A Pneumatic Semi-Active Control Methodology for Vibration Control of Air Spring Based Suspension Systems William Daniel Robinson Iowa State University
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Iowa State University Capstones, Theses and Graduate Theses and Dissertations Dissertations 2012 A pneumatic semi-active control methodology for vibration control of air spring based suspension systems William Daniel Robinson Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/etd Part of the Mechanical Engineering Commons Recommended Citation Robinson, William Daniel, "A pneumatic semi-active control methodology for vibration control of air spring based suspension systems" (2012). Graduate Theses and Dissertations. 12555. https://lib.dr.iastate.edu/etd/12555 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. A pneumatic semi-active control methodology for vibration control of air spring based suspension systems by William Daniel Robinson A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Mechanical Engineering Program of Study Committee: Atul G. Kelkar, Major Professor Jerald M. Vogel James E. Bernard Judy M. Vance Greg R. Luecke Brian L. Steward Iowa State University Ames, Iowa 2012 Copyright © William Daniel Robinson, 2012. All rights reserved. ii DEDICATION To my wonderful wife and life partner, Charlyn, and to our wonderful children, Bill, Greg, David, and Ann. iii TABLE OF CONTENTS DEDICATION .......................................................................................................................... ii LIST OF FIGURES ................................................................................................................. vi LIST OF TABLES ................................................................................................................... ix ABSTRACT .............................................................................................................................. x CHAPTER 1. INTRODUCTION ............................................................................................. 1 1.1 Basic Suspension Types ............................................................................................. 2 1.1.1 Passive Suspensions ............................................................................................ 2 1.1.2 Active Suspensions ............................................................................................. 4 1.1.3 Semi-active Suspension ...................................................................................... 7 1.2 Pneumatic Suspensions .............................................................................................. 9 1.2.1 Air Springs ......................................................................................................... 9 1.2.2 Air Suspensions ............................................................................................... 10 CHAPTER 2. PLANT MODEL ............................................................................................. 12 2.1 Introduction .............................................................................................................. 12 2.2 System Equations ..................................................................................................... 15 2.2.1 Nonlinear Equations.......................................................................................... 15 2.2.2 Nonlinear Simulation Equations ....................................................................... 22 2.2.3 Pressure Composition ....................................................................................... 23 2.2.4 Linearized Dynamics ........................................................................................ 25 2.3 Linear Analysis ........................................................................................................ 31 2.3.1 Boundary Conditions and System Natural Frequencies ................................... 31 iv 2.3.2 Frequency Response ......................................................................................... 38 2.4 Nonlinear Analysis ................................................................................................... 43 2.4.1 Frequency Response as a Function of Valve Opening ..................................... 43 2.4.2 Frequency Response as a Function of Amplitude............................................. 45 2.4.3 Step Response ................................................................................................... 46 2.4.4 Additional Considerations ................................................................................ 58 2.5 System Identification................................................................................................ 59 2.5.1 Static Tests ........................................................................................................ 59 2.5.2 Step Response Tests .......................................................................................... 62 CHAPTER 3. CONTROLLER DEVELOPMENT ................................................................ 74 3.1 Introduction .............................................................................................................. 74 3.1.1 Motivation for Research ................................................................................... 75 3.1.2 Approach ........................................................................................................... 76 3.2 Review of Covariance Control Fundamentals ......................................................... 77 3.2.1 Introduction ....................................................................................................... 77 3.2.2 Mathematical Preliminaries .............................................................................. 79 3.2.3 LQI Plant Model and Control Formulation ...................................................... 81 3.2.4 Disturbance Modeling ....................................................................................... 82 3.2.5 Optimal Solution ............................................................................................... 83 3.3 Semi-Active Controller Development ...................................................................... 88 3.3.1 Introduction ....................................................................................................... 88 3.3.2 Switching Logic ................................................................................................ 89 3.3.3 LQI with Semi-Active Tracking Controller ...................................................... 90 3.3.4 Modified Skyhook with Semi-Active Tracking Controller .............................. 97 v 3.3.5 Relative Position with Semi-Active Tracking Controller ................................. 99 3.3.6 Semi-active Controller Comparisons .............................................................. 101 3.3.7 General Observations on Semi-Active Control .............................................. 104 3.4 Controller Test Implementation on the Test Rig .................................................... 105 3.4.1 Introduction ..................................................................................................... 105 3.4.2 Experimental Results ...................................................................................... 105 3.4.3 Observations and Design Issues ...................................................................... 108 CHAPTER 4. CONCLUSIONS ........................................................................................... 111 4.1 Summary ................................................................................................................ 111 4.2 Primary Research Contributions ............................................................................ 114 4.3 Future Research Directions .................................................................................... 115 BIBLIOGRAPHY ................................................................................................................. 118 ACKNOWLEDGEMENTS .................................................................................................. 122 vi LIST OF FIGURES Figure 1.1 Passive system ........................................................................................................ 3 Figure 1.2 Active suspension ................................................................................................... 4 Figure 1.3 Bose active suspension ........................................................................................... 6 Figure 1.4 Bose active seat ...................................................................................................... 6 Figure 1.5 Semi-active suspension .......................................................................................... 7 Figure 1.6 Assortment of air springs........................................................................................ 9 Figure 1.7 Reversible sleeve and convoluted designs ........................................................... 10 Figure 1.8 Separate and integrated components .................................................................... 11 Figure 2.1 Open loop system schematic ...............................................................................