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Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 59 Active Vibration Control of Multibody Systems CLAES OLSSON Application to Automotive Design ISSN 1651-6214 ISBN 91-554-6267-7 urn:nbn:se:uu:diva-5818 ACTA UNIVERSITATIS UPSALIENSIS UPPSALA 2005

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Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 59

Active Vibration Control of Multibody Systems

CLAES OLSSON

Application to Automotive Design

ISSN 1651-6214ISBN 91-554-6267-7urn:nbn:se:uu:diva-5818

ACTAUNIVERSITATIS

UPSALIENSISUPPSALA

2005

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ISBN

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To Martina

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Appended Papers

This thesis contains an introductory part and the following six appended papersformatted for uniformity.

I. C. Olsson, Active Automotive Engine Vibration Isolation Using FeedbackControl, Provisionally accepted for publication in Journal of Sound andVibration, 2004.

II. C. Olsson, On Hazards of Using Fundamental Anti-windup Techniquefor H2 State-space Controllers With an Explicit Observer, Proceedingsof the European Control Conference, Cambridge, UK, 2003.

III. C. Olsson, A. Medvedev, Saturation-induced Limit Cycles in Observer-based State Feedback Control. (An abridged version published in Pro-ceedings of the IFAC Workshop on Periodic Control Systems, PSYCO,September 2004, Yokohama, Japan)

IV. C. Olsson, Structure Flexibility Impacts on Robust Active Vibration Iso-lation Using Mixed Sensitivity Optimisation, Technical Report, Depart-ment of Information Technology, Uppsala University, Number 2005-003,2005.

V. C. Olsson, Comparative Study of Recursive Parameter Estimation Al-gorithms with Application to Active Vibration Isolation, Technical Re-port, Department of Information Technology, Uppsala University, Num-ber 2004-051, 2004.

VI. C. Olsson, Disturbance Observer-Based Automotive Engine VibrationIsolation Dealing With Non-linear Dynamics and Transient Excitation,Technical Report, Department of Information Technology, Uppsala Uni-versity, Number 2005-009, 2005.

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Contents

1 Introduction 9

2 Active Vibration Control 11

3 Active Vibration Control in Automotive Design 15

4 Summary of Appended Papers 194.1 Paper I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.2 Paper II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.3 Paper III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.4 Paper IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.5 Paper V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.6 Paper VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5 Discussion and Future Work 23

Summary in Swedish 25

Acknowledgments 29

Bibliography 31

vii

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1

Introduction

Fierce competition is a significant characteristic of today’s market for passen-ger cars. In order to be competitive and to meet legal demands, automotiveindustry is forced to develop vehicles that possess improved comfort, safety,and quality, reduced weight and fuel consumption, as well as lowered emissionlevels. Simultaneously, the product cost has to be reduced while the time forproduct development, including steps from initial product concept developmentto a commercially available product, is shortened.

On the other hand, the relative maturity of many traditional technologieswithin different technical areas, implies little or no potential for improvements.Consequently, to deal with the technical challenges associated with some ofthe above mentioned requirements, non-conventional techniques have to be in-troduced where the conventional ones have already reached their limits. Thisis especially true in the field of noise, vibration, and harshness (NVH), wherethe targets, considering cross-attributes balancing, are way beyond the scopeof traditional passive insulators, absorbers, and dampers. Thus, active noiseand vibration control (ANVC) techniques are then necessary. This technologyenables improved balancing of various contradicting properties that are closelyassociated to one or several interactive subsystems. Moreover, it could also as-sist in overcoming limitations associated with the traditional passive solutions.

However, the potential benefits of incorporating ANVC technology in theproduct development are determined by the way it is introduced. As for anynew technology, the ratio between product customer value and product costhas to increase for an implementation to be motivated. Furthermore, a largenumber of vehicle subsystems and complete vehicle attributes influence theNVH properties and the actual ANVC systems development requires a broadtechnical knowledge. All together, the above issues make a suitable utilisation

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10 Introduction

of ANVC a great challenge, not least since the overall design prerequisiteschange due to the possibility of integrating active solutions into the completeautomotive design.

In this thesis, components of a design strategy are identified that takesthe above mentioned issues into account. Some of its potential is demon-strated dealing with several technical problems related to active vibration con-trol (AVC), an ANVC technique to deal with unwanted vibrations as well asvibration-induced structure borne noise.

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2

Active Vibration Control

As defined in [16], the main objective of AVC systems is to reduce the vibra-tions of a mechanical system by modification of its structural response. Thesesystems are composed by one or several sensors (to detect the vibration), oneor several actuators (to affect the response of the mechanical system), andan electronic controller (to compute a signal which is to be fed to the actua-tors to achieve desired modification of the structural response). Thus, AVC ismultidisciplinary [40] involving structural dynamics, control, signal processing,acoustics, material sciences, and actuator and sensor technology. In additionto vibration control, AVC are also used to reduce structure borne noise whichis often induced by the vibrations (see e.g. [9, 12, 23, 27, 28, 34]). Yet, thereis a clear distinction between these systems and systems solely devoted to ac-tive noise control (ANC) where the latter uses, for instance, loudspeakers todirectly affect the sound field [11, 14, 18, 28, 41, 45, 46].

Traditionally, vibrations of mechanical structures are treated using pas-sive damping and/or passive isolation. These techniques are effectively usedin many applications but are inevitably associated with certain limitations.Passive damping is effective at high frequencies but tend to be large, heavy,and expensive for low frequencies. Vibration isolation is normally subject toconflicting requirements where the isolation elements need to be soft enoughto reduce the transmission of forces, but stiff enough to prevent large rela-tive displacements. In e.g. automotive engine suspension design, the latteris important considering the limited space of the engine compartment and thealignment requirement for possible connection of the engine to the intermediateand drive shafts. AVC is used to overcome limitations like these and has beenapplied to a wide variety of applications. In addition to passenger car appli-cations it is, for instance, also applied to marine applications [9, 26], railway

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12 Active Vibration Control

vehicles [15, 33], vehicle seats [48], aircraft frames [7], helicopters [4], bridgetowers [44], bandsaw blades [10], and telescope attitude control [42].

Similar to the different passive techniques to deal with mechanical vibra-tions, active vibration isolation and active vibration suppression are two termscategorising two distinct AVC strategies. As defined in [3], active isolationrefers to the reduction of the force transmitted between structures at discreteconnections whereas active vibration suppression refers to the reduction of astructure’s global vibratory response using control actuators at locations thatdo not coincide with the discrete power insertion points.

A common active vibration isolation application is active machinery vibra-tion isolation which is achieved using a force actuator generating a secondaryforce to counteract for the primary excitation, i.e. the internal and/or exter-nal excitation of the mechanical structure generating the unwanted vibrations.Two main strategies for application of the secondary force exist [16]: (i) inparallel to a passive stage (i.e. combinations of passive damping and stiffnesselements) both located between the machine and the receiving structure (seee.g. [13, 20, 43]) and (ii), directly on the receiving structure opposite to thepoint of attachment of the machine mount (see e.g. [1, 2]). The choice ofmethod influences the magnitude of the secondary force required to cancel thevibrations of the receiver. To deal with vibrations for frequencies near andabove the mounted natural frequencies of the machine, the parallel configura-tion requires lower secondary force magnitudes [16, 21].

One automotive AVC application is reduction of vibrations and structureborne noise induced by the engine internal excitation, which is due to gaspressure fluctuations and unbalanced rotating masses. As mentioned above,the engine suspension system of a vehicle is a typical example to which activeisolation could be applied to deal with the limitations [17, 30, 31, 32, 35, 49, 50]of a passive system design, yielding an active engine vibration isolation system.A lot of attention has been paid to the solution of this problem by the use ofactive engine mounts [17, 19, 23, 24, 27, 28, 34, 36, 37, 39], i.e. by adoptingthe parallel actuator configuration. Still, the alternative isolation strategy usingactive absorbers attached to the receiver has also been investigated [5, 8, 22, 29].

Although many successful applications of AVC have been reported, therestill seems to be issues which require further investigation to exploit more ofthe potential benefits of AVC technology. The following are some of such issuesthat concern a beneficial incorporation of AVC technology into the early stagesof the automotive product development.

• How should the accessibility of various AVC solutions be made a naturalpart of the conceptual prerequisites of the complete vehicle?

• How could different combinations of passive and active system conceptsbe evaluated? This includes, for instance, the balancing of contradictingproperties that are closely associated to one or several interactive sub-systems, as well as choosing between different conceptual AVC solutions

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based on different control strategies and different numbers, types, andlocations of actuators and sensors.

• How should passive system design be carried out, to facilitate conceptualand detailed AVC system design, and to yield effective active systems?

• How should, for the purpose of controller design, sufficiently accuratemodels of the system to be controlled best be generated to ensure satis-factory AVC system performance?

In addition to the above mentioned overall questions which are closelyrelated to the design process, there are also more technical issues such as

• What are the impacts on controller design of various dynamic attributessuch as structure flexibility, non-linearity, actuator limitations, time vary-ing excitation characteristics, time varying plant characteristics due toe.g. ageing and heating, and uncertain passive element properties?

• What are the most suitable control strategy (e.g. time and frequencydomain adaptive filtering, feedback, etc.) with respect to each specificAVC problem and the corresponding excitation characteristics?

• How to deal with model reduction considering control object modelshaving large number of degrees of freedom to fulfill the requirements forreal-time implementation of model-based controllers?

To deal with many of the above mentioned issues, it seems to be necessaryto, in early product development phases, consider AVC system design as anintegrated part of the complete vehicle design.

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3

Active Vibration Control inAutomotive Design

In the AVC literature, it appears customary to consider AVC systems as isolatedsubsystems to be added to existing definitive passive designs. Naturally, it issometimes motivated to utilise AVC to overcome problems associated with apassive design discovered in a late product development phase. Still, this wayof introducing AVC solutions is likely to imply increased weight and cost of thefinal design which is unfavourable considering the hyper-competitive operatingenvironment of the automotive companies.

To motivate the utilisation of AVC in automotive design and to maximiseits advantages, the issues listed in Chapter 2 (and possibly others) have to beaddressed. Consequently, AVC technology has to be considered in the conceptdevelopment phase and treated as an integral part of the overall vehicle designprerequisites. These new premises created by introducing AVC systems areused to achieve optimal product performance by integrating active and passivedesign in early design stages. This also enables passive system design that max-imises the effectiveness of the active system. Here, an effective active systeme.g. refers to a system with high performance to a low power consumption.

In the AVC litterature, very limited attention has been paid to the issue ofintegrated passive and active system design, and to suitable design strategiesfor maximisiation of the potential benefits of AVC. Yet, there are initiativesstressing the importance of considering the systems for vibration damping as anintegral part of the complete vehicle design [5, 25, 30, 32]. In [5], the authorssuggest redesign of a passive engine suspension design to achieve dominanttransmission paths where active isolation is to be applied. This is one exampleof integrated active and passive system design where the passive system isadapted to increase the efficiency of the AVC system. Studies on suitabledesign strategies have also been carried out. In [6, 8], the design, simulation,

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16 Active Vibration Control in Automotive Design

and implementation of automotive AVC systems are considered. Yet, only thedesign steps following concept development are mentioned and, once again, amore or less definite passive system design is assumed.

Dealing with the above mentioned issues together with car industry’s de-mand for shortened lead-times, the automotive design process has to be sup-ported by an efficient multi-domain virtual design environment based on re-liable modelling and simulation of dynamics and control systems. Such anenvironment, enabling concept evaluation, analysis, and verification, has alsoto facilitate the treatment of the following issues

• Accurate modelling of control objects which are likely to have a largenumber of degrees of freedom

• Balancing of different targets and interacting attributes

• General input/output relationships to deal with e.g. various combina-tions of actuator and sensor locations and different number of sensorsand actuators

• Non-linear characteristics and flexible bodies

• General load cases including random and deterministic excitation

• Efficient control synthesis

• Generation of analytical representations of equations of motion for con-troller design purposes

• Evaluation of different active concepts in the early product developmentphases when, possibly, no prototypes exist

• Evaluation and analysis of passive/active system interaction with respectto each conceptual solution including both passive and active ingredients

• Closed-loop verification in time domain to e.g. verify the active systemstability and performance

• Model reduction to obtain models suitable for model based control

• Optimisation to maximise the performance of a specific active/passiveconcept

An environment that complies with the above mentioned requirementsneeds to combine several tools for controller synthesis, simulation of controllerfunctionality, control algorithm rapid prototyping, as well as dynamic systemsmodelling using e.g. softwares for finite element and multi body system (MBS)modelling and simulation. Such a combination, which has been utilised in mostof the appended papers, is schematically illustrated in Figure 3.1.

An important quality of the required virtual environment is its simulationcapabilities. To accurately design and predict the performance and stability ofan AVC system, the structural response due to the controller output signal and

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Real Time Code

Generation

HIL Simulation Equipment

Controller Simulation Software

Controller Design

Software

Target Hardware

FEM Software

CADSoftware

Random and Deterministic Disturbance

MBS Model

Figure 3.1 A schematic picture of a multi-domain virtual design en-vironment including tools for modelling, control synthe-sis, co-simulation (illustrated by the dashed lines), andrapid prototyping (FEM stands for Finite Element Mod-elling).

other disturbance sources has to be evaluated using sufficiently detailed modelrepresentations of the mechanical structure, actuators, and sensors. This evalu-ation should also cover the information that has been neglected in the controllerdesign phase, such as e.g. unmodelled non-linear and high frequency character-istics. One way to achieve this is to use co-simulation[47], where two softwaretools are run concurrently, one simulating the control system functionality, andthe other predicting the response of the mechanical structure including actu-ators and sensors. In Figure 3.1, the dashed lines illustrate the co-simulationsignal flow between a tool for accurate MBS modelling and simulation, and onefor simulation of the controller functionality.

Another important feature of a virtual environment like the one depictedin Figure 3.1, is the possibility to extract analytical model representations of

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18 Active Vibration Control in Automotive Design

general input/output relationships. By this functionality, models for controllersynthesis could effectively be obtained and thus, model based controller designeasily adopted. It is also possible to use this feature to, for instance, study theimpacts on controllability and observability of specific vibration modes, withrespect to different sensor and actuator configurations. Not only linearisedmodel representations could be directly extracted, but also analytical modelsof structures including non-linear characteristics could sometimes be obtained[38].

In contrast to the design strategy outlined above, the most widely usedAVC system design approach is based on experiments where representationsof the control object dynamic characteristics are obtained using system iden-tification. This approach has been used to produce satisfactory designs butare also associated with a number of limitations. The main drawback is therequirement of a physical prototype. Thus, the design of the passive mechan-ical structure has to be more or less finalised, leaving the question about thebest combination of passive and active solutions unanswered. Furthermore, anumber of questions seems to be difficult to address using this approach, wherethe following list raises some

• What is the expected achievable performance?

• What are the mechanism limiting the performance?

• What are the impact of a specific modification to the passive concept?

• Is there a more effective sensor and actuator configuration?

• What are the reasons for instability?

Using modelling and simulation, it is possible to gain an increased understand-ing of issues like these by e.g. studying non-measurable quantities. Thus, adesign approach based on modelling and simulation, should be adopted as apreliminary and complementary step to the experiment-based one, where thelatter is to be used primarily for final verifications.

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4

Summary of Appended Papers

In this chapter, the appended papers are briefly summarised in chronologicalorder to point out their main conclusions and reflect the evolution of the thesiswork.

4.1 Paper I

The potential of broad frequency band feedback active automotive engine vibra-tion isolation is considered. A multi-input multi-output controller design hasbeen carried out making use of a virtual development environment (schemati-cally shown in Figure 3.1) for design, analysis, and co-simulation based closed-loop verification. Utilising relevant control object dynamic modelling, thisdesign strategy provides a powerful opportunity to deal with various plantdynamics such as non-linear characteristics. The main objective is to closelyapproach the true physical behaviour for control design and verification toachieve optimum product performance.

H2 loop shaping technique proves potential when achieving the desiredclosed-loop characteristics. However, to achieve closed-loop stability two kindsof non-linear characteristics have to be taken into account. Those are non-linear material properties of the engine mounts and large angular engine dis-placements. It is demonstrated how the adopted design strategy facilitates theinvestigation of the latter non-linearity’s impact on closed-loop characteristicsusing Gain Scheduling. The proposed solution deals with system non-linearitiesand all possible engine excitations except those corresponding to very rapidchanges and extremely high values (evoking non-linear material characteris-tics) of the nominal engine torques, for which the controller has to be turnedof to ensure closed-loop stability.

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20 Summary of Appended Papers

4.2 Paper II

This paper considers H2 controllers implemented using an explicit observerfor systems subjected to input magnitude saturation. It is pointed out thatthe approach of only focusing on controller windup, by using the fundamentalobserver anti-windup technique where the observer is fed by the saturatedcontrol signal, could imply severely deteriorated closed-loop characteristics andeven sustained oscillations. This is illustrated by providing a simple single-degree-of-freedom dynamic system to which active vibration isolation has beenapplied.

Describing function analysis is adopted for approximate analysis. In thepresented H2 control application, the existence of limit cycles is found to de-pend on the combination of control object characteristics and the choice of H2

weighting functions.

4.3 Paper III

The existence of saturation-induced limit cycles is further investigated forobserver-based state feedback control systems. Two different observer basedcontroller implementations are considered, one using the computed control sig-nal for state estimation and the other using the control signal actually appliedto the plant. Based on piecewise affine system descriptions, analytical tools toconclude about limit cycles and exponential closed-loop stability are providedfor both implementations. The condition for limit cycles is found to involvethe yet unsolved problem of spectral radius characterization of the product oftwo matrix exponentials. Furthermore, it is shown how to apply the method ofseparable nonlinear least squares to effectively resolve the provided analyticalconditions for investigation of limit cycle existence.

Applying the derived conditions to a numerical example, it is demonstratedthat while limit cycles exist in the case of an implementation using for stateestimation the control signal applied to the plant, global stability could beproven for the alternative implementation utilising the computed control signal.

4.4 Paper IV

Active vibration isolation from an arbitrarily, structurally complex receiver isconsidered with respect to the impacts of structure flexibility on the open- andclosed-loop system characteristics. Specifically, the generally weak influence offlexibility on the open-loop transfer function in case of total force feedback, incontrast to acceleration feedback, is investigated.

The open-loop system characteristics are analysed based on open-loop trans-fer function expressions obtained using modal expansion, and on modal modelorder reduction techniques. It is shown that when the contribution to the to-tal transmitted force from either a rigid body, global flexible, or local flexible

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4.5 Paper V 21

eigenmode is small compared to the actuator force, it does not significantlycontribute to the open loop transfer function. The factors determining thecontribution from an individual mode are given where the mode direction rel-ative to the actuator force direction is emphasised as a key factor. It is alsopointed out that minor modal transfer function contribution has the physicalinterpretation of negligible passive stage force in the direction of the actuatorcompared to the actuator force. In this context, the relation between model or-der reduction based on modal and on balanced truncation is investigated. It isshown that for lightly damped systems with certain characteristics, the resultswhen using balanced reduction techniques could potentially be very poor. Inaddition, the upper bound on the model perturbation due to state truncationis potentially very conservative in this case.

To closely demonstrate and illustrate the impacts of flexibility on the open-loop characteristics and on the closed-loop system performance and stability,the engine suspension system of Paper I is again envisaged. Here, automo-tive engine vibration isolation is considered taking flexibility of the subframereceiver structure into account. The consequences on performance and sta-bility of neglecting flexibility in the controller design phase are investigatedrepresenting the introduced error as a relative output multiplicative modelperturbation. For this application, the degradation of robust performance andstability is shown to be insignificant by the use of total force feedback.

4.5 Paper V

The AVC application of Paper IV is revisited. In this paper, the time domainadaptive filtering strategy widely used for active noise and vibration controlhas been adopted to deal with engine excitations corresponding to idle engineoperating conditions and to rapid car accelerations including gear shifts.

The adaptive filtering problem is formulated using a linear regression modelrepresentation. This allows for an application of a general family of state-of-the-art recursive parameter estimation algorithms. The performances of twospecific members of this family have been compared. Those are the well-knownnormalised least mean square (NLMS) algorithm and a recently suggestedKalman filter based algorithm originally proposed as a method to avoid co-variance windup referred to as Stenlund-Gustafsson (SG). A virtual non-linear43 degrees-of-freedom engine and flexible subframe suspension model and mea-sured engine excitation are used in evaluation of algorithm performance.

For this application, it is demonstrated how SG and the Riccati equationassociated with it imply superior performance compared to NLMS in terms oftrade-off between convergence and steady-state parameter estimation variance.It is also shown how SG could be adapted to suit piecewise stationary condi-tions. However, none of the algorithms possessed sufficient tracking propertiesto deal with transient excitations corresponding to rapid car accelerations.

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22 Summary of Appended Papers

4.6 Paper VI

In this paper, the engine vibration isolation application of papers IV and V isfurther studied to address problems not yet fully solved. Consequently, bothtransient and stationary engine-induced excitations, receiver structure flexibil-ity, as well as plant non-linearity are closely dealt with.

A control strategy targeting the dominating spectral components of theexcitation and achieves narrow band vibration isolation using feedback of dis-turbance states estimates, is adopted. To effectively deal with the active sys-tem complexity, time-varying gain-scheduled observer design is carried out toachieve robustness to plant non-linearity in contrast to the alternative designapproach of incorporating plant non-linearity into the controller. Both observerdesign and investigation of closed-loop characteristics are based on a linearparameter varying (LPV) description of the considered non-linear engine andsubframe suspension system. Parameter dependent quadratic stability analysisis made tractable using an affine closed-loop system representation. To gener-ate the LPV-representation of the non-linear system, an approach of dividing itinto its linear and non-linear components where the latter is represented usinga parameter dependent non-linear function, is proposed.

Excellent performance is demonstrated using co-simulations incorporatinga detailed non-linear plant model and measured engine excitations. This isalso achieved for engine operating conditions corresponding to rapid car accel-erations, whereas the system exhibits non-linear characteristics and the funda-mental frequency of the harmonic disturbance undergoes rapid time variations.Parameter dependent closed-loop quadratic stability is being shown assumingplant linearity. Thus, the adopted approach for closed-loop stability analysisis shown to to be useful when dealing with the considered controller structurefor linear time invariant plants. Yet, in the non-linear plant case, stabilityis guaranteed but only for limited intervals of the parameters and their timederivatives.

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5

Discussion and Future Work

A trend towards fully integrated active and passive automotive design is natu-ral since, on one hand, the efficiency of the active systems is determined by thepassive system design and, on the other, the prerequisites of the passive systemdesign are directly influenced by the active system operation. Yet, a develop-ment of the design process towards an increasing degree of such integration isconceivable.

A design example that represents limited degree of active/passive integra-tion is minimising the non-linear characteristics of input/output relationships ofactive systems and, thus, facilitating controller synthesis. Carrying out passivedesign to minimise the number of actuators while maximising their efficiency isanother one. A suitable choice of feedback sensor type could to a large extentreduce the required complexity of the control object model used in the con-troller synthesis [39], which could be considered as integrated active/passivesystems design.

Using AVC to improve cross-attribute balancing constitutes a higher degreeof active and passive system integration. This could, e.g., be applied to dealwith the inherent compromise between NVH-properties and handling charac-teristics when determining stiffnesses of chassis bushings. Here, a special caseis active engine mounts enabling higher dynamic stiffness in a frequency rangeof importance for handling and, at the same time, maintained or improved ve-hicle NVH-properties. Modified engine combustion-process control to increaseengine efficiency by adopting AVC technology to deal with the, from NVH per-spectives, generated less favourable engine excitation is another example. Inthis case, the increased degree of design freedom achieved by introducing AVCtechnology when optimising the combustion process could be used to reducefuel consumption and thus, to improve product environmental impacts.

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24 Discussion and Future Work

In addition to enhancing the conditions for cross-attribute balancing in au-tomotive design, AVC could also be used to enable new technical solutions bycreating extended margins or, equivalently, increased design flexibility. Suchan example is given in [27] where an active engine mount system enabling vary-ing number of engine cylinders in operation, is described. Using less numberof cylinders during low load engine operations, the fuel consumption could bereduced. However, increased workload per cylinder implies higher combustionpressure and consequently higher engine vibrations amplitudes requiring iso-lation performance beyond conventional engine mounts. It is also conceivablethat AVC could be used to enable new engine combustion technologies whichare likely to require superior vibration isolation. Another example of utilisingthe extended margins provided by introducing AVC technology is the reduc-tion of engine idling speed which positively affects the environmental impact.This normally causes excessive engine shake that requires, once again, excellentvibration isolation characteristics.

Finally, integrating AVC into the early design phases of the overall vehicledesign is a great challenge for automotive product development organisations.This requires, for instance, an even better interaction between groups respon-sible for many different technical areas such as NVH, handling, strength anddurability, powertrain design, powertrain installations, electrical architecturedesign, and active vehicle control system development. In addition, contactswith AVC-subcontractors of, e.g. actuators, have to be established in the verybeginning of the product development process since the active element designand its achievable performance determine the prerequisites for the active andpassive system integration.

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Summary in Swedish

Aktiv vibrationsreglering av flerkroppssystem

Tillampat pa personbilsutveckling

Personbilsmarknaden kannetecknas idag bl.a. av en extremt tuff globalkonkurrens som rader mellan producenterna. For att halla sig konkurren-skraftiga maste foretagen inom personbilsindustrin standigt forbattra utveck-lingen av bilar med avseende pa t.ex. okad komfort, hogre sakerhet, min-dre bransleforbrukning och lagre vikt. Samtidigt maste kostnad for utveck-ling, produktion, samt produkt sankas och ledtiderna kortas. For att hanterade tekniska utmaningarna forknippade med denna utveckling ar det iblandnodvandigt att utnyttja ny teknologi for att skapa okad utvecklingspotential.Detta galler speciellt inom ljud- och vibrationsomradet dar dagens anvandningav isolatorer, dampare och absorbenter, inte racker till for att klara de okandekraven.

For att forbattra ljud- och vibrationsegenskaperna och samtidigt hanterat.ex. kostnad samt vikt, kravs aktiv ljud- och vibrationsreglering vilket avenmojliggor forbattrad egenskapsbalansering. Komplexiteten forknippad meddenna teknologi staller dock hoga krav pa hur tekniken integreras i den ovrigakonstruktionsprocessen. Detta ar framst en konsekvens av teknologins mul-tidisciplinara natur (innefattar strukturdynamik, akustik, reglerteori, signal-behandling, materialteknik, datorteknik, samt styrdons- och sensorteknologi)samt att egenskaperna hos den aktiva delen av konstruktionen ar en funktionav den passiva konstruktionens egenskaper och vice versa. Darfor bor aktivljud- och vibrationsteknologi inforlivas i utvecklingsprocessens tidigaste faser.

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26 Summary in Swedish

Under arbetet med denna avhandling har bestandsdelar av en produk-tutvecklingsstrategi identifierats som mojliggor att aktiv vibrationsreglering,ett specifikt omrade inom aktiv ljud- och vibrationsreglering, betraktas somen integrerad del av ett nybilutvecklingsprojekts totala konstruktionsforutsatt-ningar. For detta utnyttjas en effektiv multidisciplinar datormiljo for virtuellutveckling vars potential delvis har demonstrerats i behandlingen av flera speci-fika problem inom aktiv vibrationsreglering.

Aktiv isolering av motorvibrationer har tjanat som huvudsaklig tillampningi hanteringen av de specifika forskningsfragorna dar potentialen i att anvandabredbandig H2 -aterkopplingsreglering med tre insignaler och tre utsignaler,forst undersoktes. Genom att anvanda den identifierade utvecklingsmiljon kon-staterades att denna strategi kan appliceras for att hantera korfall motsvarandekombinationer av laga motormoment och langsamt foranderliga motormoments-nivaer. Dock leder reglerstrategin till sma stabilitetsmarginaler vilket bl.a.kraver att regualtorn utnyttjar information om systemets olinjara egenskaperfor att undvika instabilitet under vissa lastfall forknippade med hoga motor-moment.

Vidare har aktiv isolering av vibrationer fran en mottagarstruktur medhansyn tagen till dennas strukturflexibilitet studerats. Har ges en fysikaliskforklaring till den laga paverkan av flexibilitet pa det oppna och slutna sys-temets karaktaristik vid utnyttjande av kraftaterkoppling till skillnad fran ac-celerationsaterkoppling. I samband med detta betonas den inneboende skill-naden mellan modellreducering baserad pa balanserad respektive modal trunk-ering.

I syfte att undertrycka motorexcitationens dominerande frekvenskompo-nenter under bade tomgangskorning och snabba bilaccelerationer appliceradessedan en inom aktiv vibrationsisolering vanlig metod baserad pa adaptiv fil-trering. I denna studie dar en jamforelse av flera olika algoritmer for para-meteridentifiering ingar, demonstreras bl.a. hur hyfsad prestanda kan uppnasgenom att utnyttja de mest effektiva Kalmanfilterbaserade algoritmerna forrekursiv parameteridentifiering. Dock ger denna strategi inte tillrackligt braprestanda for att mojliggora hantering av multipla spektrala komponenter avmotorexcitation motsvarande snabba accelerationer.

Slutligen demonstreras hur bra isolering av motorvibrationer orsakade avtransient motorexcitation, motsvarande t.ex. snabba bilaccelerationer inklusivevaxlingsforlopp, kan uppnas med samtidig hansyn tagen till motorupphangning-ens olinjara karaktaristik. Detta astadkoms genom utnyttjandet av smal-bandig reglering baserad pa tidsvarierande aterkoppling av skattade tillstandtillhorande en dynamisk storningsmodell. For att hantera motorupphangningensolinjara egenskaper presenteras en strategi for att genera analytiska linjara pa-rameterberoende representationer av stora (med avseende pa antalet frihets-grader) olinjara system. En sadan representation utnyttjas for att sakerstallastabilitet hos det slutna systemet under stationara forhallanden samt i en studieav Lyapunov-stabilitet baserad pa parameterberoende kvadratiska Lyapunov-funktioner. For att mojliggora stabilitetsanalys harleddes en affin representa-

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27

tion av det slutna systemet.Under arbetet med motorvibrationsisoleringstillampningen har ett problem

med sjalvsvangningar som kunde relateras till magnitudbegransningar i styrdo-nen, sa kallad mattning, hanterats. Detta mattningsinducerade sjalvsvangnings-fenomen har noga studerats i samband med reglerstrategin baserad pa aterkopp-ling fran skattade tillstand. Tva olika observatorsimplementationer har un-dersokts dar den ena utnyttjar information om den verkliga styrsignalen foratt undvika problem med mattning, medan den andra bortser fran styrdons-begransningar. Det demonstreras att sjalvsvangningar i vissa fall framkallasgenom att utnyttja informationen om styrdonsbegransningar da global expo-nentiell stabilitet kan visas om den istallet forsummas. Genom att harledastyckvis affina beskrivningar av de slutna systemen har analytiska villkor foratt undersoka existensen av sjalvsvangningar samt exponentiell stabilitet tagitsfram for de bada observatorsimplementationerna.

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Acknowledgments

Looking back, I am indebted to two persons in particular, Professor AlexanderMedvedev at the Division of Systems and Control, Department of Informa-tion Technology, Uppsala University, and Dr. Ahmed El-Bahrawy, Volvo CarCorporation.

The research behind the last four papers appended to this thesis have beencarried out under the splendid supervision of Professor Medvedev. His vast the-oretical knowledge, highest of ambitions, and professional attitude to research,have been valuable assets in the strengthening of this research’s quality. I amalso most grateful to Professor Medvedev’s strong contribution to the develop-ment of my academic capabilities.

Dr. El-Bahrawy, the initiator of this project and my industrial supervisor,has positively influenced the conducted research by seemingly never ending en-thusiasm, visionary thinking, excellent guidance and support and, furthermore,by his aspiration for perfection. In addition, and perhaps even more impor-tantly, I feel Dr. El-Bahrawy has contributed a lot to my personal progress.

I also gratefully acknowledge Volvo Car Corporation for giving me the op-portunity to run this project within the Volvo Car Corporation Ph.D. Program.Many thanks also to the colleagues at Volvo for creating a friendly atmosphereand being responsible for many good laughs.

The first two papers appended to this thesis came as the result of a cooper-ation with Linkoping University. I am most thankful to my former supervisorProfessor Lennart Ljung, head of the Division of Automatic Control, for givingme the opportunity to make the acquaintance with his professional guidancewithin the area of automatic control.

Most of all, I would like to give my sincerest gratitude to my dear fianceeMartina. Thanks for your patience and unconditional support!

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