Pitch Rate CAS Design Project
|
|
- Felix Kennedy
- 6 years ago
- Views:
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)
EE C128 / ME C134 Fall 2014 HW 6.2 Solutions. HW 6.2 Solutions
EE C28 / ME C34 Fall 24 HW 6.2 Solutions. PI Controller For the system G = K (s+)(s+3)(s+8) HW 6.2 Solutions in negative feedback operating at a damping ratio of., we are going to design a PI controller
More informationProportional plus Integral (PI) Controller
Proportional plus Integral (PI) Controller 1. A pole is placed at the origin 2. This causes the system type to increase by 1 and as a result the error is reduced to zero. 3. Originally a point A is on
More informationOutline. Classical Control. Lecture 5
Outline Outline Outline 1 What is 2 Outline What is Why use? Sketching a 1 What is Why use? Sketching a 2 Gain Controller Lead Compensation Lag Compensation What is Properties of a General System Why use?
More informationIMPROVED TECHNIQUE OF MULTI-STAGE COMPENSATION. K. M. Yanev A. Obok Opok
IMPROVED TECHNIQUE OF MULTI-STAGE COMPENSATION K. M. Yanev A. Obok Opok Considering marginal control systems, a useful technique, contributing to the method of multi-stage compensation is suggested. A
More informationR a) Compare open loop and closed loop control systems. b) Clearly bring out, from basics, Force-current and Force-Voltage analogies.
SET - 1 II B. Tech II Semester Supplementary Examinations Dec 01 1. a) Compare open loop and closed loop control systems. b) Clearly bring out, from basics, Force-current and Force-Voltage analogies..
More informationSRV02-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 informationAMME3500: System Dynamics & Control
Stefan B. Williams May, 211 AMME35: System Dynamics & Control Assignment 4 Note: This assignment contributes 15% towards your final mark. This assignment is due at 4pm on Monday, May 3 th during Week 13
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.04A Systems and Controls Spring 2013
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.04A Systems and Controls Spring 2013 Problem Set #4 Posted: Thursday, Mar. 7, 13 Due: Thursday, Mar. 14, 13 1. Sketch the Root
More information7.4 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 informationDue Wednesday, February 6th EE/MFS 599 HW #5
Due Wednesday, February 6th EE/MFS 599 HW #5 You may use Matlab/Simulink wherever applicable. Consider the standard, unity-feedback closed loop control system shown below where G(s) = /[s q (s+)(s+9)]
More information(b) A unity feedback system is characterized by the transfer function. Design a suitable compensator to meet the following specifications:
1. (a) The open loop transfer function of a unity feedback control system is given by G(S) = K/S(1+0.1S)(1+S) (i) Determine the value of K so that the resonance peak M r of the system is equal to 1.4.
More informationFeedback 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 informationDynamic Compensation using root locus method
CAIRO UNIVERSITY FACULTY OF ENGINEERING ELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 00/0 CONTROL ENGINEERING SHEET 9 Dynamic Compensation using root locus method [] (Final00)For the system shown in the
More informationController Design using Root Locus
Chapter 4 Controller Design using Root Locus 4. PD Control Root locus is a useful tool to design different types of controllers. Below, we will illustrate the design of proportional derivative controllers
More informationDesign 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 informationa. 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 informationRoot 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 informationYTÜ 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 informationOutline. Classical Control. Lecture 1
Outline Outline Outline 1 Introduction 2 Prerequisites Block diagram for system modeling Modeling Mechanical Electrical Outline Introduction Background Basic Systems Models/Transfers functions 1 Introduction
More informationRoot 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 informationEE 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 informationUnit 8: Part 2: PD, PID, and Feedback Compensation
Ideal Derivative Compensation (PD) Lead Compensation PID Controller Design Feedback Compensation Physical Realization of Compensation Unit 8: Part 2: PD, PID, and Feedback Compensation Engineering 5821:
More informationCDS 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 informationVideo 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 informationMODERN CONTROL DESIGN
CHAPTER 8 MODERN CONTROL DESIGN The classical design techniques of Chapters 6 and 7 are based on the root-locus and frequency response that utilize only the plant output for feedback with a dynamic controller
More informationChapter 3. State Feedback - Pole Placement. Motivation
Chapter 3 State Feedback - Pole Placement Motivation Whereas classical control theory is based on output feedback, this course mainly deals with control system design by state feedback. This model-based
More informationExample 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 informationCYBER EXPLORATION LABORATORY EXPERIMENTS
CYBER EXPLORATION LABORATORY EXPERIMENTS 1 2 Cyber Exploration oratory Experiments Chapter 2 Experiment 1 Objectives To learn to use MATLAB to: (1) generate polynomial, (2) manipulate polynomials, (3)
More informationHomework 7 - Solutions
Homework 7 - Solutions Note: This homework is worth a total of 48 points. 1. Compensators (9 points) For a unity feedback system given below, with G(s) = K s(s + 5)(s + 11) do the following: (c) Find the
More information6.1 Sketch the z-domain root locus and find the critical gain for the following systems K., the closed-loop characteristic equation is K + z 0.
6. Sketch the z-domain root locus and find the critical gain for the following systems K (i) Gz () z 4. (ii) Gz K () ( z+ 9. )( z 9. ) (iii) Gz () Kz ( z. )( z ) (iv) Gz () Kz ( + 9. ) ( z. )( z 8. ) (i)
More informationEssence 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 informationSoftware Engineering 3DX3. Slides 8: Root Locus Techniques
Software Engineering 3DX3 Slides 8: Root Locus Techniques Dr. Ryan Leduc Department of Computing and Software McMaster University Material based on Control Systems Engineering by N. Nise. c 2006, 2007
More informationChapter 7 Control. Part Classical Control. Mobile Robotics - Prof Alonzo Kelly, CMU RI
Chapter 7 Control 7.1 Classical Control Part 1 1 7.1 Classical Control Outline 7.1.1 Introduction 7.1.2 Virtual Spring Damper 7.1.3 Feedback Control 7.1.4 Model Referenced and Feedforward Control Summary
More informationA SIMPLIFIED ANALYSIS OF NONLINEAR LONGITUDINAL DYNAMICS AND CONCEPTUAL CONTROL SYSTEM DESIGN
A SIMPLIFIED ANALYSIS OF NONLINEAR LONGITUDINAL DYNAMICS AND CONCEPTUAL CONTROL SYSTEM DESIGN ROBBIE BUNGE 1. Introduction The longitudinal dynamics of fixed-wing aircraft are a case in which classical
More informationSECTION 2: BLOCK DIAGRAMS & SIGNAL FLOW GRAPHS
SECTION 2: BLOCK DIAGRAMS & SIGNAL FLOW GRAPHS MAE 4421 Control of Aerospace & Mechanical Systems 2 Block Diagram Manipulation Block Diagrams 3 In the introductory section we saw examples of block diagrams
More informationContents. PART I METHODS AND CONCEPTS 2. Transfer Function Approach Frequency Domain Representations... 42
Contents Preface.............................................. xiii 1. Introduction......................................... 1 1.1 Continuous and Discrete Control Systems................. 4 1.2 Open-Loop
More informationEECS 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 informationYTÜ 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 informationControls Problems for Qualifying Exam - Spring 2014
Controls Problems for Qualifying Exam - Spring 2014 Problem 1 Consider the system block diagram given in Figure 1. Find the overall transfer function T(s) = C(s)/R(s). Note that this transfer function
More informationControl 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 informationDesign via Root Locus
Design via Root Locus 9 Chapter Learning Outcomes 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 informationBangladesh University of Engineering and Technology. EEE 402: Control System I Laboratory
Bangladesh University of Engineering and Technology Electrical and Electronic Engineering Department EEE 402: Control System I Laboratory Experiment No. 4 a) Effect of input waveform, loop gain, and system
More informationDESIGN PROJECT REPORT: Longitudinal and lateral-directional stability augmentation of Boeing 747 for cruise flight condition.
DESIGN PROJECT REPORT: Longitudinal and lateral-directional stability augmentation of Boeing 747 for cruise flight condition. Prepared By: Kushal Shah Advisor: Professor John Hodgkinson Graduate Advisor:
More informationInverted Pendulum: State-Space Methods for Controller Design
1 de 12 18/10/2015 22:45 Tips Effects TIPS ABOUT BASICS HARDWARE INDEX NEXT INTRODUCTION CRUISE CONTROL MOTOR SPEED MOTOR POSITION SYSTEM MODELING ANALYSIS Inverted Pendulum: State-Space Methods for Controller
More informationTable of Laplacetransform
Appendix Table of Laplacetransform pairs 1(t) f(s) oct), unit impulse at t = 0 a, a constant or step of magnitude a at t = 0 a s t, a ramp function e- at, an exponential function s + a sin wt, a sine fun
More information1 Steady State Error (30 pts)
Professor Fearing EECS C28/ME C34 Problem Set Fall 2 Steady State Error (3 pts) Given the following continuous time (CT) system ] ẋ = A x + B u = x + 2 7 ] u(t), y = ] x () a) Given error e(t) = r(t) y(t)
More informationRoot 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 informationLongitudinal 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 informationMAE 142 Homework #5 Due Friday, March 13, 2009
MAE 142 Homework #5 Due Friday, March 13, 2009 Please read through the entire homework set before beginning. Also, please label clearly your answers and summarize your findings as concisely as possible.
More informationDr Ian R. Manchester Dr Ian R. Manchester AMME 3500 : Review
Week Date Content Notes 1 6 Mar Introduction 2 13 Mar Frequency Domain Modelling 3 20 Mar Transient Performance and the s-plane 4 27 Mar Block Diagrams Assign 1 Due 5 3 Apr Feedback System Characteristics
More informationLinear State Feedback Controller Design
Assignment For EE5101 - Linear Systems Sem I AY2010/2011 Linear State Feedback Controller Design Phang Swee King A0033585A Email: king@nus.edu.sg NGS/ECE Dept. Faculty of Engineering National University
More informationState 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 information1 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 informationExample: DC Motor Speed Modeling
Page 1 of 5 Example: DC Motor Speed Modeling Physical setup and system equations Design requirements MATLAB representation and open-loop response Physical setup and system equations A common actuator in
More informationRoot Locus Design. MEM 355 Performance Enhancement of Dynamical Systems
Root Locus Design MEM 355 Performance Enhancement of Dynamical Systems Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University Outline The root locus design method is an iterative,
More informationMECH 6091 Flight Control Systems Final Course Project
MECH 6091 Flight Control Systems Final Course Project F-16 Autopilot Design Lizeth Buendia Rodrigo Lezama Daniel Delgado December 16, 2011 1 AGENDA Theoretical Background F-16 Model and Linearization Controller
More informationMech 6091 Flight Control System Course Project. Team Member: Bai, Jing Cui, Yi Wang, Xiaoli
Mech 6091 Flight Control System Course Project Team Member: Bai, Jing Cui, Yi Wang, Xiaoli Outline 1. Linearization of Nonlinear F-16 Model 2. Longitudinal SAS and Autopilot Design 3. Lateral SAS and Autopilot
More information1 x(k +1)=(Φ LH) x(k) = T 1 x 2 (k) x1 (0) 1 T x 2(0) T x 1 (0) x 2 (0) x(1) = x(2) = x(3) =
567 This is often referred to as Þnite settling time or deadbeat design because the dynamics will settle in a Þnite number of sample periods. This estimator always drives the error to zero in time 2T or
More informationLaboratory 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 informationPower 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 informationSystem Modeling: Motor position, θ The physical parameters for the dc motor are:
Dept. of EEE, KUET, Sessional on EE 3202: Expt. # 2 2k15 Batch Experiment No. 02 Name of the experiment: Modeling of Physical systems and study of their closed loop response Objective: (i) (ii) (iii) (iv)
More informationMassachusetts Institute of Technology Department of Mechanical Engineering Dynamics and Control II Design Project
Massachusetts Institute of Technology Department of Mechanical Engineering.4 Dynamics and Control II Design Project ACTIVE DAMPING OF TALL BUILDING VIBRATIONS: CONTINUED Franz Hover, 5 November 7 Review
More informationState Regulator. Advanced Control. design of controllers using pole placement and LQ design rules
Advanced Control State Regulator Scope design of controllers using pole placement and LQ design rules Keywords pole placement, optimal control, LQ regulator, weighting matrixes Prerequisites Contact state
More informationAutonomous 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 informationSeparation 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 informationH 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 informationTopic # Feedback Control
Topic #5 6.3 Feedback Control State-Space Systems Full-state Feedback Control How do we change the poles of the state-space system? Or,evenifwecanchangethepolelocations. Where do we put the poles? Linear
More informationECE317 : Feedback and Control
ECE317 : Feedback and Control Lecture : Steady-state error Dr. Richard Tymerski Dept. of Electrical and Computer Engineering Portland State University 1 Course roadmap Modeling Analysis Design Laplace
More informationSECTION 5: ROOT LOCUS ANALYSIS
SECTION 5: ROOT LOCUS ANALYSIS MAE 4421 Control of Aerospace & Mechanical Systems 2 Introduction Introduction 3 Consider a general feedback system: Closed loop transfer function is 1 is the forward path
More informationNote. Design via State Space
Note Design via State Space Reference: Norman S. Nise, Sections 3.5, 3.6, 7.8, 12.1, 12.2, and 12.8 of Control Systems Engineering, 7 th Edition, John Wiley & Sons, INC., 2014 Department of Mechanical
More informationEEL2216 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 informationDO NOT DO HOMEWORK UNTIL IT IS ASSIGNED. THE ASSIGNMENTS MAY CHANGE UNTIL ANNOUNCED.
EE 537 Homewors Friedland Text Updated: Wednesday November 8 Some homewor assignments refer to Friedland s text For full credit show all wor. Some problems require hand calculations. In those cases do
More information9/9/2011 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 informationEE C128 / ME C134 Fall 2014 HW 8 - Solutions. HW 8 - Solutions
EE C28 / ME C34 Fall 24 HW 8 - Solutions HW 8 - Solutions. Transient Response Design via Gain Adjustment For a transfer function G(s) = in negative feedback, find the gain to yield a 5% s(s+2)(s+85) overshoot
More informationIC6501 CONTROL SYSTEMS
DHANALAKSHMI COLLEGE OF ENGINEERING CHENNAI DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING YEAR/SEMESTER: II/IV IC6501 CONTROL SYSTEMS UNIT I SYSTEMS AND THEIR REPRESENTATION 1. What is the mathematical
More informationControl. 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 informationDesign of a Lead Compensator
Design of a Lead Compensator Dr. Bishakh Bhattacharya Professor, Department of Mechanical Engineering IIT Kanpur Joint Initiative of IITs and IISc - Funded by MHRD The Lecture Contains Standard Forms of
More informationChapter 7 Interconnected Systems and Feedback: Well-Posedness, Stability, and Performance 7. Introduction Feedback control is a powerful approach to o
Lectures on Dynamic Systems and Control Mohammed Dahleh Munther A. Dahleh George Verghese Department of Electrical Engineering and Computer Science Massachuasetts Institute of Technology c Chapter 7 Interconnected
More informationDr Ian R. Manchester Dr Ian R. Manchester AMME 3500 : Root Locus
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 informationControl Systems. Design of State Feedback Control.
Control Systems Design of State Feedback Control chibum@seoultech.ac.kr Outline Design of State feedback control Dominant pole design Symmetric root locus (linear quadratic regulation) 2 Selection of closed-loop
More information(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 informationSystems Analysis and Control
Systems Analysis and Control Matthew M. Peet Illinois Institute of Technology Lecture 12: Overview In this Lecture, you will learn: Review of Feedback Closing the Loop Pole Locations Changing the Gain
More informationLecture 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 information6.302 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 informationIntroduction 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 informationsc Control Systems Design Q.1, Sem.1, Ac. Yr. 2010/11
sc46 - Control Systems Design Q Sem Ac Yr / Mock Exam originally given November 5 9 Notes: Please be reminded that only an A4 paper with formulas may be used during the exam no other material is to be
More informationCHAPTER 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 informationStability of Feedback Control Systems: Absolute and Relative
Stability of Feedback Control Systems: Absolute and Relative Dr. Kevin Craig Greenheck Chair in Engineering Design & Professor of Mechanical Engineering Marquette University Stability: Absolute and Relative
More informationImproving a Heart Rate Controller for a Cardiac Pacemaker. Connor Morrow
Improving a Heart Rate Controller for a Cardiac Pacemaker Connor Morrow 03/13/2018 1 In the paper Intelligent Heart Rate Controller for a Cardiac Pacemaker, J. Yadav, A. Rani, and G. Garg detail different
More information(a) Find the transfer function of the amplifier. Ans.: G(s) =
126 INTRDUCTIN T CNTR ENGINEERING 10( s 1) (a) Find the transfer function of the amplifier. Ans.: (. 02s 1)(. 001s 1) (b) Find the expected percent overshoot for a step input for the closed-loop system
More informationTHE REACTION WHEEL PENDULUM
THE REACTION WHEEL PENDULUM By Ana Navarro Yu-Han Sun Final Report for ECE 486, Control Systems, Fall 2013 TA: Dan Soberal 16 December 2013 Thursday 3-6pm Contents 1. Introduction... 1 1.1 Sensors (Encoders)...
More informationThe 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 informationPitch Control of Flight System using Dynamic Inversion and PID Controller
Pitch Control of Flight System using Dynamic Inversion and PID Controller Jisha Shaji Dept. of Electrical &Electronics Engineering Mar Baselios College of Engineering & Technology Thiruvananthapuram, India
More informationExperiment # 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 informationDr 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 informationVALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur
VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur 603 203. DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING SUBJECT QUESTION BANK : EC6405 CONTROL SYSTEM ENGINEERING SEM / YEAR: IV / II year
More informationState 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 informationControl Systems Engineering ( Chapter 8. Root Locus Techniques ) Prof. Kwang-Chun Ho Tel: Fax:
Control Systems Engineering ( Chapter 8. Root Locus Techniques ) Prof. Kwang-Chun Ho kwangho@hansung.ac.kr Tel: 02-760-4253 Fax:02-760-4435 Introduction In this lesson, you will learn the following : The
More informationFirst-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 informationAim. Unit abstract. Learning outcomes. QCF level: 6 Credit value: 15
Unit T23: Flight Dynamics Unit code: J/504/0132 QCF level: 6 Credit value: 15 Aim The aim of this unit is to develop learners understanding of aircraft flight dynamic principles by considering and analysing
More information