# Patent

## Title
Plant gain calibration for an optical storage servo system

## Abstract

A gain calibration method for optical storage servo systems in which, plant gain calibration is used by injecting a reference sine wave r into an optical storage servo system, obtaining an effort signal m at the input of the servo plant and an error signal y at the output of the servo plant, using a DFT (Discrete Fourier Transformation) to translate the time domain signals m and y into frequency responses M and Y, calculating a Y-to-M ratio, and using the magnitude of the Y-to-M ratio as the plant gain K of the servo system. The servo system's sensor gain K1 at the outermost layer of a disk may be calibrated by, e.g., the conventional peak-to-peak measurement. Since K=K1·K2, the servo system's actuator gain K2 at the outermost layer of the disk may be obtained. Because the actuator gain K2 is the same for all layers of a disk, the variation of the sensor gain K1 at an inner layer may follow that of the plant gain K at that layer. Accordingly, the sensor gain K1 may be calibrated for each layer of a multilayer disk, and the calibration is independent from the compensator C.

## Background
CROSS REFERENCE TO RELATED APPLICATION
This disclosure is a continuation of U.S. application Ser. No. 12/192,896 filed on Aug. 15, 2008, which claims priority under 35 U.S.C. §119(e) to U.S. Provisional Application No. 60/955,935, filed on Aug. 15, 2007. The disclosures of the applications referenced above are incorporated herein by reference in their entireties.


BACKGROUND
1. Field of the Invention
The present invention relates generally to optical storage systems, and more particularly to a gain calibration method for an optical storage servo system.
2. Description of Related Art
An optical storage servo system is used to control the positioning of an optical lens, so that a track on an optical disk will be positioned accurately beneath the lens. In contrast to a hard disk drive, an optical storage system uses removable media. As a result, both a loader for the disk, and the disk itself, may introduce disturbances during operation of the optical storage system. An optical storage servo system may have several feedback control loops, such as a focus loop and a radial loop, to achieve high performance and robustness against OPU (optical pickup unit) actuator variations and other mechanical disturbances coming from disks or an actuating mechanism.
FIG. 1 illustrates an example of a simplified servo feedback loop for an optical storage system. As shown, the loop may have a dynamic plant P and a compensator C. The plant P may have an actuator P1 and a sensor P2. As a result:

P=P1·P2  (1)

The actuator P1 may include a digital/analog converter (D/A), a motor driver circuit, and a VCM (Voice Coil Motor) in an OPU/loader. Since optical storage systems use low cost motors, each loader may have a different actuator gain K2 and may introduce disturbances or uncertainty. The sensor P2 may include an optical photo diode, and a servo signal generator module in firmware. The sensor P2 may detect an error signal between the OPU's actual position and a target position, and may have different gains K1 and introduce plant uncertainties. The sensor gain K1 may include a focus sensor gain and a radial sensor gain. The compensator (or controller) C may receive the output of the sensor, as a servo signal, and generate a control effort to drive the actuator and suppress the disturbances or uncertainty. The compensator C may be a control HR (Infinite Impulse Response) filter implemented in firmware. The open loop transfer function of the servo feedback loop shown in FIG. 1 is as follows:

L=C·K1·K2·P1·P2  (2)

where K1 represents a sensor gain, K2 represents an actuator gain, C represents a compensator, P1 represents the actuator, and P2 represents the sensor.

The gain calibration for an optical storage servo system may include calibration of the actuator gain K2 and the sensor gain K1. Since there are big gain variations in inexpensive optical storage systems, it is very difficult to accurately measure the actuator gain K2 in open loop settings. Currently available technologies use Loop Gain Calibration (LGC) in closed loop operation to calibrate the actuator gain K2 by measuring either the magnitude or the phase of the transfer function (2), as shown in FIGS. 2A and 2B.
The curve for magnitude measurement is shown in FIG. 2A. A fixed frequency sine wave may be injected into the servo feedback loop shown in FIG. 1 at point A as a reference signal. The frequency of the sine wave may be the zero dB cross-over frequency determined by the compensator C. The magnitude of the transfer function (2) may be measured at point B. Since the target is zero dB or 1, the actuator gain K2 is the inverse of the loop magnitude measurement at the cross-over frequency.
The curve for phase measurement is shown in FIG. 2B. A fixed frequency, fixed magnitude sine wave may be injected into the servo feedback loop shown in FIG. 1 at point A as a reference signal, and the phase difference between the servo error signal at point B and the injected sine wave may be obtained. The sine wave may be, for example, 1.36 kHz. The phase difference may be compared with a target. A trial-and-error method may be used to make the phase difference to approach the target, so as to search for the actuator gain K2. One problem of the phase detection based LGC is that it suffers from defective disks, since it is difficult to implement a defect protection scheme when using the try-and-error method.
Currently available technologies use an open loop sensor peak-to-peak measurement to calibrate the sensor gain K1. In focus sensor gain calibration, an open loop focus ramp may be performed so that the peak-to-peak value of a focus error S-curve signal may be measured and compared with a target value. The S-curve peak-to-peak value is shown in FIG. 3 as the “pFocusError.” Similarly, the radial sensor gain may be calibrated by measuring the peak-to-peak value of a radial error signal in a radial open loop. One problem is that the method can only be used with single layer disk servo systems, e.g., CDs or single layer DVDs. However, multilayer format optical systems, e.g., red laser DVDs, blue laser BDs and HD-DVDs, are becoming popular, and the focus sensor gain K1 at inner layers may have a different S-curve than that of the outermost layer. Accordingly, the sensor gain K1 cannot be accurately calibrated at inner layers with the currently available technology.
In addition, the currently available technologies assume that the compensator C is fixed, and therefore include the compensator C in the path from point A to B and calibrate the loop gain of the optical servo system. The currently available technologies also assume that the variation of the actuator gain K2 is the same as that of the transfer function (2) since the compensator C is constant and the sensor gain K1 can be calibrated very accurately by the open loop sensor peak-to-peak measurement. However, in some optical storage servo systems, the spindle speed may depend on disk conditions, and a particular compensator C may be provided for each spindle speed. When the frequency of the injected sine wave stays the same, if C changes, the zero crossing point may move and may affect the calibration of the actuator gain K2.
Therefore, it may be desirable to provide a method to improve the calibration of the optical storage servo system.



BRIEF DESCRIPTION OF THE DRAWING FIGURES
Embodiments of the present invention are described herein with reference to the accompanying drawings, similar reference numbers being used to indicate functionally similar elements.
FIG. 1 illustrates an example of a simplified servo feedback loop for an optical storage system.
FIG. 2A illustrates an exemplary curve of magnitude measurements obtained by using LGC.
FIG. 2B illustrates an exemplary curve of phase measurements obtained by using LGC.
FIG. 3 illustrates an exemplary S-curve obtained in an open loop sensor peak-to-peak measurement for calibrating a sensor gain.
FIG. 4 illustrates signals used in plant gain calibration (PGC) for an optical storage servo system according to one embodiment of the present invention.
FIG. 5 is a flow chart of a method of plant gain calibration for an optical storage servo system according to one embodiment of the present invention.
FIG. 6A illustrates an exemplary frequency response at the input of a servo plant according to one embodiment of the present invention.
FIG. 6B illustrates an exemplary frequency response at the output of a servo plant according to one embodiment of the present invention.
FIG. 7 illustrates exemplary waveforms for defect detection according to one embodiment of the present invention.
FIG. 8 is a flow chart of a method for controlling transfer function of an optical servo system according to one embodiment of the present invention.
FIG. 9 illustrates a block diagram of an apparatus for controlling transfer function of an optical storage servo system according to one embodiment of the present invention.



DETAILED DESCRIPTION
The present invention provides a gain calibration method for optical storage servo systems. Instead of loop gain calibration, the method of the present invention uses plant gain calibration by injecting a reference sine wave r into an optical storage servo system, obtaining an effort signal m at the input of the servo plant and an error signal y at the output of the servo plant, using a DFT (Discrete Fourier Transform) to translate the time domain signals m and y into frequency responses M and Y, calculating a Y-to-M ratio, and using the magnitude of the Y-to-M ratio as the plant gain K of the servo system. The servo system's sensor gain K1 at the outermost layer of a disk may be calibrated by, e.g., the conventional peak-to-peak measurement. Since K=K1·K2, the servo system's actuator gain K2 at the outermost layer of the disk may be obtained. Because the actuator gain K2 is the same for all layers of a disk, the variation of the sensor gain K1 at an inner layer may follow that of the plant gain K at that layer. Accordingly, the sensor gain K1 may be calibrated for each layer of a multilayer disk, and the calibration is independent from the compensator C. The method may be used with signal layer optical disks and multilayer optical disks. Advantages of the present invention will become apparent from the following detailed description.
FIG. 4 illustrates signals used in plant gain calibration for an optical storage servo system according to one embodiment of the present invention. As shown, a reference sine wave signal r may be injected into the servo system. A time domain response at the input m of the servo plant may be used as an effort signal, and a time domain response at the output y of the servo plant may be used as an error signal. Signals m and y may be used for the PGC of the present application.
FIG. 5 is a flow chart of a method of plant gain calibration for an optical storage servo system according to one embodiment of the present invention. The method may be used in the optical storage servo system shown in FIG. 4.
Removable media used in optical storage systems may have defects. A defect in an optical storage servo system means that a servo signal from a disk is damaged and cannot be used for feedback control. The defect may be, e.g., scratches, dots, or fingerprints. A large defect may be a challenge for the optical storage servo system. In terms of the strength of light reflected from a disk, e.g., Qsum, there are two kinds of defects: black dots and bright dots. In the case of black dots, there is no reflection from the disc, and therefore the Qsum signal may drop. In addition, the Qsum signal may have transient at both start and end of defect, which may cause a spike. In FIG. 7, the second defect may be a black dot. In the case of bright dots, the disk surface may have manufacture problems, such as an air bubble, which may cause reflections from the disk high enough to distort the servo signal. In FIG. 7, the first defect may be a bright dot. A defect flag with a long delay may be used to mute the servo transient effect for a discrete-time Fourier transformation (DFT) engine. For the second defect in FIG. 7, the servo performance is not good during the long delay period. If the DFT engine is started, it may bring the PGC accuracy down.
At 510, it may be determined whether Qsum has dropped below a predetermined threshold.
If yes, at 511, a defect flag may be asserted, as shown in FIG. 7. The defect flag may be de-asserted (at 512) after a predetermined time delay, so as to return to normal track following.
Plant gain calibration may occur simultaneously with the defect detection. At 500, time domain responses to the reference signal r at the input m of the servo plant and the output y of the servo plant may be obtained, wherein m is an effort signal, and y is an error signal.
At 501, signals m and y may be translated from the time domain into the frequency domain and become frequency responses M and Y.
In one embodiment, a Fourier transform (phase and magnitude) of a servo plant at a particular frequency may be measured and the measurement may be compared with a target value. A continuous Fourier transform may be defined as follows:




  
    
      
        
          V
          ⁡
          
            (
            f
            )
          
        
        =
        
          
            ∫
            
              -
              ∞
            
            ∞
          
          ⁢
          
            
              v
              ⁡
              
                (
                t
                )
              
            
            ⁢
            
              e
              
                
                  -
                  j2π
                
                ⁢
                
                  
                
                ⁢
                ft
              
            
            ⁢
            
              
            
            ⁢
            
              d
              t
            
          
        
      
    
    
      
        (
        3
        )
      
    
  




In one embodiment, a DFT may be used to approximate the continuous Fourier transform as follows:




  
    
      
        
          
            V
            ⁡
            
              [
              k
              ]
            
          
          =
          
            
              ∑
              
                n
                =
                0
              
              
                N
                -
                1
              
            
            ⁢
            
              
            
            ⁢
            
              
                v
                ⁡
                
                  [
                  k
                  ]
                
              
              ⁢
              
                e
                
                  
                    -
                    j2π
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    kn
                    /
                    N
                  
                
              
            
          
        
        ,
        
          0
          ⁢
          
            <
            _
          
          ⁢
          k
          ⁢
          
            <
            _
          
          ⁢
          
            N
            -
            1
          
        
      
    
    
      
        (
        4
        )
      
    
  




wherein N is the number of samples.

The accuracy of the approximation may depend on the number of samples and the sampling frequency. In one embodiment, 96 sine waves at 1.36 kHz may be injected into the servo plant. By measuring the DFT of the servo plant output y and the DFT of the servo plant input m, the continuous Fourier transform of the servo plant (magnitude and phase) may be approximated. FIG. 6A illustrates an example of the reference signal r and its frequency response M, which is a radial effort signal. FIG. 6B illustrates an example of the reference signal r and its the frequency response Y, which is a radial error signal.
When the SNR (Signal-to-noise Ratio) is above a target level, one DFT session may be enough. One DFT session may be defined as one period of injected sine wave shown in FIGS. 6A and 6B. However, in order to overcome the large disturbances and noise in the closed loop system, PGC may need to have many DFT sessions to obtain a reliable and accurate plant gain result.
In the example shown in FIGS. 6A and 6B, one OFT cycle of the radial effort signal may include the following 64 values:




  
    
      7
    
    
      
        -
        30
      
    
    
      
        -
        8
      
    
    
      
        -
        19
      
    
    
      
        -
        30
      
    
    
      
        -
        22
      
    
    
      
        -
        2
      
    
    
      
        -
        15
      
    
    
      
        -
        44
      
    
    
      55
    
    
      
        -
        35
      
    
    
      14
    
    
      13
    
    
      
        -
        15
      
    
    
      
        -
        27
      
    
    
      
        -
        7
      
    
    
      
        -
        55
      
    
    
      
        -
        80
      
    
    
      -
    
  
  
    
      67
    
    
      
        -
        61
      
    
    
      18
    
    
      29
    
    
      59
    
    
      24
    
    
      
        -
        8
      
    
    
      
        -
        9
      
    
    
      
        -
        33
      
    
    
      
        -
        39
      
    
    
      
        -
        66
      
    
    
      
        -
        58
      
    
    
      
        -
        22
      
    
    
      15
    
    
      4
    
    
      12
    
    
      54
    
    
      
        -
        47
      
    
    
      -
    
  
  
    
      18
    
    
      
        -
        12
      
    
    
      33
    
    
      
        -
        21
      
    
    
      29
    
    
      9
    
    
      
        -
        1
      
    
    
      12
    
    
      
        -
        4
      
    
    
      15
    
    
      3
    
    
      15
    
    
      5
    
    
      66
    
    
      
        -
        35
      
    
    
      
        -
        35
      
    
    
      
        -
        18
      
    
    
      37
    
    
      -
    
  
  
    
      49
    
    
      
        -
        5
      
    
    
      
        -
        1
      
    
    
      46
    
    
      28
    
    
      33
    
    
      46
    
    
      
        -
        46
      
    
    
      55
    
    
      
        -
        67
      
    
    
      
        
      
    
    
      
        
      
    
    
      
        
      
    
    
      
        
      
    
    
      
        
      
    
    
      
        
      
    
    
      
        
      
    
    
      
        
      
    
    
      
        
      
    
  




Thus, the frequency response M may be:

M=(45.4)+j(394.2)

In the example shown in FIGS. 6A and 6B, one DFT cycle of radial error signal may include the following 64 values:




  
    
      
        -
        33
      
    
    
      
        -
        13
      
    
    
      
        -
        7
      
    
    
      5
    
    
      21
    
    
      31
    
    
      34
    
    
      43
    
    
      61
    
    
      38
    
    
      61
    
    
      53
    
    
      52
    
    
      60
    
    
      70
    
    
      69
    
    
      88
    
    
      109
    
  
  
    
      121
    
    
      130
    
    
      109
    
    
      
        
      
    
    
      91
    
    
      65
    
    
      55
    
    
      55
    
    
      50
    
    
      54
    
    
      57
    
    
      69
    
    
      73
    
    
      63
    
    
      42
    
    
      31
    
    
      16
    
    
      
        
          
        
        ⁢
        
          -
          14
        
        ⁢
        
          
        
      
    
  
  
    
      1
    
    
      
        -
        8
      
    
    
      
        -
        15
      
    
    
      
        -
        38
      
    
    
      
        -
        34
      
    
    
      
        -
        55
      
    
    
      
        -
        62
      
    
    
      
        -
        67
      
    
    
      
        -
        76
      
    
    
      
        -
        78
      
    
    
      
        -
        87
      
    
    
      
        -
        90
      
    
    
      
        -
        85
      
    
    
      
        -
        90
      
    
    
      
        -
        114
      
    
    
      
        -
        92
      
    
    
      
        -
        81
      
    
    
      
        -
        77
      
    
  
  
    
      
        -
        90
      
    
    
      
        -
        65
      
    
    
      
        -
        65
      
    
    
      
        -
        63
      
    
    
      
        -
        76
      
    
    
      
        -
        76
      
    
    
      
        -
        79
      
    
    
      
        -
        86
      
    
    
      
        -
        55
      
    
    
      
        -
        73
      
    
    
      
        -
        35
      
    
    
      
        
      
    
    
      
        
      
    
    
      
        
      
    
    
      
        
      
    
    
      
        
      
    
    
      
        
      
    
    
      
        
      
    
  




Consequently, the frequency response Y may be:

Y=(−790.4)+j(−2845)

Before each DFT session, the defect flag may be checked at 502. If the defect flag is asserted, the procedure may go to the next DFT session, so as to discard signals from defect areas and avoid using signals from defect areas in calculating the plant gain.
At 503, a Y-to-M ratio, which is the plant transfer function L, may be determined. In one example, the plant transfer function L may be:




  L
  =
  
    
      Y
      M
    
    =
    
      
        
          (
          
            -
            790.4
          
          )
        
        +
        
          j
          ⁡
          
            (
            
              -
              2845
            
            )
          
        
      
      
        
          (
          45.4
          )
        
        +
        
          j
          ⁡
          
            (
            394.2
            )
          
        
      
    
  




At 504, the magnitude of the plant transfer function L, which is the gain K of the dynamic servo plant at the outermost layer may be calculated. In one example, the magnitude may be:




  K
  =
  
    
      
      
        Y
        M
      
      
    
    =
    
      
        
        
          
            
              (
              
                -
                790.4
              
              )
            
            +
            
              j
              ⁡
              
                (
                
                  -
                  2845
                
                )
              
            
          
          
            
              (
              45.4
              )
            
            +
            
              j
              ⁡
              
                (
                394.2
                )
              
            
          
        
        
      
      ⁢
      
        

      
      ⁢
      
        
      
      =
      
        
          
            
              
                
                  (
                  
                    -
                    790.4
                  
                  )
                
                2
              
              +
              
                
                  (
                  
                    -
                    2845
                  
                  )
                
                2
              
            
          
          
            
              
                
                  (
                  45.4
                  )
                
                2
              
              +
              
                
                  (
                  394.2
                  )
                
                2
              
            
          
        
        =
        
          
            2952.6
            396.8
          
          =
          7.44
        
      
    
  




At 505, the servo plant's sensor gain K1 at the outermost layer of the disk may be calibrated, e.g., by the conventional peak-to-peak measurement.
As shown in the equation (1), the gain of the servo plant includes the actuator gain K2 and the sensor gain K1. When the servo plant's sensor gain K1 at the outermost layer and the plant gain K are obtained at 505 and 504 respectively, the servo plant's actuator gain K2 at the outermost layer of the disk may be determined at 506.
Since the actuator gain K2 is the same for all layers of a disk, the variation of the sensor gain K1 of an inner layer may follow that of the plant gain K at that layer. If it is determined at 507 that the disk has another layer, 500-504 may be performed at 508 to determine the servo plant's gain K at the second layer, and the sensor gain K1 at the second layer may be calibrated at 509. 507-509 may be repeated for each layer of a multilayer disk.
Since signals at the input and output of the servo plant are used during the calibration, the PGC is independent of the compensator C. In addition, it is easier to implement a robust defect protection scheme during the PGC, so that the PGC result is accurate even for disks with various kinds of defects.
FIG. 8 is a flow chart of a method for controlling the transfer function of an optical storage servo system according to one embodiment of the present invention. The method shown in FIG. 8 may be used in the optical storage servo system shown in FIG. 4, and may use part of the method shown in FIG. 5 to calibrate the plant gain of an optical storage servo system.
At 801, a disk may be loaded into an optical storage system.
At 802, the plant gain K at the outermost layer of the disk may be calibrated through 501 to 504.
At 803, it may be determined whether the plant gain K at the outermost layer equals one of a number of nominal plant gains Knn, stored in a memory. The memory may also store a compensator Cnn for each nominal plant gain Knn. In one embodiment, a pair of nominal plant gain Knn and its corresponding compensator Cnn may be stored for a family of disks, e.g., CD, DVD, and Blu-ray DVD, so that a compensator Cnn may be used for the whole family of disks. A compensator Cnn designed with a nominal plant gain Knn may deliver the same closed loop performance on different drives, even though there may be significant actuator and sensor variations.
If the plant gain K at the outermost layer equals a nominal plant gain Kn1, at 804, the compensator Cn1 corresponding to the nominal plant gain Kn1 may be selected as the compensator for the optical storage servo system, and the procedure may proceed to 807.
If the plant gain K at the outermost layer is different from all the stored nominal plant gains Knn, the plant gain K at the outermost layer may be adjusted to a closest nominal gain, e.g., Kn2, at 805, and the compensator Cn2 corresponding to the closest nominal gain Kn2 may be selected for the optical storage servo system at 806 The procedure then may proceed to 807.
At 807, the sensor gain K1 at the outermost layer of the disk may be calibrated by, e.g., the conventional peak-to-peak measurement. In one embodiment, a compensator Cn0, which may tolerate high disturbances and noise, may be used for the calibration.
At 808, the actuator gain K2 at the outermost layer may be calculated.
At 809, it may be determined whether the disk has another layer. If not, the procedure may end at 899.
It the disk has a second layer, then at 810, the plant gain K at the second layer may be calculated through 501-504, and at 811, it may be determined whether the plant gain K at the second layer is the same as the plant gain at the outermost layer. If yes, Cn1 which corresponds to the nominal plant gain of the outermost layer Kn1 may be selected for the second layer at 812, and the procedure may return to 809.
If the plant gain K at the second layer is different from that of the outermost layer, then at 813, the plant gain K at the second layer may be adjusted to equal the plant gain K at the outermost layer, so that the compensator Cn1 selected for the outermost layer may be used for the second layer as well. The procedure may then return to 809.
In one embodiment, at 813, instead of adjusting the plant gain K at the second layer, a compensator Cnn corresponding to a nominal plant gain which equals or is the closest to the plant gain at the second layer may be selected for the second layer.
Since the compensator C may be selected according to the plant gain of the optical storage servo system, the performance of the optical storage servo system may be significant improved.
FIG. 9 illustrates a block diagram of an apparatus for controlling transfer function of an optical storage servo system according to one embodiment of the present invention. The apparatus may include a control unit 901 and a memory 902. The control unit 901 may control various procedures of the optical storage servo system, including the procedures shown in FIGS. 5 and 8. The memory 902 may store a number of nominal plant gains Knn and a compensator Cnn corresponding to each nominal plant gain. The control unit 901 may access the memory 902 during operation of the methods shown in FIGS. 5 and 8.
Several features and aspects of the present invention have been illustrated and described in detail with reference to particular embodiments by way of example only, and not by way of limitation. Alternative implementations and various modifications to the disclosed embodiments are within the scope and contemplation of the present disclosure. Therefore, it is intended that the invention be considered as limited only by the scope of the appended claims.

## Claims

1. A method for calibrating gains of an optical storage servo system having a plant, the method comprising:
translating an effort signal of the plant from a time domain effort signal into a frequency domain effort signal using a Discrete Fourier Transformation (DFT);
translating an error signal of the plant from a time domain error signal into a frequency domain error signal using the DFT;
determining a plant gain of the optical storage servo system based on the effort signal and the error signal;
comparing a reflecting signal from an optical dish of the optical storage servo system with predetermined threshold; and
asserting a defect flag to avoid using error signals received for calibrating gains of the optical storage servo system when the reflecting signal drops below the predetermined threshold.

2. The method of claim 1, further comprising:
obtaining the effort signal at an input of the plant; and
obtaining the error signal at an output of the plant.

3. The method of claim 2, further comprising:
determining a transfer function of the plant by calculating a ratio between the frequency domain error signal and the frequency domain effort signal.

4. The method of claim 3, further comprising:
determining the plant gain by calculating a magnitude of the transfer function.

5. The method of claim 2, further comprising:
determining a first sensor gain of the optical storage servo system at an outermost layer of an optical disk.

6. The method of claim 5, further comprising:
determining an actuator gain of the optical storage servo system at the outermost layer with the plant gain and the first sensor gain at the outermost layer.

7. The method of claim 6, further comprising:
determining the plant gain of the optical storage servo system at a second layer of the optical disk.

8. The method of claim 7, further comprising:
determining a second sensor gain of the optical storage servo system at the second layer of the optical disk.

9. The method of claim 1, further comprising:
checking the defect flag before determining the plant gain; and
ignoring error signals received when the defect flag is asserted.

10. The method of claim 1, further comprising:
de-asserting the defect flag after a predetermined time delay.

11. The method of claim 1, further comprising:
storing in a memory at least two nominal plant gains and their corresponding compensators;
injecting a reference signal into the optical storage servo system;
obtaining at an input of the plant the effort signal, which is the time domain effort signal in response to the reference signal;
obtaining at an output of the plant the error signal, which is the time domain error signal in response to the reference signal; and
selecting a compensator corresponding to the plant gain.

12. The method of claim 11, the method further comprising:
determining whether the plant gain of the optical storage servo system at an outermost layer of the optical disk is a same as a nominal plant gain in the memory.

13. The method of claim 12, further comprising:
selecting the compensator corresponding to the nominal plant gain as the compensator for the optical storage servo system when the plant gain is the same as the nominal plant gain.

14. The method of claim 12, further comprising:
adjusting the plant gain of the optical storage servo system at the outermost layer of the optical disk to a closest nominal plant gain in the memory when the plant gain is different from all nominal plant gains in the memory.

15. An apparatus for an optical storage servo system having a plant, the apparatus comprising:
a memory for storing at least two nominal plant gains and their corresponding compensators; and
a control unit configured to translate a time domain effort signal of the plant and a time domain error signal of the plant to a frequency domain effort signal and a frequency domain error signal using a Discrete Fourier Transformation (DFT), determine a plant gain of the optical storage servo system based on the frequency domain effort signal and the frequency domain error signal, compare a reflecting signal from an optical disk of the optical storage servo system with a redetermined threshold, and assert a defect flag to avoid using error signals received for calibrating gains of the optical storage servo system when the reflecting signal drops below the predetermined threshold.

16. The apparatus of claim 15, wherein the control unit is further configured to select a compensator corresponding to the plant gain.

17. The apparatus of claim 16, wherein the control unit is further configured to determine whether the plant gain at a first layer of the optical disk is a same as a nominal plant gain in the memory.

18. The apparatus of claim 17, wherein the control unit is further configured to select the compensator corresponding to the nominal plant gain as the compensator for the optical storage servo system when the plant gain is the same as the nominal plant gain.

19. The apparatus of claim 17, wherein the control unit is further configured to adjust the plant gain to a closest nominal plant gain in the memory when the plant gain is different from all nominal plant gains in the memory.