Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Active Control of Vibration, Applications of

  • Stephan AlgermissenEmail author
  • Björn T. Kletz
  • Martin Pohl
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_246-1

Synonyms

Abbreviations

AMP

Amplifier

ANC

Active noise control

ANVC

Active noise-vibration control

ASAC

Active structural acoustic control

AVC

Active vibration control

CFRP

Carbon fiber reinforced polymer

CROR

Counter-rotating open rotor

EF

Eigenfrequency

EMI

Electromagnetic interference

FIR

Finite impulse response filter

FRF

Frequency response function

IIR

Infinite impulse response filter

LSA

Loudspeaker array

PBC

Printed circuit board

PVDF

Polyvinylidene fluoride

RME

Radiation modal expansion

SHM

Structural health monitoring

SLDV

Scanner laser Doppler vibrometer

SPL

Sound pressure level

SPU

Signal processing unit

TBL

Turbulent boundary layer

TL

Transmission loss

Definitions

In this chapter, different methods to achieve a reduction of unwanted structural vibrations using augmented active components are discussed. The proper selection of a suitable method depends on the application goal, the excitation source and the underlying frequency range. Some applications demand the reduction of absolute oscillations, others target relative oscillations leading to active isolation components.

Motivation

Due to the fact that the methods to achieve active control of vibrations are highly application dependent, it is reasonable to describe the most prominent approaches using dedicated applications in mind.

Structural Damping

Idealized structures with no damping have resonance frequencies with unbounded oscillations in associated mode shapes. But all real structures have inherent damping based on material properties and friction. The system response is therefore always finite, but response amplitudes may still be very high in case of weak damping. Generally, methods to increase structural damping reduce the amplitude of structural vibrations. Especially stiff and lightweight structures often suffer from weak damping. Passive methods like additional layers with high material damping can significantly increase the overall damping at higher frequencies. At lower frequencies, the additional mass of passive measures is often not acceptable, and active structures may be used for this purpose if the control algorithm is designed correspondingly.

Global Vibration Control

If only parts of an oscillating structure are augmented with active measures, the vibration patterns of the global structure may be changed with only minor impact on the resulting vibration amplitudes. To prevent this from happening, a global control strategy can be designed using an error function which penalizes vibrations at every location. Global control usually needs computationally intensive plant models with a large number of state variables. It is elaborate to properly determine the underlying model parameters by means of system identification or model updating strategies. Another drawback is given by the fact that it is very demanding to adapt the plant model and the derived control algorithm to parameter changes, which might occur naturally during operation. A lack of adaptation of the control algorithm leads to non-robust adaptive systems, which may get unstable or have poor overall performance.

Distributed Collocated Control

A method to achieve global damping in a structure using many distributed local adaptive substructures consisting of collocated actuators and sensors and unrelated controllers, which are designed to increase the local damping. This guarantees control stability and robustness, which probably cannot be achieved with global control for such large flexible structures in mind as, e.g., wind power plants. Previous work shows that non-model-based velocity feedback control with distributed collocated actuator-sensor pairs achieves comparable control results. Although the implementation of velocity feedback loops is not demanding concerning computational power, a very simple feedback solution is often not sufficient. Additional filters for sensors and actuators as well as limiters are needed in practical applications. In the following a realization of a velocity feedback controller, a so-called sky-hook damper, is presented. With this unit a smart structure with collocated actuator-sensor pairs is set up. In the well-known velocity feedback approach, an actuator and a collocated sensor build a stand-alone control unit. In its simplest realization, the inverse velocity signal of the sensor is fed back with a gain to the actuator. This adds additional damping to the mounting point of the actuator and reduces the vibrations of the structure. By distributing several of these control units over the structure, a global vibration and noise reduction can be achieved.

Here, a slightly modified approach of a pure velocity feedback is chosen. To include the dynamics of the actuator, an additional sensor is mounted on its top. A single control unit consists of an actuator and two sensors; see Fig. 1. Both sensor signals are fed back to the controller where their difference is calculated. This signal is filtered by an integrator approximation and a gain to realize a velocity feedback using accelerometers. The output of the controller drives the actuator on the structure. The objective of the controller is the reduction of vibration signal y2n−1 measured with the structural accelerometer. The test environment for the presented control device is a vertically mounted aluminum plate shown in Fig. 2. It has a width of 500 mm, a height of 400 mm, and a thickness of 1.1 mm. All sides of the panel are fixed, while small rotations of the boundaries are possible due to the type of mounting. Two control units are placed on the panel with respect to the controllability of modes up to 1 kHz. One accelerometer that delivers signal y2n is placed on the inertial mass of the actuator. The other one is mounted on the opposite side of the panel to measure its vibrations y2n−1. The disturbance is realized with a small shaker that is mounted at point D. The disturbance shaker at point D is driven with a band-limited pseudo random signal up to 5 kHz. Figure 3 shows the local results in terms of open and closed loop disturbance transfer functions from the disturbance to the accelerometer on the structure of the two units (unit 1 with collocated actuator A1 and sensors S1 and S2 and unit 2 with collocated actuator A2 and sensors S3 and S4). The vibrations at the mounting points of the two control units can be reduced in the entire interval from 250 to 4,000 Hz. In certain peaks an attenuation of more than 20 dB can be achieved.
Fig. 1

Control unit n with one actuator and two accelerometers

Fig. 2

Experimental setup of the active panel: Front view with sensors S1 and S3 (left) and back view with sensors S2/S4, actuators A1/A2 and disturbance point D (right)

Fig. 3

Bode magnitude plot of disturbance transfer functions of both control units

Active Vibration Isolation

To attenuate vibrations of dedicated mechanical substructures, these parts can be linked to the outer environment by active components, providing an active vibration isolation. These active links must be indispensably integrated in the load-carrying path, and therefore their internal stiffness and mass must be adequately chosen to provide suitable support. They can be as simple as spring damper systems with embedded piezoactuator and suitable control law. Other multidimensional interfaces provide isolation in up to six degrees of freedom with a corresponding number of actuators and sensors.

There are many places where such active interfaces can be used with advantage. A vibration isolation is for instance needed, if measurement units or other sensitive parts need to be separated from oscillating components. This is especially the case for mirror systems, because small deviations in angles often induce large displacement in images. Therefore many vehicles suffer from disturbed images in interior and exterior mirrors. Vibrating mirrors are found at low driving speeds particularly at trucks, cabriolets, and motorcycles. Higher speed tends to increase those vibration levels.

The classical and commonly used approach to enhance the stiffness of the system in question (here the mirror system) would not reduce vehicle mirror oscillations significantly as vibration from the vehicle body would even then continue to transfer to the mirror glass. To enable a clear backward view with such mirror systems, it is rather necessary to mitigate the vibrations of the mirror glass in two rotatory and one translatory directions.

This is achieved by the integration of an active interface in between the mirror housing and the mirror glass. The interface is based on a soft three-axes isolation system. It isolates the mirror glass from the vehicle body and mirror housing vibrations even in case of a failing active system. Exterior vehicle mirors are subject to additional aerodynamic loads that act directly against the mirror glass. To maintain a vibration-free mirror glass regarding this type of excitation, the mount of the mirror system must counteract these forces and thus generate a bearing of the mirror glass that is ideally infinite stiff. It is here necessary to generate not only a highly stiff interface but an interface that virtually stiffens the mirror housing and the adjoining car body to generate the desired behavior. With an appropriate control, the passively soft active isolation system can generate the described contracting forces.

For this application, it is consequently required to generate an interface that is very soft (with regard to the vibration of the mirror housing) to achieve the required vibration isolation and at the same time very stiff (with regard to aerodynamic forces).

Leaf spring-based double spiral interfaces (cf. Fig. 4) that are equipped with piezoelectric patch actuators serve this task (Kletz et al., 2012). Those interfaces are very flat and can be easily accommodated into commercial mirror system housings. For generating the control forces, an interface conformal dual channel controller (IC2) is appropriate (Kletz and Melcher, 2015). The controller is conformal regarding the interface as it emulates the dynamical properties of the vibration mitigating mirror glass mount (Kletz, 2017). The two signals that are provided to the controller are the displacement (xF) of the mirror housing and the force that is measured between the interface and the mirror glass. It shall be noted that the exciting aerodynamic forces at the mirror cannot be measured directly.
Fig. 4

Active double spiral mirror glass interface equipped with piezoelectric patch actuators inside a mirror housing of a large van

The IC2-controller remains stable independent of the systems mounted to the mirror housing side (base) and to side of the mirror glass (payload). As this is not always the case for velocity feedback skyhook controllers those controllers should be used with care (Elliott et al., 2004; Preumont and François, 2002). Skyhook controllers that use integral force feedback are unconditionally stable but they don’t achieve a sufficient vibration reduction when excitations are concurrently present at the base (mirror housing side) and payload (mirror glass side) (Kletz, 2017).

Figure 5 indicates the displacement of the mirror glass (xM) that is obtained with an IC2 controlled interface that is similar to the described double spiral mirror mount. The interface is modified so that it enables the vibration mitigation in one direction only. Together with the mirror glass, it is mounted in between a vibrating foundation that simulates the vibrations of the mirror housing and almost stiffness-free voice coil actuators that simulate the aerodynamic loads.
Fig. 5

Vibration reduction at the mirror glass using an adaptive variant of the IC2 controller during simultaneous excitation of the mirror housing and the mirror glass. The filter coefficients of the IC2 controller are aI0, aII0 and aII1

Semi-active Vibration Control

If the controller of an active structure mainly consists of non-digital mechanical or electric components (electric network) which parameters are possibly adapted to environmental conditions itself by an outer control loop with a comparatively low update frequency, a semi-active vibration control system is given.

One prominent kind of this is piezoelectric shunt damping. This subsumes all concepts where an oscillating structure is damped with attached piezoelectric actuators connected to electric networks. The basic principle can be seen in Fig. 6, where the shunt network is represented by the electrical impedance Z1. These networks may represent any circuit consisting of active and passive electronic components. In most cases, this reduces to electrical impedances consisting of capacitive, inductive, and resistive parts. In contrary to active vibration control (AVC) or active structural acoustic control (ASAC), no separate sensors, controllers, or actuator amplifiers are needed. The electrical network incorporates all of these components and is called semi-active for this reason.
Fig. 6

Working principle of piezoelectric shunt damping

Several active or passive circuits are known, which can be used for piezoelectric shunt damping. In the easiest case, resonant shunts consisting of inductors and resistors are used. Their drawback is the limitation to one or a few discrete eigenfrequencies, which do not allow them to be used for a multiple eigenfrequency system, such as a circular saw blade. In addition, radial acceleration due to the rotation of the blade leads to dynamic stiffening, which changes eigenfrequency and mode shape. Therefore, the negative capacitance circuit is the best solution because of its wide band damping effect. In this case, no tuning of the electric circuit is required with respect to the eigenfrequencies, which allows to damp vibrations as long as they are observable by the piezoelectric transducers (see also Moheimani 2003 or Pohl et al. 2011).

Circular saws are precise, efficient, and frequently used machine tools for cutting wood, metal, composites, or even ceramics. Since the invention of circular saws, technology of saw blades, tooth materials, and machines developed with time, but one general problem could not be solved: In machining condition, when the saw blade has contact to the workpiece, it is randomly excited by the contact of the cutting edges. This leads to intense vibration amplitudes of the very lightly damped thin blade disc. The vibration amplitudes result in the emission of severe noise, which can excess sound pressure levels of 110 dB(A) as shown in Schlünz (2005). In addition, vibrations of the saw blade teeth widen the cutting gap, which reduces precision.

To overcome this a global vibration reduction of circular saw blades will be helpful to decrease noise emission and increase precision. This can be achieved based on applied piezoelectric transducers which are connected to a negative capacitance network. Multiple piezoelectric patches can be applied to the blade core. If they are connected to individual circuits, a charge flow between patches with opposite strain sign is prevented, which would reduce the damping effect (Pohl and Rose, 2016).

In order to avoid rotating electrical connections with risk of wear, as, e.g., slip rings, it is useful to arrange all components in the rotating system of the saw tool. This also means to ensure power supply of the active electronic components required for the shunt networks. Due to low power drain of the shunt networks and high drive power of the machine, energy can be harvested from the saw blade’s rotation. Therefore, an electric generator is used for power supply which has been built from a modified synchronous disc motor with permanent magnets. The stator of this motor is fixed on the saw tool, while the rotor containing the windings is rotating. Additionally, the rotor can be used to carry the printed circuit board (PBC) with all electronics. An overview of the setup with the saw aggregate, generator, PCB, and protective box is given in Fig. 7.
Fig. 7

Design of shunt-damped circular saw tool demonstrator

A comparison between vibration amplitude of the circular saw blade with shunted and open electrode piezoelectric transducers, respectively, in the non-rotating system is given in Fig. 8. It can be seen that an amplitude reduction of more than 20 dB can be achieved in the eigenfrequencies of the saw blade in a wide frequency range up to 5 kHz. In contrast to the non-rotating condition, the amplitude reduction in rotation, when the saw blade is in contact to the workpiece, is much less as shown in Fig. 9. In this case, maximum 5 dB is achieved for some eigenfrequencies. The difference between both measurements is mainly caused by the much higher vibration amplitudes in machining condition compared to the non-rotating condition. This leads to much higher voltages at the piezoelectric transducers, which lead to saturation of the negative capacitance shunt circuit electronics.
Fig. 8

Vibration amplitude with excitation by piezo transducer

Fig. 9

Acceleration level spectrum for machining

Nonlinear Mechanisms

Most control algorithms for elastic structures are based on linear system equations. But if vibrations of a mechanism like a robotic structure should be attenuated, the plant is inherently nonlinear. Therefore in general, nonlinear control algorithms based on inverse dynamic modelling must be used. If the mechanism is moved only with frequencies well separated from the main vibration frequencies, an interpolated control strategy may be applied instead.

To enhance the achievable accelerations in robotic tasks with the ultimate goal to reduce cycle times within production steps, parallel robotic structures are being investigated. The standard serial robot is often massively built, because the electric motors of subsequent chains have to be moved as well. Their masses prevent the engineers to realize very fast and responsive machines in handling and assembly tasks. In parallel robotic structures, however, the major drives of the axes are mounted at fixed positions, allowing very lightweight kinematic structures to control the end effector on its trajectories. To reduce moved masses even more, carbon fiber reinforced polymers (CFRP) are considered here as sophisticated materials due to their high stiffness. But this often comes at the cost of increased vibrations. This induced unwanted deviations from the planned trajectories again reduce the precision of such robot systems. In Fig. 10 a parallel 2D robot structure, augmented with suitable patch actuators to introduce actuating moments, is shown in combination with its linearized equations of motion at a specific workspace position. The actuators should counteract the vibrations of the underlying elastic structure, which are introduced by high accelerations during the handling and assembly task. Several complicated questions have to be answered for a fully functional realization. One severe implication of the high nonlinearity of the underlying structure is the large variation in the control object with respect to the location of the end effector.
Fig. 10

Application of smart piezo patches to elastic parts of a robotic paraplacer structure (left) and some aspects on the modelling of the actuator with the finite element method (right)

One successful approach to overcome the limitations due to large model changes is discussed in Algermissen et al. (2009). The workspace of the 2D robot system is partitioned into triangular subdomains. For each triangular cell, an elastic model is identified. The granularity of the mesh is chosen in a way that the variation in the underlying state space models in each triangle has a negligible influence on the overall control performance. The control algorithm tracks the coordinates of the end effector position in each cell and smoothly interpolates the elastic model during traversal of neighboring domains.

Obviously, the partition of large workspaces suffer from the course of dimensionality if a 3D domain has to be meshed. This limits the generality of the method, when it is applied to robot systems such as a hexapod with real six degrees of freedom, but even for 3D workspaces with prismatic grids, the interpolating control algorithm is applicable.

The elastic control with a continuously varying state space model has been applied to a real 3D robot system. This so-called Triglide (see Fig. 11) has one Cartesian x-axis and a 2D parallel configuration orthogonal to this axis. In addition to the experimental results, a stability proof using the Small-Gain Theorem of robust control theory is performed. With different transformations on the time-variant switching factors β, the Small-Gain Theorem provides satisfying non-conservative results under the assumption of infinitely fast varying parameters.
Fig. 11

Working Triglide robot system with local vibration control of the end effector

Cross-References

References

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Stephan Algermissen
    • 1
    Email author
  • Björn T. Kletz
    • 1
  • Martin Pohl
    • 1
  1. 1.Institute of Composite Structures and Adaptive SystemsGerman Aerospace Center (DLR)BrunswickGermany

Section editors and affiliations

  • Hans Peter Monner
    • 1
  1. 1.Institut für Faserverbundleichtbau und Adaptronik, Abteilung AdaptronikDeutsches Zentrum für Luft- und Raumfahrt e.V. (DLR)BraunschweigGermany