Abstract:
Systems, methods, and computer program products for directional force weighting of an active vibration control system involve arranging a plurality of force generators in an array, identifying individual component forces corresponding to force outputs of each of the plurality of force generators, determining a combination of the individual component forces that will produce a desired total force vector, and adjusting the outputs of each of the plurality of force generators such that the combination of the individual component forces are at least substantially similar to the desired force vector.

Description:
PRIORITY CLAIM 
       [0001]    The present application claims the benefit of U.S. Provisional Patent Application Ser. No. 61/754,234, filed Jan. 18, 2013, the disclosure of which is incorporated herein by reference in its entirety. 
     
    
     TECHNICAL FIELD 
       [0002]    The subject matter disclosed herein relates generally to active vibration control systems and methods. More particularly, the subject matter disclosed herein relates to implementation and control schemes for an active vibration control system, such as is used to control vibration in a helicopter. 
       BACKGROUND 
       [0003]    It is sometimes desired to place multiple actuators, such as linear actuators or circular force generators (CFGs), close together at particular locations to increase controllability of certain modes of vibration. When this is done, however, adaptive algorithms that are commonly used to control such modes of vibration (e.g., filtered least mean squares) can have difficulty finding the optimal solution. These difficulties can generally arise either because the algorithm takes a significantly longer path to find the minimal solution (i.e., slow convergence) or because it can have a difficult time finding a unique solution, and it will thus oscillate back and forth looking for the minimum (i.e., poor performance). 
         [0004]    As a result, it would be advantageous for systems and methods for controlling multiple actuators to quickly and accurately identify an optimal solution to generate the desired force output from the combined operation of the multiple actuators. 
       SUMMARY 
       [0005]    In accordance with this disclosure, systems, methods, and computer program products for directional force weighting of an active vibration control system are provided. In one aspect, an active vibration control system includes a plurality of force generators arranged in an array, with each of the plurality of force generators being configured to generate individual component force outputs. An even number of the plurality of force generators are arranged in pairs that are placed in close proximity to one another for multi-directional force generation. A controller is configured to individually control each of the plurality of force generators to achieve a combination of the individual component force outputs that produces a desired total force vector. 
         [0006]    In another aspect, a method for directional force weighting of an active vibration control system is provided. The method involves arranging a plurality of force generators in an array, identifying individual component forces corresponding to force outputs of each of the plurality of force generators, determining a combination of the individual component forces that will produce a desired total force vector, and adjusting the outputs of each of the plurality of force generators such that the combination of the individual component forces are at least substantially similar to the desired force vector. 
         [0007]    Although some of the aspects of the subject matter disclosed herein have been stated hereinabove, and which are achieved in whole or in part by the presently disclosed subject matter, other aspects will become evident as the description proceeds when taken in connection with the accompanying drawings as best described hereinbelow. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0008]      FIG. 1  is a flow chart representing a method of controlling an active vibration control system according to an embodiment of the presently disclosed subject matter. 
           [0009]      FIG. 2  is a schematic view of an arrangement of multiple force generators according to an embodiment of the presently disclosed subject matter. 
           [0010]      FIG. 3  is an illustration of a mapping matrix used for force mapping according to an embodiment of the presently disclosed subject matter. 
           [0011]      FIG. 4  is a schematic view of an arrangement of multiple force generators according to an embodiment of the presently disclosed subject matter. 
           [0012]      FIGS. 5 through 7  are illustrations of mapping matrices used for force mapping according to embodiments of the presently disclosed subject matter. 
           [0013]      FIG. 8  is a schematic view of an arrangement of multiple force generators according to an embodiment of the presently disclosed subject matter. 
           [0014]      FIG. 9  is a mapping matrix used for linear force mapping according to an embodiment of the presently disclosed subject matter. 
       
    
    
     DETAILED DESCRIPTION 
       [0015]    Numerous objects and advantages of the subject matter will become apparent as the following detailed description of the preferred embodiments is read in conjunction with the drawings, which illustrate such embodiments. 
         [0016]    Actuator mapping is able to transform redundant and/or poorly conditioned degrees of freedom into simpler primary Degrees of Freedom (DOFs) in a very simple way. As shown in  FIG. 1 , for example, achieving a desired force output from a system of independently-controlled force actuators using this kind of actuator mapping involves a selection step S 1  in which the degrees of freedom that are desired for the system to output are selected. A mapping step S 2  then maps the desired degrees of freedom to the degrees of freedom that are realizable by the force actuators in the system. Based on this mapping, a control step S 3  controls each of the force actuators in the system to achieve the desired output. Furthermore, such actuator mapping is generally applicable to any vibration control system, including linear, circular, or mixed actuation systems. 
         [0017]    In one non-limiting example, a system of linear actuators is controllable to achieve an aggregate force output that includes both linear and rotational modes of vibration. As shown in  FIG. 2 , for example, a first linear actuator  10   a  is configured to generate linear vibrations in a first direction (e.g., along an x-axis), and a second linear actuator  10   b , a third linear actuator  10   c , and a fourth linear actuator  10   d  are each configured to generate linear vibrations in a second direction that is substantially perpendicular to the first direction (e.g., along a z-axis), with each of the linear actuators being independently controlled by a controller  30 . In addition, third linear actuator  10   c  and fourth linear actuator  10   d  are positioned near one another such that they are mapped into one or more independent control degrees of freedom as a single paired linear actuator  20  to improve control performance of the system. Furthermore, if resonant actuators are used, the resonant frequency of the coupled actuators can be tuned close to one another, or a phase offset correction can be added. In this way, the controlled actuation of all of the linear actuators enables modes of vibration to be achieved beyond the first and second directions. 
         [0018]    To achieve these complex modes of vibration, a transformation matrix is applied to the inputs from each of the linear actuators to achieve a desired output. In general, an active vibration control system operating at a single frequency is described as 
         [0000]    
       
      
       e=Cf+d  
      
     
         [0000]    where e is a [n×1] complex vector of vibration signals at the frequency of interest and measured by the vibration sensors, f is a [m×1] complex vector of input force commands at the frequency of interest, C is the [n×m] complex transfer function matrix between f and e, and d is the n×1 complex vector of vibration signals measured when there is no control. The control system is functional to adapt f such that the product of C and f looks as close to −d as possible such that e is minimal (in a least squares sense). 
         [0019]    In this regard, a force transform vector is produced: 
         [0000]        M 1= M 2 M 3 
         [0000]    where an output force vector M 1  represents a complex vector with elements for which control weighting is desired, and a transformation matrix M 2  maps the natural modes of vibration generated by an input force vector M 3  to achieve the desired control weighting. 
         [0020]    Referring again to the actuator configuration shown in  FIG. 2 , for example, a control scheme is implemented in one embodiment based on the relationship described above to achieve a complex output force vector M 1  as shown in  FIG. 3  that is selected to best neutralize the uncontrolled vibration (e.g., the negative of the complex vector of vibration signals d from the relationship discussed above). In this embodiment, output force vector M 1  includes vibrations in a first x-direction (e.g., aligned with first linear actuator  10   a ), a first z-direction (e.g., aligned with second linear actuator  10   b ), and a second z-direction (e.g., substantially aligned with paired linear actuator  20 ), as well as generating a rotational mode of vibration (e.g., about paired linear actuator  20 ). This output is achieved by multiplying transformation matrix M 2  (e.g., complex transfer function matrix C from the relationship discussed above) by input force vector M 3  (e.g., complex vector of input force commands f from above), where input force vector M 3  represents the natural degrees of freedom of each of the linear actuators in the system. In particular, as shown in  FIG. 3 , input force vector M 3  comprises elements representing a first x-direction (e.g., aligned with first linear actuator  10   a ), a first z-direction (e.g., aligned with second linear actuator  10   b ), a second z-direction (e.g., aligned with third linear actuator  10   c ), and a third z-direction (e.g., aligned with fourth linear actuator  10   d ). By particularly configuring transformation matrix M 2 , the particular inputs that are needed for each of first, second, third, and fourth linear actuators  10   a ,  10   b ,  10   c , and  10   d  (i.e., the values of input force matrix M 3 ) to achieve the resultant mode of vibration defined by output force vector M 1  are found. 
         [0021]    Similarly, the pairing of proximal circular force generators (CFGs) enables bidirectional force generation. There may be situations where a systems engineer will want to create a single direction force using two CFGs. For example, multiple circular forces can be mapped to independent linear forces (and vice versa). To this end, the vibration control algorithm implicitly will converge to an elliptical resultant force profile for pairs of CFGs such that a weighted sensor set is minimized. The following provides a manner for doing so by penalizing or applying control weighting to various rectilinear directions while maintaining independent CFG control. 
         [0022]    For example, as shown in  FIG. 4 , if a system consists of five CFGs (e.g., a first CFG  11   a , a second CFG  11   b , a third CFG  11   c , a fourth CFG  11   d , and a fifth CFG  11   e ) each being independently controlled by controller  30 , the first four CFGs are grouped as a first CFG pair  21   a  and a second CFG pair  21   b , and fifth CFG  10   e  is unpaired. A goal to minimize the vibration signals (e.g., vector e from the relationship discussed above) is achieved while constraining first CFG pair  21   a  to produce forces in the x-direction only, constraining second CFG pair  21   b  to produce forces in the y-direction only, and provide an option to apply a small level of control weighting to fifth CFG  11   e.    
         [0023]    Again, identifying the proper control weighting for each of the five CFGs in this exemplary configuration is achieved by transforming the input forces generated individually into an aggregate output force vector having the desired modes of vibration. In particular, for example,  FIG. 5  provides one generalized implementation of transformation matrix M 2  in which a sub-matrix tof converts forces from circular force format to rectilinear force format. 
         [0024]    Using this form of force transform, a cost function is defined as follows: 
         [0000]    
       
         
           
             
               
                 
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         [0000]    where Q is a sensor weighting matrix and R is a control weighting matrix. With respect to the configuration discussed above with respect to the arrangement shown in  FIG. 4 , R takes the following form to achieve the control objectives stated above: 
         [0000]        R =diag{0, r   ay   ,r   by ,0, r   5 } 
         [0000]    where r ay , r by , are adjustable to ensure unidirectionality of first CFG pair  21   a  and second CFG pair  21   b , respectively, and r 5  provides control weighting on fifth CFG  11   e.    
         [0025]    The adaptation algorithm has the following form: 
         [0000]        f   k+1 =( I−{circumflex over (R)} ) f   k   −μC*Qe   k    
         [0026]      FIGS. 6 and 7  provide further non-limiting examples of the above principles being applied generally to achieve a desired force output using collocated CFGs. Specifically,  FIG. 6  illustrates a configuration of transformation matrix M 2  that is configured to map independent linear forces to four circular forces. In this non-limiting example, output force vector M 1  contains four circular force outputs to be achieved, and transformation matrix M 2  is able to map input force vector M 3  to these linear forces from an array of CFGs. Specifically, input force vector M 3  represents two linear forces acting in a single linear direction. In addition, those having skill in the art will recognize that transformation matrix M 2  is further able to transform four circular forces into two linear forces. 
         [0027]    In addition, in the configuration shown in  FIG. 7 , transformation matrix M 2  is designed to transform force inputs from six CFGs (e.g., three clockwise-rotating CFGs and three counter-clockwise-rotating CFGs) into a complex mode of vibration having both circular and linear components. Specifically, the circular force inputs are represented in input force matrix M 3  as a first counter-clockwise rotational force F ccw1 , a first clockwise rotational force F ccw2 , a second counter-clockwise rotational force F ccw3 , a second clockwise rotational force F ccw4 , a third counter-clockwise rotational force F ccw5 , and a third clockwise rotational force F ccw6 , and the complex force outputs are represented in output force matrix M 1  as a first circular force F c1 , a second circular force F 2c , a first linear force F z , and a second linear force F y . 
         [0028]    In yet a further configuration, actuators are mounted near the transmission of a helicopter to suppress the primary DOFs: X, Y, Z, pitch, and roll. Specifically, as shown in  FIG. 8  for example, eight circular force generators are operable to independently control the five primary rigid body DOF&#39;s, thereby creating the possibility of a zero-vibration application. In this non-limiting example, a first CFG  12   a  and a second CFG  12   b  are arranged substantially in the center of an array as a first CFG pair  22   a . In addition, a third CFG  12   c  and a fourth CFG  12   d  are each arranged at positions that are spaced apart from first CFG pair  22   a  on opposing sides of first CFG pair  22   a . Similarly, a fifth CFG  12   e  and a sixth CFG  12   f  are likewise disposed on opposing sides of first CFG pair  22   a , with third CFG  12   c  and sixth CFG  12   f  functioning as a second CFG pair  22   b  and fourth CFG  12   d  and fifth CFG  12   e  functioning as a third CFG pair  22   c . A seventh CFG  12   g  and an eighth CFG  12   h  are arranged at positions that are spaced apart from first CFG pair  22   a  on opposing sides of first CFG pair  22   a  and shifted approximately 90° with respect to second CFG pair  22   b  and third CFG pair  22   c.    
         [0029]    An exemplary mapping matrix for such a configuration is designed as shown in  FIG. 7 . As discussed above, the eight CFGs are operable to independently control the five primary rigid body DOFs represented in output force vector M 1 : a first linear vibrational force F x , a second linear vibrational force F y , a third linear vibrational force F z , a first moment M γ , and a second moment M η . This control is achieved by applying a configuration of transformation matrix M 2  that maps three counter-clockwise rotational forces (i.e., F ccw1  of first CFG  12   a , F ccw3  of third CFG  12   c , and F ccw5  of fifth CFG  12   e ) and five clockwise rotational forces (i.e., F cw2  of second CFG  12   b , F cw4  of fourth CFG  12   d , F cw6  of sixth CFG  12   f , F cw7  of seventh CFG  12   g , and F cw8  of eighth CFG  12   h ) represented in input force matrix M 1  to the five primary rigid body DOFs. 
         [0030]    In any configuration, if the control authority of a particular DOF is significantly larger or smaller than the others, it can also cause poor transient performance. A simple way to improve this is to normalize the actuator response in the plant model (C-model): 
         [0031]    for n=1: nact
       nor(n)=C(:,n)′*C(:,n);   Cnor(:,n)=C(:,n)./(nor(n));       
 
         [0034]    end 
         [0035]    The present subject matter can be embodied in other forms without departure from the spirit and essential characteristics thereof. The embodiments described therefore are to be considered in all respects as illustrative and not restrictive. Although the present subject matter has been described in terms of certain preferred embodiments, other embodiments that are apparent to those of ordinary skill in the art are also within the scope of the present subject matter.