PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

AN ADAPTIVE STRUCTURAL EXCITATION SYSTEM AS A TOOL FOR
STRUCTURE-BORNE NOISE RESEARCH
Marco NORAMBUENA1; René WINTER2
1,2

Institute of Aeroelasticity, German Aerospace Center (DLR), Göttingen, Germany

ABSTRACTEngine vibration has been identified as one of the main sources of structure-borne cabin noise. Researchers
could benefit from having the ability to reproduce operational vibro-acoustic excitation on the ground insteadof requiring flight testing in order to investigate its generation and transmission paths. While realistic
excitation generated by engine operation can be obtained through simulations the injection of these forces is
not a trivial task. The excitation system needs to compensate for all modifications introduced not only by the
amplification chain but also by the interaction of injected forces in different directions to achieve precise
excitation in each individual direction. The development of a multi-channel controller able to perform all
required compensations can enable a new approach for vibro-acoustic characterization of aircraft fuselages.
The adaptive controller presented here is able to provide all counteractions required in order to replicate
translational and rotational forces at the injection points on the structure. The system capabilities aredemonstrated on a laboratory structure that resembles typical fuselage subcomponents as skin fields,
stringers and frames. The following work describes the adaptive MIMO controller, presents results anddiscusses its applicability.
Keywords: Active, Structural, Excitation

1. INTRODUCTION
In the aeronautics industry, Ground Vibration Tests (GVT’s) are a well stablished testing procedure
meant to characterize structural behavior of aircrafts. Such applied methodology serves as key part not
only in the understanding of aeroelastic stability but also provides relevant data used to validate
analytical models that ultimately become part of the certification process of a irworthiness [1]. Insummary, GVT’s are able to accurately describe the fuselage response by means of artificial excitationof the structure. There are two other closely related methods to achieve similar objectives, Taxi
Vibrations Tests (TVT) and Flight Vibrations Tests (FVT), the former consists in the replacement of
the artificial shaker excitation by the natural vibrations generated during aircraft taxiing [2] and thelater uses the operational vibration generated on the fuselage during flight [3].
Any current structural testing procedure in the field of aeronautics uses one, or a variation, of thesemethods. From the excitation point of view, the most common strategy is to use arbitrary, but known,
excitation signals, e.g. white noise or sine sweeps. This provides the necessary flexibility to obtain, forinstance, frequency response functions, modal parameters, etc.
One could easily argue that a FVT will provide the perfect type of excitatio n since it is in fact anoperational condition, however the elevated costs associated with flight tests make this option
unfeasible in most cases. Moreover, such type of excitation, although ideal for many applications, iscompletely unknown and difficult to quantify since there are multiple sources acting on the fuselage
during flight. The unavailability of such excitation reference will limit the types of processing that canbe performed, e.g. modal masses can’t be obtained.
During recent years [4], vibroacoustic topics had drawn considerable attention in the aeronautic
industry. This is given by the fact that concerns have been shifted from safety and reliability topics ofprevious decades of research to cabin quality and passenger comfort. This cu rrent trend has pushed thedevelopment of new tools and methodologies in order to face these new challenges [5]. A set ofrefocused topics has emerged from the interest in understanding how vibroacoustics play a crucial role4726

in the cabin noise.
Given the fact that the starting points of all vibroacoustic phenomena are vibrations propagating ona structure, it is necessary to have a suitable excitation system capable of reproduce real flight
operational conditions. If we forget for one second the effect of the Turbulent Boundary Layer, thesolely source responsible for vibrations on the fuselage at low frequencies are the loads generated by
the rotating components of the engines.
Through simulation, it is possible to accurately calculate the loads generated at connection points
between engines and fuselage. However, a key problem arises at the moment when you try to
reproduce those loads on the structure, since there is no way to compensate for the modifications
introduced by the system created between amplifier, shaker and structure. Such unaccounted system
will certainly change the predefined reference loads. Nonetheless, if the reference loads signal isavailable, it can be used to design an active excitation system able to genera te and inject into thestructure an exact copy of the simulated loads. As we will show in the following sections, suchreal-time excitation system is based on an adaptive controller. As part of the development process, asa first step a single-input single-output (SISO) controller was investigated and implemented, thesefinding have been presented previously [6] [7]. The fundamentals of this system served later on as a
stepping stone for the more complex multi-input multi-output (MIMO) controller. Such multichannel
system is part of our long-term goal to create a system able to reproduce forces in the three directionsof space plus its associated moments. Our previous research already stablish the ca pabilities of thecontroller to perform MIMO force control, so in this work we will like to extend the focus further andpresent the Moments of Force (M x) control.
Therefore, if we could implement a system able to excite a structure in a realistic manner,
mimicking true loads, such system will allow to study the vibroacoustic behavior of a structure in themost accurate way possible. Such opportunity will help, for example, in the better understanding ofstructure—borne noise mechanisms of different parts of a fuselage or will assist in the determinationof relevant energy transmission paths between sources and receivers.

2. CONTROLLED EXCITATION
The type of problem presented in this scenario, where it is required to inject on a structure a copy ofan arbitrary reference force signal, seems to be a perfect candidate for an active control solution. The
two main reasons for this are the availability of a reference signal, in this case the load forces, and theneed to compensate a relatively stable plant. In this particular case the plant consists of the pathcreated between amplifier, electrodynamic shaker, the structure and a force cell used to quant ify the
injected force, Figure 1 shows the configuration of the plant.

Figure 1: Schematic of the plant which consists of a shaker, a structure and a force cell (denoted by the reddot) that quantify the injected force into the structure.
The type of configuration described above is known as inverse control, since the task of adaptive
process is to generate an inverse system ‫ܥ‬መ of the plant P. If this is successfully accomplished, theoutput of the plant will be an unmodified copy of the reference force signal. The typical schematic ofan idealized inverse controller is shown in Figure 2, where ‫ܥ‬መ represents the compensation filter of theplant P, driven by the adaptive procedure. The error signal represents the deviation of the output of theplant in comparison with the reference force signal at the input of ‫ܥ‬መ .

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Figure 2: Block diagram of an idealized adaptive inverse controller.
There are multiple options available to implement the adaptive algorithm. From the most simple
and reliable LMS variations to the most sophisticated and demanding RLS variations.
According with this type of application, the following algorithms were tested in order to find thebest tradeoff between speed of convergence and overall quality of output signal: NLMS,
Correlation-LMS, DCT-LMS and RLS. The comparisons showed that all algorithms performed fairly
well. After this comparison and considering that there is no requirement of high speed tracking of thereference signal, it was decided that the NLMS was the proper choice at this stage. Having thesimplicity of an NLMS algorithm will make it easier to debug any problem that could potentiallyappear during the implementation on hardware.
The idealized system shown in Figure 2 is the most basic configuration for an inverse controller.
However this simplicity helps to illustrate how such configuration works. Unfortunately, such
idealized controller is not able to work properly on a real implementation since it requires conditions
that are almost impossible to obtain, e.g. that there is no internal disturbance at the output of P. One ofthe options suggested in the literature [8] that can be used for an actual implementation, has aconfiguration similar to what is called filtered-x LMS (Fx-LMS) algorithm. This configuration is wellknown and widely used in Active Noise Control applications [9].
One of the characteristics of this configuration is that the control filter ‫ܥ‬መ is not applied directly tothe plant P but rather to a modeled version ܲ෠ of the plant. The Fx-NLMS configuration ensures stable
inverse control of the plant even in the case where there are errors in the modeling of ܲ෠. Independentlyof how ܲ෠ is modeled, online or offline. In this schema it is assumed that on a previous process theplant ܲ෠ was identified and now a copy is connected at the input of the control filter ‫ܥ‬መ . Under certain
conditions it could be desired that the plant does not track directly the Reference signal but rather adelayed or modified version of the Reference. The introduction of the Reference model M serves thispurpose.

Figure 3: Block diagram of inverse controller with added reference model.
The aforementioned implementations rely on the fact that SISO system are commutative, i.e. P(z)C(z) = C(z) P(z). However, such a property is in general not true for MIMO systems as pointed out by
Plett [10]. Special care needs to be taken in the order of how the transfer function matrix of thecontroller C is manipulated. Plett also introduces a highly efficient controller by using a Recursive
Least Square (RLS) update strategy. It is a well-known fact that RLS algorithms, although fast, arecomputationally demanding. During the development phase it was clear that our hardware system was4728

not able to run the controller at the required sampling rate with a RLS algorithm. Therefore, asimplified version was implemented with an LMS algorithm, in a similar manner as the SISO
controller. The cost of this decision is carried by the speed of convergence, however for our application
it has a low impact if we have to wait a little longer before the control coefficients settle and the
optimal solution is reached. The scheme of the MIMO controller can be seen in Figure 4. This is a moresophisticated online version of the Fx-LMS controller of Figure 3.

Figure 4: Block diagram of MIMO hybrid controller.

3. SIMULATIONS
Although multiple simulations were performed during the development processes in order to test
different algorithms, a simple example is presented here for the purpose of illustrating the generalbehavior of the controller. In the following figures, comparisons are presented between the Reference
that represents the desired signal that should be injected into the structure, Control OFF that represents
the signal obtained at the output of the plant when no control is performed (bypassing ‫ܥ‬መ ) and Control
ON is the same as the latter but now the controller ‫ܥ‬መ is operating. All these curves are shown in Figure
5 and Figure 6.
In Figure 5, an arbitrary plant P with a low-pass characteristic was chosen. This fact is evidenced by
the spectral profile of the Control OFF curve. The reference signal was defined as the sum of four
sinusoids with frequencies 30, 50, 170 and 240 Hz. After the controller has reached a stable condition
and the coefficients of ‫ܥ‬መ have converged, it can be seen that the Control ON condition matches
perfectly the Reference signal. This means that the injected force on the structure will be an exact copyof the reference. In Figure 6, a similar example is shown where a plant with an almost flat response isused and an arbitrary reference profile with seven modes is selected. This time the controller tries toadjust the Moment of force M x applied to a point on the structure. A more complete description of
moment controller will be given in the following sections. Once again, after the controller reaches astable condition, the resulting applied moment over a given point on the structure ma tches almost
perfectly the Reference M x profile.

4. HARDWARE REALIZATION AND EXPERIMENTAL RESULTS OF A MIMOSYSTEM
4.1 Force control
The last stage in the development process of the active controller was the implementation of thepreviously described algorithm into specialized hardware running in real time. For this purpose thealgorithm was developed using Simulink and an ADwin-Pro II T12 system. The test structure used wasa single aluminum plate of 1 x 0.8 x 0.03 m, with an asymmetric milled pattern that resemb les the skinfields, stringers and frames typically found in fuselage structures. The thickness of the skin fields,4729

Figure 5: Example comparison of simulated

Figure 6: Example comparison of simulated

force spectra.
moment of force spectra.
stringers and frames was 1, 5 and 10 mm respectively. The plate was suspended using bungee cords inorder to generate free displacement boundary conditions, as seen in Figure 7.
The next step in the development of the system was to extend its capabilities to be able to provide
three-dimensional controlled excitation, i.e. in each direction of space. The extension f rom a SISO
controller, as described previously, to a MIMO implementation required certain modifications of thealgorithms. Two incremental versions of the MIMO controller were developed during this part of the
project. The first version took a simple approach similar to the SISO system in the sense that there
were two steps for the controller to work. In the initial step the mimo plant P was identified and thecorresponding coefficient stored. The second step consisted in loading the stored coefficients of P to
use them as part of the inverse controller. This approach ensured a simple structure that could help to
debug any potential problem during development. Later on, a second version was implemented with amore advanced approach. In this case, both previous steps were merged into a single algorithm that
performed simultaneously the system identification of P while the inverse control was operating. The
scheme used is shown in Figure 4, where the blocks naming are similar to the SISO system introducedin Figure 3. Further specifics of this control strategy can be found in Plett’s reference. Since this is acontroller driven by a reference system, and not a reference signal, the inputs r k and n k correspond to
broadband noise. In principle both developed version used the same reference model M, still due tochanges in the sampling frequency and how these models are created, small differences occurred. Thismeans that, although both reference models do not match perfectly, they follow a resembling
frequency profile as will be seen in Figure 9 and Figure 10. Nonetheless, for our comparison thesesmall differences are irrelevant and only a global qualitative performance is derived from bothversions.
For the evaluation of the MIMO implementation, the same aluminum plate was used but this time
three shakers were attached, one per spatial direction as seen in Figure 7. In this case, three different
frequency profiles were arbitrarily defined. As in the previous SISO case, these profiles serve as thetarget reference that the controller will try to replicate at the injection point of the structure. The
profiles were integrated into the controller as part of the reference model M. The results of theevaluation are summarized in Figure 9 and Figure 10, where the Reference profiles and the Control ON
conditions are shown. There, each color represents one direction in space, the solid and dashed lines
represent the Reference and the Control ON respectively. From Figure 9 it is possible establish thecorrect operation of the controller. The good agreement among references and resulting profiles
illustrates the proper generation of control coefficients and the successful application of thecompensation filter C to the input signal. In X direction, it is possible to notice a relatively small
difference of 0.6 dB between Reference and Control ON in the region of interest. In Y direction,
vertical excitation, the difference between both curves seems to increase in the upper frequency range.
We assume that in this direction the suspension of the plate negatively affects the result. It is notunreasonable to assume that a non-linear effect of the bungee cords suspension escapes the control
capabilities of the system making it appear as a less favorable result. In order to validate thisassumption, a new configuration of suspension is being designed to minimize its influence and will be
evaluated in the near future. The Z direction, perpendicular to the plate, presents an almost perfectmatch between Reference and Control ON profiles. The results of the second version of the controller,

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shown in Figure 10, exceed its predecessor. In this case there is a closer match between References andControl ON condition in all three directions. Despite this better agreement, once again it is possible toobserve a small deviation region in the Y curve. As already discussed, this may be caused by thesuspension system of the plate. Nevertheless, the important outcome if this comparison is that thesecond version of the controller performs substantially better, this is most probably due to thecontinuous adjustment of the identified plant that quantifies any deviation occurring during theoperation of the controller.

Figure 7: Aluminum plate configuration for

Figure 8: Aluminum plate configuration forForce control

Moment of force control

4.2 Moment control
The designed Moment controller was defined to apply a moment M x around the x-axis, as seen in
Figure 7 and Figure 8, where two forces are applied perpendicular to the plate and arranged verticallyalong the y-axis. Such configuration assumes that the moment is applied at the center point between
both forces. The moment M x is obtained by‫ܯ‬௫ ൌ ‫ݎ‬ሺ‫ܨ‬ଶ െ ‫ܨ‬ଵ ሻ,(1)where r is the distance between each applied force and the center point where the adapter beam is
attached to the plate. This adapter beam serves as interface for connecting shakers and force cells tothe plate at a single point. In order to perform the control of the moment, it is necessary to modify
slightly the control scheme previously used, shown in Figure 4. Since there are not sensors that can
provide a direct moment signal that can be used to build an error signal, this is derived from Eq. 1.
Therefore, this is added as a two stages Plant, where an impulse response representation of thisequation is set before ்ܲ in the controller path and also after the returned signals from the force cells inorder to build an error signal by comparing the real generated moment on the structure and thepredefined reference moment. For a single moment control, i.e. M x in our case, this configuration canbe considered as Multi-input Single-Output (MISO) since two forces are actually injected on theinterface in order to generate a single moment applied. However, one could make some assumption andsimplify the controller even further, as for example defining that both injected forces have the same
magnitude but opposite direction. On one hand this implies that the net force applied is zero and on theother hand the controller will have to consider only single input, transforming it internally into aSingle-Input Single-Output controller although there are still two input and two output channels.

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Figure 9: Spectral comparison of first version of

Figure 10: Spectral comparison of second version of

MIMO controller, References vs. Control ON

Hybrid MIMO controller, References vs. Control ON

condition.
condition.
The evaluation of the controller is performed as in the previous cases, where the frequency
Reference model is compared against the actual moment generated by the Control ON condition. The
result is shown in Figure 11. There it is possible to notice the relatively good agreement between bothcurves, which means that the controller is properly generating the correct moment at the injection point.
A slight deviation appears in the upper frequency region, the difference there average around 2.5 dB.
At the moment there is no clear explanation about the causes of this difference, however there are twomain factors that could be responsible. The first one is the fact that only the moment in one direction is
being controller and maybe small cross-coupling is taking place with the moments in y and z direction.
The second factor could be the suspension system used during the experiments. This type of deviation
was also noted in the results of force control, as seen in Figure 10. Future work will try to address thisissue by implementing a multiple control of all moment’s directions.

Figure 11: Spectral comparison of Moment Mx controller, Reference vs. Control ON.

5. CONCLUSIONSIn this paper we examine the application of an active system to perform controlled structural
excitation. Simulations and laboratory test show that it is possible to successfully apply a calibrated
excitation for either multi-tonal or broadband signals in accordance with an arbitrary predefined signal
reference or model reference. A MIMO controller was presented and evaluated. The successful
implementation was demonstrated through laboratory experiments. The controller was able toreproduce reference forces with great accuracy. Moreover, two versions of MIMO controllers were
implemented as part of the development within this project. The most advanced version of the MIMO
controller showed significant better performance than its predecessor.

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Besides the force control scheme, a Moment of Force control strategy was developed, implemented
and evaluated. This controller uses a modified version of the previously used controller. The
evaluation showed a good agreement between the reference and injected moment. The future
integration of Forces and Moments control will provide an essential tool in the aircraft vibroacoustic
research field.

ACKNOWLEDGEMENT
This project has received funding from the Clean Sky 2 Joint Undertaking under the European
Union’s Horizon 2020 research and innovation programme under grant agreement N° CS2Ǧ
LPA-GAMǦ2014Ǧ2015Ǧ01.

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