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Frequency Domain Active Noise Control with Ultrasonic Tracking Thomas Chapin Waite Iowa State University Iowa State University Capstones, Theses and Graduate Theses and Dissertations Dissertations 2010 Frequency Domain Active Noise Control with Ultrasonic Tracking Thomas Chapin Waite Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/etd Part of the Mechanical Engineering Commons Recommended Citation Waite, Thomas Chapin, "Frequency Domain Active Noise Control with Ultrasonic Tracking" (2010). Graduate Theses and Dissertations. 11782. https://lib.dr.iastate.edu/etd/11782 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]. Frequency domain active noise control with ultrasonic tracking by Tom Waite 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 Julie A. Dickerson J. Adin Mann III Jerald M. Vogel Qingze Zou Iowa State University Ames, Iowa 2010 Copyright c Tom Waite, 2010. All rights reserved. ii TABLE OF CONTENTS LIST OF FIGURES . v ACKNOWLEDGEMENTS . xi ABSTRACT . xii CHAPTER 1. INTRODUCTION . 1 1.1 Background . 1 1.1.1 Frequency Domain ANC . 5 1.1.2 Ultrasonic Tracking . 7 1.2 Outline . 8 CHAPTER 2. ULTRASONIC TRACKING . 11 2.1 Introduction . 11 2.2 Localization . 11 2.2.1 Bandwidth Considerations . 16 2.3 Error . 18 2.3.1 Sources of Incorrect Solutions . 19 2.3.2 Sources of Error . 20 2.3.3 Error w.r.t. Microphone Position . 24 2.4 Experimental Results . 27 2.5 Remarks . 32 CHAPTER 3. NON-MINIMUM PHASE DECOMPOSITION AND SYSTEM IDENTIFICATION . 33 iii 3.1 Introduction . 33 3.2 The Time Delay Problem . 33 3.3 Non-minimum Phase System Decomposition . 38 3.4 System Identification . 40 3.4.1 Obtaining the Frequency Response . 41 3.4.2 Experimental Results . 44 3.5 Remarks . 50 CHAPTER 4. TIME ADVANCING WITH THE STFT . 52 4.1 Introduction . 52 4.2 Controller as Time Advance Filter . 52 4.3 Signal Deconstruction and Reconstruction . 54 4.4 STFT Time Advancement . 59 4.5 STFT Filter Performance . 61 4.6 Remarks . 66 CHAPTER 5. TIME ADVANCING WITH THE PHASE VOCODER 67 5.1 Introduction . 67 5.2 The Phase Vocoder . 67 5.2.1 PV Frequency Estimation . 68 5.2.2 Performance . 70 5.3 PV Time Advance Filter . 73 5.3.1 Performance . 75 5.3.2 Error . 80 5.4 Remarks . 85 CHAPTER 6. INTERNAL MODEL CONTROL . 86 6.1 Introduction . 86 6.2 Feedback Active Noise Control . 86 iv 6.3 Internal Model Control . 89 6.3.1 Periodic Signal Selector . 91 6.3.2 Stability . 96 6.4 Experimental Results . 104 6.5 Remarks . 120 CHAPTER 7. CONCLUSION AND FUTURE WORK . 121 7.1 Conclusion . 121 7.2 Future Work . 123 BIBLIOGRAPHY . 127 v LIST OF FIGURES Figure 1.1 Active noise control performance review under various conditions. 3 Figure 1.2 Diagram showing interaction of tracking system and controller. 4 Figure 1.3 Tractor cab example. 5 Figure 1.4 Comparison chart of positioning systems. 8 Figure 2.1 Each speaker to microphone acoustic delay appears as a peak on the cross-correlation plot. 13 Figure 2.2 Speaker to microphone distances can be extracted from the slope of the cross-spectrums. 14 Figure 2.3 Ultrasonic localization of a target within a 3D environment. 15 Figure 2.4 Effect of bandwidth on the cross-correlation. 17 Figure 2.5 Time separated pulses can each utilize the entire available band- width. 17 Figure 2.6 Intersecting additive error margins are shown at various distances to illustrate potential microphone positions. 23 Figure 2.7 Multiplicative error gets worse with distance. 23 Figure 2.8 Blown up view of error margins intersecting to form a region of possible microphone locations. 24 Figure 2.9 Maximum error as a function of microphone position in a 2D environment. Speakers located at (0,0) and (1,0). 26 Figure 2.10 Block diagram of 3D ultrasonic tracking system. 28 vi Figure 2.11 Ultrasonic speaker array and microphone to be tracked. 29 Figure 2.12 Tracking a microphone as it follows a circular trajectory results in ±0.5 cm error. 30 Figure 2.13 Tracking a distant circular path results in ±1 cm error. 30 Figure 2.14 Measured position captures microphone movement behind an ob- struction by detecting diffracted acoustic waves. 31 Figure 3.1 Collocated, minimum phase systems show phase responses which are much easier to control than their non-collocated counterpart. 35 Figure 3.2 A 3D acoustic system model separated into its minimum phase part and its time delay (modeled using an all-pass filter approx- imation). As is often the case, more poles and zeros are needed to represent the time delay than the acoustic dynamics. 36 Figure 3.3 Root locus showing instability results with very little controller gain due to the RHP zeros pulling the poles into the RHP. The RHP zeros are a byproduct of the time delay. 37 Figure 3.4 Block diagram for viewing real-time acoustic frequency response data. 43 Figure 3.5 Enclosure made to mimic a large tractor cab with the controller workstation in the foreground. 45 Figure 3.6 Interior of the enclosure showing the control speaker and micro- phone. 45 Figure 3.7 The frequency response of the tractor cab is extremely complex with large phase lag. 48 Figure 3.8 The 80 state model of the enclosure frequency response has an average magnitude error of only 0.217 dB and an average phase error of only 1.79 ◦ from 30-800 Hz. 49 vii Figure 3.9 The model of the minimum-phase acoustic system shows no right half plane zeros and has an equal number of poles and zeros so it is stably invertible. 50 Figure 4.1 Block diagram of closed loop feedback system showing decom- posed plant, controller H(s), and time advance filter etds. 54 Figure 4.2 Illustration of the overlap-add reconstruction of a signal which has been deconstructed into several windowed segments. 55 Figure 4.3 Progression illustrating a window's maximum hop size parameter as well as its role in signal scaling. 57 Figure 4.4 Comparison of window parameters important to signal recon- struction. 58 Figure 4.5 Multiplication with ej!td linearly increases phase without chang- ing magnitude. 59 Figure 4.6 STFT time advancement block diagram with example signal to illustrate each step. 60 Figure 4.7 The STFT filter perfectly reconstructs a time advanced 32 Hz sine wave. 61 Figure 4.8 The STFT filter incorrectly reconstructs a time advanced 34 Hz sine wave. 62 Figure 4.9 Increasing the buffer time increases the number of accurately time advanced frequencies. No matter how large the buffer, though, there will always be large error in the spaces between center fre- quency bins of the FFT. 65 Figure 5.1 Comparing successive phases yields a different frequency estimate for each n (see Eq. 5.1). 69 viii Figure 5.2 With a short preview window, STFT frequency estimation is coarse while the phase vocoder is able to follow the chirp to within 0.1 Hz. 71 Figure 5.3 Frequency estimation vs preview time (window size) using the STFT and PV methods. 72 Figure 5.4 Block diagram of time advance filter using phase vocoder. 75 Figure 5.5 Time advance filter with the phase vocoder accurately reproduces previously inaccurate 34 Hz tone. 76 Figure 5.6 Multi-tone PV filter error in time domain. Signal is analyzed in first portion and canceled in second. 78 Figure 5.7 Multi-tone PV filter error in frequency domain shows accuracy at tones but no where else. Magnitude plot also shows input and output of filter. 79 Figure 5.8 PV time advance filter error versus tonal separation for several window sizes. 81 Figure 5.9 PV time advance filter error versus chirp speed for several window sizes. 82 Figure 5.10 PV time advance filter error versus tonal separation for each win- dow type. 84 Figure 5.11 PV time advance filter error versus chirp speed for each window type. 84 Figure 6.1 Feedback control block diagram. 87 Figure 6.2 Standard feedback configuration yields oscillation.
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