WO2005121901A1

WO2005121901A1 - System and method for damping structural modes using active vibration control

Info

Publication number: WO2005121901A1
Application number: PCT/IB2005/051773
Authority: WO
Inventors: Jan Van Eijk; Michael J. Vervoordeldonk
Original assignee: Koninklijke Philips Electronics N.V.
Priority date: 2004-06-09
Filing date: 2005-05-31
Publication date: 2005-12-22

Abstract

Active vibration control system of a construction of a first and second structural element (M1,M2) and a first and second resilient element (U1,U2), and equipped with an actuator (L1), a controller (CL) and at least one sensor (G1,G2). The first structural element is connected to a base through the first resilient element. The actuator is mounted between the first structural element and the base. The second structural element is connected to the first structural element through the second resilient element. In open loop, the system has an open loop frequency response with a gain > 0 dB both at a suspension mode frequency (Wp) and at a structural mode frequency (Ws). Above the structural mode frequency (Ws), the response displays a 0 dB crossing with a negative slope at a 0 dB crossing frequency. Actuator, controller and sensor form a control loop. The sensor measures the vibration of the first and/or second structural element, and provides a vibration signal to the controller. The controller provides a compensation signal to the actuator, which provides an actuating force based on the compensation signal. Values of amplifier bandwidth and sensor bandwidth are selected above the crossing frequency to obtain a stable control loop and to damp suspension and structural modes.

Description

System and method for damping structural modes using active vibration control

The present invention relates to a system for damping structural modes using active vibration control as defined in the preamble of claim 1. Moreover, the present invention relates to a method for damping structural modes using active vibration control.

A system and method which use active vibration isolation for damping suspension modes of a payload are well known. A so-called suspension mode, also referred to as a rigid body mode, describes the vibration of the payload (i.e., a construction) on its suspension. In this mode the payload moves substantially as a rigid body; large deformations occur in the suspension. When the construction is excited at the suspension frequency (for instance, by floor vibrations), the vibration amplitudes of the payload generally become larger than the excitation signals (i.e;, the moving floor). Therefore, a damping of this mode is required. US RE 33,937 discloses a system for active vibration isolation, which uses a geophone as velocity sensor in combination with a stretch filter to determine payload velocity and to apply active damping known as "sky-hook" damping. Here, in addition to a passive isolation (a resilient element), a force actuator, a sensor and a controller are added. The force actuator is arranged between payload and site to apply a force on the payload in response to a measured payload velocity. Control of the system is performed in an active loop wherein the velocity sensor signal is input for a stretch filter, whose output acts as feedback signal. The feedback signal is input (via a controller and an amplifier) to the actuator for actuating the payload to achieve a reduction of vibrations of the payload. In a construction, a payload typically comprises structural parts, e.g., a platform and a plurality of elements mounted thereon. Due to external excitations (such as the aforementioned floor induced vibrations) or internal excitations, the payload may show internal elastic deformations since the internal stiffness of the payload is finite. To minimize the influence of floor vibrations on the deformation of the payload, the payload is to be isolated. The internal vibrations are referred to as structural modes, as opposed to the suspension modes (or rigid body modes). Although isolation of floor vibration for a payload is achieved by the system from the prior art, the structural modes of the payload may still be excited, due to (internal or external) excitations, e.g., a remaining floor induced excitation. Isolators reduce floor vibrations, but do not eliminate influence of the internal forces caused by e.g., a moving internal part, such as a stage, or an external excitation by an acoustical source. The frequency of suspension modes is typically in a range from 0.5 - 5 Hz for soft mounts. The frequencies of the structural modes are generally higher, as constructions are in general designed for high stiffness. Structural modes typically range from about 30 Hz up to 1 kHz or higher, depending on the actual construction. In the prior art, active damping or active vibration control is usually aimed at damping the suspension modes. To achieve damping of structural modes, additional measures are necessary. To this extent, the construction may be equipped with further damping systems, located between those structural parts that may move relative to each other in order to reduce vibrations. Disadvantageous^, reduction of structural vibration by additional damping systems on the structural parts requires additional efforts with respect to design and engineering, and additional parts and cost. Adversely, in many constructions and designs no space is available for implementing the additionally required damping parts. US 2003/0053035 Al discloses a controller for a lithographic apparatus to reduce vibrational movements caused by resonances in the apparatus. The controller uses an algorithm based on the H infinity method.

It is an object of the present invention to provide a system for damping a structural mode using active vibration control, which overcomes the burden of the prior art with respect to design and engineering for obtaining damping structural modes in addition to damping suspension modes. The object is achieved by: a system for active vibration control of a construction, the construction comprising a first and a second structural element and a first and a second resilient element; the system further comprising an actuator, a controller and at least one sensor, in which: the controller comprises an amplifier having an amplifier bandwidth; the at least one sensor has a sensor bandwidth; the first structural element is connected to a base site through the first resilient element, and with the actuator mounted between the first structural element and the base site, and the second structural element is connected to the first structural element through the second resilient element; the system having an open loop frequency response with at least one suspension mode at a suspension mode frequency and at least one structural mode at a structural mode frequency, the system having an open loop gain > 0 dB at the at least one suspension mode and an open loop gain > 0 dB in the at least one structural mode, the open loop frequency response showing a 0 dB crossing with a negative slope at a 0 dB crossing frequency above the structural mode frequency; in use, the actuator, the controller and the at least one sensor being arranged in a control loop, the at least one sensor being arranged to measure a vibration of at least one of the first and the second structural element and the at least one sensor being connected to the controller for providing a vibration signal to the controller, and the controller being further connected to the actuator for providing a compensation signal as actuation signal to the actuator, the actuator being arranged for receiving the compensation signal as actuation signal and for providing an actuating force based on the compensation signal; the amplifier bandwidth having an amplifier bandwidth value and the sensor bandwidth having a sensor bandwidth value, both the amplifier bandwidth value and the sensor bandwidth value being chosen above the 0 dB crossing frequency such that the control loop is stable and both the suspension mode and the structural mode are damped. The present invention uses the system for damping suspension modes using active vibration control to increase the damping of the structural modes of the payload. Moreover, it is an object of the present invention to provide a method for damping suspension modes using active vibration control to be used with the system according to the present invention. The object is achieved by a method of active vibration control of a construction, the construction comprising a first and a second structural element and a first and a second resilient element; the system further comprising an actuator, a controller and at least one sensor, in which system: the controller comprises an amplifier having an amplifier bandwidth; the at least one sensor has a sensor bandwidth; the first structural element is connected to a base site through the first resilient element, and with the actuator mounted between the first structural element and the base site, and the second structural element connected to the first structural element through the second resilient element; the construction having an open loop frequency response with at least one suspension mode at a suspension mode frequency and at least one structural mode at a structural mode frequency, the system having an open loop gain > 0 dB in the at least one suspension mode and an open loop gain > 0 dB in the at least one structural mode, the open loop frequency response showing a 0 dB crossing with a negative slope at a 0 dB crossing frequency above the structural mode frequency; in use, the actuator, the controller and the at least one sensor being arranged in a control loop, the method comprising measuring with the at least one sensor a vibration of at least one of the first and the second structural element and providing a vibration signal to the controller, providing with the controller a compensation signal as actuation signal to the actuator, and providing with the actuator an actuating force based on the compensation signal; the amplifier bandwidth having an amplifier bandwidth value and the sensor bandwidth having a sensor bandwidth value, both the amplifier bandwidth value and the sensor bandwidth value being chosen above the 0 dB crossing frequency such that control loop is stable and both the suspension mode and the structural mode are damped.

Below, the invention will be explained with reference to some drawings, which are intended for illustration purposes only and not to limit the scope of protection as defined in the accompanying claims. Fig. 1 schematically depicts an exemplary construction build up of first and second structural parts Ml and M2; Fig. 2 schematically depicts variables in the construction of Figure 1, as well as parts of the construction; Figs. 3a and 3b show a Bode diagram of an open loop frequency response function (series of controller and plant) where the velocity of the first structural part Ml is measured; Fig. 4 depicts a first embodiment of a control loop according to the present invention, for use with the construction shown in Figures 1 and 2; Fig. 5 shows a block diagram for a modified control loop of the control loop according to figure 4 and comprising a high-pass filter; Fig. 6 depicts a second embodiment of a control loop according to the present invention, for use in the exemplary construction shown in Figures 1 and 2; Fig. 7 shows a frequency response function of the filter block (part of the controller) of Figure 6; Figs. 8a and 8b show a Bode diagram of frequency response functions in accordance with Figure 6; Fig. 9 shows a force mobility of the second structural part M2 in accordance with the first embodiment for a construction without active vibration control (un-damped), a construction under active vibration control with optimal damping using pure velocity feedback of the velocity of the first structural part Ml, and a construction under active vibration control with damping of the structural modes and using a high-pass filter for minimizing the damping of the suspension mode, using velocity feedback of the velocity of the first structural part Ml; Fig. 10 shows a third embodiment of a control loop according to the present invention.

The present invention relates to high precision equipment, which requires isolation in the presence of vibrations originating from, for example, the floor, acoustics, or internally generated disturbance forces. Such equipment comprises a payload which is to be isolated, like a metrology frame in lithographic projection apparatuses, or the construction comprises a stage in high resolution surface inspection tools such as scanning electron microscopes, scanning ion-beam microscopes, etc. Such a payload is not to be exposed to any of the aforementioned vibrations. As will be appreciated by persons skilled in the art, exposure of equipment to vibrations which may excite structural modes is hardly avoidable. Vibrations will always be present, only the level of the excited vibrations should be below a value, which may be acceptable during operation of the construction. To reduce the vibrations, the construction may be isolated from the source or may be arranged for damping the vibrations caused by the source. Structural vibrations within the apparatus may strongly reduce the performance of the apparatus to be effective at levels relating to details of small dimensions. For example, a lithographic projection apparatus may not succeed in imaging the smallest features of a mask pattern with sufficient accuracy and/or sufficient resolution. Figure 1 schematically depicts an exemplary construction build up of first and second structural parts Ml and M2. The construction comprises a payload, a first vibration sensor Gl and/or a second vibration sensor G2 (figure 2), a controller CL including an amplifier CA, and an actuator Ll. The amplifier CA may be a current amplifier or a voltage amplifier. The payload is located on a floor G and is built up from the first structural part Ml and the second structural part M2. The first structural part Ml of the payload is elastically mounted on the floor

G through a soft spring Ul which is the intended isolation. The second structural part M2 of the construction is mounted on first structural part Ml through a mechanical connection which due to the finite stiffness of the connection acts as a parasitic spring U2. For the remainder of the specification, the soft spring Ul is called the first spring and the mechanical connection between Ml and M2 will be called the second spring. X2 is defined as the absolute displacement of mass M2, whereas XI is defined as the absolute displacement of mass Ml. The actuator Ll is an actuator with a first and a second moveable part (not shown in detail), the first moveable part being connected to the floor G and the second moveable part being connected to the payload. The first and second moveable parts are arranged to exert a force between them. The actuator Ll may be, for example, a Lorentz engine or another type of actuator. Furthermore, a parasitic damping may be present between the floor G and the payload. It is noted that such parasitic damping is not relevant here with respect to the present invention. A vibration sensor is mounted somewhere on the payload on either first structural part Ml or second structural part M2, for recording vibrations of the payload. There may be provided a vibration sensor on both first and second structural parts Ml, M2. The actual location of the vibration sensor is depending on the embodiment of the present invention, and will be indicated separately for each embodiment. When the vibration sensor is mounted on first structural part Ml, it is labeled as Gl. When mounted on second structural part M2, it will be labeled as G2. For example, the vibration sensor Gl is a velocity measuring sensor. It is noted that a velocity sensor may measure a velocity signal directly. It is also possible that the velocity sensor Gl measures an acceleration and then derives the velocity signal from the measured acceleration. The same applies to velocity sensor G2. The output of the vibration sensor Gl is connected to an input of the controller CL. An output of the controller CL is connected to an input of the actuator Ll. The controller CL is arranged for determining an input signal for the actuator Ll, based on an output signal of the sensor Gl, in order to reduce the vibration of the payload by the actuator Ll. The vibration sensor Gl, G2 is arranged to obtain at least information of the vibration modes, i.e., both suspension mode and structural mode, of the construction. The first vibration sensor Gl is arranged to determine a first velocity _jJ_t of the first structural

part Ml. The second vibration sensor G2 is arranged to determine a second velocity /j_t of the second structural part M2. The payload (consisting of Ml and M2) will have a structural mode, which has a structural resonance frequency ω_s, which is typically higher than a suspension resonance frequency ω_p of the payload. For apparatuses like a lithographic projection system, the suspension frequency ω_p of a payload is relatively low, typically 1 Hz and the resonance frequency ω_s of a structural mode, e.g. the bending of the payload or the deflection of a lens element relative to a measurement tool is typically in a range between about 30 Hz and about 1 kHz. Figure 2 schematically depicts variables in the construction of Figure 1, as well as parts of the construction. In Figure 2 entities with the same reference number refer to the same entities as shown in Figure 1. The possibility of using an additional second vibration sensor G2 is shown in figure 2, where G2 is mounted on second structural part M2. The output of the second vibration sensor G2 is connected to a further input of the controller CL. The second vibration sensor G2 may be a velocity sensor, and will be discussed in more detail later. If only the first vibration sensor Gl or the second vibration sensor G2 is used, the respective other sensor may be omitted from the scheme. The exemplary construction shown in Figure 1 relates to a 2-DOF system (DOF = degrees of freedom) with displacement in vertical direction with further displacements and rotations in other directions being excluded. However, it is noted that the principle of the present invention also is applicable to other systems with more degrees of freedom and is not limited to the example as described below. In case no (active) damping is provided, a vibration, for example, a displacement h of the base G produces a displacement XI and 2 of the first and second structural parts Ml and M2, respectively, through the first and second springs Ul and U2. The first and second structural parts Ml, M2 mutually influence the respective displacements due to dynamic interaction of the mechanical coupling (second spring U2) between them. Since the coupling between Ml and M2 is not rigid, a relative displacement ΔX=X2-X1 exists between the second structural part M2 and the first structural part Ml of the payload. Figures 3a and 3b show a Bode diagram of an open loop frequency response function where a velocity of the first structural part Ml is measured. The open loop relates to a series connection of a controller and a plant, where the plant in this respect comprises the structural parts Ml, M2, the first and second springs Ul, U2 and vibration sensor Gl. The controller comprises a gain function GB. Figure 3 a schematically depicts an amplitude diagram of the open loop frequency response function. Figure 3b depicts a phase diagram of the open loop frequency response function in accordance with Figure 3 a. In this example the following data are used: the mass of the first structural part

Ml is 500 kg, the mass of the second structural part M2 is 500 kg. The suspension mode (relating to first spring Ul) has a frequency ω_p of 1 Hz. The structural mode (relating to second spring U2) has a frequency ω_s of 80 Hz. When using a pure P-controller (only proportional control) for feeding back the velocity , the maximum damping of the structural mode is reached at a gain of

approximately 3*10⁵ N/m/s, which corresponds to a relative damping of the structural mode of approximately 20%. In this example, the bandwidth is "only" 35 Hz. The bandwidth is defined as the first zero dB crossing at a frequency oo_tri above the suspension frequency ( , cf, figure 3 a, whereas the structural mode α^ is situated at 80 Hz. Persons skilled in the art will appreciate that simply increasing the gain and thus the bandwidth in an attempt to obtain higher damping of the structural mode will lead to a decrease of the structural damping (instead of an increase). In Figure 3a a further zero dB crossing above the structural mode is present at 130 Hz. Thus, in the open loop situation, the open loop gain at the suspension mode frequency Op is > 0 dB and the open loop gain at the structural mode frequency co^ is also > 0 dB. At the further zero dB crossing C0_tr2, the open loop has a negative slope. It is noted that the further zero dB crossing C0_tr2 above the structural mode ω_s is significantly above the bandwidth of 35 Hz. Care must be taken with regard to the gain and phase behavior around this frequency ω_tr2 that may be 130 Hz to avoid violation of the Nyquist criterion. In the example of Figures 3a and 3b, a feedback from the velocity ^x j_f of the first structural part Ml is used for damping the structural modes. In this example, only a single structural mode at ω_s= 80 Hz is present, but the present invention also applies in situations with a plurality of structural modes. Figure 4 depicts a first embodiment of a control loop according to the present invention, for use with the construction shown in Figures 1 and 2. The first embodiment of a control loop according to the present invention schematically comprises a subtractor B, a controller HC, and a process HP.

The process HP describes the relation between the actuator input and the various measured velocities (^dxV_dt ; ^dx/^l _dt) ^{of e} P^lant (comprising Ml, M2, Ul, U2, Gl and/or G2). The subtractor B for subtracting a second signal from a first signal is connected to a first subtracting input to receive a first signal Al, and to a second subtracting input to receive a second signal A2 and with its output to an input of the controller HC. For providing an action by the actuator in reply to an incoming signal, the controller HC comprises a gain function GB. The controller HC has an output connected to an input of the process HP. The process HP which provides the response of the payload to the action of the actuator is connected with its output to an input of sensor Gl, which is capable of measuring the response of the payload over a suitable frequency range well above the structural vibration frequency. The sensor Gl is arranged to measure the absolute velocity ^dxVj_t of the first structural part Ml. An output of the sensor Gl is connected to the second input of the subtractor B. It is noted that with respect to the mechanical behavior, Gl is shown as part of process HP. Therefore, a block displaying the action by Gl is not shown in figure 4. Further, it is noted that in this case it is assumed that the sensor Gl has a working frequency range at least equal to the complete frequency range of interest. In practice, the working frequency range may be smaller (particularly, in relation to the range of low frequency). A person skilled in the art will appreciate this limitation will not detract from the present invention. In use, a set-point signal is provided as first signal Al (which may be a reference signal e.g. zero) at the first input of subtractor B. At the second input of subtractor B the output signal of sensor Gl is provided as signal A2. The subtractor B subtracts second signal A2 from first signal Al to produce an error signal ε. The error signal ε is input to the controller HC, which generates a signal to the amplifier CA via the gain function GB. The amplifier CA drives the actuator Ll, that is e.g., a Lorentz engine. Finally the actuator Ll generates an actuating force FL to counteract the measured velocity ^y^ • The actuating force FL is input to the process HP. The process

response to the actuating force FL is a displacement xl and a change in velocity ^ ^ ■

The change in velocity "^xVj_f is, again, sensed by the sensor Gl (not shown in

Figure 4) and provided to the subtractor B as second signal A2, as described above. Typically, the first and second signals Al and A2 are signals in the electronic or software domain. It is noted that in Figure 4 the controller HC of the embodiment may comprise further elements such as a low-pass filter to reduce high frequency content or a notch filter to reduce high frequency content in a specific range. In accordance with the present invention, not only the suspension mode ω_p is affected by the control loop of Figure 4, but also the structural mode ω_s is affected. To this end, the active vibration isolation system according to the present invention is realized by the control loop as shown in Figure 4 under the following condition. The active vibration isolation system must be designed to be able to cope with a relatively large bandwidth: when only damping the suspension mode (in the example at 1 Hz), a bandwidth of the control loop of approximately 10 Hz would be sufficient to realize suspension damping. However, in order to create substantial structural damping too, i.e. to be sure that the loop is stable at the zero dB crossing frequency C0t_r2 too, a higher bandwidth of the control loop is needed. In this example, it turns out that a larger bandwidth BWO of about 35 Hz is suitable. To obtain this bandwidth, it is preferred to let the sensor Gl have a position, which is collocated with the actuator Ll, i.e., to let it have the same degree-of- freedom as the actuator. Furthermore, the bandwidth BWA of the amplifier CA for driving the actuator Ll must be well above the zero dB crossing C0tr₂. Also, the bandwidth BWG of the sensor Gl must be well above the zero crossing cotr₂, preferably at least about 4 times the frequency value of that zero-dB crossing cotr₂. It is noted that all controlling components (gain function GB, filter function, amplifier CA, actuator Ll) must be able to operate with each having a sufficiently large bandwidth, and that the respective bandwidth values depend on the actual construction (having a specific value for bandwidth BWO), and that it may require some trial and error when determining their optimum (i.e., minimum) values. Note that the bandwidth of a component is defined as the frequency at which the output of the component still follows the input of the component, i.e., e.g. has a value within a range between a low frequency value of the output and 3 dB below that low frequency value of said output. The collocation of the sensor Gl and the actuator Ll effectively results from a construction with a very high stiffness between these elements Gl and Ll, which means that substantially no vibrations between actuator Ll and sensor Gl occur. A person skilled in the art will appreciate that a plurality of positions for each element may be available in a given construction to obtain a collocated arrangement. With reference to figures 3a and 3b, the bandwidth BWA of the amplifier CA should be typically 1 kHz. The bandwidth BWG of the sensor Gl should also be typically 1 kHz in this case. It is noted that in the first embodiment as described above the damping realized for the suspension mode may be relatively large in comparison with the optimal structural vibration damping. To reduce the suspension damping somewhat, the control loop according to this first embodiment may be provided with a high-pass filter. In other words, addition of a high-pass filter allows for creating structural damping while keeping the suspension damping relatively small. Figure 5 shows a block diagram for a modified control loop comprising such a high-pass filter. In Figure 5 entities with the same references refer to the same entities as shown in the preceding figures. In comparison with the control loop of figure 4, the modified control loop CL further comprises a high-pass filtering controller HC. The high-pass filtering controller HC for providing an action by the actuator in response to an incoming signal has an output connected to an input of the process block HP. The high-pass filtering controller HC comprises gain function GB, a high-pass filter FHP, the amplifier CA and actuator Ll. In Figure 5 the signal in the high-pass filtering controller HC is first processed by the gain function GB and then by the high-pass filter FHP. Persons skilled in the art will appreciate that the order of processing in HC may be reversed. The gain function GB and the high-pass filter FHP are arranged in a series connection. The gain function GB generates a first amplified signal from the error signal ε. The output of the gain function GB is supplied to the high-pass filter FHP which filters the received signal. The high-pass filter FHP may have the following structure for its frequency response F(s):

F(s) = - s² + 2 - β - ω₀ - s + ύ)_Q wherein s is the Laplace operator, with ω₀ and β being a first and second filter constant, respectively. The first filter constant ω₀ denotes the corner frequency of the high pass filter FHP. The second filter constant β denotes the relative damping of the high pass filter FHP. The high-pass filter FHP filters the first amplified signal as processed by gain function GB to reduce transmission of low frequency signals affecting the suspension mode and to allow transmission of (relatively) high frequency components of the amplified signal. The filtered signal is output to the amplifier CA for generating a power amplified signal to the actuator Ll which provides actuating force signal FL to the process HP. According to the present invention, a second embodiment provides a control loop with such settings that the structural mode is damped by means of feedback of the velocity ^dx%_f of the second structural part M2. Figure 6 depicts such a second embodiment of the control loop according to the present invention, for use in the exemplary construction shown in Figures 1 and 2. In Figure 6 entities with the same references refer to the same entities as shown in the preceding figures. The controller HC comprises gain function GB and a filter block FB for providing a gain setting and a frequency dependent filter setting, respectively, to the actuator Ll. Gain function GB is shown as providing an output signal to the filter block FB, however, again, the order in which gain function GB and filter block FB process a signal within HC is not relevant. It is noted, that the filter block FB may also be located after the process HP, or before the gain function GB. Figure 7 shows a possible frequency response of the filter block FB of Figure 6. This filter block FB is also known as a twofold skewed notch filter, or a general second order filter with two zeroes and two poles. In this embodiment, the filter has two zeroes at a first frequency below the structural vibration frequency ω_s. Figure 7 shows a conjugated pair of zeroes at 40 Hz. A conjugated pair of two poles of the filter is shown at a second frequency above the structural vibration frequency ω_s. The zeroes are at a lower frequency than the structural vibration frequency ω_s and the poles are at a frequency above the structural vibration frequency ω_s, having a +2 slope between the zeroes and the poles. In use, a set-point signal is provided as first signal Al at the first input of the subtractor B. At the second input of the subtractor B the measured response signal A2 is provided to the subtractor B which then subtracts second signal A2 from first signal Al to produce error signal ε. The error signal ε is input to the controller HC, which applies the gain function GB and the filter function FB (as described above) and generates a control signal for the amplifier CA. The amplifier CA supplies a power amplified signal to actuator Ll which generates actuating force FL to dampen the velocity yj_f of the second structural part M2 as measured by velocity sensor G2. The actuating force signal FL is input to the process HP. The process response to the actuating force FL is a displacement xl andxl (and a velocity ^dxV_jf and jj_t , respectively). The velocity jι_t of the second structural part M2 is measured by the sensor G2 which converts the measured velocity into the second signal A2 for the subtractor B, as described above. Typically, the first and second signals Al, A2 are signals in the electronic or software domain. Figures 8a and 8b show the Bode diagram of a frequency response function in accordance with Figure 6. Figure 8 a shows the amplitude diagram, and Figure 8b shows the corresponding phase diagram. In Figure 8a and Figure 8b, a solid line depicts the open loop (i.e., the frequency response HC-HP) of the system of Figure 6 The frequency response function HC-HP with filter block FB equal to unity in the controller HC (thus HC-HP is equal to frequency response function GB-HP) is indicated by a dashed line. The dashed line indicating the loop without filter block FB shows that the control loop can not be closed without becoming unstable, as is obvious to a person skilled in the art. The solid line shows that the control loop can be closed and is stable when applying the filter block FB. The present invention achieves to obtain a control loop, which is stable upon closure, for damping of structural modes by the application of the skewed notch filter function FB in controller HC. In this second embodiment of figure 6, a bandwidth of approximately 20 Hz is obtained. The next zero dB crossing is at about 180 Hz. For the exemplary values of Ml and M2 given earlier, a relative damping of the structural mode of 60% can be obtained at a gain of approximately 1.8xl0⁵ N/m/s. Figure 9 shows a force mobility plot of the second structural part M2 in accordance with the first embodiment for a construction without active vibration control (undamped), a construction under active vibration control with optimal damping using pure velocity feedback of the velocity of the first structural part Ml (Figure 4), and a construction under active vibration control with optimal damping and filtering using velocity feedback of the velocity of the first structural part Ml (Figure 5). Force mobility is defined here as the velocity of M2 over an external force acting on M2. The force mobility without active vibration control (i.e., without damping) is depicted by a dotted line. The force mobility under active vibration control with damping (using only pure gain in the controller HC as shown in figure 4) is depicted by a solid line. The force mobility under an active vibration control with optimal damping and filtering, (in the sense of maximizing the structural damping, using pure gain and high-pass filter in the controller HC as shown in figure 5) is depicted by a dashed line. It is clear that active vibration control using only a pure gain control (solid line, cf. figure 4) strongly reduces the vibrations in the low frequency range around the suspension mode frequency ω_p and also reduces the vibrations around structural mode frequency ω_s. Such a pure gain control has a side-effect that the suspension mode damping is unintentionally high, which in practical situations might be undesired from the point of view of controller stability and or performance. For an optimal (i.e., less) damping of the suspension mode, the high pass filter

FHP is added to the control loop (figure 5). As a result, the damping as illustrated by the dashed line is obtained, as shown, In comparison to the situation without any damping (dotted line), such optimal damping would create a benefit with respect to the implementation of the present invention. In summary: by adding high pass filter FHP in the loop, the damping of the suspension mode will be reduced relative to damping by the pure gain control (solid line). But this reduction of the suspension mode damping (from solid to dashed line) may be preferred to avoid practical implementation problems. Moreover, a good damping of vibrations around the structural mode frequency ω_s is maintained (dashed line). Figure 10 shows a third embodiment of a control loop according to the present invention. In Figure 10 entities with the same references refer to the same entities with identical references as shown in the preceding figures. In the control loop of Figure 10 both velocities ^dxVj_f and jj_f are used in a feedback control loop for active vibration control. The velocity ^dx] _t of the first structural part Ml is measured by the first

velocity sensor Gl, and the velocity ^xjj_f of the second structural part is measured by the second velocity sensor G2, additional to the first sensor Gl. The control loop in this embodiment comprises a first subtractor Bl, a second subtractor B2, controller HC, process HP, and a third subtractor B3. The controller HC comprises a first controller portion HC1 and a second controller portion HC2, which two controller portions together schematically indicate the controller HC. The first subtractor Bl for subtracting a second signal from a first signal comprises a first subtracting input to receive a first signal Al, and a second subtracting input to receive a second signal A2 (which will be defined below). Further, the first subtractor Bl comprises an output for providing a difference signal εl between the first and second signals to an input of the second controller portion HC2. For providing an action by the actuator in reply to an incoming signal, the second controller portion HC2 comprises an output F+ connected to a first input of the second subtractor B2. A second input of the second subtractor B2 is provided for receiving a second actuator response signal F-, which will be described later in more detail. The second subtractor B2 determines a force signal ΔF from subtracting said second actuator response signal F- from said first actuator response signal F+. The force signal ΔF is fed to an input of the process HP. An output of the first sensor Gl for outputting a first signal corresponding to the first velocity _{y jt} is connected to a first input of the third subtractor B3. An output of the second sensor G2 for outputting a second signal corresponding to the second velocity ^dx%_t is connected to a second input of the third subtractor B3. The third subtractor B3 determines the difference between the first signal of the first velocity Vj_f and the second signal of the second velocity _f ■ On its output the third subfractor B3 provides a velocity difference signal A2. The velocity difference signal A2 is provided as the second input signal to the second input of the first subtractor Bl. Further, the output of the first velocity sensor Gl is also connected to an input of the first controller portion HC1. An output of the first controller portion HC1 is connected to the second input of the second subtractor B2. The signal relating to the first velocity "^xl^/j_f is provided as second actuator response signal F- to the second subtractor B2. In use, a set-point signal (a reference signal which may be zero) is provided as a first signal Al at the first input of first subtractor Bl. The process HP describes how the construction responds to the force signal ΔF exerted on the construction. The following relation between ΔF, ^dxVj_f and yj_f is found: . „ . .dx\ . c2 . dx2 ΔF = -c3 • ( ( ) ) (2), dt el + c2 dt where cl, c2 are the control functions as performed by controllers HC1 and HC 2, respectively, c3=cl+ c2 with cl > 0 and c2 > 0. Preferably, these control functions cl and c2 are based on pure gains. In other words, in the third embodiment, a weighted combination of the measured velocities ^x/j_t , /_M is used to obtain a stable control loop for the construction, using, e.g., only pure gains cl, c2 as confrol action. It is noted that the controller portion HC1 and HC2 each may comprise an additional filter, like a notch filter or a low-pass filter, to suppress for example undesirable dynamical effects, which, for reasons of clarity, have not been taken into consideration in the specification above. Below the scope of the invention will be defined by the wording of the claims and its equivalents. In the claims, instead of the term "spring", as used in the description for expressing any flexibility between floor G, and structural parts Ml and M2, the term

"resilient element" will be used. Instead of "floor", in the claims, the more general term "base site" will be used.

Claims

CLAIMS:

1. System for active vibration control of a construction, said construction comprising a first and a second structural element (Ml, M2) and a first and a second resilient element (Ul; U2); said system further comprising an actuator (Ll), a controller (CL) and at least one sensor (Gl; G2), in which: said controller (CL) comprises an amplifier (CA) having an amplifier bandwidth (BWA); said at least one sensor (Gl; G2) has a sensor bandwidth (BWG); said first structural element (Ml) is connected to a base site (G) through said first resilient element (Ul), and with said actuator (Ll) mounted between said first structural > element (Ml) and said base site (G), and said second structural element (M2) is connected to said first structural element (Ml) through said second resilient element (U2); said system having an open loop frequency response with at least one suspension mode at a suspension mode frequency (ω_p) and at least one structural mode at a structural mode frequency (ω_s), said system having an open loop gain > 0 dB in said at least one suspension mode and an open loop gain > 0 dB inj said at least one structural mode, the open loop frequency response showing a 0 dB crossing with a negative slope at a 0 dB crossing frequency ( ) above said structural mode frequency (ω_s); in use, said actuator (Ll), said controller (CL) and said at least one sensor (Gl; G2) being arranged in a control loop, said at least one sensor (Gl; G2) being arranged to measure a vibration ( "^xVj_t , ' /_j* ) °f ^at least one of said first and said second structural element (Ml; M2) and said at least one sensor (Gl; G2) being connected to said controller for providing a vibration signal to said controller, and said controller being further connected to said actuator (Ll) for providing a compensation signal as actuation signal to said actuator (Ll), said actuator (Ll) being arranged for receiving said compensation signal as actuation signal and for providing an actuating force based on said compensation signal; said amplifier bandwidth (BWA) having an amplifier bandwidth value and said sensor bandwidth (BWG) having a sensor bandwidth value, both said amplifier bandwidth value and said sensor bandwidth value being chosen above said 0 dB crossing frequency (ω_tr ) such that control loop is stable and both said suspension mode and said structural mode are damped.

2. System for active vibration control according to claim 1, characterized in that said at least one sensor (Gl) is collocated with said actuator (Ll).

3. System for active vibration control according to claim 1 or 2, characterized in that said controller comprises a further filter (FB; FHP) arranged for reducing a damping of the suspension mode (ω_p) by said control loop.

4. System for active vibration control according to claim 3, characterized in that said filter (FHP) is a high pass filter.

5. System for active vibration control according to claim 3 or 4, characterized in that said filter (FB) has two zeros at a frequency below said structural mode frequency (ω_s), and two poles at a frequency above said structural mode frequency (ω_s).

6. System for active vibration control according to any one of the preceding claims, characterized in that said system comprises a first sensor (Gl) arranged to measure a first velocity ( ^dxV_f ) of said first structural element (Ml), a second sensor (G2) to measure a

second velocity (^dxy/_f ) of said second structural element (M2) said controller being

arranged to receive both said first and second velocity ( ^dxVj_f , ' yj_* ) ^and ^to determine an actuator signal for said actuator (Ll) based on both said first and second velocity

(dx\/ - dx2/ \ ^y /dt ' /dt '-

7. System for active vibration control according to claim 6, characterized in that said actuator signal is derived from a weighted combination of said first velocity ( ^dx) _f ) and

said second velocity ( yj_t )•

8. System for active vibration control according to claim 7, characterized in that said actuator signal is proportional to: „ ,dx\ , c2 . dx2. - c3 ^■ ( ( ) ) dt c\ + c2 dt where cl and c2 are predetermined control functions, c3=cl+c2 with cl > 0 and c2 > 0.

9. System for active vibration control according to claim 7 or 8, characterized in that said controller (HC) comprise at least one additional filter of at least one of a notch filter, a band pass filter, a high pass filter and a low-pass filter.

10. Method of active vibration control of a construction, said construction comprising a first and a second structural element (Ml, M2) and a first and a second resilient element (Ul; U2); said system further comprising an actuator (Ll), a controller (CL) and at least one sensor (Gl; G2), in which system: - said controller (CL) comprises an amplifier (CA) having an amplifier bandwidth (BWA); said at least one sensor (Gl; G2) has a sensor bandwidth (BWG); said first structural element (Ml) is connected to a base site (G) through said first resilient element (Ul), and with said actuator (Ll) mounted between said first structural element (Ml) and said base site (G), and said second structural element (M2) is connected to said first structural element (Ml) through said second resilient element (U2); said construction having an open loop frequency response with at least one suspension mode at a suspension mode frequency (ω_p) and at least one structural mode at a structural mode frequency (ω_s), said system having an open loop gain > 0 dB in said at least one suspension mode and an open loop gain > 0 dB in said at least one structural mode, the open loop frequency response showing a 0 dB crossing with a negative slope at a 0 dB crossing frequency (ω_tβ) above said structural mode frequency (ω_s); in use, said actuator (Ll), said controller (CL) and said at least one sensor (Gl; G2) being arranged in a control loop, said method comprising measuring with said at least one sensor (Gl; G2) a vibration

( /d_t ' ^^X/ _t ) °^ ^at ^^{east one} °^ ^sa ° ^^{rst anc sa}^ ^secon(i structural element (Ml ; M2) and providing a vibration signal to said controller, providing with said controller a compensation signal as actuation signal to said actuator (Ll), and providing with said actuator (Ll) an actuating force based on said compensation signal; said amplifier bandwidth (BWA) having an amplifier bandwidth value and said sensor bandwidth (BWG) having a sensor bandwidth value, both said amplifier bandwidth value and said sensor bandwidth value being chosen above said 0 dB crossing frequency (ro_tr2) such that confrol loop is stable and both said suspension mode and said structural mode are damped.