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THE INTEGRATION OF ADVANCED ACTIVE AND PASSIVE STRUCTURAL NOISE CONTROL METHODS

A.J. Keane, S.J. Elliott, M.J. Brennan and E. Rogers

Computational Engineering & Design Centre, Faculty of Engineering and Applied Science, University of Southampton, Highfield, Southampton, SO17 1BJ, U.K.

RESEARCH TEAM

This work will be supervised by Prof. A.J. Keane who has considerable expertise in the field of structural dynamics having worked on Statistical Energy Analysis methods for many years[1]. He has also worked on optimization since completing his M.Sc. in this field and has studied design related problems for nearly 20 years. This has included further studies in the concept design of warships[2], the use of modern stochastic design methods in structural design[3], as well as studies of the fundamentals under-pinning these methods[4]. As a result of this work a large package of software[5] has been developed and is now in use with a number of UK companies. Work in this area has been funded by organizations as diverse as the Defence Research Agency, Cable and Wireless, Glaxo Wellcome, British Aerospace and the EPSRC (grants GR/J06856 for £117k and GR/L04733 for £215k). Based on this experience, model satellite booms have been designed using SEA and design optimization methods and then built and tested, showing the same dramatically improved vibration isolation predicted by theory to be present in practice. The present project therefore represents a logical extension to this work drawing on the expertise of other staff at Southampton University. The work will take place in the Computational Engineering and Design Centre (CEDC) at Southampton, which is a faculty-wide activity, and the facilities of the Signal Processing and Control Group of the Institute of Sound and Vibration Research. The CEDC, which Prof. Keane directs, is dedicated to investigating the uses of high performance computing (HPC) in engineering and has access to several HPC facilities that have been recently installed at Southampton. Other projects within the centre are focusing on CFD, FE, control theory and related areas and will be able to give significant support to the project. The Signal Processing and Control Group houses experimental facilities dedicated to the study of active noise control systems and is led by Prof. S.J. Elliott. Other projects within the group deal with the active control of vibration transmission in helicopter struts, funded by the EC in collaboration with Westland Helicopters, the use of distributed sensors and actuators for active vibration control of structures and the active control of sound radiation funded by the DTI, and the control algorithms and actuator technologies required for active mounts, funded by the EC and DRA Farnborough. Recent work on adaptive controllers is being funded by EPSRC (grants GR/K11857 for £104k and GR/L62979 for £161k). The experimental aspects of the study will be carried out under the supervision of Prof. S. J. Elliott and Dr. M. J. Brennan. Prof. Elliott's main research interests lie in the interaction between physical systems and the signal processing or control methods used to analyse or control them[6]. Of particular interest is the active control of sound and vibration, and research in this area has resulted in full-scale demonstrations of active control systems on aircraft, cars and helicopters[7]. This has involved the real-time implementation of various adaptive control algorithms, as well as an analytic evaluation of their potential performance at the error sensors and of the effect this will have at other points on the distributed system under control[8]. Dr. Brennan has extensive experience of the practical implementation and testing of active vibration control systems. He has been particularly involved in the design and evaluation of novel sensors and actuators for active control systems in pipes, plates and struts using both piezoelectric and magnetostrictive technology[9, 10]. Assistance on the theoretical active control aspects of this project be provided by Dr E. Rogers. Dr. Rogers is Reader in Control Systems and a member of the ISIS group in the Department of Electronics and Computer Science. His major research interests lie in the general area of control systems theory and design[11, 12]. He is the author/co-author of 3 research monographs and more than 120 refereed papers, the editor of the International Journal of Control, and joint editor of the Taylor and Francis research book series in Systems and Control.

COLLABORATORS

The project will take place in collaboration with staff from various divisions of Matra Marconi Space plc. Matra Marconi Space (MMS) is a joint venture company 51% owned by Matra Hachette of France and 49% owned by GEC of the United Kingdom. MMS combines the complementary expertise of three former companies, each having over 25 years of experience on major space programmes: (1) Matra Espace, now MMS-France, (2) Marconi Space Systems, MMS-UK since 1991 (3) British Aerospace Space Systems Ltd., part of MMS-UK since 1994 Matra Marconi Space is a major international space company and is Europe's largest satellite manufacturer. Since the early 1960's the company has been a major contributor to missions aimed at furthering Man's knowledge and understanding of the Earth, the Solar System and the Universe. The companies spacecraft engineering achievements span more than 50 national, European, and international projects and has contributed significantly to the activities of agencies such as ESA, NASA, CNES and EUMETSAT. MMS operates as a number of directorates each specialising in a particular aspect of the space business. The project will take place in collaboration with staff from the Directorate of Science and Radar (DSR) at Bristol and Portsmouth. The work will also involve consultation with staff from the equivalent directorate in MMS- France. MMS staff will supply data on the structural requirements for the systems being studied as well as typical noise levels and spectra and other launch and flight data. They will attend progress meetings and evaluate the work being carried out and the software being developed.

BACKGROUND

Introduction

Vibration and noise control problems arise in many engineering projects. These problems are most severe when light weight structures, such as those found in the automobile and aerospace sectors, are used. Perhaps the most challenging vibration control issues arise in the design of space missions that involve satellites with highly sensitive instrumentation packages. To function correctly these packages must be supported on structures where the vibration levels have been reduced to extremely low levels (micro vibrations). This need becomes most severe when the instruments concerned form the individual sensors of a multi sensor interferometric telescope or synthetic aperture radar. In such cases there is a need to support instruments spaced tens of metres apart using structural booms, with the relative motions between their ends being restricted to microns over wide ranges of excitation frequency[13]. A number of design approaches have been proposed to try to meet these demanding requirements but it is still not clear how best to proceed in this field[14]. The current project is concerned with the development of a vibration control system for use where there are demanding noise and vibration control targets. It is based on a novel design approach combining several existing methods which it is believed will provide a real breakthrough for problems of this class. Essentially, the idea is to combine active vibration control using robust control techniques, drawn from the work of the Control community, together with booms geometrically optimized for passive vibration isolation, based on methods developed by the Structural Dynamics community; the whole being designed using evolutionary algorithms, coming from the Computer Science community. This process will be carried out so as to allow for the dynamics of the active system when carrying out the passive isolation optimization. The combined evolutionary design process will be carried out off-line to locate sensors & actuators and to define the geometric configuration needed for passive noise rejection. Following construction of the system, the models used during the design phase will then form the basis for the H2/Hinf (or related) on-line robust active control system. Of course, mixed active/passive noise control is not a new idea[15] nor is the use of evolutionary methods in control system design[16]. We believe, however, that there are a number of new ideas in this project. First, we do not know of any other work mixing all three of these ideas together in one system. Secondly, the kind of passive vibration control to be used is based on reflecting rather than absorbing energy; this is an idea that is very much in its infancy and one that was originally proposed by those supervising this research. Thirdly, we aim to use the two different noise control methods over different, but adjacent, ranges of the frequency spectrum. Lastly, we intend to build a working prototype system whereas almost all previous work in this area has been essentially computational in nature. The project is thus highly inter-disciplinary in nature and much of its novelty stems from its drawing on the results of three separate research communities to design and build a complex but practical, integrated engineering system. Active noise control methods are now well established but their high frequency capabilities are fundamentally limited by the signal processing, actuator and sensor requirements of such systems[17]. Passive methods using geometric optimization are less widely used but, with increasing computational power, they are of growing interest and, moreover, are directly applicable to frequencies above those amenable to active control[18]. (Work in both these areas has recently been funded by the EPSRC and this project seeks to build on and exploit the successes of that work.) The combination of these methods should allow a wide spectrum of noise control problems to be dealt with without the weight and bulk penalties associated with traditional added damping approaches for problems of this kind. It is, of course, difficult to make exact predictions of the likely vibration reductions that such an approach will give. However, earlier work on model scales suggest that 10-20dB reduction in vibrational energy transmission should be expected over a 200 Hz bandwidth on a structure some 3- 5m long. Although the investigation described in this project is based on satellite structures, progress in the general area of integrated active / passive vibration control will be of major benefit in all those fields where reduced noise transmission is important, such as in aircraft and car design. Work in this area is also in keeping with UK and EU goals in terms of improving quality of life and reducing pollution (lighter vehicles consume less fuel and pollute less). A vibration isolation capability of this type will therefore be of very great benefit to the UK car, aerospace and marine construction industries where lighter-weight and cheaper designs could be produced with improved noise performance, leading to increased prospects for sales.

Scientific/Technological Relevance

Structure borne noise and vibration control is an aspect of design where there are few design synthesis techniques available and one that is relevant to almost all lightweight engineering structures. This is an area where many traditional techniques have been tried with relatively little success. Moreover, structures such as satellites, cars, aeroplanes, ships, etc., all suffer from exposure to noise and vibration sources. These sources often excite unwanted structural vibrations which can cause damage or the transport of vibrational energy to distant parts of the structure where they cannot be tolerated. For example, the reaction wheels and cryogenic coolers in satellites always vibrate to some degree and, despite isolation treatments, excite motions of their mounting points. Since most space structures have inherently low damping characteristics such motions may well be relatively large. This vibrational energy can then flow through the structure and cause significant motions of the mountings points of sensitive instruments. These in turn fail to meet their design specifications resulting in failure or reduced value of the mission. The most common treatment for such problems is to use anti- vibration mountings or to coat the structural elements with heavy viscoelastic damping materials with consequent weight and cost penalties. Moreover, the effectiveness of such treatments diminishes with the vibration levels which makes continuously improving noise and vibration targets difficult to meet. Clearly, if the vibrational energy could be contained near to the points of excitation there would be a reduced need for damping treatments and, additionally, they could be concentrated in regions where they were most effective. This is precisely the aim of the vibration isolators used between most pieces of equipment and their supporting structure. However, such isolators cannot deliver the desired behaviour in all situations, particularly for sensitive equipment. The upshot of this problem is the need for some kind of widely applicable, generic structural filter design capability that can be used to build desirable characteristics into a structure, retaining its ability to carry static loads while blocking higher frequency motions. To gain maximum benefit from the available technologies such a capability would ideally be based on a integrated active / passive approach, with these two techniques being used in tandem and together tackling the widest possible range of excitation frequencies. Analysis of the vibrational energy flows around complex structures is dominated by the many resonances exhibited by such structures and also the large number of physical parameters needed to specify typical structural designs (many thousands in a full satellite structural model). Moreover, experience shows that even the most detailed finite element models do not accurately predict the behaviour of real structures over wide frequency ranges (because of the inevitable differences between the structure modelled and that actually built). This means that the approaches used when choosing design configurations must be robust enough to tolerate such mis-matches. That to be used for the passive optimization aspect of the work is based on statistical energy analysis models combined with genetic algorithm optimization methods. This is an approach that has already been shown to work in purely passive approaches to noise isolation[19]. In this approach, prediction is aimed at the frequency and space averaged energy levels of the structure at one end for given excitation levels at the other. The method does not, however, work effectively at very low frequencies because the method relies on the wavelengths of the vibrations being controlled being of a similar order to the changes introduced in the geometry of the structure. Fortunately, this is a range of frequencies ideally suited to active vibration control and this is why a mixed active / passive approach is thought to be so potentially beneficial. Active control holds great promise for the reduction of vibration caused by the relatively low order modes of a structure because the volume and mass required for conventional passive vibration control of these modes would be very high. Moreover, robust active control has been the subject of enormous research effort over the last 10-15 years, the result of which has been the in-depth development of a range of controller analysis / design methods based on a nominal linear model approximation to the system dynamics, e.g., Hinf, mixed H2/Hinf and loop transfer recovery approaches[20]. These (and other approaches) are now very mature areas in systems theory terms and increasing effort is now being directed towards applications. This work is supported by the widespread availability of Matlab compatible software with the onward ability to generate executable C code for software based implementation of the resulting controller(s). Such control schemes require a feedback strategy whose stability and performance are relatively insensitive to typical changes in the response of the structure and vibration environment. Various actuators and sensors have been designed for this application, including piezoceramic stack actuators[9], reaction-mass actuators[21], active struts[13] as actuators and accelerometers, strain gauges and rate gyros as sensors. The design of the feedback control loops which connect these actuators and sensors requires a knowledge of the dynamics of the structure to provide effective active control. Ideally the gain of these feedback loops would be large, to provide high attenuation of vibration disturbances, but the stability of these loops is then very sensitive to small changes in the response of the structure. These may be caused by geometric distortion, heating or, in space missions, the change from 1g conditions on the ground to 0g in space[22]. To ensure that the stability of the controller is robust to these changes, a good model of the uncertainty in the structural response is required, in addition to a good model of the structural response itself. Fortunately, the models needed for the higher frequency, passive aspects of the study can be directly applied at lower frequencies where they give very high resolution results. Nonetheless, given the inherent modelling uncertainties that arise when working in this field it is considered essential that modest `proof of concept' experiments be performed, based on the theoretical designs produced. This will involve the construction of an initial base-line structure which, for a satellite boom, will be of the order of 3-5m long and have, for example, 10 identical bays. The response of this structure will be measured when suspended in the laboratory, both at low frequencies, to characterise the lower modes which are to be actively controlled, and at high frequencies, to characterise the vibration transmission characteristics which will be modified by structural changes. Initial active control experiments will also be conducted on this base-line design. The construction of the optimised structures will require more complicated fabrication facilities to ensure that they accurately match the required designs. It is anticipated that these optimised structures will be built on a similar scale and with a similar number of bays to the base-line configuration. The results of the low and high frequency structural response tests will then be directly comparable between the base-line and optimised structures, so that the improvement in the low frequency control performance and high frequency vibration transmission can be established directly. Clearly, the use of combined active / passive approaches will bring its own difficulties and it is considered essential that the two methods are not considered in isolation. Instead a sophisticated computational model of the satellite structure with its active control system will be built and genetic algorithm optimization methods applied to the complete system. The optimizer would try to minimize the frequency averaged vibration transmission across the whole spectrum of noise frequencies while the control system of the active part of the design would strive to deal with just the low frequency components. Variations in the locations of both sensors and actuators will form a key part of the design process and would be controlled by the GA at the same time as it adjusted the structural geometry. Thus the final design will inherently allow for aspects of both the passive and active components of the system. Although computationally expensive, such an approach is within the capabilities of the large scale clustered / parallel computing facilities available to the CEDC at Southampton University. This, combined with the University's 5 and 5* class expertise in all the technologies necessary for the study, makes Southampton an ideal location for work of this kind.

PROGRAMME AND METHODOLOGY

To investigate an inter-disciplinary approach to vibration control and to assess the capabilities of active / passive systems designed following these ideas will require a mixed theoretical, computational and experimental approach. Thus, the programme will start with the design and construction of a base-line model structure (an interferometer constructed to large model scale: typically around 10% of full size) in close collaboration with MMS. Then, while this is being built and tested, attention will move to the design of geometrically optimized versions of the structure. This process will also incorporate selection of suitable methods for implementing control strategies in this field and also for analysing such structures by the most efficient means, given the particular needs of active control systems design. Having fixed on the appropriate methods a custom built computational model will be built and coupled to the existing OPTIONS[5] design exploration system. This system will allow selection and tuning of the most appropriate variant of genetic algorithm for the work in hand. The OPTIONS codes will then allow parallel implementation of the models on the high performance computing platforms available to the group. Having carried out a series of design studies and traded off noise isolation characteristics against the other requirements of the design such as manufacturability, deployability, weight, strength, etc., an example passively optimized structure will be built for test. Following this, an integrated active / passive design will be produced and built. These structures, together with practical implementations of the control systems, will then be evaluated experimentally so as to provide `proof of concept' for the approach to be followed. They will clearly demonstrate what gains can be achieved solely by active and also by simply passive means and what by a combined active / passive approach. At the same time, further wholly computational studies will investigate the utility of the approach for the related structural configuration of a synthetic aperture radar (SAR), again in collaboration with MMS. This list of activities is addressed by the following programme which will be carried out mainly by the research assistant and research student appointed to the project (see also the attached project plan) :-

Months Research Programme Stages

1-4 Familiarization with literature (and WWW) by appointed researcher (RA). Establish working relationships between the RA and staff at MMS (W100). Establish sensible overall design parameters for an interferometer structural boom in keeping with the proposed Darwin mission in collaboration with MMS (W200). 3-7 Produce design specification for the base-line boom and have this built in the University's workshops (W300). Interface the computational model of the passive only structure to the OPTIONS design exploration suite and carry out trial design runs with various search engines (W400). Produce six monthly report (W500). 8-11 Commission experimental facilities (transducers, shakers, active elements, etc.) using the base-line structure and measure its passive performance over a variety of input conditions to provide validation data for the structural model (W600). 12 Prepare annual report and conference paper and present intermediate results to design staff within the collaborating company (W700). 13-15 Use available high performance computing systems to produce suitable optimized boom designs making use of experimental data from the base-line structure. Develop practical designs in conjunction with MMS staff (W800). 16-18 Prepare detail specifications for passive only optimized structural design and have this built in the University's workshops (W900). Establish sensible overall design parameters for synthetic aperture radar (SAR) structure in collaboration with MMS (W1000). Construct customized computational model of the structural dynamics and potential active control system (W1100). Produce six monthly report (W1200). 19-21 Carry out initial tests on passive only optimized structural design in purely passive mode and compare with computational model (W1300). Have active control system prototyped by University technician staff in accordance with the design work already carried out (W1400). 22-24 Commission active control system using base-line structure (W1500). Prepare annual report and journal paper and present intermediate results to staff within the collaborating company (W1600). 25-30 Use available high performance computing systems to produce integrated active / passive optimized boom designs using modified code. Develop practical designs in conjunction with MMS staff (W1700). Design base-line and optimized SAR in collaboration with staff from MMS (W1800). Carry out full tests on the passive only optimized boom but with active control. Compare results with those for base-line structure (W1900). Produce six monthly report (W2000). 31-35 Prepare detail specifications for integrated active / passive optimized structural design and have this built in the University's workshops (W2100). Carry out full tests on the integrated active / passive boom. Compare results with those for base-line and passive only structure (W2200). Refine computational models to establish maximum likely noise isolation figure that might be achieved using this approach for both interferometer and SAR booms, in the light of the experimental studies (W2300). 36 Prepare final report, journal papers and electronic digests describing the work. Brief collaborating company on further development of the ideas explored during the programme (W2400).

RELEVANCE TO BENEFICIARIES

The work planned here is primarily aimed at future aerospace structures which are vibration critical. However, the use of integrated active / passive techniques of this kind has applications over a wide range of other fields. It is a common need of modern vehicle designers, whether they are working on satellites, aircraft, trains, cars or ships, to reduce noise and vibration levels. These reductions are necessary to meet increasingly severe noise pollution and habitability legislation as well as to improve customer satisfaction, and thus market share, for the products concerned. The principal beneficiaries of this research will be organizations working in the aerospace sector such as the collaborating company, Matra Marconi Space, but also including British Aerospace and Westland Helicopters who both produce light weight structures with vibration sensitive payloads or where there are very severe vibration noise sources (and who the investigators are also collaborating with on other, related projects). More indirectly, the UK car and truck industry will also benefit from advances in structural noise control techniques. Matra Marconi Space (MMS) consider progress in this field to be critical to the success of a number of satellite proposals currently under active consideration. Consequently, they have indicated their willingness to contribute £40k in cash, £25k in staff effort and £5k in kind to a three year programme of work. Since MMS have particular interests in the ESA Horizon 2000+ Darwin mission this will be the main domain in which the project will be set. The major deliverables of the project being (1) to provide designers at MMS with access to methods that will enable the home aerospace sector to enhance its competitiveness over manufacturers outside the UK and (2) to demonstrate to aerospace and other designers how such active / passive vibration control methods could be integrated into the design process.

DISSEMINATION AND EXPLOITATION

The results of this work will be fed directly back into MMS by the active collaboration of their staff during the project. It is intended that the work be based on realistic design studies and that the new methods developed be assessed by MMS design staff. This will be achieved by the close involvement of MMS staff during the design and practical elements of the work. Such exercises will be backed up by seminars and extended technology transfer sessions carried out by the research staff of the project for the benefit of practising design staff. It must be stressed, however, that MMS are extremely keen to see the results of this work published in the open literature and they will only seek to delay those publications which contain valuable IPR and then only until such time as satisfactory protection has been obtained. It is therefore planned that the research staff involved attend and give presentations at the AIAA Smart Structures conference in St. Loius, MO., USA, April 1999 and also at the International Conference on Genetic Algorithms in the USA in the spring of 2001. It also the normal practice of those involved to publish journal papers describing their research at regular intervals and to make their work available on the world wide web. Southampton University also has an active technology transfer and IPR exploitation programme managed by its Office of Innovation and Research Support. They will be closely involved in developing any IPR arising from the programme.

RESEARCH STAFF

This work will be supervised by Prof. A.J. Keane acting as P.I. in collaboration with Prof. S.J. Elliott and Drs. M.J. Brennan and E. Rogers. as co-investigators, assisted by a full-time post-doctoral research assistant, preferably with some skills in the areas of structural dynamics, control systems design, optimization or experimentation together with a research student working on related topics. The main role of the P.I. will be to give strategic guidance on the direction of the work, to supervise liaison with the industrial collaborators and to provide input based on previous experience of using evolutionary optimizers in a passive noise control context. Prof. Elliott and Dr. Brennan will lead on the experimental side of the study while Dr. Rogers will provide input on active control theory. The R.A. will carry out the required code development, design work, experimentation and interaction with MMS staff. The student will, of course, be primarily focused on completing a PhD thesis, but this activity will provide background support to the main project and forms an important aspect of the project, particularly given the broad spectrum of activities encompassed. At this stage the most promising avenue of related research suitable for the student appears to be in the field of structural modelling techniques for control systems design[23] although, as always with PhD studies, it is difficult to predict the precise nature of the work to be covered. The association with the main project will, of course, provide a very good platform for such research.

REFERENCES

1. A. J. Keane and W. G. Price, ``Statistical Energy Analysis of Periodic Structures,'' Proc. R. Soc. Lond. (ISSN 0962-8444) A423 pp. 331-360 (1989). 2. A. J. Keane, W. G. Price, and R. D. Schachter, ``Optimization Techniques in Ship Concept Design,'' Trans. R.I.N.A. 132(A)(1990). 3. A. J. Keane, ``Experiences with optimizers in structural design,'' pp. 14-27 in Proceedings of the Conference on Adaptive Computing in Engineering Design and Control 94, ed. I. C. Parmee,P.E.D.C., Plymouth (1994). 4. A. J. Keane, ``Genetic algorithm optimization of multi-peak problems: studies in convergence and robustness,'' Artificial Intelligence in Engineering 9(2) pp. 75-83 (1995). 5. A. J. Keane, The OPTIONS Design Exploration System User Guide and Reference Manual, http://www.soton.ac.uk/ ~ajk/options.ps (1994). 6. S.J. Elliott, ``Active Control of Structure Borne Sound (Tyndall Medal lecture),'' J. Sound Vib. 177(5) pp. 651-673 (1994). 7. S.J. Elliott and L. Billet, ``Adaptive control of flexural waves propagating in a beam,'' J. Sound Vib. 163 pp. 293-310 (1993). 8. P. Gardonio and S.J. Elliott, ``Active control of waves in a one-dimensional structure with a scattering termination,'' J. Sound Vib. 192 pp. 701-730 (1996). 9. M.J. Brennan, M.J. Day, S.J. Elliott, and R.J. Pinnington, ``Piezoelectric actuators and sensors,'' pp. 263-274 in Proceedings of the IUTAM Symposium on the Active Control of Vibration, (1994). 10. M.J. Brennan, S.J. Elliott, and R.J. Pinnington, ``Strategies for the active control of flexural vibration on a beam,'' J. Sound Vib. 186 pp. 657-688 (1995). 11. N. Amann, D. H. Owens, E. Rogers, and A. Whal, ``An Hinf Approach to Linear Iterative Learning Control design,'' International Journal of adaptive Control and Signal Processing Vol 10(6) pp. 767-781 (1996). 12. E. Rogers, K. Galkowski, and D. H. Owens, ``Control Theory and Applications for Systems with Repetitive Dynamics,'' in Springer Verlag Lecture Notes in Control and Information Sciences Series, (1997). 13. S.W. Sirlin and R.A. Laskin, ``Sizing of active piezoelectric struts for vibration suppression on a space-based interferometer,'' pp. 47-63 in Proceedings of the 1st US / Japan Conference on Adaptive Structures, (1990). 14. J. W. Melody et al, ``Integrated modelling methodology validation using the micro-precision interferometer testbed,'' in Proceedings of the IEEE CDC conference, , Kobe (1996). 15. P. G. Maghami, S. M. Joshi, and E. S. Armstrong, ``An Optimization-Based Integrated Controls-Structures Design Methodology for Flexible Space Structure,'' NASA Report L-17080, NASA Langley Research Center (1993). 16. A. J. Chipperfield and P. J. Fleming, ``Genetic algorithms in control systems engineering,'' Control and Computers 23 pp. 88-94 (1996). 17. G.M. Zhu and R.E. Skelton, ``Integrated modeling and control for the large spacecraft control laboratory experiment facility,'' J. Guidance Control and Dynamics 17(3) pp. 442-450 (1994). 18. A. J. Keane, ``Passive vibration control via unusual geometries: the application of genetic algorithm optimization to structural design,'' J. Sound Vib. 185(3) pp. 441-453 (1995). 19. A. J. Keane and A. P. Bright, ``Passive vibration control via unusual geometries: experiments on model aerospace structures,'' J. Sound Vib. 190(4) pp. 713-719 (1996). 20. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, Prentice Hall (1996). 21. A. Bosse, S. Fisher, S. Shelly, and T. Lim, ``On the feasibility of adaptive vibration control of a space truss using modal filters and a neural network,'' in SPIE Symposium on Smart Structures and Materials, (1996). 22. D. W. Miller, E.F. Crawley, J.P. How, K. Liu, M.E. Campbell, S.C.O. Grocott, R.M. Glaese, and T.D. Tuttle, ``The mid-deck active control experiment (MACE): Summary,'' 7-96, MIT Space Engineering Research Centre (1996). 23. G. S. Aglietti, S. B. Gabriel, R. S. Langley, and E. Rogers, ``A modelling technique for active control design studies with application to spacecraft microvibrations,'' J. Acoust. Soc. Am. 102(4) pp. 2158-2166 (1997).

This article may be found at http://www.soton.ac.uk/~ajk/mms_fps.html


Correspondence to Andy.Keane@soton.ac.uk, or Prof. A.J. Keane, Department of Mechanical Engineering, University of Southampton, Highfield, Southampton, SO17 1BJ, U.K.
Tel +44-1703-592944, FAX +44-1703-593230.