Pitch Rate CAS Design Project

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Pitch Rate CAS Design Project"

Transcription

1 Pitch Rate CAS Design Project Washington University in St. Louis MAE 433 Control Systems Bob Rowe 4.4.7

2 Design Project Part 2 This is the second part of an ongoing project to design a control and stability system for pitch control of an aircraft. This second part of the design project will cover the following areas: 4. Establishing the system configuration and identifying the actuator 5. Obtaining a model of the process, the actuator, and the sensor 6. Describing a controller and selecting parameters to meet the performance specifications 7. Optimizing the parameters and analyzing the performance 8. Repeating these steps if the performance is unacceptable In part three, the last part of the design project, a prototype will be built and tested from the results of parts one and two. Design Goals As a refresher, it is fitting to go over our design goals and a few of the key variables associated with our problem (see Figure 1a). A summary of the control goals follows: 1. Dead beat pitch response to precision tracking with t r 1. 5s 2. Steady state error of less than 5% 3. Phugoid damping Short Period damping. 35 We will consider an aircraft flying at an altitude of 4, ft at a velocity of 774 ft/s. The aircraft will be modeled during constant, steady flight. The aircraft will be examined mostly in the x-z plane where moments are about the y axis. This can be done assuming that the mass distributions around the x and z axes are symmetric. Figure 1a: Key variables in describing control of aircraft

3 System Configuration, Actuator, Sensor, and Process Model The results from part one of the design project have shown a need to improve the phugoid and short period responses. Let us see how employing pitch rate feed back to our system will improve the response. Pitch rate feed back should give us more control of the phugoid and short period responses and help us meet our design goals. To provide feed back and control of our system we will need a sensor and an actuator. For the sensor we will use is a gyroscopic pitch rate sensor which can be modeled with a transfer function equal to one. For the actuator we will use a hydraulic elevator as commonly used in aircraft. We will model the elevator as a lag transfer function with a time constant of 1/2 seconds. Thus our plant transfer function becomes the following: G P G actuator G aircraft e q u e e To account for the fact that a negative moment is created for a positive elevator deflection it is necessary to apply a phase reversal by multiply the actuator state variable by negative one. This yields the following relation: e x a The state equation and output equation for our new state variable X a, the actuator state variable, are as follows: 1 x a x y x e a a 1 u e We can now add this new state equation to our existing state equations by augmenting the state matrices. From this we will attain the following newly formed matrices. vt x q x a

4 3.e e 5 F 2.1e e e e e e e e e 2 2 G 2 ue H 18 / e J As in part one of the design project the previous matrices belong to our matrix state equations that are expressed as follows: x F x Gu y H x Ju Uncompensated Control System - G c = K p With the current model of our system we are not meeting the design goals. This fact can be seen by examining the root locus and the response to a step input. Let s take a look at the unit step response of our system in figures 1 and 2.

5 Figure 1: Unit step response of uncompensated system Figure 2: Unit step response of uncompensated system (note: larger time scale)

6 In figure 1 we can see that the response to a unit step input reaches amplitude of one and then starts to decrease in amplitude. In figure 2, where we are viewing the response on a much larger time scale, we can see that the amplitude quickly drops from an amplitude of one and begins to oscillate around zero. The amplitude continues to oscillate until the response settles at zero. The system at this point yields unsatisfactory results. The response does not meet our design goals because it is not dead beat, does not have the right final output, and thus does not meet our goal of steady state error being less than five percent! The root locus, Figure 3, doubles as a pole-zero plot because we can identify the location of all of the system s poles and zeros. Examining and manipulating the root locus proved futile in fully meeting our design goals. We need to find a way to make our system have a dead beat response, assume a steady state error of less than 5%, and make the damping fall within design constraints. Let us try to do this by adding a PI compensator to our system. Figure 3: Root locus of uncompensated system PI Compensated System G c = K p (S+Z)/S By adding a PI compensator we are effectively adding another pole and zero to our system. The form of a PI compensator is as follows: K p S Z S

7 The value of K p (the gain) and Z (zero location) are to be chosen. These values can be manipulated in such a fashion to design the system response to meet the specified design goals. The PI compensator was designed by manipulating the root locus using SISO tool in Matlab. When values of K p and Z were chosen the step response was examined to see if it met the design goals. Figures 4 and 5 show the results of adding the PI compensator to our system. Figure 4: PI compensated root locus plot (left) Figure 4 shows the root locus plot of the PI compensated system. The zero added can be seen slightly to the left of the imaginary axis and the pole added lies at the origin. Manipulating this root locus plot resulted in choosing a gain value K p = 6.5 and a zero location value Z = These values resulted in the following PI compensator. S S The unit step response to our system while utilizing the above compensator results in a better response than what we had without a compensator. The PI compensated unit step response can be seen in Figure 4.

8 Figure 5: PI compensated unit step response As can be seen in Figure 5 adding a PI compensator dramatically improves the system s response. The response s final value is now somewhere around one. Even when viewing a larger time scale the response s amplitude settles close to one. However, due to the zero the PI compensator did add a substantial amount of overshoot to our system. It can be seen in Figure 5 that the amplitude within the first second reaches a max value around 1.3. The rise time in the response looks ideal because we attain our peak value in under 1 second. This easily meets the design goal of the rise time being less than 1.5 seconds. To meet all of our design goals we should have a dead beat response and no overshoot. We also need to verify our damping and rise time to ensure that it is within our design goals. The system is closing in on what we desire but is still unsatisfactory. PI compensator with a minor loop and closing the loop How then shall we go about changing our response to eliminate the overshoot? We need to change something to create a dead beat response after which we will verify the rest of our design goals. Let us add a minor loop into our system to eliminate the overshoot effect of the zero. Figure 6 shows our current system block diagram with the PI compensator.

9 1/S Z K p G p Figure 6: PI compensated block diagram This configuration causes our system to have overshoot, yet if we use block diagram algebra we can manipulate our system to a new form. This form is shown in Figure 6 and has the same closed loop poles as does the configuration in Figure 6. 1/S Z K p G p K p Figure 7: PI compensated block diagram with minor loop closed loop Figure 7 shows our PI compensated system with a minor loop. This new configuration will rid our response of overshoot and therefore cause a dead beat response. It is important to note that the closed loop poles in both Figure 6 and Figure 7 are equivalent. This can be seen by looking at single loops in both figures. As you can see, in both instances, there is one loop with a loop gain of G p K p and another with a closed loop gain equal to ZKG P /S. Because both have the same loop gains their poles and zeros are also equivalent. Once the configuration in Figure 7 is attained we have closed the loop. Theory behind closing the loop brings us to the configuration shown in Figure 8.

10 G 1/S H F Figure 8: Closed loop block diagram For the closed loop system in Figure 8 it can be seen that, u r y also, x Fx G r x y F GHx Gr Also, for the forward path gain K, G goes to K*G x F KGHx KGr And for the feedback path gain K, we let u = r Ky and thus, x F x G r ky x F KGHx Gr y H x Verification of closed loop design G c = K p Z/S Once we have added a minor loop and closed the loop it is time to check and see if our system meets the specified design goals. From the PI compensator root locus we were able to choose values for K p and Z, we will use those values as a starting point in our analysis of the new system. Let us begin by looking at our new system s response to a unit step input. This is shown in Figure 9.

11 Figure 9: Closed loop response The response seems to be within our design goals. As you can see in Figure 9, the amplitude at 1.5 seconds is.955. This fact meets the design goal of wanting a rise time that is less than 1.5 seconds. Also, the steady state amplitude of the system was right around.97, meeting the design goal that the steady state error must be less than 5%. To make sure that the steady state error was less than 5% the response was plotted on a very large time scale. The amplitude flattened out as expected and never dropped below.95. (I tried to have Matlab place the true rise time and steady state amplitude on the plot but it was buggy and would not do it. Thus, I have shown that the rise time is less than 1.5 seconds and the steady state error is less than 5% in a slightly roundabout way.) Now let us take a look the root locus which can be seen in Figure 1.

12 Figure 1: Closed Loop Root locus From the root locus in Figure 1 we can verify that the phugoid damping is greater than.4 with an actual value of.553 and that the short period damping is greater than.35 with an actual value of 1.. Conclusion The design goals have been met using a K P = 6.5 and a Z = If our design goals were not met we would have chosen different values for the gain and zero to see how our system would change. In this way the design process of control systems can be somewhat iterative. In our case, the gain and zero location we chose worked and we successfully designed a type zero system (characterized by the system s finite error to a step input) that met our specified design goals.

13 Appendix Matlab m-file % Bob Rowe % Controls Pitch Rate CAS Design Project_part2 clc clear all %Xdot=Fx+Gu %Augmented F matrix F=[-.3,3.186,-32.2,, ; ,-.319,,1,.4589;,,,1,;.21, ,,-.429,.2246;,,,,-2] %Augmented G matrix G=[; ; ; ; 2] %y=hx+ju %H matrix H=[,,,(18/pi),] %J matrix J=[] %Set up SISO sys=ss(f,g,h,j) sisotool(sys) %Set up minorloop using values from SISO kp=6.5 z=3.62 sysgainloop=tf(kp,1) sysminor=feedback(sys,sysgainloop) %Set up PI Compensator using values from SISO num=kp*[1, z] den=[1, ] syscompensator=tf(num,den) %Close the loop sysfp=series(syscompensator,sysminor) syscl=feedback(sysfp,1) %Verify Design requirements figure(1) t=(:.1:5) step(syscl,t) figure(2) rlocus(syscl)

7.4 STEP BY STEP PROCEDURE TO DRAW THE ROOT LOCUS DIAGRAM

7.4 STEP BY STEP PROCEDURE TO DRAW THE ROOT LOCUS DIAGRAM 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)

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

Feedback Control of Linear SISO systems. Process Dynamics and Control

Feedback Control of Linear SISO systems. Process Dynamics and Control 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

More information

Design via Root Locus

Design via Root Locus 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

More information

a. Closed-loop system; b. equivalent transfer function Then the CLTF () T is s the poles of () T are s from a contribution of a

a. Closed-loop system; b. equivalent transfer function Then the CLTF () T is s the poles of () T are s from a contribution of a Root Locus Simple definition Locus of points on the s- plane that represents the poles of a system as one or more parameter vary. RL and its relation to poles of a closed loop system RL and its relation

More information

Root Locus Design Example #4

Root Locus Design Example #4 Root Locus Design Example #4 A. Introduction The plant model represents a linearization of the heading dynamics of a 25, ton tanker ship under empty load conditions. The reference input signal R(s) is

More information

Root Locus Design Example #3

Root Locus Design Example #3 Root Locus Design Example #3 A. Introduction The system represents a linear model for vertical motion of an underwater vehicle at zero forward speed. The vehicle is assumed to have zero pitch and roll

More information

Example on Root Locus Sketching and Control Design

Example on Root Locus Sketching and Control Design Example on Root Locus Sketching and Control Design MCE44 - Spring 5 Dr. Richter April 25, 25 The following figure represents the system used for controlling the robotic manipulator of a Mars Rover. We

More information

Homework 7 - Solutions

Homework 7 - Solutions Homework 7 - Solutions Note: This homework is worth a total of 48 points. 1. Compensators (9 points) For a unity feedback system given below, with G(s) = K s(s + 5)(s + 11) do the following: (c) Find the

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

Control System Design

Control System Design ELEC4410 Control System Design Lecture 19: Feedback from Estimated States and Discrete-Time Control Design Julio H. Braslavsky julio@ee.newcastle.edu.au School of Electrical Engineering and Computer Science

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

Dr Ian R. Manchester Dr Ian R. Manchester AMME 3500 : Review

Dr Ian R. Manchester Dr Ian R. Manchester AMME 3500 : Review Week Date Content Notes 1 6 Mar Introduction 2 13 Mar Frequency Domain Modelling 3 20 Mar Transient Performance and the s-plane 4 27 Mar Block Diagrams Assign 1 Due 5 3 Apr Feedback System Characteristics

More information

Longitudinal Automatic landing System - Design for CHARLIE Aircraft by Root-Locus

Longitudinal Automatic landing System - Design for CHARLIE Aircraft by Root-Locus International Journal of Scientific and Research Publications, Volume 3, Issue 7, July 2013 1 Longitudinal Automatic landing System - Design for CHARLIE Aircraft by Root-Locus Gaber El-Saady, El-Nobi A.Ibrahim,

More information

1 Steady State Error (30 pts)

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

More information

1 Chapter 9: Design via Root Locus

1 Chapter 9: Design via Root Locus 1 Figure 9.1 a. Sample root locus, showing possible design point via gain adjustment (A) and desired design point that cannot be met via simple gain adjustment (B); b. responses from poles at A and B 2

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

Power System Operations and Control Prof. S.N. Singh Department of Electrical Engineering Indian Institute of Technology, Kanpur. Module 3 Lecture 8

Power System Operations and Control Prof. S.N. Singh Department of Electrical Engineering Indian Institute of Technology, Kanpur. Module 3 Lecture 8 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

More information

Essence of the Root Locus Technique

Essence of the Root Locus Technique Essence of the Root Locus Technique In this chapter we study a method for finding locations of system poles. The method is presented for a very general set-up, namely for the case when the closed-loop

More information

H inf. Loop Shaping Robust Control vs. Classical PI(D) Control: A case study on the Longitudinal Dynamics of Hezarfen UAV

H inf. Loop Shaping Robust Control vs. Classical PI(D) Control: A case study on the Longitudinal Dynamics of Hezarfen UAV Proceedings of the 2nd WSEAS International Conference on Dynamical Systems and Control, Bucharest, Romania, October 16-17, 2006 105 H inf. Loop Shaping Robust Control vs. Classical PI(D) Control: A case

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

Separation Principle & Full-Order Observer Design

Separation Principle & Full-Order Observer Design Separation Principle & Full-Order Observer Design Suppose you want to design a feedback controller. Using full-state feedback you can place the poles of the closed-loop system at will. U Plant Kx If the

More information

EEL2216 Control Theory CT1: PID Controller Design

EEL2216 Control Theory CT1: PID Controller Design EEL6 Control Theory CT: PID Controller Design. Objectives (i) To design proportional-integral-derivative (PID) controller for closed loop control. (ii) To evaluate the performance of different controllers

More information

9/9/2011 Classical Control 1

9/9/2011 Classical Control 1 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),

More information

CHAPTER 1 Basic Concepts of Control System. CHAPTER 6 Hydraulic Control System

CHAPTER 1 Basic Concepts of Control System. CHAPTER 6 Hydraulic Control System 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

More information

6.302 Feedback Systems Recitation 16: Compensation Prof. Joel L. Dawson

6.302 Feedback Systems Recitation 16: Compensation Prof. Joel L. Dawson Bode Obstacle Course is one technique for doing compensation, or designing a feedback system to make the closed-loop behavior what we want it to be. To review: - G c (s) G(s) H(s) you are here! plant For

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

The requirements of a plant may be expressed in terms of (a) settling time (b) damping ratio (c) peak overshoot --- in time domain

The requirements of a plant may be expressed in terms of (a) settling time (b) damping ratio (c) peak overshoot --- in time domain Compensators To improve the performance of a given plant or system G f(s) it may be necessary to use a compensator or controller G c(s). Compensator Plant G c (s) G f (s) The requirements of a plant may

More information

First-Order Low-Pass Filter!

First-Order Low-Pass Filter! Filters, Cost Functions, and Controller Structures! Robert Stengel! Optimal Control and Estimation MAE 546! Princeton University, 217!! Dynamic systems as low-pass filters!! Frequency response of dynamic

More information

Alireza Mousavi Brunel University

Alireza Mousavi Brunel University 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

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

Control Systems. State Estimation.

Control Systems. State Estimation. State Estimation chibum@seoultech.ac.kr Outline Dominant pole design Symmetric root locus State estimation We are able to place the CLPs arbitrarily by feeding back all the states: u = Kx. But these may

More information

10/8/2015. Control Design. Pole-placement by state-space methods. Process to be controlled. State controller

10/8/2015. Control Design. Pole-placement by state-space methods. Process to be controlled. State controller Pole-placement by state-space methods Control Design To be considered in controller design * Compensate the effect of load disturbances * Reduce the effect of measurement noise * Setpoint following (target

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

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

Course Outline. Higher Order Poles: Example. Higher Order Poles. Amme 3500 : System Dynamics & Control. State Space Design. 1 G(s) = s(s + 2)(s +10)

Course Outline. Higher Order Poles: Example. Higher Order Poles. Amme 3500 : System Dynamics & Control. State Space Design. 1 G(s) = s(s + 2)(s +10) Amme 35 : System Dynamics Control State Space Design Course Outline Week Date Content Assignment Notes 1 1 Mar Introduction 2 8 Mar Frequency Domain Modelling 3 15 Mar Transient Performance and the s-plane

More information

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

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

More information

Application Note #3413

Application Note #3413 Application Note #3413 Manual Tuning Methods Tuning the controller seems to be a difficult task to some users; however, after getting familiar with the theories and tricks behind it, one might find the

More information

Theory and Practice of Rotor Dynamics Prof. Dr. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati

Theory and Practice of Rotor Dynamics Prof. Dr. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati Theory and Practice of Rotor Dynamics Prof. Dr. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati Module - 2 Simpul Rotors Lecture - 2 Jeffcott Rotor Model In the

More information

Control System Design

Control System Design ELEC ENG 4CL4: Control System Design Notes for Lecture #24 Wednesday, March 10, 2004 Dr. Ian C. Bruce Room: CRL-229 Phone ext.: 26984 Email: ibruce@mail.ece.mcmaster.ca Remedies We next turn to the question

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

Implementation of a Communication Satellite Orbit Controller Design Using State Space Techniques

Implementation of a Communication Satellite Orbit Controller Design Using State Space Techniques ASEAN J Sci Technol Dev, 29(), 29 49 Implementation of a Communication Satellite Orbit Controller Design Using State Space Techniques M T Hla *, Y M Lae 2, S L Kyaw 3 and M N Zaw 4 Department of Electronic

More information

Simulation Study on Pressure Control using Nonlinear Input/Output Linearization Method and Classical PID Approach

Simulation Study on Pressure Control using Nonlinear Input/Output Linearization Method and Classical PID Approach Simulation Study on Pressure Control using Nonlinear Input/Output Linearization Method and Classical PID Approach Ufuk Bakirdogen*, Matthias Liermann** *Institute for Fluid Power Drives and Controls (IFAS),

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

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering Dynamics and Control II Fall K(s +1)(s +2) G(s) =.

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering Dynamics and Control II Fall K(s +1)(s +2) G(s) =. 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:

More information

12.7 Steady State Error

12.7 Steady State Error Lecture Notes on Control Systems/D. Ghose/01 106 1.7 Steady State Error For first order systems we have noticed an overall improvement in performance in terms of rise time and settling time. But there

More information

Proportional, Integral & Derivative Control Design. Raktim Bhattacharya

Proportional, Integral & Derivative Control Design. Raktim Bhattacharya AERO 422: Active Controls for Aerospace Vehicles Proportional, ntegral & Derivative Control Design Raktim Bhattacharya Laboratory For Uncertainty Quantification Aerospace Engineering, Texas A&M University

More information

Root Locus Methods. The root locus procedure

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

More information

6.245: MULTIVARIABLE CONTROL SYSTEMS by A. Megretski. Solutions to Problem Set 1 1. Massachusetts Institute of Technology

6.245: MULTIVARIABLE CONTROL SYSTEMS by A. Megretski. Solutions to Problem Set 1 1. Massachusetts Institute of Technology Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.245: MULTIVARIABLE CONTROL SYSTEMS by A. Megretski Solutions to Problem Set 1 1 Problem 1.1T Consider the

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

Control Systems! Copyright 2017 by Robert Stengel. All rights reserved. For educational use only.

Control Systems! Copyright 2017 by Robert Stengel. All rights reserved. For educational use only. Control Systems Robert Stengel Robotics and Intelligent Systems MAE 345, Princeton University, 2017 Analog vs. digital systems Continuous- and Discretetime Dynamic Models Frequency Response Transfer Functions

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

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

CHAPTER 7 STEADY-STATE RESPONSE ANALYSES

CHAPTER 7 STEADY-STATE RESPONSE ANALYSES 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

More information

B1-1. Closed-loop control. Chapter 1. Fundamentals of closed-loop control technology. Festo Didactic Process Control System

B1-1. Closed-loop control. Chapter 1. Fundamentals of closed-loop control technology. Festo Didactic Process Control System B1-1 Chapter 1 Fundamentals of closed-loop control technology B1-2 This chapter outlines the differences between closed-loop and openloop control and gives an introduction to closed-loop control technology.

More information

The output voltage is given by,

The output voltage is given by, 71 The output voltage is given by, = (3.1) The inductor and capacitor values of the Boost converter are derived by having the same assumption as that of the Buck converter. Now the critical value of the

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

PD, PI, PID Compensation. M. Sami Fadali Professor of Electrical Engineering University of Nevada

PD, PI, PID Compensation. M. Sami Fadali Professor of Electrical Engineering University of Nevada 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

More information

Low Pass Filters, Sinusoidal Input, and Steady State Output

Low Pass Filters, Sinusoidal Input, and Steady State Output Low Pass Filters, Sinusoidal Input, and Steady State Output Jaimie Stephens and Michael Bruce 5-2-4 Abstract Discussion of applications and behaviors of low pass filters when presented with a steady-state

More information

Chapter 12. Feedback Control Characteristics of Feedback Systems

Chapter 12. Feedback Control Characteristics of Feedback Systems 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

More information

Learn2Control Laboratory

Learn2Control Laboratory 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

More information

Statistical methods. Mean value and standard deviations Standard statistical distributions Linear systems Matrix algebra

Statistical methods. Mean value and standard deviations Standard statistical distributions Linear systems Matrix algebra Statistical methods Mean value and standard deviations Standard statistical distributions Linear systems Matrix algebra Statistical methods Generating random numbers MATLAB has many built-in functions

More information

Homework Assignment 3

Homework Assignment 3 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

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

16.30/31, Fall 2010 Recitation # 2

16.30/31, Fall 2010 Recitation # 2 16.30/31, Fall 2010 Recitation # 2 September 22, 2010 In this recitation, we will consider two problems from Chapter 8 of the Van de Vegte book. R + - E G c (s) G(s) C Figure 1: The standard block diagram

More information

Laplace Transform Analysis of Signals and Systems

Laplace Transform Analysis of Signals and Systems Laplace Transform Analysis of Signals and Systems Transfer Functions Transfer functions of CT systems can be found from analysis of Differential Equations Block Diagrams Circuit Diagrams 5/10/04 M. J.

More information

Inverted Pendulum. Objectives

Inverted Pendulum. Objectives Inverted Pendulum Objectives The objective of this lab is to experiment with the stabilization of an unstable system. The inverted pendulum problem is taken as an example and the animation program gives

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

Methods for Solving Linear Systems Part 2

Methods for Solving Linear Systems Part 2 Methods for Solving Linear Systems Part 2 We have studied the properties of matrices and found out that there are more ways that we can solve Linear Systems. In Section 7.3, we learned that we can use

More information

Stability and Control Analysis in Twin-Boom Vertical Stabilizer Unmanned Aerial Vehicle (UAV)

Stability and Control Analysis in Twin-Boom Vertical Stabilizer Unmanned Aerial Vehicle (UAV) International Journal of Scientific and Research Publications, Volume 4, Issue 2, February 2014 1 Stability and Control Analysis in Twin-Boom Vertical Stabilizer Unmanned Aerial Vehicle UAV Lasantha Kurukularachchi*;

More information

ANALYSIS OF AUTOPILOT SYSTEM BASED ON BANK ANGLE OF SMALL UAV

ANALYSIS OF AUTOPILOT SYSTEM BASED ON BANK ANGLE OF SMALL UAV ANALYSIS OF AUTOPILOT SYSTEM BASED ON BANK ANGLE OF SMALL UAV MAY SAN HLAING, ZAW MIN NAING, 3 MAUNG MAUNG LATT, 4 HLA MYO TUN,4 Department of Electronic Engineering, Mandalay Technological University,

More information

Feedback Basics. David M. Auslander Mechanical Engineering University of California at Berkeley. copyright 1998, D.M. Auslander

Feedback Basics. David M. Auslander Mechanical Engineering University of California at Berkeley. copyright 1998, D.M. Auslander Feedback Basics David M. Auslander Mechanical Engineering University of California at Berkeley copyright 1998, D.M. Auslander 1 I. Feedback Control Context 2 What is Feedback Control? Measure desired behavior

More information

Dr. Ian R. Manchester

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

More information

FREQUENCY-RESPONSE DESIGN

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

More information

APPLICATIONS FOR ROBOTICS

APPLICATIONS FOR ROBOTICS 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

More information

Homework 11 Solution - AME 30315, Spring 2015

Homework 11 Solution - AME 30315, Spring 2015 1 Homework 11 Solution - AME 30315, Spring 2015 Problem 1 [10/10 pts] R + - K G(s) Y Gpsq Θpsq{Ipsq and we are interested in the closed-loop pole locations as the parameter k is varied. Θpsq Ipsq k ωn

More information

Aircraft Flight Dynamics!

Aircraft Flight Dynamics! Aircraft Flight Dynamics Robert Stengel MAE 331, Princeton University, 2016 Course Overview Introduction to Flight Dynamics Math Preliminaries Copyright 2016 by Robert Stengel. All rights reserved. For

More information

EE3CL4: Introduction to Linear Control Systems

EE3CL4: Introduction to Linear Control Systems 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

More information

Distributed Real-Time Control Systems

Distributed Real-Time Control Systems Distributed Real-Time Control Systems Chapter 9 Discrete PID Control 1 Computer Control 2 Approximation of Continuous Time Controllers Design Strategy: Design a continuous time controller C c (s) and then

More information

D G 2 H + + D 2

D G 2 H + + D 2 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.302 Feedback Systems Final Exam May 21, 2007 180 minutes Johnson Ice Rink 1. This examination consists

More 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 3. 8. 24 Übersetzungshilfe / Translation aid (English) To be returned at the end of the exam! Do not mark up this translation aid

More information

AN INTRODUCTION TO THE CONTROL THEORY

AN INTRODUCTION TO THE CONTROL THEORY Open-Loop controller An Open-Loop (OL) controller is characterized by no direct connection between the output of the system and its input; therefore external disturbance, non-linear dynamics and parameter

More information

Digital Pendulum Control Experiments

Digital Pendulum Control Experiments EE-341L CONTROL SYSTEMS LAB 2013 Digital Pendulum Control Experiments Ahmed Zia Sheikh 2010030 M. Salman Khalid 2010235 Suleman Belal Kazi 2010341 TABLE OF CONTENTS ABSTRACT...2 PENDULUM OVERVIEW...3 EXERCISE

More information

KINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING

KINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING KINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING QUESTION BANK SUB.NAME : CONTROL SYSTEMS BRANCH : ECE YEAR : II SEMESTER: IV 1. What is control system? 2. Define open

More information

SAMPLE SOLUTION TO EXAM in MAS501 Control Systems 2 Autumn 2015

SAMPLE SOLUTION TO EXAM in MAS501 Control Systems 2 Autumn 2015 FACULTY OF ENGINEERING AND SCIENCE SAMPLE SOLUTION TO EXAM in MAS501 Control Systems 2 Autumn 2015 Lecturer: Michael Ruderman Problem 1: Frequency-domain analysis and control design (15 pt) Given is a

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

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

Control System Design. Risk Assessment

Control System Design. Risk Assessment Control System Design Risk Assessment Using Fuzzy Logic VPI - AOE - 239 Dr. Mark R. Anderson Associate Professor Department of Aerospace and Ocean Engineering Virginia Polytechnic Institute and State University

More information

Transient Response of a Second-Order System

Transient Response of a Second-Order System 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

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

Lab Experiment 2: Performance of First order and second order systems

Lab Experiment 2: Performance of First order and second order systems Lab Experiment 2: Performance of First order and second order systems Objective: The objective of this exercise will be to study the performance characteristics of first and second order systems using

More information

CM 3310 Process Control, Spring Lecture 21

CM 3310 Process Control, Spring Lecture 21 CM 331 Process Control, Spring 217 Instructor: Dr. om Co Lecture 21 (Back to Process Control opics ) General Control Configurations and Schemes. a) Basic Single-Input/Single-Output (SISO) Feedback Figure

More information

Design of Decentralised PI Controller using Model Reference Adaptive Control for Quadruple Tank Process

Design of Decentralised PI Controller using Model Reference Adaptive Control for Quadruple Tank Process Design of Decentralised PI Controller using Model Reference Adaptive Control for Quadruple Tank Process D.Angeline Vijula #, Dr.N.Devarajan * # Electronics and Instrumentation Engineering Sri Ramakrishna

More information

Vehicle longitudinal speed control

Vehicle longitudinal speed control 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

More information

EE Control Systems LECTURE 14

EE Control Systems LECTURE 14 Updated: Tueday, March 3, 999 EE 434 - Control Sytem LECTURE 4 Copyright FL Lewi 999 All right reerved ROOT LOCUS DESIGN TECHNIQUE Suppoe the cloed-loop tranfer function depend on a deign parameter k We

More information

CDS 110b: Lecture 2-1 Linear Quadratic Regulators

CDS 110b: Lecture 2-1 Linear Quadratic Regulators CDS 110b: Lecture 2-1 Linear Quadratic Regulators Richard M. Murray 11 January 2006 Goals: Derive the linear quadratic regulator and demonstrate its use Reading: Friedland, Chapter 9 (different derivation,

More information

Goodwin, Graebe, Salgado, Prentice Hall Chapter 11. Chapter 11. Dealing with Constraints

Goodwin, Graebe, Salgado, Prentice Hall Chapter 11. Chapter 11. Dealing with Constraints Chapter 11 Dealing with Constraints Topics to be covered An ubiquitous problem in control is that all real actuators have limited authority. This implies that they are constrained in amplitude and/or rate

More information

Chap 8. State Feedback and State Estimators

Chap 8. State Feedback and State Estimators Chap 8. State Feedback and State Estimators Outlines Introduction State feedback Regulation and tracking State estimator Feedback from estimated states State feedback-multivariable case State estimators-multivariable

More information

ELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 2010/2011 CONTROL ENGINEERING SHEET 5 Lead-Lag Compensation Techniques

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

More information

Lecture 14 - Using the MATLAB Control System Toolbox and Simulink Friday, February 8, 2013

Lecture 14 - Using the MATLAB Control System Toolbox and Simulink Friday, February 8, 2013 Today s Objectives ENGR 105: Feedback Control Design Winter 2013 Lecture 14 - Using the MATLAB Control System Toolbox and Simulink Friday, February 8, 2013 1. introduce the MATLAB Control System Toolbox

More information