the front page

More information

Review: stability; Routh Hurwitz criterion Today s topic: basic properties and benefits of feedback control

Review: stability; Routh Hurwitz criterion Today s topic: basic properties and benefits of feedback control Plan of the Lecture Review: stability; Routh Hurwitz criterion Today s topic: basic properties and benefits of feedback control Goal: understand the difference between open-loop and closed-loop (feedback)

More information

(Refer Slide Time: 1:42)

(Refer Slide Time: 1:42) Control Engineering Prof. Madan Gopal Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 21 Basic Principles of Feedback Control (Contd..) Friends, let me get started

More information

Control Systems Design

Control 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 information

Problem Weight Score Total 100

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

More information

Modeling and System Identification for a DC Servo

Modeling 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 3-7 March 7, Abstract First, you

More information

MinSeg balancing using pole-placement

MinSeg balancing using pole-placement MinSeg balancing using pole-placement This version: December 12, 2017 REGLERTEKNIK Name: P-number: AUTOMATIC LINKÖPING CONTROL Date: Passed: Chapter 1 Introduction The purpose of this lab is to balance

More information

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

EECS C128/ ME C134 Final Wed. Dec. 15, am. Closed book. Two pages of formula sheets. No calculators. Name: SID: EECS C28/ ME C34 Final Wed. Dec. 5, 2 8- am Closed book. Two pages of formula sheets. No calculators. There are 8 problems worth points total. Problem Points Score 2 2 6 3 4 4 5 6 6 7 8 2 Total

More information

Theory An important equation in physics is the mathematical form of Newton s second law, F = ma

Theory An important equation in physics is the mathematical form of Newton s second law, F = ma EXPERIMENT 5 NEWTON S SECOND LAW WITH A CONSTANT MASS Objectives 1. To find the acceleration of a cart using the graph of its velocity versus time 2. To establish a mathematical relation between the acceleration

More information

Plan of the Lecture. Review: stability; Routh Hurwitz criterion Today s topic: basic properties and benefits of feedback control

Plan of the Lecture. Review: stability; Routh Hurwitz criterion Today s topic: basic properties and benefits of feedback control Plan of the Lecture Review: stability; Routh Hurwitz criterion Today s topic: basic properties and benefits of feedback control Plan of the Lecture Review: stability; Routh Hurwitz criterion Today s topic:

More information

MAE143A Signals & Systems, Final Exam - Wednesday March 16, 2005

MAE143A 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 information

EE C128 / ME C134 Feedback Control Systems

EE C128 / ME C134 Feedback Control Systems EE C128 / ME C134 Feedback Control Systems Lecture Additional Material Introduction to Model Predictive Control Maximilian Balandat Department of Electrical Engineering & Computer Science University of

More information

Lecture 25: Tue Nov 27, 2018

Lecture 25: Tue Nov 27, 2018 Lecture 25: Tue Nov 27, 2018 Reminder: Lab 3 moved to Tuesday Dec 4 Lecture: review time-domain characteristics of 2nd-order systems intro to control: feedback open-loop vs closed-loop control intro to

More information

Experiment #6. Thevenin Equivalent Circuits and Power Transfer

Experiment #6. Thevenin Equivalent Circuits and Power Transfer Experiment #6 Thevenin Equivalent Circuits and Power Transfer Objective: In this lab you will confirm the equivalence between a complicated resistor circuit and its Thevenin equivalent. You will also learn

More information

SOTM LAB: P16 OHM S LAW I. TEACHER NOTES & GUIDELINES TITLE OF LAB: Ohm s Law DEVELOPERS OF LAB:

SOTM LAB: P16 OHM S LAW I. TEACHER NOTES & GUIDELINES TITLE OF LAB: Ohm s Law DEVELOPERS OF LAB: SOTM LAB: P16 OHM S LAW I. TEACHER NOTES & GUIDELINES TITLE OF LAB: Ohm s Law DEVELOPERS OF LAB: John Lane, JD853@maristb.marist.edu Taylor Pancoast, JD573@maristb.marist.edu OVERVIEW OF LAB DESCRIPTION

More information

Autonomous Mobile Robot Design

Autonomous Mobile Robot Design Autonomous Mobile Robot Design Topic: Guidance and Control Introduction and PID Loops Dr. Kostas Alexis (CSE) Autonomous Robot Challenges How do I control where to go? Autonomous Mobile Robot Design Topic:

More information

CDS 101/110a: Lecture 8-1 Frequency Domain Design

CDS 101/110a: Lecture 8-1 Frequency Domain Design CDS 11/11a: Lecture 8-1 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 information

Positioning Servo Design Example

Positioning Servo Design Example Positioning Servo Design Example 1 Goal. The goal in this design example is to design a control system that will be used in a pick-and-place robot to move the link of a robot between two positions. Usually

More information

Uncertainty and Robustness for SISO Systems

Uncertainty and Robustness for SISO Systems Uncertainty and Robustness for SISO Systems ELEC 571L Robust Multivariable Control prepared by: Greg Stewart Outline Nature of uncertainty (models and signals). Physical sources of model uncertainty. Mathematical

More information

Linear Motion Servo Plant: IP02. Linear Experiment #4: Pole Placement. Single Pendulum Gantry (SPG) Student Handout

Linear Motion Servo Plant: IP02. Linear Experiment #4: Pole Placement. Single Pendulum Gantry (SPG) Student Handout Linear Motion Servo Plant: IP0 Linear Experiment #4: Pole Placement Single Pendulum Gantry (SPG) Student Handout Table of Contents 1. Objectives...1. Prerequisites...1 3. References... 4. Experimental

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

QNET Experiment #05: HVAC System Identification. Heating, Ventilation, and Air Conditioning Trainer (HVACT) Student Manual

QNET Experiment #05: HVAC System Identification. Heating, Ventilation, and Air Conditioning Trainer (HVACT) Student Manual Quanser NI-ELVIS Trainer (QNET) Series: QNET Experiment #05: HVAC System Identification Heating, Ventilation, and Air Conditioning Trainer (HVACT) Student Manual Table of Contents 1. Laboratory Objectives...1

More information

NORTHERN ILLINOIS UNIVERSITY PHYSICS DEPARTMENT. Physics 211 E&M and Quantum Physics Spring Lab #4: Electronic Circuits I

NORTHERN ILLINOIS UNIVERSITY PHYSICS DEPARTMENT. Physics 211 E&M and Quantum Physics Spring Lab #4: Electronic Circuits I NORTHERN ILLINOIS UNIVERSITY PHYSICS DEPARTMENT Physics 211 E&M and Quantum Physics Spring 2018 Lab #4: Electronic Circuits I Lab Writeup Due: Mon/Wed/Thu/Fri, Feb. 12/14/15/16, 2018 Background The concepts

More information

CDS 101: Lecture 2.1 System Modeling

CDS 101: Lecture 2.1 System Modeling CDS 101: Lecture 2.1 System Modeling Richard M. Murray 4 October 2004 Goals: Define what a model is and its use in answering questions about a system Introduce the concepts of state, dynamics, inputs and

More information

2.004 Dynamics and Control II Spring 2008

2.004 Dynamics and Control II Spring 2008 MIT OpenCourseWare http://ocw.mit.edu 2.004 Dynamics and Control II Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Massachusetts Institute

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

Lecture 12. AO Control Theory

Lecture 12. AO Control Theory Lecture 12 AO Control Theory Claire Max with many thanks to Don Gavel and Don Wiberg UC Santa Cruz February 18, 2016 Page 1 What are control systems? Control is the process of making a system variable

More information

Model-building and parameter estimation

Model-building and parameter estimation Luleå University of Technology Johan Carlson Last revision: July 27, 2009 Measurement Technology and Uncertainty Analysis - E7021E MATLAB homework assignment Model-building and parameter estimation Introduction

More information

Example: Modeling DC Motor Position Physical Setup System Equations Design Requirements MATLAB Representation and Open-Loop Response

Example: Modeling DC Motor Position Physical Setup System Equations Design Requirements MATLAB Representation and Open-Loop Response 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

More information

Chapter 5 HW Solution

Chapter 5 HW Solution Chapter 5 HW Solution Review Questions. 1, 6. As usual, I think these are just a matter of text lookup. 1. Name the four components of a block diagram for a linear, time-invariant system. Let s see, I

More information

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

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

More information

Laboratory Exercise 1 DC servo

Laboratory Exercise 1 DC servo Laboratory Exercise DC servo Per-Olof Källén ø 0,8 POWER SAT. OVL.RESET POS.RESET Moment Reference ø 0,5 ø 0,5 ø 0,5 ø 0,65 ø 0,65 Int ø 0,8 ø 0,8 Σ k Js + d ø 0,8 s ø 0 8 Off Off ø 0,8 Ext. Int. + x0,

More information

PHY 221 Lab 7 Work and Energy

PHY 221 Lab 7 Work and Energy PHY 221 Lab 7 Work and Energy Name: Partners: Goals: Before coming to lab, please read this packet and do the prelab on page 13 of this handout. Note: originally, Lab 7 was momentum and collisions. The

More information

5-Sep-15 PHYS101-2 GRAPHING

5-Sep-15 PHYS101-2 GRAPHING GRAPHING Objectives 1- To plot and analyze a graph manually and using Microsoft Excel. 2- To find constants from a nonlinear relation. Exercise 1 - Using Excel to plot a graph Suppose you have measured

More information

PHYSICS LAB: CONSTANT MOTION

PHYSICS LAB: CONSTANT MOTION PHYSICS LAB: CONSTANT MOTION Introduction Experimentation is fundamental to physics (and all science, for that matter) because it allows us to prove or disprove our hypotheses about how the physical world

More information

Experiment 81 - Design of a Feedback Control System

Experiment 81 - Design of a Feedback Control System Experiment 81 - Design of a Feedback Control System 201139030 (Group 44) ELEC273 May 9, 2016 Abstract This report discussed the establishment of open-loop system using FOPDT medel which is usually used

More information

Root Locus. Motivation Sketching Root Locus Examples. School of Mechanical Engineering Purdue University. ME375 Root Locus - 1

Root Locus. Motivation Sketching Root Locus Examples. School of Mechanical Engineering Purdue University. ME375 Root Locus - 1 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

More information