Active controller for the attenuation of mechanical vibrations

A plural orthogonal feed forward control system with an actuator system for installation on an upper floor or area of a building as an integral part of a building's structural supports to control seismic, wind, or wave disturbances to the structure or building. Control means include upstream and dual orthogonal downstream sensor arrays for determination of input and output error signals, plural orthogonal anti-feedback filters, and the plural adaptive weight updates to best determine the orthogonal components of the cancellation signal. The cancellation signal is acted on by the variable controlling force apparatus consisting of hydraulic or other actuators with stiff rods attached to the building structure and connected with a movable mass. The device works on orthogonal components of the disturbance, and is capable of attenuating simultaneously signals whose spectra contain multiple narrowband and/or combined narrowband and broadband character.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The invention relates to an active control system for protecting a 
structure, such as a building, from disturbances, such as vibrational 
disturbances, by imparting canceling forces to the structure. More 
particularly, it relates to a plural orthogonal controlling force 
apparatus, having a corresponding number of plural time domain digital 
controllers, with input and output sensor arrays which work on orthogonal 
components of the disturbance. The apparatus is capable of attenuating 
simultaneously signals with spectra consisting of multiple narrowband 
character, or combined narrowband and broadband character. The invention 
has particular applicability to controlling or counteracting seismic or 
other environmentally induced disturbances. 
2. Description of Related Art 
Vibration control systems for attenuating undesirable wind, earthquake and 
mechanical vibrations are known. Many of these prior vibration control 
systems are passive systems such as the base isolation and the dynamic 
absorber type control systems that are commonly used to attenuate unwanted 
vibrations. Patents relating to various techniques for wind and earthquake 
disturbance control include U.S. Pat. Nos. 4,783,937; 4,799,339; 
4,841,685; 4,429,496; 4,635,892; 4,922,667; 4,956,947; 4,766,706; 
5,025,599; 5,036,633; 5,107,634; 5,233,797; 5,239,789; 5,245,807; 
5,255,764; and 5,311,709. However, because the character of the undesired 
vibrations may change over time, active vibration control may provide 
better attenuation abilities than passive systems. A combination of active 
and passive methods may provide the best protection against unwanted 
vibrations, particularly from earthquakes. 
A known prior art controller for wind and earthquake disturbances by 
Nishimura (Nishimura, Isao et al., "An Experimental Study of the Active 
Control of a Building Model," Proceedings of the First Joint U.S./Japan 
Conference on Adaptive Structures, Maui, Hawaii, Nov. 13-15, 1990) is 
depicted in FIG. 1. It is based on feedback analysis. This system does not 
have an upstream sensor array to measure the disturbance signal, x.sub.k, 
before the disturbance enters the structure; all responses are measured by 
the downstream sensors to give the output or error e.sub.k. The error 
signal e.sub.k is fed into an analysis box to give the cancellation signal 
u.sub.k which is imparted to the system by an actuator. It is a closed 
loop controller. The control law is a linear feedback control system based 
on the first order differential equation model of the system. This control 
system requires development of a good model for the building or structure 
before the controller is installed. State space based controllers have 
difficulty with time lags. If the time lag, between the time the 
disturbance is sensed and the time the correcting force is applied, is too 
long this type of controller does not work well. 
A prior art controller for earthquake disturbances by Kobori et. al. (U.S. 
Pat. No. 4,799,339) is shown in FIG. 2. This controller is a feed forward 
frequency domain controller 10" based on a single frequency with upstream 
sensors 4" near the building and close to the source of the seismic 
disturbance. (In addition to the feed forward controller, a feedback 
controller to modify the rigidity of the building by stiffness connectors 
5 is also incorporated.) The downstream sensors 6" are on the building 2". 
Though this is a feed forward controller it is significantly different 
than the present invention since it is not only frequency domain based but 
also limited to a single frequency. This system has two upstream sensor 
sites 4"; one at the epicenter 4"A of the earthquake and the second 
consisting of two sensors in the ground near the building 4"B. This 
assumes that the network of seismic monitoring sites is extensive so that 
any earthquake epicenter will be monitored by a nearby sensor. This may be 
feasible in Japan or California but may be difficult elsewhere. The 
schematic shows the sensors 6" within the building 2" and the controller 
10". In addition, this system strives to change the rigidity to reduce the 
vibration of the building as well as control the excess disturbance. The 
addition of the rigidity modifications 5" then changes the transfer 
functions of the controller with time making this a very difficult control 
problem. The patent description of this prior art does not discuss the 
details of the controller other than to say that it "analyzes frequency 
characteristics and calculatively forecasts the oscillatory property" 
(U.S. Pat. No. 4,799,339, column 5, lines 57-58). 
Other control systems of the digital feed forward type are also known in 
the art. Much of the early work in digital feed forward control systems 
occurred in the acoustic field arena for noise attenuation in a fan duct 
using a speaker to introduce the canceling sound wave. Prior control 
systems for acoustic systems use adaptive filtering based on the Least 
Mean Square (LMS) algorithm in various configurations to estimate the 
required cancellation signal to be introduced into the system. Examples of 
these techniques include U.S. Pat. Nos. 5,337,365; 5,325,437; 5,355,417; 
5,377,275; and 5,377,276. Prior control systems based on the LMS will 
adapt successfully for strictly broadband or narrowband characteristic 
input signals but, if the input signal spectrum consists of a broadband 
signal and a narrowband signal or of multiple close tones, the filter 
output may not converge, or, at best, converge extremely slowly. This is 
true because, when the condition number of the input correlation matrix is 
large, the LMS will not converge. Since many mechanical systems have 
multi-tonal input signals, this type of controller is not generally 
applicable. 
Input signals with both broadband and narrowband characteristics in the 
frequency domain will be referred to as combined input. An example of 
combined input consists of colored noise (broadband) and multiple tonals 
(narrowband). Thus, prior control systems with the adaptive LMS filter may 
be used effectively and efficiently only in systems with input signals 
that have a strictly broadband or narrowband spectrum where the tones are 
well separated. In addition, prior control systems also have difficulty 
converging for narrowband signals consisting of multiple tones. A 
significant drawback of control systems with the LMS as the adaptive 
filter is their inability to converge rapidly (within k*n filter lengths, 
k&lt;10) for combined input. The convergence time may be such that the 
necessary action by the compensator or actuator to cancel the noise or 
vibration is applied too late and thus, instead of reducing the vibration, 
the problem becomes exacerbated. 
FIG. 3 shows a known prior art filtered-X controller system developed by 
Burgess (Burgess, J. C., "Active adaptive sound control in a duct: A 
computer simulation," J. Acoust. Soc. Am., 70(3), Sep. 1981, pp. 715-726). 
This controller is designed for use with a Finite Impulse Response (FIR) 
filter adapted in the time domain using the LMS algorithm. This controller 
includes upstream 4' and downstream 6' sensors feeding into the controller 
10'. The disturbance is sensed at the upstream sensor array 4' and then 
enters the object 2' generating the unwanted response. The canceling 
signal is added 8' and then the resulting output or error signal is sensed 
by the downstream sensor array 6'. P.sub.1 represents the transfer 
function between the upstream 4' and downstream 6' sensors. P.sub.2 
represents the transfer function between the canceling force device and 
the downstream sensors. P.sub.2 represents an estimate of P.sub.2. The 
output error signal e.sub.k is fed into the LMS controller algorithm 20'B 
along with v.sub.k (the disturbance signal x.sub.k filtered by the 
estimate of P.sub.2 gives v.sub.k). The LMS algorithm determines the 
weights or coefficients which give the best canceling signal. These 
weights are then used to filter 20'A the disturbance signal to give 
q.sub.k. The signal, q.sub.k, is then applied to the object through the 
actuator array which is represented by P.sub.2 16' to give the 
cancellation signal y.sub.k. This controller does not have an 
anti-feedback filter so it has difficulty with non-ideal systems where 
there is contamination of the upstream sensor by the canceling signal. 
This controller works well for an ideal system if the input signal's 
spectrum consists of a single tone or of strictly white noise of broadband 
character. Because this control configuration is based on the LMS 
algorithm, as discussed above, it does not perform well for the combined 
problem or for the multiple tone problem. 
Many practical systems experience the combined input such as tones in 
colored noise. This is frequently true in structural control. A stable 
control system which will handle combined input is necessary for 
structural vibration attenuation. Prior stable FIR systems adapt too 
slowly to actively control the physical system to reduce the vibrations of 
the system when the input consists of combined narrowband (tonals) and 
broadband spectrum signals. Thus, there is a need for a stable control 
system that can adapt rapidly for all types of input but, in particular, 
for the combined broadband/narrowband problem or the multiple tonal case. 
In active adaptive filters such as those of Burgess discussed above and 
depicted in FIG. 3, to control unwanted signals there must be a canceling 
signal that is summed with the input signal to attenuate the input signal 
as it traverses the object to be controlled. The input and output signals 
must be measured by appropriately located sensors and the canceling signal 
must be generated by actuators and propagated into the structure. The 
structure to be controlled, and the sensors and actuators constitute the 
physical system. The physical system can be thought of as a number of 
"plants" interacting to produce the output. A "plant" is defined to be the 
transfer function between two nodes such as between the input and output 
sensor arrays, such terminology being well known in the art. The digital 
controller or electrical system consists of estimates of plant models, 
other filters and the adaptive algorithm that determines the cancellation 
signal. 
The general goal of such control systems is to control the motion of the 
structure by minimizing the error signal. The canceling signal device is 
adapted by the system controller which may consist of various plant model 
estimates, a system model, and an adaptive algorithm in a specific 
controller configuration. 
The present invention is based on the well-known concept of Finite Impulse 
Response (FIR) filters in the time domain. As such, only time domain FIR 
based methods will be discussed in detail. A FIR filter model, as is 
known, consists of a set of N+1 weights which represent a plant such that 
when convolved with the input data, produce an estimate to the actual 
plant output. A FIR filter is also referred to as an all zero filter 
because it requires only data entering the plant, x, and not output data, 
y. If we let b.sup.k .tbd.{b.sub.0.sup.k . . . b.sub.N.sup.k } be the set 
of N+1 filter weights at time k, and let x.sub.k be the input value at 
time k, and y.sub.k be the output value at time k, then the output at time 
k may be written as a linear combination of the filter weights with the 
past input values: 
EQU y.sub.k =b.sub.0.sup.k x.sub.k +b.sub.1.sup.k x.sub.k-1 +. . . 
+b.sub.N.sup.k x.sub.k-N. 
The vector b may be fixed for all time or it may be adapted in time by an 
adaptive filter algorithm. In the z-domain the transfer function may be 
written as 
##EQU1## 
It has a denominator of 1 indicating that no output values are required. 
It is called a finite impulse response filter (FIR) because when an 
impulse is applied to this system its response dies out in finite time. 
For a detailed explanation of the Z-domain and FIR filters, see Widrow & 
Stearns, Adaptive Filter Processing, Prentice Hall, 1985, Chapters 7 and 9 
of this well-known text. Many times, in order to obtain a good 
approximation to the plant, N must be large. The value of N must be 
weighed in conjunction with the convergence rate of adaptive filter so 
that convergence is rapid enough for the system to be realizable. 
The controller cannot control without a method to adjust the weights, b, 
which determine the canceling signal to be propagated into the system. The 
method of adjustment, the adaptive filter algorithm, is an integral part 
of any controller without which there can be no active control. The 
adaptive filter algorithm adjusts the weights at each time step based on 
some defined error criteria. The weights are adapted in time and will 
change at every time step until the adaptive filter algorithm has 
converged. If at a later time the input varies in time the weights will be 
adapted anew to match the new input characteristics. Adaptive algorithms 
that have been used in adaptive feed forward controllers include the Least 
Mean Square (LMS) and the LMS in normalized form (NLMS). 
The LMS is a gradient descent method developed by Widrow (see Widrow & 
Stearns, Chapter 6). It uses a single past sample when adjusting the 
weights for the cancellation based on the error signal at the output 
sensor. It also has a scaling or acceleration parameter .mu. (also called 
the adaptive gain constant) that is determined by the user based on the 
problem of interest as is well known in the art (see, Widrow and Stearns, 
p. 111, Eq. 6.36). The LMS computes the weight update as: 
EQU e.sub.k =y.sub.k -y.sub.k 
EQU w.sub.k+1 =w.sub.k +2.mu.e.sub.k v.sub.k 
where the above variables and coefficients are as shown in FIG. 3. It 
requires O(N) computations per sample and performs well for problems where 
the input data correlation matrix, R, has a small condition number 
(R=E[X.sup.T X] where X is the input data vector). [O(N) is read as 
Order(N) and means that the number of operations required per time step is 
proportional to N. This can be written as K*N, where K is a constant.] 
The NLMS algorithm, as is well known, is the LMS normalized by 
.parallel.v.sub.k .parallel..sup.2. It computes the weight update as 
##EQU2## 
The Block Underdetermined Covariance (BUC) algorithm was developed by Slock 
(Slock, D. T. M., "The Block Underdetermined Covariance (BUC) Fast 
Transversal Filter (FTF) Algorithm for Adaptive Filtering," Proceedings of 
the 26th Asilomar Conference on Signals, Systems and Computers, 1992, 
incorporated by reference herein). The BUC is a modified block least 
squares method which uses an L.times.L estimate to the N.times.N input 
correlation matrix and a sliding window. It requires O(L.sup.2) 
computations, where L may be relatively small compared to N. It also has a 
scaling parameter that is set by the user. Unlike the LMS, the BUC is 
relatively insensitive to the condition number of the input correlation 
matrix. 
The objective of the BUC algorithm, which governs the operation of the 
transversal filter, is to obtain the filter weights in such a way as to 
minimize the error, e, and find the weighted sum of the input signals that 
best fits the desired response. This objective is similar to that of the 
LMS. However, the methods by which the two algorithms determine the filter 
coefficients and minimize the error differ markedly. In the LMS, changes 
in the weight vector to accomplish this end are made along the direction 
of the estimated gradient vector based on the method of steepest descent 
on the quadratic error surface. The LMS relies on a single past sample 
value to determine the estimate of the filter weights. The BUC uses 
multiple past sample values (equal to a small percentage of the number of 
weights) to determine the estimate of the filter weights by minimizing the 
least squares criterion. 
The BUC algorithm uses a window length L that is shorter than the FIR 
filter order N, leading to an underdetermined least squares problem to be 
solved. The BUC can treat successive blocks of data with no overlap or it 
can slide along the data advancing the block by as little as a single 
sample. A projection mechanism onto a subspace of dimension L renders the 
BUC's convergence less sensitive to the coloring of the input signal 
spectrum than is the case for the LMS algorithm. The underdetermined least 
squares character of the BUC also endows it with relatively fast tracking 
ability. In addition, the tracking ability of least squares type 
algorithms (such as the BUC) is independent of the condition number of the 
input correlation matrix. 
The goal in selecting an adaptive filter algorithm for adjusting the filter 
weights is to enable fast convergence, without too many computational 
steps, and to produce the correct cancellation signal. When used as part 
of a feed forward controller, the LMS or NLMS algorithms converge quickly 
and accurately so long as the input signal is not a combined broadband and 
narrowband signal or is not a multiple tonal signal. With these latter 
inputs, the LMS/NLMS algorithm converges slower than the BUC, if it 
converges. 
The BUC algorithm has not, to the applicant's knowledge, been used as an 
adaptive filter algorithm in a controller system. The BUC is expected to 
be slower than the LMS algorithm since it generally requires more 
computations per time step. 
SUMMARY OF THE INVENTION 
The present invention is an adaptive feed forward control system for 
reducing or attenuating disturbances acting upon or within a physical 
structure, such as a building. The invention includes sensors to sense or 
detect the disturbances and a method to then separate such sensed 
disturbances into orthogonal signal components. Plural orthogonal feed 
forward controllers, corresponding in number to the number of orthogonal 
components, impart cancellation forces, through orthogonally oriented 
actuators, to the structure to cancel the undesired disturbances. 
The plural orthogonal feed forward control system of the present invention 
has particular applicability for attenuating a vibration field in a 
building structure resulting from externally applied seismic or other 
environmentally induced disturbances, such as earthquakes or high wind 
disturbances. The vibration field induced by these external disturbances 
is defined as the input vibration field. As is well known, earthquake 
ground waves produce vibrations within a structure that may cause 
substantial damage. Earthquake energy propagates through the earth as 
compressional and shear waves which impart energy to structures in the 
form of compressional, shear and bending waves. Bending waves are 
generally the most destructive. The energy of the earthquake imparted to 
the building is filtered by the building resonances (mostly by the first 
three major resonance frequencies). The spectrum of the signal propagating 
through the structure may consist of narrowband and/or broadband 
character. 
Structures such as oil rigs in the ocean face disturbances similar to that 
for building structures during earthquakes. The wave motion of the water 
causes the platform to sway introducing shear and bending waves into the 
structure. This problem can be formulated exactly as that of control of a 
structure during an earthquake. 
The present invention provides for plural orthogonal feed forward 
controllers, for example, dual orthogonal controllers, for driving dual 
orthogonal actuators for imparting a vibration field to the building 
structure so as to counteract the primary vibration field on the structure 
resulting from earthquakes or high wind conditions. This counteracting 
vibration field is defined as the cancellation vibration field. A movable 
mass is situated at an upper level of the building, such as a central 
chamber within the building located at one of the top-most floors. 
Actuators connected between the movable mass and the structural supports 
of the building move the movable mass so as to counteract or cancel the 
vibrations induced by the input vibration field. 
To reduce the complexity of a controller, orthogonalization of the input 
and output will simplify the design. For rigid body motion, three 
translational displacements or their derivatives can be sensed and three 
rotational displacements or their derivatives can be sensed. Total control 
of the motion of a rigid body requires six independent (i.e., orthogonal) 
channels. If the channels are not independent (i.e., not orthogonal) then 
36 channels could be required. Non-rigid body motion can be orthogonalized 
by sensing and controlling patterns of vibration which are orthogonal to 
one another. Those patterns of motion may or may not correspond to the 
modes of vibration of a structure. Complete orthogonalization is not 
required to improve the performance of a controller. The separation of the 
sensed disturbances into orthogonal components, the provision of separate 
orthogonal controllers responsive to such components, and the providing of 
orthogonal outputs to control orthogonally oriented actuators provides 
many advantages. For example, it reduces the number of channels required 
simplifying the controller configuration. Also, orthogonality reduces the 
condition number (due to spatial effects) of the problem making the 
problem easier to solve. If full orthogonalization is not possible, 
partial orthogonalization may be used simplifying the controller to a 
lesser extent. 
The present invention is also directed to an adaptive feed forward control 
system for counteracting undesirable disturbances by applying cancellation 
signals to a physical structure or system, whereby the adaptive feed 
forward controller adjusts the adaptive filter weights in accordance with 
the BUC algorithm. The BUC algorithm has several advantages previously 
unrecognized in the controller art. Specifically, the BUC algorithm may be 
successfully employed where the input signal spectrum is of combined 
broadband and narrowband character or of multiple narrowband character 
(multiple tones). These combined type signal spectra are found to exist in 
earthquake seismic signals. Moreover, despite the increase in the number 
of computations required per time step for the BUC algorithm as compared 
to the LMS algorithm, it has been discovered that the parameter L of the 
BUC, which determines the L.times.L estimate of the input correlation 
matrix, is smaller than expected for success. Thus, the total number of 
computations required for a solution within a given tolerance may not be 
substantially greater than for the LMS. 
Accordingly, it is an object of the present invention to provide a feed 
forward control system for reducing disturbances, such as vibrational 
disturbances, acting upon a structure using plural orthogonal controllers, 
preferably dual orthogonal controllers. It is a further object of this 
invention for utilizing such plural controllers to counteract earthquake 
or other environmental disturbances, such as high wind disturbances. Still 
further, it is an object of the present invention to control or counteract 
disturbances of both broadband and narrowband character, or multiple 
narrowband character, by using an adaptive filter employing the BUC 
algorithm.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
A generalized schematic of an active feed forward controller system is 
depicted in FIG. 4. The vibrational disturbance x.sub.k, such as an 
earthquake, wind, or other disturbance that may induce undesirable 
vibrations is measured at an upstream vibrational sensor array 4. The 
disturbance passes through the structure 2 to a second sensor array 6 
within the structure to give the error or output signal. The error value, 
e.sub.k, anti-aliased and digitized, e.sub.k 12, is input into the 
controller 10 along with the anti-aliased and digitized disturbance 
signal, x.sub.k, 12. The controller 10 determines the best canceling 
signal u.sub.k which is passed through a D/A converter and an amplifier 14 
to give u.sub.k and then u.sub.k is applied to the mechanical or 
structural system by the shaker or actuator array 8 to attenuate the 
undesired vibrational response. As will be discussed, the upstream sensor 
array 4 senses the disturbance and provides an electrical input or 
reference signal which is then separated into orthogonal components. The 
controller 10 includes plural orthogonal controllers providing orthogonal 
canceling signals to orthogonally oriented actuators. 
The present invention has applicability for any type structural vibration 
cancellation problem. Two examples, for earthquakes and wind disturbances, 
will be discussed in detail, however use of this invention is not limited 
to these specific types of problems. 
A seismic disturbance to a building generates shear and bending waves 
within the building or structure which excite the vibrational modes of the 
building or structure. Similarly, an ocean wave disturbance to an 
ocean-based structure (such as an oil rig) also generates shear and 
bending waves within the structure which excite the vibrational modes of 
the structure. In each of these cases, the major excitation energy occurs 
in the first three modes of the structure and may cause the building or 
structure to sway side to side or front to back. The vibrational modes of 
a building or structure may be determined by experimental methods (driving 
the building with a force and measuring its modes) or by mathematically 
modeling the building or structure using a finite element model. (As used 
herein, the term "building" or "building structure" is meant to be generic 
to both buildings, such as high-rise office buildings or ocean-based 
structures, such as oil rigs, or any other type of structure that behaves 
similarly.) 
The vibrational building modes are orthogonal to each other. This 
orthogonality can be used to assist in the placement of the downstream 
sensors and control actuators. 
As shown in FIG. 5A, a plurality of input sensors 4 are disposed around a 
building 2. These sensors 4 may include velocimeters, accelerometers, or 
displacement measuring devices which sense an incoming earthquake 
vibration and convert the sensed vibrational disturbance to an electrical 
input or reference signal. As will be discussed, the input signal is 
broken down into orthogonal components and provided to the controllers 
which control the actuator 8. The actuator 8 consists of two separately 
controlled actuators 28A,28B attached to orthogonal sides of a mass 
integrated into an upper floor of the building structure and to the main 
supports of the building so that the canceling forces can be applied 
directly to the main supports of the building. Two downstream arrays of 
sensors 6A,6B installed along orthogonal sides of the building must be 
placed such that they are not located at a node of the first three 
vibrational modes. Sensors located at a node will not sense the motion 
because of the null that occurs at a node. The number of sensors required 
will depend on the size and height of the building. The downstream sensor 
arrays, located in orthogonal planes of the building, provide an error or 
output signal to each of the controllers as will be described. 
The upstream array of input sensors 4 are circularly located in the ground 
about the building. The number of upstream sensors required depends on the 
size of the base of the building. There must be a sufficient number of 
sensors in the ground-based upstream array to determine a good 
approximation of the direction of arrival of the seismic disturbance. The 
sensor that first detects the disturbance determines its direction of 
arrival. The signal from this sensor is used by the plural orthogonal 
controllers as their upstream input. Contamination of the upstream sensors 
by the controlling vibration, or cancellation vibration field, is not a 
concern for the seismic disturbance problem since the upstream array is in 
the ground away from the building. Thus, there is little or no feedback 
from the cancellation vibrations induced by the actuators that would reach 
the remote input sensors. The upstream sensor signal, along with the 
appropriate error signal from the downstream sensor array, is fed into the 
controller, as will be discussed, which determines the canceling signal. 
It is assumed that anyone skilled in the art of digital controllers 
understands that all signals to and from the controller would be 
anti-aliased and converted from analog to digital (A/D) or digital to 
analog (D/A) and amplified as appropriate and thus these steps are not 
further shown or discussed. 
For a feed forward controller to operate in an optimum way it should not be 
predicting the disturbance waveform traveling through the ground. The 
upstream sensor array 4 must be far enough away from the structure 2 so 
the delay in propagation of the disturbance from the sensors 4 to the 
building is greater than the delay in processing the signal in the 
controller. The physical distance on the ground or media corresponds to 
the compressional velocity of sound for a structure on land, and the 
surface wave velocity for a structure in water, times the delay in signal 
processing within the digital signal processing chip within the 
controller. This delay is on the order of 3 samples for many systems with 
A/D and D/A converters with the controller algorithm in between. The 
velocity of sound in rock (which has the highest speed) is on the order of 
15,000 ft/sec. The upper frequency limit of servo valves for hydraulic 
cylinders is on the order of 200 Hz, while most earthquake energy is below 
30 Hz. A 500 Hz sample rate would be more than adequate, thus 
3.times.1/500.times.15000=90 ft. Accordingly, the sensors in this example 
must be at least 90 ft away from the building or structure to ensure that 
the counteracting control vibrations are applied at or prior to the 
building's receipt of its input vibrations. 
As shown in FIG. 5A, the earthquake wave front approaches substantially 
tangentially to the circular sensor array 4. By detecting which of the 
sensors 4 is "hit" first, a determination can be made of the wave front 
direction with respect to the building and thus the input signal can be 
decomposed into its orthogonal components. The number of sensors around 
the building to determine source direction and the particular reference 
sensor, or signal channel to be used as the input signal source, should be 
8 or greater (8 would give 45 degrees of resolution, 32 would give 11 
degrees of resolution which would be better). The upstream sensors 4 
located in the ground around the building 2 should be spaced close enough 
such that direction of arrival may be determined within a few degrees. The 
signals from the ring of sensors 4 around the building or structure, are 
sampled synchronously by a digital signal processor 34, as schematically 
shown in FIG. 8. These signals are continuously cross correlated to each 
other. The particular signal channel (sensor) which satisfies the 
following two criteria is used as the reference channel. The criteria are 
1.) the signal level is above a minimum level and 2.) the signal has the 
lowest lag to the adjacent channels for peak cross correlation. Once the 
specific sensor, or reference channel is found, then the system is 
enabled, and the input to the dual orthogonal controller systems is 
generated, as will be described. Since the location of the sensor relative 
to the building is known, the wavefront can be decomposed into two 
orthogonal components or directions. These two orthogonal signals become 
the input or reference signals for the controllers. 
The number of output or downstream sensors 6A,6B on each side of the 
building is determined by the first three mode shapes in each direction. 
The number of sensors must be sufficient so that spatial aliasing does not 
occur. It is expected that 6 sensors per side will be adequate (however, 
more would provide better resolution). The downstream sensor sets sense 
the movement of the structure to provide an error signal for use in the 
appropriate orthogonal controller. Each error signal used in an orthogonal 
controller is formed by combining the signal from each sensor in the set 
weighted by .beta..sub.i (i=1 to number of sensors) so that the maximum 
output of the sensors occurs for the first three vibrational modes of the 
building. For example, suppose there are 6 downstream sensors represented 
by 1 through 6. Each of these 6 sensors has a weight associated with it 
based on the model shape for each mode. This could be thought of as the 
sum of three vectors representing the appropriate weights d.sub.1,j 
through d.sub.6,j for each of the first j modes (j=1 to 3) with each 
vector weighted by the participation factor of the mode .alpha..sub.j : 
##EQU3## 
where .beta..sub.j =the weight for the i.sup.th sensor 
d.sub.i,j =the i.sup.th weight for the j.sup.th mode 
.alpha..sub.j =the participation factor for the j.sup.th mode. 
The d weights are determined by the mode shape. The mode shapes for each 
set of sensors may differ especially if the building is not square. (A 
rectangular shaped building would be expected to have more flex in the 
shorter direction.) The d weights are normalized so the maximum value 
permitted is 1; these weights may also be orthogonalized. The .alpha. 
factor is determined based on the structure and the disturbance type. The 
first mode generally is the most important in that it has the most energy, 
more than the second which has more than the third. Recall that most of 
the energy from disturbances into the structure occurs at low frequency so 
that generally only the first three modes are important. There is very 
little energy in the higher frequencies thus, there is little interest in 
controlling the modes related to higher frequencies. 
FIG. 5B shows the preferred embodiment for a multi-dimensional dual 
controller to counter a wind disturbance to a structure. In FIG. 5B, the 
upstream sensor array 4 consists of four detectors located at each corner 
of an upper floor of the building and extending from poles 50. These 
upstream sensors may be hot wire anemometers. If the sensors provide 
instantaneous velocity (including direction) then only four sensors are 
required. Such sensors are well known and, if used, the detected 
disturbance data is then decomposed into orthogonal components by the 
digital signal processor 34 as schematically shown in FIG. 9. If the 
sensors provide only instantaneous speed, then at least eight sensors 
would be required to determine the direction as in the earthquake 
configuration. 
The wind sensors need to be far enough away from the building to allow for 
the controller delay. For wind with a speed of 60 miles per hour (88 
ft/sec), sampled at 500 Hz, a three sample delay would require that the 
sensors be a minimum of 0.006 sec.times.88 ft/sec=0.528 ft from the 
building. The sensors may have a few millisecond delay which must be 
accounted for, thus if the poles are four to five feet long the delay 
requirement is more than satisfied. 
In both FIGS. 5A and 5B, there are two downstream sensor actuator arrays 6A 
and 6B on adjacent, orthogonal sides of the building. The countering force 
apparatus 8 may be located in a center chamber room 22 on an upper floor 
or roof 24 of the building. The walls of the center chamber must be an 
integral part of the structural supports of the building. For example, the 
chamber could be designed for the space between dual elevator shafts, thus 
allowing the use of the window sides of the building for offices. 
The countering force apparatus 8, as depicted in FIGS. 6A and 6B, includes 
mass 26 on rollers 27 or other low friction bearings and two orthogonally 
oriented hydraulic cylinders 28A,28B, or other type actuator, each having 
a movable piston (not shown) connected to stiff actuator rods 29A-B. Each 
hydraulic cylinder is controlled by a separate controller 40A,40B (as 
schematically shown in FIGS. 8, 9, and 10) in a manner to be described. 
The hydraulic cylinders or other type actuator with rods 29A-B are 
pivotally attached to the structural support of the building, such as to 
walls 31 tied into, or integral with, the structural support of the 
building, at adjacent, orthogonal sides of the chamber 22 and also 
pivotally connected to the mass 26 at the corresponding adjacent, 
orthogonal sides 26A,26B of the mass through pivots 30C,D. Pivots at all 
four junctions, 30A-B, 30C-D allow the mass to move freely within the 
confines of the chamber. 
An alternative countering force apparatus 8' is shown in FIG. 7. The dual 
mass countering force apparatus 8' includes two independent mass blocks 
26A',26B' on rollers or other low friction base for movement along 
orthogonally oriented tracks. The hydraulic cylinders 28A',28B' or other 
type actuators, include stiff actuator rods 29A'-B' each controlled by a 
separate controller 40A,40B in the same manner as schematically shown in 
FIGS. 8, 9, and 10, as will be described. The hydraulic cylinders or other 
type actuator with rods 29A'-B' are attached to the structural support of 
the building at adjacent, orthogonal walls 30 of the chamber and to the 
appropriate mass 26A',26B' so that the mass may move freely along the 
straight track within the confines of the chamber. In this embodiment, the 
cylinders 28A',28B' are not pivotally connected to the walls 30', nor is 
there a need for pivotal connections with the two masses. 
The size of the chamber and the mass (or pair of masses) are related to the 
force required to counter the maximum disturbance expected as defined by 
Newton's Law. Newton's law is F=ma, where F is the force imparted to the 
building by the disturbance, m is the mass of the block or blocks in the 
chamber and a is the acceleration of the mass which is related to the 
displacement of the mass. The maximum expected displacement (size of the 
chamber) and the mass of the block or blocks (maximum mass allowable is 
determined by the strength of the structures vertical supports) may be 
traded off based on the maximum force, F.sub.max, expected. The size of 
the reaction mass/masses in the upper part of the building is determined 
by the tradeoff of three constraints. 
1) The minimum power requirements are for a large mass. The apparent power 
of a reaction mass device is 
##EQU4## 
where P=power 
F=force 
.omega.=frequency in radians 
m=mass 
2) The minimum displacement requirements are for a large mass. The 
displacement for a reaction mass device is 
##EQU5## 
where X=displacement from equilibrium. 
A small displacement means less area of the building must be given up for 
the chamber room. 
3) The minimum structural requirements to support the mass are for a small 
mass. A successful design will balance these three constraints. 
FIG. 8 is a block diagram of the multi-dimensional dual orthogonal control 
system in accordance with the invention for a seismic disturbance. FIG. 9 
is a block diagram of the multi-dimensional dual orthogonal control system 
in accordance with the invention for a wind disturbance. Like reference 
numerals are used from FIGS. 1-7 to facilitate clarity. As illustrated in 
these FIGS. 8 and 9, the output of each of the dual orthogonal controllers 
40A,40B is a digital electrical signal over lines 41A,41B which is 
converted to an analog signal which drives a power amplifier 43A,43B. The 
amplifier output controls a servo valve on the hydraulic cylinder of the 
actuator in a manner well known in the art. Thus, the electrical output 
signal from each of the dual controllers controls the amount of fluid flow 
into and out of the cylinder and the force exerted on the reaction mass 
and into the building. 
With reference to FIG. 8, the control system includes dual controllers 
40A,40B, each based on time domain feed forward FIR filters adapted by the 
BUC, LMS, or NLMS to provide a cancellation signal to attenuate or counter 
the vibrational disturbance. Because seismic or earthquake waves are of a 
combined broadband and narrowband character, the BUC algorithm is 
preferred in the adaptive filter. When the input is high winds, which is 
generally not of combined character but rather, a narrowband character 
input, then the LMS or NLMS may be utilized. 
The sensors 4 detect the incoming seismic disturbance in advance of the 
disturbance propagation through the structure 2. When the disturbance 
reaches the structure, the structure 2, defined by the transfer function 
P.sub.1 produces the structural response y.sub.k. The various sensors 
include transducers to detect the disturbance and convert the disturbance 
into electrical signals which are anti-aliased and converted to digital 
format and then are input into an orthogonal component separator 34 which 
may be a digital signal processor. The processor determines which of the 
sensors should be looked at, in the manner as discussed above, and then 
separates the input or reference signal into orthogonal components 
x.sub.k.sup.A, x.sub.k.sup.B. The orthogonality is predetermined with 
respect to the orthogonal components, or sides, of the building structure. 
The orthogonal input or reference signals are provided to corresponding 
orthogonal feed forward controllers 40A,40B. In the depicted embodiments, 
the input signal is divided into two orthogonal components and the dual 
controllers are provided. If the input is broken down into more than two 
components, or if more than two orthogonal sets of actuators are utilized, 
then more than two controllers are required. 
The appropriate orthogonal component of the input signal is then fed into a 
pre-filter 18A,18B which filters the input with a predetermined stationary 
estimate of the appropriate orthogonal component of the actuator response 
transfer function P.sub.2, (P.sub.2.sup.A, P.sub.2.sup.B) to obtain signal 
v.sub.k (v.sub.k.sup.A, v.sub.k.sup.B), which is then used in conjunction 
with the appropriate orthogonal component of the error e.sub.k, 
(e.sub.k.sup.A, e.sub.k.sup.B) in the BUC, LMS, or NLMS to adjust the 
weights. (For the BUC algorithm, a memory stack is required, as will be 
discussed.) The determination of the estimated transfer function between 
the actuators and the output sensors may be determined by experimentally 
driving the building with the respective orthogonal actuators and 
measuring its response, or by mathematical modeling using a finite element 
model, both techniques being well known. 
The filtered orthogonal reference signal component from 18A,18B, is then 
input into the adapter, or filter weight adjustment means, 32A,32B, along 
with the respective orthogonal error or output signals e.sub.k.sup.A, 
e.sub.k.sup.B, whereby the filter weights (or coefficients) are adjusted 
in accordance with the selected mathematical algorithm. The weight 
vectors, w.sup.A and w.sup.B are then used to filter 30A,30B, the 
appropriate orthogonal component of the input signal and the output 
q.sub.k, after conversion to analog output and amplified by amplifier 
43A,43B comprises the orthogonal actuator driving signal. This signal 
actuates the actuators. The actuators impart a cancellation vibration 
field to the structure 2, modified by the appropriate transfer function 
P.sub.2, (P.sub.2.sup.A, P.sub.2.sup.B), 8A,8B to produce the cancellation 
vibration. This signal is summed with the signal y.sub.k, (y.sub.k.sup.A, 
y.sub.k.sup.B) within the structure and the resulting or combined effect 
of the input and cancellation field signals is sensed as the error. The 
orthogonal components of the error signal e.sub.k, (e.sub.k.sup.A, 
e.sub.k.sup.B) are then fed correspondingly into the two different 
controllers A and B 40A,40B, by way of the BUC, LMS, or NLMS adapters 
32A,32B. The appropriate component of the error signal, (e.sub.k.sup.A, 
e.sub.k.sup.B), after anti-aliasing and conversion to digital format, is 
used in the corresponding adaptive algorithm to update the filter weights 
and provide a better cancellation signal. The system adapts its response 
to the input signal to cancel vibrations by minimizing the error signal. 
For the case of the wind disturbance to the building, FIG. 5B, the only 
difference in the physical system from the seismic case is a change in the 
upstream sensor array 4 and its location, as well as the use of a feedback 
filter. The upstream sensor array, consisting of wind sensors which 
measure the wind velocity, must be located in the air stream about the 
building 2. This can be accomplished by locating the sensors on poles 50 
off the corners of an upper floor of the building, as previously 
discussed. The wind stream velocity decreases as it gets closer to the 
ground according to a known prescribed formula. This information can be 
used to better adapt to the disturbance. The wind velocity is measured by 
the upstream sensors 4 and the wind profile derived to provide the input 
signal, x.sub.k, that causes the disturbance to the building. Like the 
seismic case, the downstream sensors 6 on orthogonal sides of the building 
measure the response and the orthogonal controllers determine the 
appropriate canceling force. Because the upstream sensors 4 are located on 
the building they will be contaminated by the controlling force applied to 
the building. That is, the cancellation vibration field applied by the 
actuators will be fed back and detected by the input sensors attached to 
the building. This feedback path must be compensated for. 
The transfer function between the apparatus applying the cancellation force 
8 and the upstream sensors 4 is given by P.sub.3 (P.sub.3.sup.A, 
P.sub.3.sup.B). In order to compensate for the feedback path represented 
by P.sub.3, the transfer function between the actuators and the upstream 
sensors, the controller must have an anti-feedback filter, P.sub.3. The 
main differences between FIG. 8 and FIG. 9 are with the predetermined 
stationary anti-feedback filters P.sub.3.sup.A and P.sub.3.sup.B 38A,38B 
to compensate for the contamination of the upstream sensors 4 as defined 
by P.sub.3 36A,36B and the summation of the cancellation signal with the 
input signal at 40 to give the contaminated signal. The orthogonal 
cancellation signals are fed into the appropriate anti-feedback filter 
P.sub.3.sup.A and P.sub.3.sup.B 38A,38B and then subtracted at 42A,42B 
with the input signal that is contaminated with feedback (as shown at 40). 
Note that the contamination signal that is summed with the input is within 
the physical system. As such it is an analog signal depicted as is shown 
in FIG. 9 as coming from the analog cancellation signal to be input 40. 
FIG. 10 shows a block diagram of the connections between the physical and 
electrical systems of this invention. The controller can be thought of as 
having three parts and three interconnections between the sensors and the 
actuators as shown in FIG. 10. The first part of the controller is the 
sensor ring around the structure (or the wind sensors on poles) with the 
part that determines the direction of arrival and decomposition of the 
earthquake signal into the spatially orthogonal components by the 
separator 34. Then the two orthogonal input signals which are generated by 
the first part of the system are the inputs to the two adaptive controller 
channels 40A,40B. The input to the two adaptive controllers are the 
sensors from the building which are spatially orthogonal to each other. 
The sensors on the building detect the motion of the structure. It is the 
controllers' function to drive the building motion to a minimum by 
providing signals to the two spatially orthogonal actuators 8A,8B in the 
structure. The resultant building motion from the input vibration field of 
the disturbance wave and the cancellation vibration field from the 
actuator array is detected by the orthogonally oriented output sensors 
6A,6B. 
The digital signal processing configuration of the controller would consist 
of three DSP boards. The first DSP board would be for the A/D and D/A 
converters (for example, the ICS 140), the second board would provide the 
anti-aliasing filters and the last board would be a multiple programmable 
chip board such as the four chip Pentek DSP board. On this last board, two 
chips would be programmed as the orthogonal separator for the input and 
two other chips would be programmed as the dual orthogonal controllers. 
The invention proposed for both embodiments updates the filter weights with 
the BUC, LMS or NLMS depending on the type of signal expected. 
Implementation of the LMS and NLMS into the control configuration as the 
adaptive algorithm is direct, requires no modification, and is well known 
in the controller art. When employing the BUC for multiple tonal signals 
or combined broadband/narrowband signals, such as is expected for 
earthquake disturbances, the updates are determined based on a number of 
past values equal to a small percentage of the length of the filter. The 
present invention enables the use of the known BUC to provide an 
adjustment to a control actuator which is responsive for both narrowband 
and/or broadband spectrum signals in a stable feed forward FIR-based 
control system that is computationally feasible (i.e., L small). 
When the controller is based on the BUC adaptive algorithm, the controller 
has memory capability, (i.e., use of multiple past values of the input) as 
shown in FIGS. 8 and 9. Thus a modification must be made to initialize the 
BUC and fill the memory stacks. Both v.sub.k and q.sub.k memory stacks are 
required, whose lengths are dependent on the number of weights used, N, 
the amount of memory to be used for the determination of the weights, L, 
and the length of the filter P.sub.2, M. Note that the q.sub.k memory 
stack is required for q.sub.k to be filtered by P.sub.2. In a real system 
P.sub.2 represents the transfer function between the actuator input and 
the downstream sensors. P.sub.2 is not known a priori. The q.sub.k memory 
stack represents the delay of P.sub.2. In the real system q.sub.k is 
applied via the actuator and the e.sub.k is sensed. The q memory stack 
which represents the delay of P.sub.2 and P.sub.2 as a filter are for 
illustration purposes only. Each time a memory stack is updated the most 
recent value is added to the top of the stack and the oldest is removed 
from the bottom of the stack. For example at time k for k&gt;max(M,N,2L-1), 
the BUC uses 2L-1 past values of a signal v so k-2L+1 values are in 
storage for use in the algorithm. At each time k, the newest value of v, 
v.sub.k, is saved at the top of the stack pushing the other values down 
the stack, with the oldest value, v.sub.k-2L discarded. 
The BUC computes the N weights at time k, w.sub.N,k, by the equation: 
##EQU6## 
where N=the length of the FIR filter (number of weights) used in the 
controller 
L=the size estimate to the sample covariance matrix 
J=the sample advance per time step 
M=the length of the filter P.sub.2 
x.sub.k =is the input signal value from the upstream sensor at time k 
v.sub.k =is the input signal value to the BUC at time k 
y.sub.k =is the output signal values from the downstream sensors at time k 
q.sub.k =is the output value of the BUC into the physical system 
y.sub.k =is the estimate to y.sub.k in the physical system 
.mu..sub.k =is the convergence parameter at time k 
y.sub.L,k =[y.sub.k. . . y.sub.k-N+1 ].sup.H 
##EQU7## 
EQU R.sub.L,N,k =V.sub.L,N,k V.sub.L,N,K.sup.H 
R.sub.L,N,k.sup.-1 V.sub.L,N,K is found using Levinson's recursion 
EQU q.sub.L,k =X.sub.N,L,K w.sub.N,k-L.sup.H 
##EQU8## 
The value of .mu. may vary with time depending on the problem to be 
solved. It is usually taken to be greater than or equal to zero (See, 
Slock article, discussed above and incorporated herein). The value of .mu. 
determines how much of a correction is made to the previous set of weights 
to determine the new weight vector. If .mu. is set equal to 1 then 1/2 of 
the correction value e.sub.L,k R.sub.1,N,K.sup.-1 V.sub.N,1,K is used to 
compute w.sub.N,k from w.sub.N,k-j in Eq. 1. The weights are then used to 
filter input data using x.sub.k through x.sub.k-n+1 to give q.sub.k. The 
q.sub.j (j=k-M+1 to k) fill a memory stack of length M. The q.sub.j 
(j=k-M+1 to k) are filtered by the M length filter P.sub.2 to give 
y.sub.k, the canceling signal to be applied. (This equation occurs only in 
simulation because P.sub.2 represents the physical system. The value 
q.sub.k enters the D/A converter and amplifier, then enters the system.) 
Since the v.sub.k memory stack is not full during the initialization, the 
BUC is modified to accommodate this lack of information. During the 
initialization of the controller which occurs for k&lt;max(M,N,2L-1) equation 
(1) is modified with L=1 as follows 
##EQU9## 
FIG. 11 shows a flow chart of the controller algorithm with initialization. 
Notice that the initialization branch has a memory buffer for v.sub.k and 
q.sub.k which require initialization. The v.sub.k stack is not used during 
initialization only filled. Note that the q buffer is initially zero and 
the zeros are pushed off the stack by the newest q value. 
FIG. 12A shows the spectrum of a combined input signal. FIG. 12B shows the 
error output signal for a simulated problem using this combined input for 
an NLMS based controller and a BUC based controller. In a perfect system, 
when the output error signal is exactly zero, the controller is providing 
total disturbance control. Notice that the BUC based controller with L=10 
for N=100 provides attenuation (error to -15 and -35 dB) whereas the NLMS 
based controller developed by Burgess has difficulty converging to 0 dB in 
this case. In addition, convergence occurs within 10 to 15 filter lengths 
for our invention. FIG. 12c shows the power spectra of the input signal 
and the output error signal for the NLMS based controller and for the BUC 
based controller with L=10. Notice that the BUC based controller 
outperforms the filtered-X NLMS controller across the entire frequency 
range but particularly at the higher frequencies. Note that the NLMS 
performs very well for the single tonal, harmonic tonals, or the strictly 
broadband problem, and for those cases it is appropriate to use the LMS or 
NLMS in the controller. However, for other kinds of problems, the BUC is a 
better alternative. 
While this invention has been described in terms of a number of preferred 
embodiments, those skilled in the art will recognize that various 
equivalents, alternatives and modifications are possible within the scope 
of the appended claims. It is assumed that anyone skilled in the art of 
digital controllers understands that all signals to and from the 
controller would be anti-aliased and converted from analog to digital 
(A/D) or digital to analog (D/A) as appropriate and thus these steps are 
not shown or discussed.