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whirlybird_v3.0

whirlybird_v3.0 - A Guide to the BYU Whirlybird Version 2.1...

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A Guide to the BYU Whirlybird Version 2.1 Randal W. Beard 1 Brigham Young University Updated: November 12, 2010 1 With future contributions from Mark Colton and Tim McLain.
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Contents 1 Introduction 1 2 Animations in Simulink 5 2.1 Handle Graphics in Matlab . . . . . . . . . . . . . . . . . . . . . 5 2.2 Animation Example: Inverted Pendulum . . . . . . . . . . . . . . 6 2.3 Animation Example: Spacecraft Using Lines . . . . . . . . . . . 9 2.4 Animation Example: Spacecraft using vertices and faces . . . . . 14 2.5 Lab 1: Assignment . . . . . . . . . . . . . . . . . . . . . . . . . 15 3 S-functions in Simulink 19 3.1 Level-1 M-file S-function . . . . . . . . . . . . . . . . . . . . . . 20 3.2 C-file S-function . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.3 Lab 2: Assignment . . . . . . . . . . . . . . . . . . . . . . . . . 24 4 Whirlybird Simulation Model 27 4.1 Kinetic and Potential Energy . . . . . . . . . . . . . . . . . . . . 28 4.2 Euler-Lagrange Equations . . . . . . . . . . . . . . . . . . . . . 30 4.3 Model of the Motor-Propeller . . . . . . . . . . . . . . . . . . . . 32 4.4 Lab 3: Assignment . . . . . . . . . . . . . . . . . . . . . . . . . 33 5 Whirlybird Design Models 35 5.1 Design Models for the Longitudinal Dynamics . . . . . . . . . . . 35 5.2 Design Models for the Lateral Dynamics . . . . . . . . . . . . . . 37 5.3 Lab 4: Assignment . . . . . . . . . . . . . . . . . . . . . . . . . 40 6 Design Specifications and Limits of Performance 41 6.1 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 6.2 Lab 5: Assignment . . . . . . . . . . . . . . . . . . . . . . . . . 46 iii
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iv CONTENTS 7 Successive Loop Closure using PID 49 7.1 PID Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 7.2 Longitudinal Control using PID . . . . . . . . . . . . . . . . . . 55 7.3 Successive Loop Closure . . . . . . . . . . . . . . . . . . . . . . 56 7.4 Lateral Control using Successive Loop Closure . . . . . . . . . . 59 7.5 Lab 6: Assignment . . . . . . . . . . . . . . . . . . . . . . . . . 61 8 Loopshaping Design 63 8.1 Lead-lag Control Overview . . . . . . . . . . . . . . . . . . . . . 63 8.2 Discrete Compensator Implementation . . . . . . . . . . . . . . . 65 8.3 Lab 7: Assignment . . . . . . . . . . . . . . . . . . . . . . . . . 66 9 Full State Feedback 69 9.1 Lateral Control using Linear State Feedback . . . . . . . . . . . . 69 9.2 Longitudinal Control using Linear State Feedback and an Integrator 70 9.3 Lab 8: Assignment . . . . . . . . . . . . . . . . . . . . . . . . . 71 10 Observer Design and Visual Feedback 73 10.1 Relative Yaw Angle . . . . . . . . . . . . . . . . . . . . . . . . . 73 10.2 Sensor Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 10.3 State Estimation using an Extended Kalman filter . . . . . . . . . 79 10.4 Lab 9: Assignment . . . . . . . . . . . . . . . . . . . . . . . . . 80 11 Nonlinear Control Design 83 11.1 Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . . 83 11.2 Assignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 A Whirlybird Parameters 87 B Using the Hardware 89 Bibliography 97
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Chapter 1 Introduction This objective of this document is to provide a detailed introduction to the BYU whirlybird including laboratory assignments that are intended to complement an introductory course in feedback control. The whirlybird is a three degree-of- freedom helicopter with complicated nonlinear dynamics, but the dynamics are amenable to linear analysis and design. The whirlybird has been designed with encoders on each joint that allow full-state feedback, but it is also equipped with an IMU (rate gyros and accelerometers) and a downward looking camera that resemble the types of sensors that will be on a real aerial robot. The sensor con- figuration allows estimated state information obtained from the IMU and camera to be compared to truth data obtained from the encoders, thereby decoupling the state feedback and state estimation problems, and allowing each to be tuned and analyzed independently. We believe that this decoupling is essential to help stu- dents understand the subtleties in feedback and estimator design. The design process for control system is shown in Figure 1.1. For the whirly- bird, the system to be controlled is a physical system with actuators (motors) and sensors (encoders, IMU, camera). The first step in the design process is to model the physical system using nonlinear differential equations. While approximations
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