OPTIMAL ACTUATOR PLACEMENT AND ACTIVE STRUCTURE DESIGN FOR CONTROL OF ...

322 Pages·2002·5.5 MB·English

by  David E. Heverly

The Pennsylvania State University

The Graduate School

Department of Mechanical and Nuclear Engineering

OPTIMAL ACTUATOR PLACEMENT AND ACTIVE STRUCTURE DESIGN

FOR CONTROL OF HELICOPTER AIRFRAME VIBRATIONS

A Thesis in

Mechanical Engineering

by

David E. Heverly II

 2002 David E. Heverly II

Submitted in Partial Fulfillment
of the Requirements
for the Degree of

Doctor of Philosophy

August 2002
We approve the thesis of David E. Heverly II.

Date of Signature

Kon-Well Wang
William E. Diefenderfer Chaired Professor in
Mechanical Engineering
Thesis Co-Advisor
Co-Chair of Committee

Edward C. Smith
Associate Professor of Aerospace Engineering
Thesis Co-Advisor
Co-Chair of Committee

Farhan Gandhi
Associate Professor of Aerospace Engineering

Panagiotis Michaleris
Assistant Professor of Mechanical Engineering

Richard C. Benson
Professor and Head
Department of Mechanical and Nuclear Engineering
ABSTRACT
A comprehensive research program on active control of rotorcraft airframe
vibration is detailed in this thesis. A systematic design methodology, to realize an active
vibration control system, is proposed and studied. The methodology is a four-part design
cycle and relies heavily on numerical computation, modeling, and analysis. The various
analytical tools, models, and processes required to execute the methodology are
described. Two dynamic models of the helicopter airframe and an optimization procedure
for actuator placement are utilized within the methodology. The optimization procedure
simultaneously determines the type of actuation, the locations to apply actuation, and the
corresponding active control actions.

A feasibility study is conducted to examine the effectiveness of helicopter
vibration control by distributing actuators at optimal locations within the airframe, rather
than confining actuation to a centralized region. Results indicate that distributed actuation
is capable of greater vibration suppression and requires less control effort than a
centralized actuation configuration.

An analytical and experimental investigation is conducted on a scaled model of a
helicopter tailboom. The scaled tailboom model is used to study the actuation design and
realization issues associated with integrating dual-point actuation into a semi-monocoque
airframe structure. A piezoelectric stack actuator configuration is designed and installed
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within the tailboom model. Experimental tests indicate the stack actuator configuration is
able to produce a bending moment within the structure to suppress vibration without
causing excessive localized stress in the structure.
TABLE OF CONTENTS

LIST OF FIGURES......................................................................................................viii
LIST OF TABLES.......................................................................................................xii
ACKNOWLEDGMENTS............................................................................................xiii
Chapter 1 INTRODUCTION.......................................................................................1
1.1 Background.....................................................................................................1
1.1.1 Helicopter Vibration Sources................................................................2
1.1.2 Vibration Control Methods...................................................................4
1.1.2.1 Passive Control Methods............................................................5
1.1.2.2 Active Control Methods.............................................................7
1.2 Problem Statement and Research Objectives..................................................10
1.3 Literature Review............................................................................................13
1.3.1 Helicopter Airframe Dynamic Models.................................................14
1.3.2 Active Vibration Control of Helicopter Airframe................................15
1.3.3 Actuator Placement Methods................................................................28
1.4 Summary and Thesis Outline..........................................................................37
Chapter 2 OPTIMALLY DISTRIBUTED ACTUATION REALIZATION
METHODOLOGY................................................................................................40
2.1 Introduction.....................................................................................................40
2.2 Optimally Distributed Actuation Realization Methodology...........................41
Chapter 3 AIRFRAME MODEL, EXCITATION LOADS, AND
OPTIMIZATION PROCESS................................................................................46
3.1 Airframe Structural Dynamic Model..............................................................46
3.2 Excitation Loads.............................................................................................50
3.3 Actuation Modeling........................................................................................52
3.4 System Modeling............................................................................................57
3.5 Hybrid Active/Passive Optimization Process.................................................60
3.5.1 Active Control Law..............................................................................60
3.5.2 Simultaneous Controller Design and Actuator Placement Method......61
vi
Chapter 4 OPTIMAL ACTUATION PLACEMENT RESULTS................................67
4.1 Uncontrolled Airframe Response....................................................................67
4.2 Baseline Active Control..................................................................................70
4.3 Active Control with Optimally Placed Actuation...........................................72
4.4 Multi-objective Optimization Analysis...........................................................82
4.5 Simplified Actuator Placement Method..........................................................89
4.6 Parametric Study on Number of Actuators.....................................................91
4.7 Summary and Conclusions..............................................................................92
Chapter 5 ANALYTICAL REALIZATION OF DISTRIBUTED ACTUATION......96
5.1 Introduction.....................................................................................................96
5.2 NASTRAN Finite Element Airframe Model..................................................97
5.3 Airframe Models Response Comparison........................................................98
5.4 Distributed Actuation Analytical Realization.................................................102
5.5 Airframe Dynamic Stress................................................................................109
5.6 Summary and Conclusion...............................................................................114
Chapter 6 SCALED TAILBOOM MODEL STRUCTURE AND
EXPERIMENTAL STUDY..................................................................................116
6.1 Introduction.....................................................................................................116
6.2 Tailboom Construction and Design................................................................118
6.3 Experimental Setup.........................................................................................123
6.4 Actuation Design and Installation...................................................................124
6.4.1 Actuation Concept................................................................................124
6.4.2 Predicted Actuation Parameters............................................................125
6.4.3 Actuator Selection.................................................................................126
6.4.4 Stack Actuator Installation....................................................................132
6.5 Static Deflection Analysis...............................................................................134
6.6 Dynamic Analysis and Vibration Control.......................................................136
6.7 Summary and Conclusion...............................................................................143
Chapter 7 CONCLUSION AND FUTURE RESEARCH...........................................145
7.1 Thesis Summary and Conclusions..................................................................145
7.2 Future Research Recommendations................................................................153
BIBLIOGRAPHY........................................................................................................156
Appendix A HELICOPTER AIRFRAME MODEL AND COMPUTER SOURCE
CODES..................................................................................................................162
vii
Appendix B ADDITIONAL ACTUATION PLACEMENT RESULTS.....................210
Appendix C DISTRIBUTED ACTUATION REALIZATION ANALYSIS
RESULTS.............................................................................................................218
Appendix D SCALED TAILBOOM MODEL SPECIFICATIONS AND
ANALYSIS RESULTS.........................................................................................253
LIST OF FIGURES

Figure 1.1: Principal sources of airframe excitation. [3].............................................3
Figure 1.2: Vibration levels in forward flight..............................................................4
Figure 1.3: ACSR actuator installation on Westland 30 helicopter. [7]......................18
Figure 1.4: S-76 helicopter main gearbox supports and ACSR actuator locations
[9]..........................................................................................................................20
Figure 1.5: Sikorsky UH-60 Servo Inertial Force Generator (SIFG) [22]...................22
Figure 2.1: Optimally Distributed Actuation Realization Methodology (ODARM)...42
Figure 3.1: Apache AH-64 Reduced Order Elastic Line Model..................................49
Figure 3.2: Reduced order airframe model node numbering.......................................50
Figure 3.3: Airframe model excitations.......................................................................51
Figure 3.4: Centralized Actuation Configuration (CAC)............................................53
Figure 3.5: Force Actuation Unit (FAU).....................................................................54
Figure 3.6: Moment Actuation Unit (MAU)...............................................................54
Figure 3.7: Single-point actuation concept..................................................................55
Figure 3.8: Simulated annealing optimization algorithm............................................64
Figure 3.9: Hybrid active/passive optimization process..............................................66
Figure 4.1: Modal participation of uncontrolled response to external excitation........68
Figure 4.2: Nodes selected for vibration suppression..................................................69
Figure 4.3: Uncontrolled airframe response to hub and tail excitation.......................69
ix
Figure 4.4: Uncontrolled vibration at target nodes......................................................70
Figure 4.5: CAC controlled airframe response to hub and tail excitation...................71
Figure 4.6: CAC controlled vibration at target nodes..................................................71
Figure 4.7: DAUC controlled airframe response to hub and tail excitation................73
Figure 4.8: DAUC controlled vibration at target nodes...............................................73
Figure 4.9: Optimized DAUC emphasizing vibration reduction.................................76
Figure 4.10: Optimized DAUC emphasizing control effort reduction........................76
Figure 4.11: Optimized DAUC emphasizing both control effort and vibration
reduction................................................................................................................76
Figure 4.12: Vibration reduction of multi-objective optimized DAUC......................88
Figure 4.13: Control effort reduction of multi-objective optimized DAUC...............88
Figure 4.14: Evaluation indices for various actuation configurations.........................91
Figure 4.15: Optimization objective function and vibration index versus number
of Actuation Units.................................................................................................92
Figure 4.16: Evaluation indices of CAC and 4 optimally distributed Actuation
Unit configuration.................................................................................................92
Figure 5.1: Apache helicopter NASTRAN Finite Element model..............................98
Figure 5.2: Reduced Order Model, uncontrolled vibration response to hub and tail
excitation...............................................................................................................100
Figure 5.3: NASTRAN model, uncontrolled vibration response to hub and tail
excitation...............................................................................................................100
Figure 5.4: Reduced Order Model: Uncontrolled vibration at target nodes................101
Figure 5.5: NASTRAN model: Uncontrolled vibration at target nodes......................101
Figure 5.6: Dual-point actuation concept applied to semi-monocoque structure........103
Figure 5.7: Reduced Order Model: Centralized actuation, Controlled vibration at
target nodes...........................................................................................................105
x
Figure 5.8: NASTRAN model: Centralized actuation, Controlled vibration at
target nodes...........................................................................................................105
Figure 5.9: Reduced Order Model: Distributed actuation, Controlled vibration at
target nodes...........................................................................................................105
Figure 5.10: NASTRAN model: Distributed actuation, Controlled vibration at
target nodes...........................................................................................................105
Figure 5.11: Reduced Order Model: Comparison of performance indices..................106
Figure 5.12: NASTRAN Model: Comparison of performance indices.......................106
Figure 5.13: NASTRAN Model: Comparison of performance indices, re-
optimized locations...............................................................................................108
Figure 5.14: Finite Element dynamic stress from hub and tail excitation
(uncontrolled)........................................................................................................109
Figure 5.15: Finite Element dynamic stress, Centralized control of hub and tail
excitation...............................................................................................................110
Figure 5.16: Change of element stress from uncontrolled to centralized control........111
Figure 5.17: Finite Element dynamic stress, Distributed control of hub and tail
excitation...............................................................................................................111
Figure 5.18: Change of element stress from uncontrolled to distributed control........112
Figure 5.19: Dynamic stress levels for distributed control of hub and tail
excitation...............................................................................................................113
Figure 6.1: Tailboom model, 0.3 scale semi-monocoque structure.............................118
Figure 6.2: Scaled tailboom Beam Equivalent Model (BEM).....................................120
Figure 6.3: Cantilevered ROM and BEM mode shape comparison............................121
Figure 6.4: Scaled tailboom Finite Element Model (FEM).........................................123
Figure 6.5: Tailboom model and experimental setup..................................................123
Figure 6.6: APC Pst 150/14/100 piezoelectric stack actuator.....................................126
Figure 6.7: Piezoelectric stack element.......................................................................127
Figure 6.8: Stack actuator force and displacement relation.........................................130