Abstract:
Systems and methods for determining the position of the rotor of brushless DC motor drives over a wide speed range from near zero to high speed without additional hardware. This sensorless method and system provides continuous rotor position information with good accuracy and resolution even at very low speed operation, making them suitable for high performance applications. Motor current is detected from two of three motor phases and is compared with reference values. A speed-independent function is calculated to generate continuous rotor position information that covers almost all speed ranges from near zero to high speed. Suitable control of current and speed may then be provided to the motor.

Description:
[0001]    This application claims the priority of U.S. provisional patent application No. 60/438,949 filed Jan. 9, 2003. 
     
    
     
       BACKGROUND OF THE INVENTION  
         [0002]    1. Field of the Invention  
           [0003]    The invention relates to systems and methods for determining the rotor position of a brushless DC motor. In other aspects, the invention relates to systems and methods for control of a brushless DC motor.  
           [0004]    2. Description of the Related Art  
           [0005]    The brushless DC motor (“BLDCM”) drive is one of the fastest growing areas of motion control in the world today. To drive a BLDCM, rotor position information is required to provide the proper stator phase current commutation sequence. Conventionally, this has been accomplished by using a variety of rotor-position sensing devices, including optical encoders, resolvers, and Hall- effect sensors. These devices typically provide the feedback signals required for proper rotor position information to generate the correct switching patterns. Well-known disadvantages to these rotor-position sensing devices include 1) the cost of the sensors, 2) additional required space in or around the electric motor for the sensors to reside, and 3) the addition of fragile small gauge signal wires. Additionally, these rotor-position sensing devices are often unreliable and vulnerable to high temperatures, vibration, and so forth.  
           [0006]    When the problems with conventional position sensors are considered, alternative methods to obtain rotor position information become highly desirable. In the last two decades, in order to eliminate sensor-caused problems, many researchers have presented various position sensorless operation methods for BLDCM drives. These sensorless methods may be grouped into four categories as follows: 
           [0007]    1. Back-electromotive force (“EMF”) information-based sensorless techniques.  
           [0008]    A) Back-EMF integration methods;  
           [0009]    B) Zero-crossing point in back-EMF sensing methods;  
           [0010]    C) The third-harmonic back-EMF sensing method.  
           [0011]    2. Measured current information-based sensorless techniques.  
           [0012]    A) Freewheeling diode current conduction sensing method;  
           [0013]    B) Current waveform misalignment-detection method;  
           [0014]    3. Using alterations in machine design.  
           [0015]    4. Using fundamental machine equations, and algebraic manipulations. 
           [0016]    Most popular and practical methods for sensorless drive belong to category one. However, the methods in the first category directly depend on the back-EMF information. Neither those methods nor the methods of category two can work properly when the magnitude of back-EMF is small. This occurs at low speeds. Except for special alterations that have been made in some machine designs, the back-EMF is zero at standstill and proportional to speed. Thus, methods in category one and two cannot be realized at very low speed operation. This speed limitation has been a major drawback for sensorless operation of the BLDCM drives. Another disadvantage of the methods that depend on back-EMF information to estimate position is the additional cost of hardware for sensing terminal voltages. To estimate position, these arrangements need six-additional hardware sensing circuits and A/D converter channels to sense three-phase voltages and currents. Since the shape and magnitude of a phase back-EMF or line-to-line back-EMF is changing with motor speed, sensorless drive methods using back-EMF or line-to-line back-EMF information usually give only discrete position information at commutation points or zero-crossing points. Therefore, continuous position information that may be needed for advanced motor controls and system level purposes is not provided.  
           [0017]    A solution to the problems of the prior art would be desirable.  
         SUMMARY OF THE INVENTION  
         [0018]    The present invention provides systems and methods for determining the position of the rotor of brushless DC motor drives. The novel sensorless drive technique covers a wide speed range from near zero to high speed without additional hardware. This sensorless method and system also provides continuous rotor position information with good accuracy and resolution even at very low speed operation, making them suitable for high performance applications. Furthermore, the systems and methods of the present invention are simple enough to implement in real-time using an economical, fixed-point microprocessor. Motor current is detected from two of three motor phases and is compared with reference values. A speed-independent function is calculated to generate continuous rotor position information that covers almost all speed ranges from near zero to high speed. Since the speed term is technically eliminated from the calculation, identical shape of the position information can be presented over the entire speed range. Suitable control of current and speed may then be provided to the motor. The systems and methods of the present invention remove the need for external hardware to sense back-EMF information while presenting a high accuracy estimation of rotor position even at very low speed. These features make it suitable for high performance applications. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0019]    The advantages and further aspects of the invention will be readily appreciated by those of ordinary skill in the art as the same becomes better understood by reference to the following detailed description when considered in conjunction with the accompanying drawings in which like reference characters designate like or similar elements throughout the several figures of the drawing and wherein:  
         [0020]    [0020]FIG. 1 is a schematic diagram of an exemplary brushless DC motor drive system having a sensing system in accordance with the present invention.  
         [0021]    [0021]FIG. 2 is a timing diagram for a system depicting three-phase back-EMFs and currents.  
         [0022]    [0022]FIG. 3 is a detailed diagram of the voltage source inverter used in the drive system shown in FIG. 1.  
         [0023]    [0023]FIG. 4 a  is a diagram of waveforms of a phase H(θ) function, line-to-line H(θ) functions, and a square wave current.  
         [0024]    [0024]FIG. 4 b  is a diagram of G(θ) waveform.  
         [0025]    [0025]FIG. 5 depicts the exemplary G(θ) function, commutation signal, phase current and speed for a motor drive operated in accordance with the present invention.  
         [0026]    [0026]FIG. 6 is a correlation of G(θ) function with two phase currents.  
         [0027]    [0027]FIG. 7 is a flow chart depicting steps in an exemplary method in accordance with the present invention. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0028]    [0028]FIG. 1 schematically depicts a brushless DC motor drive system  10  in accordance with the present invention. The system  10  includes a brushless DC motor  12  and voltage source inverter  14  of a type known in the art. The motor  12  includes an outer stator (not shown) and a rotatable rotor (not shown) that rotates within the stator. The exemplary motor  12  has three electromagnetic phases, and each of the phases is provided with an electric lead  16 ,  18 ,  20 , respectively, which extends from the motor  12  to the voltage source inverter  14 . A rectifier  22 , for conversion of AC power to DC power, and 110 V AC power supply  24  are operably associated with the voltage source inverter  14 . Because the structure and operation of rectifiers and voltage source inverters are well understood by those of skill in the art, they are not described in any detail herein.  
         [0029]    A processor  26  is also included in the drive system  10 . The processor  26  may be a microprocessor or digital signal processor (DSP) of types that are known in the art. Current taps  28 ,  30  extend from motor leads  16 ,  18 , respectively, to the processor  26  and are used to detect the current, Ia and lb, respectively, on each motor lead  16 ,  18 . It is noted that only two of the three currents of the motor phases are sensed for current controlled sensorless operation. In this case, leads  16  and  18  have current sensed, while lead  20  does not. Under balanced conditions, the three-phase currents always meet the following condition, such as: 
           I   3 =−( I   1   +I   2 )  (1) 
         [0030]    This equation implies that one of the three-phase currents (Ic) can be composed by the summation of the other phase currents. Reference voltage (Vdc) from the rectified voltage source  24  is also provided to the processor  26 .  
         [0031]    The processor  26  includes suitable on-board memory and processing means for carrying out the processes, functions and steps that will be described. As is known in the art, such functions, processes and steps may be accomplished using suitable programming of a programmable processor  26  as well as by hardwired means or preprogrammed media. In a currently preferred embodiment, and depicted schematically in FIG. 1, the processor  26  includes on-board comparator means  32 ,  34 , respectively, for comparing each of the sensed currents Ia and Ib to predetermined reference currents Ia-ref and Ib-ref. A third comparator means  36  is also provided for comparing a calculated third current Ic to a predetermined reference current Ic-ref for the third motor phase.  
         [0032]    A rotor position estimation function  38  and speed calculation function  40  are depicted schematically on processor  26 . These functions  38 , 40  receive, as inputs, the detected motor currents Ia and Ib as well as the calculated current Ic and the reference voltage Vdc. The position estimation function  38  provides a commutation signal  42  as an output to a current control and gate pulse  44 . The current control and gate pulse  44  is known circuitry that provides gate pulse signals  46  to the inverter  14  in order to selectively control the current, and consequently the torque, of the motor  12 . The speed calculation function  40  provides a calculated speed signal (ω)  48  to a comparator  50 . The comparator  50  compares the speed signal  48  to a predetermined reference speed  52  and generates a signal that is indicative of the differential. Any differential between the calculated speed signal  48  and the reference speed  52  is provided to a speed regulator  54 , which is a device that is known in the art. The speed regulator  54  is capable of adjusting the speed of the motor  12  to compensate or correct for the differential between calculated speed and reference speed.  
         [0033]    [0033]FIG. 2 illustrates a profile for an exemplary motor system having three-phase back EMFs, depicted as lines  56 ,  58 , and  60  and show how the back EMFs and currents (Ia, Ib, Ic) change as the motor  12  moves through cycles (rotor positions I, II, III, IV, V, VI corresponding to 60° electrical angles). In prior art operation of the BLDC motor  12 , each phase back-EMF  56 ,  58 ,  60  was aligned with the phase current (Ia, Ib, or Ic). The switching instance of the inverter  14  was obtained by knowing the zero-crossing points  62  of the back-EMF and a speed-dependent period of time delay. To monitor or sense the sloped phase back-EMF of the silent phase, the prior art techniques usually sense terminal voltages. Since back-EMF is zero at stand-still and proportional to speed, it is not possible to use the terminal voltage sensing method to obtain a switching pattern at low speeds. Also, back-EMF or line-to-line back-EMF based sensorless methods usually provide only zero-crossing points  56  as position information in variable speed drives.  
         [0034]    To overcome this drawback of the previous methods, the methods and systems of the present invention feature a sensorless method for the BLDC drive  10 , which can successfully apply from near zero to high speeds without sensing terminal voltages to know the back-EMF information. This eliminates redundant hardware circuits for estimation of rotor position and provides continuous position information with good accuracy using the processor  26 .  
         [0035]    [0035]FIG. 3 shows an equivalent circuit of the voltage source inverter  14  and BLDC motor  12 . Here, each phase voltage equation can be expressed as:  
                   V   =       Ri   s     +       L   s                 i   s            t         +            λ   r            t                                         (       L   s     =     L   -   M       )                 (   2   )                            =       Ri   s     +       L   s                 i   s            t         +            θ          t       ·         ϕ   r     ·          f        (   θ   )                θ                     (   3   )                            =       Ri   s     +       L   s                 i   s            t         +     ω            ϕ   r                          f        (   θ   )                θ                     (   4   )                               
 
         [0036]    Where, V is the applied voltage to the stator phase winding; i s  is the energized current in the stator phase winding; R and L s  are the register and inductance in the stator phase winding; where, L and M are the self and mutual inductances of the stator winding; λ r  is the flux linkage due to rotor magnetic field excitation. The  
              λ   r            t                           
 
         [0037]    term, so-called back-EMF, can be divided with speed term and a periodical function changing by rotor position as in equation (3). Here, f(θ) is a new definition that we call flux linkage function and θ r  is the constant flux value from the rotor. Where, we define H(θ) function as:  
               H        (   θ   )       =         ϕ   r               f        (   θ   )                θ               (   5   )                               
 
         [0038]    Thus, finally we have:  
             V   =       Ri   s     +       L   s                 i   s            t         +     ω   ·     H        (   θ   )                   (   6   )                               
 
         [0039]    The peak magnitude of back-EMF depends on rotor speed ω. However, H(θ) itself has the identical functional waveform by rotor position θ. The defined H(θ) function contains rotor position information, and the shape and peak value of the H(θ) function are speed independent. From equation (6), the H(θ) function can be expressed as:  
               H        (   θ   )       =       1   ω          (     V   -     Ri   s     -       L   s                 i   s            t           )               (   7   )                               
 
         [0040]    To eliminate the speed term ω, we divide a phase H(θ) function by another phase H(θ) function. For example,  
                 H   a       H   b       =           1   ω          (       V   a     -     Ri   a     -       L   s                 i   a            t           )           1   ω          (       V   b     -     Ri   b     -       L   s                 i   b            t           )         =         (       V   a     -     Ri   a     -       L   s                 i   a            t           )       (       V   b     -     Ri   b     -       L   s                 i   b            t           )       =     G        (   θ   )                   (   8   )                               
 
         [0041]    Here, we name this divided function as G(θ).  
         [0042]    [0042]FIG. 4( a ) shows waveforms of a phase H(θ) function, line-to-line H(θ) functions, and a square wave current. Here, we utilize two sloped lines of line-to-line H(θ) functions in each mode and divide them to eliminate the speed term ω and to extract sensitive waveforms that are speed independent. The time duration of each mode in FIG. 4( a ) corresponds to 60° electrical angles.  
                         TABLE I                       G(θ) functions at each mode.                                            Mode 1 and 4               G   (   θ   )     1     =           H        (   θ   )       bc         H        (   θ   )       ab       =         V   bc     +     Ri   bc     +     L               i   bc            t               V   ab     -     Ri   ab     -     L               i   ab            t                                                     Mode 2 and 5               G   (   θ   )     2     =           H        (   θ   )       ab         H        (   θ   )       ca       =         V   ab     +     Ri   ab     +     L               i   ab            t               V   ca     -     Ri   ca     -     L               i   ca            t                                                     Mode 3 and 6               G   (   θ   )     3     =           H        (   θ   )       ca         H        (   θ   )       bc       =         V   ca     +     Ri   ca     +     L               i   ca            t               V   bc     -     Ri   bc     -     L               i   bc            t                                                        
 
         [0043]    Table I above shows the equation of the G(θ) functions at each mode. The G(θ) functions, made by combination of two line-to-line H(θ) functions at each mode, can be used for continuous rotor position information as well as commutation points. Because of the division of the equations at each mode, the speed term, ω, is technically eliminated. Since the G(θ) functions are absolutely speed independent, they have an identical shape over all speed ranges. As shown in FIG. 4( a ), at mode  1 , we calculate H(θ) bc/ab  to make G(θ) mode1  and after a 60° electrical angle, at mode  2 , we shift to H(θ) ab/ca  for deriving G(θ) mode2 .  
         [0044]    Since the waveform of the G(θ) function is identical at the entire speed range, as FIG. 4( b ) illustrates, we can characterize the G(θ) function at rated speed with off-line, and use the characterized function as a position reference for sensorless operation at all speeds. Based on Table I, the G(θ) function can be made as FIG. 4( b ). It is noted that the commutation signal can be generated at the peak point  70  of the G(θ) function.  
         [0045]    When the well-known PWM control scheme is applied, to compute G(θ) function at each mode, each phase voltage vector is derived. The three computed phase voltage vectors Vsf_a, Vsf_b, and Vsf_c are depicted in FIG. 1. To derive these voltage vectors, we can define the switching function of each phase [ 13 ]. Each phase has a switching function, such as SF —a , SF —b , and SF —c . Using the switching function SF —a,b,c , the V ao , V bo , and V co  at the peaks  70  shown in FIG. 4 can be obtained as:  
               V   ao     =         V   d     2     ·     SF     _      a                 (   12   )                 V   bo     =         V   d     2     ·     SF     _      b                 (   13   )                 V   co     =         V   d     2     ·     SF     _      c                 (   14   )                               
 
         [0046]    where,  
         [0047]    SF —a =1 (When Switch S 1  is turned on), SF —a =−1 (When S 4  is turned on)  
         [0048]    SF —b =1 (When Switch S 3  is turned on), SF —a =−1 (When S 6  is turned on)  
         [0049]    SF —c =1 (When Switch S 5  is turned on), SF —a =−1 (When S 2  is turned on)  
         [0050]    Then, the inverter line-to-line voltage vectors (V ab , V bc , V ca ) can be derived as:  
                     V   ab     =         V   ao     -     V   bo       =         V   d     2          (       SF     _      a       -     SF     _      b         )                       V   bc     =         V   bo     -     V   co       =         V   d     2          (       SF     _      b       -     SF     _      c         )                       V   ca     =         V   co     -     V   ao       =         V   d     2          (       SF     _      c       -     SF     _      a         )                       (   15   )                               
 
         [0051]    In normal two-phase current activated operation for the BLDC motor  12 , we cannot define the switching function of a silent phase. Therefore, to compute G(θ) functions of each mode, measurement of the terminal voltage of the silent phase is required. But, in accordance with the sensorless systems and methods of the present invention, to avoid putting in additional voltage sensing hardware circuit, we activate three-phase currents (Ia, Ib, Ic) all together and control the silent phase current as zero. By this scheme, we have switching function and can calculate the line-to-line voltage vectors even in silent phase period.  
         [0052]    [0052]FIG. 5 shows a simulation result of sensorless operation at 50 rpm with the proposed sensorless drive technique. It is noted that the stated G(θ) function  74  is derived by computation even in very low speed operation. Commutation signal  76  is generated at the peak point of the speed independent G(θ) function  74 , and phase currents are controlled by a well-known three-phase PWM control scheme. FIG. 5 depicts one such phase current  78 , which has been correlated to the commutation signal  76  and G(θ) function  74 . Speed  80  of the motor  12  is controlled to remain substantially constant over time.  
         [0053]    Table II below shows the specification for an exemplary four-pole BLDC motor  12  system for use with the developed sensorless technique. A BLDC motor  12  drive test-bed is built using PowerRex IGBTs Module as main switches to compose the inverter circuit  14 , Fuji EXB-841 as a gate driver  44 , TI TMS320F243 (Texas Instrument) microprocessor as a processor  26 , and 1 HP permanent magnet DC motor as a constant torque load.  
                             TABLE II                       Motor Specification (LL: line-to-line)                                    POWER   1 HP           Rated Speed   3000 [rpm]           R —LL     7.82 [Ω]           L —LL     77.6 [mH]           K e     1.146 [V/(rad/sec)]           K t     1.605 [Nm/A]                      
 
         [0054]    [0054]FIG. 6 shows the experimental waveform of the G(θ) function  70  and currents  82 ,  84  at 50 rpm with three-phase current control scheme using a TMS320F243 as the processor  26 . This experiment was done to observe the computed G(θ) function waveform at low speed. The computed G(θ) function is written to a D/A converter port to observe using an oscilloscope. At the peak-point  70  of the G(θ) function  74 , we do commutation to continually synchronize the phase excitation with the flat part of the back-EMF. Based on our experiment, we conclude that sensorless operation down to 10 rpm or lower is possible. The minimum speed depends on measurement error of currents and temperature effect of winding resistance R. Since PM motors have large air-gaps, saturation effects caused by current level may be ignored. From FIGS. 5 and 6, the validity of the developed sensorless drive technique for BLDCM using the new speed-independent function is successfully verified.  
         [0055]    [0055]FIG. 7 is a flow diagram illustrating steps in an exemplary method  100  for motor control performed in accordance with the present invention. In the method  100 , the motor drive system  10  is provided with a timer (see block  102 ) which is typically on-board the processor  26  to control operation of iterative steps in the method and to control starting and stopping of the process. According to the exemplary method  100 , the timer begins an interrupt service routine (ISR) is step  102 . The rectifier  22  of the drive system  10  then begins analog-to-digital conversion of the power supply  24  (step  104 ). In step  106 , the phase currents Ia, Ib and DC reference voltage Vdc are detected from leads  16 ,  18 , as described previously. In step  108 , the gate pulse/current control  44  of the processor  26  controls the currents of the inverter  14  using the input of the commutation signal  42 . In step  110 , the processor  26  generates a PWM modulation control scheme, and in step  112 , the processor  26  computes the G(θ) function for the motor  12 , and, each phase voltage vector Vsf_a, Vsf_b, Vsf_c is derived. Next (step  114 ), rotor position is estimated by the position estimation means  38 .  
         [0056]    After rotor position has been estimated, the drive system  10  then determines whether the commutation point has been reached (see block  116 ). If not, the ISR ends (block  118 ). If so, however, the system  10  performs commutation (step  120 ), calculates speed of the motor  12  (step  122 ), controls the speed (step  124 ), and determines reference currents Ia-ref, Ib-ref, and I c -ref (step  126 ). The process  100  then ends.  
         [0057]    Although the systems and methods of the present invention have been described above with respect to a three-phase brushless DC motor, those of skill in the art will understand that it is applicable as well to motors having other number of phases (i.e., two, four, five, etc.). In such a case, the number of motor phase currents (Ia, Ib . . . ) that are measured by the drive system will number one less than the total number of motor phases. For a five-phase motor, for example, four phase currents would be measured.  
         [0058]    Those of skill in the art will recognize that many modifications and changes may be made