Active Control of Vibration, Applications of
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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.
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.
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.
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).
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).
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.
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).
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.
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.
- Kletz BT (2017) Aktive Schwingungsberuhigung mit reflektierenden und isolierenden Verbindungselementen in mehrfach angeregten Strukturen. Shaker VerlagGoogle Scholar
- Kletz BT, Melcher J (2015) Dual feedback control for vibration isolation systems dealing with multiple excitations. In: ICSV22, Florence, pp 1–8Google Scholar
- Kletz BT, Melcher J, Sinapius M (2012) Active vibration isolation of rear-view mirrors based on piezoceramic ”double spiral” actuators. In: Proceedings of ISMA2012-USD2012, pp 305–320Google Scholar
- Pohl M, Rose M, Breitbach E (2011) Lrm- und Schwingungsreduktion eines Kreissgeblattes mit flchigen Piezokeramiken und hybriden elektrischen Netzwerken. Shaker VerlagGoogle Scholar
- Schlünz S (2005) Analyse von berufsbedingt anerkannten Lärmschwerhörigkeiten. PhD thesis, Thüringer Universitäts-und LandesbibliothekGoogle Scholar