# Patent

## Title
Method of determining the gain of a BEMF amplifier and relative control circuit of an induction electric motor

## Abstract

A method for determining gain of a back-electromotive force amplifier may include setting an electric motor into a tri-state function mode and storing a first quasi steady-state value for back-electromotive force from the difference signal, and forcing a reference current through the electric motor and determining a first value of the gain of the amplifier for equaling a difference signal to the first quasi steady-state value. The method may further include setting the electric motor into a tri-state function mode a second time and storing a second quasi steady-state value for back-electromotive force from the difference signal, and increasing the first value of the gain by an amount proportional to a difference between the second quasi steady-state value and the first quasi steady-state value.

## Background
FIELD OF THE INVENTION
This invention relates to control systems for the speed of induction electric motors, and, more particularly, to a method and related device for determining the gain of a back-electromotive force (BEMF) amplifier in an induction electric motor.
BACKGROUND OF THE INVENTION
Induction motors are used in many applications for rotating a motor shaft in a direction or in the opposite direction at a certain speed. For example, one application may include using induction motors for moving an arm carrying read/write heads of a hard disk drive (HDD) from a parked position to a position above the disk and vice versa. In these applications, it may be important to precisely control the motor speed to prevent the arm carrying the read/write heads from hitting against a run stop when they are moved off the disk to the parking ramp, preventing possible damage of the read/write heads.
A typical approach for monitoring the speed of an induction electric motor is to sense the back electromotive force (BEMF) induced in the primary winding of the motor by the moving rotor. To this end, the BEMF is sensed with a circuit as depicted in FIG. 1, commonly referred to as “BEMF Amplifier.” The equivalent circuit of the induction electric motor is schematically shown within the dashed lines and comprises a generator of BEMF, an inductance Lm, and a resistor Rm of the primary winding. Typically, a sense resistor Rs is connected in series to the primary winding, and the voltage drop on this resistor corresponds to the current IM flowing through the motor. The motor is connected to a positive voltage supply line VCMP and to a negative voltage supply line VCMN.
The BEMF Amplifier senses voltage drops on the terminals of the motor and on the sense resistor Rs, amplifies the latter through an adjustable gain amplifier A1, and generates a difference signal between the voltage on the terminals of the motor and the amplified voltage. An output signal VOUT is generated as amplified replica of the difference signal by a second gain amplifier A2.
If the motor is driven in DC mode, the contribution given from the inductance Lm to the voltage drop on the terminals of the motor is negligible and the output signal VOUT is:

VOUT=(BEMF+IM·Rm−IM·Rs·A1)·A2  (1)

By adjusting the value of the gain A1 such to satisfy the following equation:

A1=Rm/Rs  (2)

results in:

VOUT=BEMF·A2  (3),

that is, the output signal is an amplified replica of the back-electromotive force in the motor. Therefore, the signal VOUT represents the motor speed and does not depend on the current IM flowing through the motor.

This characteristic of the signal VOUT is particularly useful to control the motor of a HDD or a similar system when the supply line is unintentionally interrupted, situation commonly referred to as “power down” condition. When a power down condition occurs, it may be necessary to park the read/write heads to prevent them from staying over the disk, thus preventing any risk of damaging the surface of the disk with a consequent loss of data. The fact that the signal VOUT does not depend on the current IM makes it track the BEMF both during the normal functioning as well as when the supply line of the motor is unintentionally interrupted.
The equivalent resistance of the motor Rm is not known a priori and varies with the functioning temperature, thus it may be necessary to adjust the gain A1 such to satisfy equation (2). Indeed, this adjustment is carried out with the rotor locked (BEMF=0) in a certain position. In these conditions, it is possible to supply current to the motor and ensure that the motor may not start running. The adjustment includes varying the gain A1 until the signal VOUT becomes null. When this occurs, the equation (2) is satisfied.
As stated hereinbefore, the equivalent resistance Rm of the motor varies during its functioning, thus the signal VOUT may not reliably track the BEMF. This may lead to an inaccurate determination of the motor speed. This problem is even more disadvantageous in the case of power down conditions. When a power down occurs, for example, in a HDD, it may be necessary to park the read/write heads and to control accurately the speed of the arm moved by the motor.
If equation (2) is no longer verified because the equivalent resistance Rm of the motor has varied, it may be necessary to repeat the step of determining the gain A1. This is not possible with the previously described technique because in general the condition BEMF=0 is not verified and it is likely not possible to be sure that the rotor is locked to force a current through the motor without moving it.
SUMMARY OF THE INVENTION
An object is to determine the gain of a BEMF amplifier and the actual speed of the motor without blocking the rotor.
Another object is a method for adjusting the gain of a BEMF amplifier when the speed of the motor is unknown and the rotor is not locked.
According to the method, the motor is set in a high impedance state (tri-state) and the back electromotive force on its terminals is read, thus a constant pre-established current is forced through the motor, and the gain A1 of the BEMF amplifier is adjusted a first time such to make the output signal VOUT correspond to the previously sensed back electromotive force BEMF0. As soon as this condition is verified, the motor is tri-stated again and the back electromotive force BEMF1 on its terminals is read again. The correction of the previously adjusted value of the gain A1 is determined in function of the values of the back electromotive force.
Another aspect is directed to a control circuit of an induction motor comprising a state machine that executes the method of determining the gain of the BEMF amplifier when a power down condition of the supply line of the motor occurs.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 depicts a schematic circuit diagram of a BEMF amplifier, according to the prior art.
FIG. 2 is a time graph of the BEMF of the motor, according to the present invention.
FIG. 3 is a schematic circuit diagram of a control circuit of a HDD, comprising a BEMF amplifier connected to a retract control circuit for parking the heads in a power down condition occur, according to the present invention.



DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
The three steps of the method for adjusting the gain of the BEMF amplifier are schematically illustrated in the exemplary time graph of FIG. 2. The motor is tri-stated and the back electromotive force (BEMF) BEMF0 on its terminals is sensed by reading the value of the output signal VOUT, given by the following equation:

VOUT=BEMF0·A2  (4)

A pre-established constant current IM is forced through the motor, and the gain A1* of the BEMF amplifier is adjusted (“GAIN CAL.”) in order to make the output signal VOUT equal to the previously sensed value.
In this functioning condition, the back electromotive force BEMF1 of the motor is unknown because the speed at which the rotor is moving is unknown and the output signal VOUT is

VOUT=(BEMF1+IM·Rm−IM·Rs·A1*)·A2  (5).

The gain A1* has been determined such to satisfy equation (4), thus:

BEMF0=BEMF1+IM·Rm−IM·Rs·A1*  (6).

By tri-stating the motor a second time, the back electromotive force BEMF1 is sensed and the difference between the gain A1* and the value of the ratio Rm/Rs between the equivalent resistance of the motor Rm and the sense resistance Rs is determined:




  
    
      
        
          
            Rm
            Rs
          
          -
          
            A
            ⁢
            
              
            
            ⁢
            
              1
              *
            
          
        
        =
        
          
            (
            
              
                BEMF
                0
              
              -
              
                BEMF
                1
              
            
            )
          
          ·
          
            
              1
              
                
                  I
                  M
                
                ·
                Rs
              
            
            .
          
        
      
    
    
      
        (
        7
        )
      
    
  




The back electromotive forces BEMF0 and BEMF1 have been measured, the current IM and the sense resistance Rs are design parameters, thus with equation (7), the difference between the ideal gain Rm/Rs and the previously determined gain A1* is calculated, correcting the latter such to make the output signal VOUT independent from the current flowing through the motor.
An aspect of the method is the fact that after the calibration step, the system may work in a continuous mode and not in a discontinuous mode. This prevents generation of switching noise at audible frequency. The method may be executed during the normal functioning of the motor to adjust the value of the gain A1 such to consider fluctuations of the equivalent resistance of the motor.
It may be conveniently implemented even in case of eventual power down condition of the supply of the motor, to adjust the gain A1 of the BEMF amplifier such to control precisely the motor speed. This characteristic is very useful in applications that contemplate the execution of an emergency procedure in case of power down condition, such as, for example, for parking the HDD read/write heads (“emergency retract”).
In HDDs, the emergency retract procedure is executed in case of power down condition for moving the heads away from the disk and bringing them in a parking zone. This may be done safely because, with this method, when a power down condition occurs, the output signal VOUT of the BEMF amplifier tracks precisely the back electromotive force BEMF.
FIG. 3 depicts a control device of a voice-coil motor VCM for carrying out the emergency retract procedure by adjusting the gain A1 of the BEMF amplifier when a power down condition occurs. The meaning of each block is specified in the following table:
















Retract Control
State machine that enables the



Circuit
“emergency retract” procedure by




commanding the determination of the




gain A1 of the BEMF Amplifier and




controlling the arm carrying the heads




in the parking zone



Target BEMF
Reference value for the back




electromotive force



DAC
Digital-to-analog converter



ADC
Analog-to-digital converter



VCM
Voice-coil motor



CSA
Amplifier of the voltage on the sense




resistance



EA
Error amplifier



PI Gain
PI controller



Digital PI
Proportional-integral controller of the



Filter
speed










The procedure for determining the gain A1 is executed by the state machine retract control circuit periodically or in case of a power down condition before driving the motor such to park safely the heads of a HDD.

## Claims

1. A method of determining gain of a back-electromotive force (BEMF) amplifier in a circuit comprising an electric motor coupled in series with a sense resistor, the BEMF amplifier having a gain to be adjusted for generating an amplified replica signal of a first voltage drop on the sense resistor, and an adder for generating a difference signal between a second voltage drop on the electric motor and the amplified replica signal, the method comprising:
setting the electric motor into a tri-state function mode and storing a first quasi steady-state value for BEMF from the difference signal;
forcing a reference current through the electric motor and determining a first value of the gain of the BEMF amplifier for equaling the difference signal to the first quasi steady-state value;
setting the electric motor into a tri-state function mode a second time and storing a second quasi steady-state value for BEMF from the difference signal; and
increasing the first value of the gain by an amount proportional to a difference between the second quasi steady-state value and the first quasi steady-state value.

2. The method according to claim 1 wherein the first value of the gain is based upon


BEMF0=BEMF1+IM·Rm−IM·Rs·A1*;


and wherein A1* is the first value of the gain, Rm is an equivalent resistance of the electric motor, Rs is a resistance of the sense resistor, IM is the reference current, BEMF0 is the first quasi steady-state value, and BEMF1 is the second quasi steady-state value.

3. The method according to claim 1 wherein the increasing of the first value of the gain value is based upon




  
    
      
        
          
            
              Rm
              Rs
            
            -
            
              A
              ⁢
              
                
              
              ⁢
              
                1
                *
              
            
          
          =
          
            
              (
              
                
                  BEMF
                  0
                
                -
                
                  BEMF
                  1
                
              
              )
            
            ·
            
              1
              
                
                  I
                  M
                
                ·
                Rs
              
            
          
        
        ;
      
    
    
      
        
      
    
  




and wherein A1* is the first value of the gain, Rm is an equivalent resistance of the electric motor, Rs is a resistance of the sense resistor, IM is the reference current, BEMF0 is the first quasi steady-state value, and BEMF1 is the second quasi steady-state value.

4. A method of determining gain of a back-electromotive force (BEMF) amplifier in a circuit comprising an electric motor coupled in series with a sense resistor, the BEMF amplifier having a gain to be adjusted for generating an amplified replica signal of a first voltage drop on the sense resistor, and a circuit for generating a difference signal between a second voltage drop on the electric motor and the amplified replica signal, the method comprising:
setting the electric motor into a tri-state function mode and storing a first quasi steady-state value for BEMF from the difference signal;
forcing a reference current through the electric motor and determining a first value of the gain of the BEMF amplifier for matching the difference signal to the first quasi steady-state value;
setting the electric motor into a tri-state function mode a second time and storing a second quasi steady-state value for BEMF from the difference signal; and
changing the first value of the gain by an amount based upon a difference between the second quasi steady-state value and the first quasi steady-state value.

5. The method according to claim 4 wherein the first value of the gain is based upon


BEMF0=BEMF1+IM·Rm−IM·Rs·A1*;


and wherein A1* is the first value of the gain, Rm is an equivalent resistance of the electric motor, Rs is a resistance of the sense resistor, IM is the reference current, BEMF0 is the first quasi steady-state value, and BEMF1 is the second quasi steady-state value.

6. The method according to claim 4 wherein the changing of the first value of the gain value is based upon




  
    
      
        Rm
        Rs
      
      -
      
        A
        ⁢
        
          
        
        ⁢
        
          1
          *
        
      
    
    =
    
      
        (
        
          
            BEMF
            0
          
          -
          
            BEMF
            1
          
        
        )
      
      ·
      
        1
        
          
            I
            M
          
          ·
          Rs
        
      
    
  
  ;




and wherein A1* is the first value of the gain, Rm is an equivalent resistance of the electric motor, Rs is a resistance of the sense resistor, IM is the reference current, BEMF0 is the first quasi steady-state value, and BEMF1 is the second quasi steady-state value.

7. A control circuit of an electric motor having a sense resistor coupled in series therewith, the control circuit comprising:
a back-electromotive force (BEMF) amplifier configured to generate an amplified replica signal of a first voltage drop on the sense resistor;
an adder configured to generate a difference signal between a second voltage drop on the electric motor and the amplified replica signal; and
a state machine configured to detect changes in a supply voltage of the electric motor, to control the electric motor, and to determine a gain when the change is detected by at least
setting the electric motor into a tri-state function mode and storing a first quasi steady-state value for BEMF from the difference signal,
forcing a reference current through the electric motor and determining a first value of the gain of said BEMF amplifier for equaling the difference signal to the first quasi steady-state value,
setting the electric motor into a tri-state function mode a second time and storing a second quasi steady-state value for BEMF from the difference signal, and
increasing the first value of the gain by an amount proportional to a difference between the second quasi steady-state value and the first quasi steady-state value.

8. The control circuit according to claim 7 wherein the first value of the gain is based upon


BEMF0=BEMF1+IM·Rm−IM·Rs·A1*;


and wherein A1* is the first value of the gain, Rm is an equivalent resistance of the electric motor, Rs is a resistance of the sense resistor, IM is the reference current, BEMF0 is the first quasi steady-state value, and BEMF1 is the second quasi steady-state value.

9. The control circuit according to claim 7 wherein the increasing of the first value of the gain value is based upon




  
    
      
        Rm
        Rs
      
      -
      
        A
        ⁢
        
          
        
        ⁢
        
          1
          *
        
      
    
    =
    
      
        (
        
          
            BEMF
            0
          
          -
          
            BEMF
            1
          
        
        )
      
      ·
      
        1
        
          
            I
            M
          
          ·
          Rs
        
      
    
  
  ;




and wherein A1* is the first value of the gain, Rm is an equivalent resistance of the electric motor, Rs is a resistance of the sense resistor, IM is the reference current, BEMF0 is the first quasi steady-state value, and BEMF1 is the second quasi steady-state value.

10. A control circuit of an electric motor having a sense resistor coupled in series therewith, the control circuit comprising:
a back-electromotive force (BEMF) amplifier configured to generate an amplified replica signal of a first voltage drop on the sense resistor;
a circuit configured to generate a difference signal between a second voltage drop on the electric motor and the amplified replica signal; and
a controller configured to detect changes in a supply voltage of the electric motor, to control the electric motor, and to determine a gain when the change is detected by at least
setting the electric motor into a tri-state function mode and storing a first quasi steady-state value for BEMF from the difference signal,
forcing a reference current through the electric motor and determining a first value of the gain of said BEMF amplifier for matching the difference signal to the first quasi steady-state value,
setting the electric motor into a tri-state function mode a second time and storing a second quasi steady-state value for BEMF from the difference signal, and
changing the first value of the gain by an amount based upon a difference between the second quasi steady-state value and the first quasi steady-state value.

11. The control circuit according to claim 10 wherein the first value of the gain is based upon


BEMF0=BEMF1+IM·Rm−IM·Rs·A1*;


and wherein A1* is the first value of the gain, Rm is an equivalent resistance of the electric motor, Rs is a resistance of the sense resistor, IM is the reference current, BEMF0 is the first quasi steady-state value, and BEMF1 is the second quasi steady-state value.

12. The control circuit according to claim 10 wherein the changing of the first value of the gain value is based upon




  
    
      
        Rm
        Rs
      
      -
      
        A
        ⁢
        
          
        
        ⁢
        
          1
          *
        
      
    
    =
    
      
        (
        
          
            BEMF
            0
          
          -
          
            BEMF
            1
          
        
        )
      
      ·
      
        1
        
          
            I
            M
          
          ·
          Rs
        
      
    
  
  ;




and wherein A1* is the first value of the gain, Rm is an equivalent resistance of the electric motor, Rs is a resistance of the sense resistor, IM is the reference current, BEMF0 is the first quasi steady-state value, and BEMF1 is the second quasi steady-state value.

13. A hard disk drive comprising:
a control arm configured to carry read/write heads;
a voice-coil motor coupled to said control arm and configured to move said control arm; and
a control circuit for said voice-coil motor and comprising
a sense resistor coupled in series to the electric motor,
a back-electromotive force (BEMF) amplifier configured to generate an amplified replica signal of a first voltage drop on said sense resistor,
a circuit configured to generate a difference signal between a second voltage drop on the electric motor and the amplified replica signal, and
a controller configured to detect changes in a supply voltage of the electric motor, to control the electric motor, and to determine a gain when the change is detected by at least
setting the electric motor into a tri-state function mode and storing a first quasi steady-state value for BEMF from the difference signal,
forcing a reference current through the electric motor and determining a first value of the gain of the BEMF amplifier for matching the difference signal to the first quasi steady-state value,
setting the electric motor into a tri-state function mode a second time and storing a second quasi steady-state value for BEMF from the difference signal, and
changing the first value of the gain by an amount based upon a difference between the second quasi steady-state value and the first quasi steady-state value.

14. The hard disk drive according to claim 13 wherein the changing of the first value of the gain comprises increasing the first value of the gain.

15. The hard disk drive according to claim 13 wherein said controller comprises a state machine.

16. The hard disk drive according to claim 13 wherein said circuit to generate the difference signal comprises an adder.

17. The hard disk drive according to claim 13 wherein said controller is to be coupled to said BEMF amplifier.

18. The hard disk drive according to claim 13 wherein said control circuit further comprises an analog-to-digital converter to be coupled to said BEMF amplifier and configured to receive an output thereof.

19. The hard disk drive according to claim 18 wherein said control circuit further comprises a proportional-integral controller configured to receive an output of said analog-to-digital converter.

20. The hard disk drive according to claim 13 wherein the first value of the gain is based upon


BEMF0=BEMF1+IM·Rm−IM·Rs·A1*;


and wherein A1* is the first value of the gain, Rm is an equivalent resistance of the electric motor, Rs is a resistance of the sense resistor, IM is the reference current, BEMF0 is the first quasi steady-state value, and BEMF1 is the second quasi steady-state value.

21. The hard disk drive according to claim 13 wherein the changing of the first value of the gain value is based upon




  
    
      
        Rm
        Rs
      
      -
      
        A
        ⁢
        
          
        
        ⁢
        
          1
          *
        
      
    
    =
    
      
        (
        
          
            BEMF
            0
          
          -
          
            BEMF
            1
          
        
        )
      
      ·
      
        1
        
          
            I
            M
          
          ·
          Rs
        
      
    
  
  ;




and wherein A1* is the first value of the gain, Rm is an equivalent resistance of the electric motor, Rs is a resistance of the sense resistor, IM is the reference current, BEMF0 is the first quasi steady-state value, and BEMF1 is the second quasi steady-state value.