Patent Publication Number: US-2010111693-A1

Title: Wind turbine damping of tower resonant motion and symmetric blade motion using estimation methods

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is related to U.S. Patent Application No. 60/849,160 of Kitchener Clark Wilson, William Erdman and Timothy J. McCoy entitled “Wind Turbine With Blade Pitch Control To Compensate For Wind Shear And Wind Misalignment” filed Oct. 2, 2006, which is assigned to Clipper Windpower Technology, Inc. and is incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     The invention relates to tower structures, such as wind turbine towers and more particularly to damping the turbine primary resonant frequencies by modulating the blade pitch angle while maintaining rated torque or power. 
     DESCRIPTION OF THE PRIOR ART 
     Large modern wind turbines have rotor diameters of up to 100 meters with towers of a height to accommodate them. In the US tall towers are being considered for some places, such as the American Great Plains, to take advantage of estimates that doubling tower height will increase the wind power available by 45%. 
     Various techniques are in use, or proposed for use, to control a wind turbine. The goal of these control methodologies is to maximize electrical power generation while minimizing the mechanical loads imposed on the various turbine components. Loads cause stress and strain and are the source of fatigue failures that shorten the lifespan of components. Reducing loads allows the use of lighter or smaller components, an important consideration given the increasing sizes of wind turbines. Reducing loads also allows the use of the same components in higher power turbines to handle the increased wind energy or allows an increase in rotor diameter for the same rated power. 
     Wind turbines, and the towers that support them, have complex dynamics influenced by the wind activity as well as control inputs. The dynamics include rotor rpm, lightly damped tower motion, lightly damped drive train motion, flexible blade bending, etc. Wind turbine control is a balancing act between providing good control of the turbine rpm, adding tower motion damping, and adding drive train damping while minimizing or not exacerbating blade bending. State space control, with complex models of all these dynamics, hold promise to accomplish this, but such controls are complex and difficult to develop. 
     It is desirable to provide a control method that adds tower damping by modulating the rpm control pitch commands generated by conventional control methods (e.g. proportional-integral-PI compensators). Such a method is adaptable to inclusion in state space control algorithms as well as used as an adjunct to conventional controls. 
     Approaches to damping, for example tower damping, generally consist of measuring tower acceleration, detecting the natural tower resonant mode within that acceleration, and generating a feedback blade pitch that adds damping. U.S. Pat. Nos. 4,420,692 and 4,435,647 disclose the use of conventional band-pass filters applied to damp the tower first bending moment through use of blade pitch control. This type of damping in many situations increases blade bending motion, which is unacceptable 
     The acceleration signal has superimposed onto the natural tower resonant motion, among others, an acceleration due to the three-per-revolution (3P) force caused by imbalances and blade aerodynamic nonlinearities. Not eliminating some of these components from the pitch-feedback-damping signal can aggravate blade motion and lead to blade fatigue and failure. In particular, the 3P signal picked up by the tower accelerometer  144  used for damping is very close to the tower resonant frequency and within the pass-band of the band-pass filters disclosed in U.S. Pat. Nos. 4,420,692 and 4,435,647. Using the band-pass filters results in the 3P signals being passed through to the blade pitch control with an arbitrary phase. The source of the 3P signal is the blade symmetric bending mode where all three rotor blades move together, bending in and out of the blade rotor disc plane. The 3P frequency component is close to the blade symmetric bending mode resonant frequency and, when passed through with phase changes caused by the band-pass filter, exacerbates the symmetric blade bending. 
     It is therefore desirable to provide a means to separate the tower resonant motion from that caused by 3P blade imbalance. Conventional approaches to eliminating a frequency component consist of placing a notch filter in series with the conventional band-pass filter. The 3P notch, being close in frequency to the band-pass, adds its phase and gain error to the final output making control difficult. This process does not produce estimates of the tower resonant motion and of the 3P motion. 
     It is desirable to provide estimates of the motion of the tower at its known resonant frequency using tower acceleration measurements alone. Such estimates, uncorrupted by other motions, are needed to generate pitch feedback signals for tower resonant motion damping. 
     It is also desirable to provide estimates of the 3P acceleration caused by the rotation of the three unbalanced blades. Such estimates uncorrupted by tower resonant motion and having selected phase so as not to exacerbate blade bending, are needed for tower and blade damping and general turbine control. 
     SUMMARY OF THE INVENTION 
     Briefly, the present invention relates to an apparatus and method of controlling a wind turbine having a number of rotor blades comprising a method of using tower acceleration measurements to damp tower resonant motion, and to damp 3P motion and hence blade symmetric bending. The tower resonant acceleration is caused by the collective response of the tower and blades to the wind changes averaged over the entire blade disc. With three unbalanced blades rotating in a wind shear (vertical, horizontal or due to yaw misalignment), the interaction of the air stream with the blades is a thrice per revolution motion superimposed on the resonant motion. The resulting overall tower acceleration includes the lightly damped resonant motion of the tower structure with superimposed thrice per revolution activity. This tower motion causes fatigue failure and shortens the tower life. 
     Further, the blades themselves are elongated flexible structures having their own bending modes and resonant motion. As the pitch commands are actuated on these blades by turning them to and from a feather position, the blade bending is strongly influenced. If the pitch commands include a frequency component near the blade symmetric bending resonant frequency, the pitch activity can exacerbate blade bending and increase blade loading and shorten their life. 
     In accordance with an aspect of the invention, the wind turbine uses feedback pitch commands to control pitch of the blades in order to control the rpm of the rotor and the power generated by the turbine. The present invention adds, to this rpm controlling feedback pitch, a feedback component to damp the tower resonant motion that does not include frequencies that exacerbate blade bending. This tower resonant motion damping feedback pitch component is applied collectively (equally to each blade). 
     In accordance with an aspect of the invention, the present invention further adds a feedback pitch component that reduces the 3P tower motion and, therefore, blade bending. This 3P motion damping feedback pitch component is also applied collectively. 
     In accordance with an aspect of the invention, in order to damp the tower motion, the turbine control includes a means to estimate the tower resonant motion and simultaneously estimate the tower 3P motion. The control further produces a tower damping pitch feedback signal and a 3P damping pitch feedback pitch signal. 
     In accordance with an aspect of the invention, this is accomplished by an estimator using only the tower acceleration measurements and tuned to specifically estimate the tower resonant acceleration and simultaneously estimate the 3P tower acceleration. The resonant tower damping pitch feedback signal is formed from the estimated tower resonant acceleration rate, and the 3P pitch feedback signal is formed from the estimated 3P tower acceleration rate. 
     Further, to correct for pitch actuator and other turbine system lags, each feedback signal is provided with individual phase control to advance or retard each as needed. The 3P pitch feedback signal does not exacerbate the blade symmetric bending mode as its phase is set to mitigate this mode. 
     Further, to account for varying wind conditions, each feedback signal is provided with a gain that adapts to the condition. 
     The feedback signals are formed as modulations of the nominal pitch signals developed by the tower controls (state space, Proportional-Integral-Derivative-PID, . . . ) for rpm or other purposes. The final pitch command to the pitch actuator is the sum of the nominal, the resonant tower damping pitch modulation, and the 3P pitch feedback modulation. 
     In accordance with an aspect of the invention, acceleration caused by the 3P motion of the imbalanced blades is rejected in the tower resonant pitch feedback signal. 
     In accordance with an aspect of the invention, acceleration caused by the resonant motion of the tower is rejected in the 3P pitch feedback signal. 
     The invention has the advantage that it rids the tower resonant motion pitch control signal of 3P (or any other selected frequency) signal while passing the tower first bending frequency (or any other selected frequency). Further it rids the 3P pitch control signal of tower resonant motion (or any other selected frequency) signal while passing the 3P frequency (or any other selected frequency). Further it provides feedback pitch signals to mitigate the tower resonant motion and the 3P motion. 
     This holds true even when such frequencies are too close to use conventional frequency filters. Further, a method of introducing desired phase to compensate for actuator lags is included. Further, a method of gain adaptation to wind conditions is included. This is a very general and relatively simple technique that can be used to detect one frequency signal when another is close by and can be used advantageously for many purposes other than tower motion damping. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention and its mode of operation will be more fully understood from the following detailed description when taken with the appended drawings in which: 
         FIG. 1  is a block diagram of a variable speed wind turbine in accordance with the present invention highlighting the key turbine elements. 
         FIG. 2  is a block diagram of a tower damping system in accordance with the present invention. 
         FIG. 3  is a graphical display of the transfer function of the estimated tower resonant rate of acceleration driven by the tower-measured acceleration before parameter selection. 
         FIG. 4  is a graphical display of the transfer function of the estimated tower resonant rate of acceleration driven by the tower-measured acceleration after parameter selection. 
         FIG. 5  is a graphical display of a sample rate of acceleration sensitivity to the steady state pitch where the pitch is a stand-in for wind speed. 
         FIG. 6  is a graphical display of the transfer function of the pitch modulation to compensate for tower resonant acceleration driven by the tower measured acceleration after parameter selection and provision of adaptive gain (at wind speed of 14 m/s or 10.77 degree pitch). 
         FIG. 7  is a graphical display of the transfer function of the pitch modulation to compensate for tower resonant acceleration driven by the tower-measured acceleration after parameter selection and provision of adaptive gain (at wind speed of 14 m/s or 10.77 degree pitch) and addition of 30 degree phase lead. 
         FIG. 8  is a graphical display of the transfer function of a conventional band-pass and notch filter replication of  FIG. 4  to illustrate the phase error introduced. 
         FIG. 9  is a graphical display of the transfer function of the estimated 3P rate of acceleration driven by the tower-measured acceleration after parameter selection. 
         FIG. 10  is a graphical display of the transfer function of the −30 degree phase shifted estimated 3P rate of acceleration driven by the tower-measured acceleration after parameter selection. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Refer to  FIG. 1 , which is a block diagram of a variable-speed wind turbine apparatus in accordance with the present invention. The wind-power generating device includes a turbine with one or more electric generators housed in a nacelle  100 , which is mounted atop a tall tower structure  102  anchored to the ground  104 . The nacelle  100  rests on a yaw platform  101  and is free to rotate in the horizontal plane about a yaw pivot  106  and is maintained in the path of prevailing wind current. 
     The turbine has a rotor with variable pitch blades,  112 ,  114 , attached to a rotor hub  118 . The blades rotate in response to wind current. Each of the blades may have a blade base section and a blade extension section such that the rotor is variable in length to provide a variable diameter rotor. As described in U.S. Pat. No. 6,726,439, the rotor diameter may be controlled to fully extend the rotor at low flow velocity and to retract the rotor, as flow velocity increases such that the loads delivered by or exerted upon the rotor do not exceed set limits. The nacelle  100  is held on the tower structure in the path of the wind current such that the nacelle is held in place horizontally in approximate alignment with the wind current. The electric generator is driven by the turbine to produce electricity and is connected to power carrying cables inter-connecting to other units and/or to a power grid. 
     The apparatus shown in  FIG. 1  controls the RPM of a wind turbine and damps the tower resonant motion and 3P motion. The pitch of the blades is controlled in a conventional manner by a command component, conventional pitch command logic  148 , which uses generator RPM  138  to develop a nominal rotor blade pitch command signal  154 . Damping logic  146  connected to the tower acceleration signal  143  generates an estimated blade pitch modulation command  152 . Combining logic  150  connected to the estimated blade pitch modulation command  152  and to the pitch command  154  provides a combined blade pitch command  156  capable of commanding pitch of the rotor blades, which combined blade pitch command includes damping of the wind turbine tower resonant motion and of the 3P blade imbalance motion. 
     The apparatus shown in  FIG. 2  compensates for tower resonance and blade imbalance in a wind turbine  200 . The nominal pitch of the blades is controlled in a conventional manner  201  by a command component  248 , which uses actual generator RPM  238  to develop the rotor blade pitch command signal. 
     The modulation of the pitch of the blades is controlled by tower-damping logic  240 . The result is a collective resonant motion modulation  247  and a collective 3P motion modulation  249 . Combining logic  250  connected to the blade pitch modulation commands  247  and  249  and to the collective pitch command  248 , provides a combined blade pitch command  252  capable of commanding pitch of the rotor blades, which includes damping of the wind turbine tower and of the blades. 
     The tower damping logic  240  comprises a tower motion estimator  246  using tower acceleration measurements  245  to estimate the tower resonant motion  260  and the tower 3P motion  262 . The resonant motion estimates  260  are phase-adjusted  264  and amplified by an adaptive gain  266  using the collective RPM command component  248  to select the appropriate gain. The 3P motion estimates  262  are phase-adjusted  265  and amplified by an adaptive gain  267  using the collective RPM command component  248  to select the appropriate gain. 
     The Estimator: The tower resonant estimator logic is based on a second order damped model of the tower resonant motion: 
         a   resonant =−ω resonant   2   x   resonant −2ω resonant ξ resonant   v   resonant    
     wherein a is acceleration (m/s/s), v is velocity (m/s), x is position (m), and ξ resonant  is the damping coefficient of the estimator tower resonant response (not necessarily of the tower dynamics) used to tune its response, and ω resonant  is the known resonant frequency of that motion. Taking two derivatives with respect to time, this model is written in terms of acceleration alone as 
         ä   resonant =−ω resonant   a   resonant −2ω resonant ξ resonant   {dot over (a)}   resonant +δ resonant    
     The added δ resonant  term (m/s/s/s/s) is a stochastic noise quantity representing inaccuracies in the model and its standard deviation σ is used to further tune the estimator response. 
     The estimator is further based on a second order damped model of the 3P wind shear motion 
         ä   3P =−ω 3P   2   a   3P −2ω 3P ξ 3P   {dot over (a)}   3P +δ 3P    
     wherein ξ 3P  and δ 3P  are similarly used to tune the estimator response. 
     The estimator uses the measurement equation relating these two accelerations to the measured acceleration 
         a   measured   =a   resonant   +a   3P +δ measurement    
     wherein the added δ measurement  term (m/s/s) represents stochastic measurement deviations beyond that modeled and is also used to tune the estimator response. The state space representation of the complete system is 
     
       
         
           
             
               
                 
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     wherein k is the estimator gain matrix and a* measurement,i  is the actual acceleration measurement at time t i . The gain can vary with each estimate (as in the classical Kalman or H ∞  filters) or can be selected as a constant matrix (as in pole placement and the steady state Kalman or H ∞  gains). Time varying gains have the advantage of adapting to changing resonant and wind shear ω and ε while constant gains have the advantage of forming a very simple and computationally efficient filter. 
     The two stages of the estimator, the resonant and the 3P, are formed together within the same observer. This means the design process (gain selection) produces an observer that ‘knows’ both phenomena exist and their interactions. And, because this is an estimator and thus cannot allow phase errors, the estimates have minimal phase error (generally zero error unless the frequency bandwidths substantially overlap). Further, since the both phenomena are estimated, each is free of the other. 
     Feedback for Tower Resonant Damping: A damping feedback term is developed to add damping to the tower resonant portion of the dynamics. A more complete model of the resonant dynamics, one that includes the affect of blade pitch and wind speed, is 
         ä   resonant =−ω resonant   2   a   resonant −2ω resonant ε inherent   {dot over (a)}   resonant   +f   resonant (β, V   wind )+ . . . 
     wherein ε inherent  is the inherent or existing natural damping, and f resonant (β, V wind ) is a forcing function representing the influence of blade pitch β and wind speed V wind  through the blade aerodynamics. If damping is added by modulating pitch, then approximately 
         ä   resonant =−ω resonant   2   a   resonant −2ω resonant (ε inherent +ε xtra ) {dot over (a)}   resonant   +f   resonant (β, V   wind )+ g   resonant ( V   wind )Δβ resonant + . . . 
     wherein ε xtra  is the desired extra damping coefficient produced by the imposed Δβ resonant  modulation. The g resonant (V wind ) gain factor as determined from simulation studies of the turbine. Equating terms, the extra damping is provided by the modulation when the pitch modulation is scheduled by wind speed as 
     
       
         
           
             
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     The feedback pitch is a modulation to the pitch demand normally produced by the turbine for its other control functions (e.g. rpm control using PID compensators). Since the feedback is based only on the resonant motion estimation, and this is free of 3P dynamics, the feedback has no undesired frequencies and does not exacerbate turbine blade modes. 
     Phase Control: It is one thing to demand a pitch and quite another to get a response. Pitch actuators and other processing requirements add lag between the demand and the actuation, and this can be corrected by adding lead to the demand modulation. Simplifying the estimator resonant dynamics by ignoring damping terms: 
         ä   resonant =−ω resonant   2   a   resonant    
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                         γ 
                         
                           
                             1 
                             + 
                             
                               γ 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   
                     
                       
                         
                           a 
                           . 
                         
                         resonant 
                       
                        
                       
                         _ 
                         phaseShifted 
                       
                     
                     = 
                       
                      
                     
                       
                         
                           
                             a 
                             . 
                           
                           resonant 
                         
                         - 
                         
                           
                             ( 
                             
                               
                                 ω 
                                 resonant 
                               
                                
                               tan 
                                
                               
                                   
                               
                                
                               
                                 φ 
                                 resonant 
                               
                             
                             ) 
                           
                            
                           
                             a 
                             resonant 
                           
                         
                       
                       
                         
                           1 
                           + 
                           
                             
                               tan 
                               2 
                             
                              
                             
                               φ 
                               resonant 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   
                     = 
                       
                      
                     
                       
                         
                           - 
                           
                             ( 
                             
                               
                                 ω 
                                 resonant 
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               
                                 φ 
                                 resonant 
                               
                             
                             ) 
                           
                         
                          
                         
                           a 
                           resonant 
                         
                       
                       + 
                     
                   
                 
               
               
                 
                   
                       
                      
                     
                       
                         ( 
                         
                           cos 
                            
                           
                               
                           
                            
                           
                             φ 
                             resonant 
                           
                         
                         ) 
                       
                        
                         
                        
                       
                         
                           a 
                           . 
                         
                         resonant 
                       
                     
                   
                 
               
             
           
         
       
     
     The phase controlled pitch modulation is then given by 
     
       
         
           
             
               Δβ 
               
                 resonant 
                  
                 _ 
                  
                 phaseShifted 
               
             
             = 
             
               - 
               
                 
                   
                     2 
                      
                     
                       ω 
                       resonant 
                     
                      
                     
                         
                     
                      
                     
                       ξ 
                       xtra 
                     
                   
                   
                     
                       g 
                       resonant 
                     
                      
                     
                       [ 
                       
                         h 
                          
                         
                           ( 
                           β 
                           ) 
                         
                       
                       ] 
                     
                   
                 
                  
                 
                   [ 
                   
                     
                       
                         
                           
                             
                               - 
                               
                                 ( 
                                 
                                   
                                     ω 
                                     resonant 
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     φ 
                                     resonant 
                                   
                                 
                                 ) 
                               
                             
                              
                             
                               a 
                               resonant 
                             
                           
                           + 
                         
                       
                     
                     
                       
                         
                           
                             ( 
                             
                               cos 
                                
                               
                                   
                               
                                
                               
                                 φ 
                                 resonant 
                               
                             
                             ) 
                           
                            
                             
                            
                           
                             
                               a 
                               . 
                             
                             resonant 
                           
                         
                       
                     
                   
                   ] 
                 
               
             
           
         
       
     
     Example of Tower Resonant Damping: Consider a turbine having tower resonance frequency of 0.38 Hz, blade bending moment close to the 3P frequency, and a 20 Hz control loop. At rated rpm (15.5 rpm) 3P is at 0.775 Hz and must be eliminated from the modulated pitch feedback so as not to exacerbate blade bending. Using preliminary values
         ε xtra =0.707   σ δmeasurement =0.1   φ=0   ω resonant =2π(0.38)   ω resonant 2π(0.775)   σ δresonant =0.001   ε resonant =0   σ δ3P =0.001   ε 3P =0
 
the state space model is digitized (using the Tustin, or bilinear, transform), the steady state Kalman gains are calculated, and the Bode plot (using zero-order-hold) of the acceleration measurement to {dot over (a)} resonant , shown in  FIG. 3 , has a peak at ω resonant  and a notch at ω 3P .
       

     Although a dynamic Kalman filter is useful to track the 3P frequency as the turbine changes rpm, here the steady state is considered as it is computationally simpler and has been shown to work well. 
     Increasing σ δresonant  and σ δ3P  to widen the bandwidth of the peak and notch, since the resonant and 3P frequencies are not that well known, and increasing ε resonant  and ε 3P  to soften the response:
         σ δresonant =0.016   ε resonant =0.2   σ δ3P =0.04
 
produces the Bode plot of  FIG. 4 . Notice, in both  FIG. 3  and  FIG. 4 , that the phase of the resonant signal at ω damp  is +90 degrees as expected of a differentiator, and without error. The resulting estimator matrices are
       

     
       
         
           
             
               
                 Γ 
                 _ 
               
               ss 
             
             = 
             
               [ 
               
                 
                   
                     0.96833 
                   
                   
                     0.047412 
                   
                   
                     
                       - 
                       0.023486 
                     
                   
                   
                     
                       - 
                       0.0011803 
                     
                   
                 
                 
                   
                     
                       - 
                       0.30196 
                     
                   
                   
                     0.94372 
                   
                   
                     0.0048336 
                   
                   
                     0.00024292 
                   
                 
                 
                   
                     
                       - 
                       0.090436 
                     
                   
                   
                     
                       - 
                       0.0044280 
                     
                   
                   
                     0.88257 
                   
                   
                     0.044354 
                   
                 
                 
                   
                     
                       - 
                       0.14511 
                     
                   
                   
                     
                       - 
                       0.0071052 
                     
                   
                   
                     
                       - 
                       1.2992 
                     
                   
                   
                     0.94492 
                   
                 
               
               ] 
             
           
         
       
       
         
           
             
               
                 k 
                 _ 
               
               ss 
             
             = 
             
               [ 
               
                 
                   
                     0.024186 
                   
                 
                 
                   
                     
                       - 
                       0.0049776 
                     
                   
                 
                 
                   
                     0.091135 
                   
                 
                 
                   
                     0.14624 
                   
                 
               
               ] 
             
           
         
       
     
     Simulation studies of the turbine produce g resonant [h(β)], the gain scheduling term, shown in  FIG. 5 , with the resulting Bode plot of the pitch modulation of  FIG. 6 . Also shown in  FIG. 6  is the conventional band-pass compensator originally developed for this turbine (dashed lines). Whereas the original system exacerbated blade bending, the estimator does not and produces equivalent tower resonant damping. 
     To illustrate the phase shifting property, increasing
         φ=30 degrees
 
produces the Bode of  FIG. 7  where the +30 degree phase shift at ω resonant  is seen when compared to  FIG. 6 .
       

     Attempts to produce the transfer function of  FIG. 4  using conventional frequency filters is not successful.  FIG. 8  is the result of using a low-pass followed by a notch filter: 
     
       
         
           
             
               lowPass 
                
               
                 ( 
                 s 
                 ) 
               
             
             = 
               
              
             
               
                 g 
                 low 
               
                
               
                 
                   ω 
                   resonant 
                   2 
                 
                 
                   
                     s 
                     2 
                   
                   + 
                   
                     2 
                      
                     
                       ξ 
                       low 
                     
                      
                     s 
                   
                   + 
                   
                     ω 
                     resonant 
                     2 
                   
                 
               
             
           
         
       
       
         
           
             
               notch 
                
               
                 ( 
                 s 
                 ) 
               
             
             = 
               
              
             
               1 
               - 
               
                 
                   g 
                   notch 
                 
                  
                 
                   
                     ω 
                     
                       3 
                        
                       P 
                     
                     2 
                   
                   
                     
                       s 
                       2 
                     
                     + 
                     
                       2 
                        
                       
                         ξ 
                         notch 
                       
                        
                       s 
                     
                     + 
                     
                       ω 
                       
                         3 
                          
                         P 
                       
                       2 
                     
                   
                 
               
             
           
         
       
     
     with
         g low =−0.5   ε low =0.3   g notch =0.85   ε notch =0.3
 
Although the magnitude plot is similar, the phase is not: there is an added 22 degree phase lag at ω resonant  in contrast to the estimator of  FIG. 4 .
       

     Feedback for Tower 3P Damping Plus Phase Control: Identically as for the resonant damping above, the 3P tower motion damping is given by 
     
       
         
           
             
               
                 a 
                 . 
               
               
                 3 
                  
                 P_phaseShifted 
               
             
             = 
             
               
                 
                   - 
                   
                     ( 
                     
                       
                         ω 
                         
                           3 
                            
                           P 
                         
                       
                        
                       sin 
                        
                       
                           
                       
                        
                       
                         φ 
                         
                           3 
                            
                           P 
                         
                       
                     
                     ) 
                   
                 
                  
                 
                   a 
                   
                     3 
                      
                     P 
                   
                 
               
               + 
               
                 
                   ( 
                   
                     cos 
                      
                     
                         
                     
                      
                     
                       φ 
                       
                         3 
                          
                         P 
                       
                     
                   
                   ) 
                 
                  
                 
                   
                     a 
                     . 
                   
                   
                     3 
                      
                     P 
                   
                 
               
             
           
         
       
       
         
           
             
               Δβ 
               
                 3 
                  
                 
                   P 
                    
                   _ 
                    
                   phaseShifted 
                 
               
             
             = 
             
               
                 - 
                 
                   
                     2 
                      
                     
                       ω 
                       
                         3 
                          
                         P 
                       
                     
                      
                     
                       ξ 
                       xtra 
                     
                   
                   
                     
                       g 
                       
                         3 
                          
                         P 
                       
                     
                      
                     
                       [ 
                       
                         h 
                          
                         
                           ( 
                           β 
                           ) 
                         
                       
                       ] 
                     
                   
                 
               
                
               
                 
                   a 
                   . 
                 
                 
                   3 
                    
                   
                     P 
                     
                       3 
                        
                       
                         P 
                          
                         _ 
                          
                         phaseShifted 
                       
                     
                   
                 
               
             
           
         
       
     
     wherein the 3P acceleration terms are taken directly from the estimator values and g 3P [h(β)] is determined from simulation studies. The transfer function from tower acceleration to {dot over (a)} 3P  is shown in  FIG. 9 : there is a notch at ω resonant  and a peak at ω 3P  with the anticipated +90 degree phase shift of a differentiator. The phase actually slightly less than 90 degrees due to lag introduced at ω 3P  by the nature of zero-order-holds of sampled data systems (added lag=0.775 Hz*360 degrees/20 Hz=14 degrees). Phase control is important so as not to exacerbate blade bending while damping it. As seen in  FIG. 6 , the conventional design that exacerbated blade bending produced a 3P feedback component having a phase of around −98 degrees. With the negative sign used on the feedback gain, the nominal estimator feedback is close at −90+14=−76 degrees and needs to be adjusted to damp and not excite the blade bending mode.  FIG. 10  illustrates the added 30 degree lag when φ 3P =−30 degrees. 
     Other Embodiments 
     While the invention has been particularly shown and described with reference to preferred embodiments thereof, it will be understood by those skilled in the art that the foregoing and other changes in form and detail may be made therein without departing from the scope of the invention. Whereas the steady state estimator gains have been used for illustrative purposes, the dynamic gains adapting to rotor rpm are included in this invention. Whereas the tower resonant and 3P frequencies have been used for illustrative purpose, other frequencies are considered. Whereas tower damping is used as an illustrative example, the invention can be used for other applications such as rotor damping and to remove undesired frequencies from such signals as rotor rpm and so forth.