# Patent

## Title
Predictive pulse width modulation for an open delta H-bridge driven high efficiency ironless permanent magnet machine

## Abstract

Embodiments of the present method and system permit an effective method for determining the optimum selection of pulse width modulation polarity and type including determining machine parameters, inputting the machine parameters into a predicted duty cycle module, determining the optimum polarity of the pulse width modulation for a predicted duty cycle based on a pulse width modulation generation algorithm, and determining the optimum type of the pulse width modulation for a predicted duty cycle based on the pulse width modulation generation algorithm.

## Background
CLAIM OF BENEFIT AND INCORPORATION BY REFERENCE
This application claims priority to U.S. Provisional Patent Application No. 61/194,102 to DABOUSSI, filed Sep. 23, 2008, entitled “PREDICTIVE PWM FOR OPEN DELTA H-BRIDGE DRIVE HIGH EFFICIENCY IRONLESS P.H. METER”, the entire disclosure of which is incorporated by reference herein.


TECHNICAL FIELD
1. Field of the Disclosure
This disclosure relates to a method and system that makes use of the availability of the machine parameters required to achieve optimal selection of pulse width modulation polarity and type. More specifically, the disclosure relates to a method and system that uses a predictive duty cycle employing machine parameters to determine both the magnitude and the pulse width of the pulse width modulation that is required to generate a waveform at a given operation condition, as well as the polarity of the pulse width modulation.
2. Description of Related Art
A permanent magnet machine is a type of alternating current (AC) motor whereby power is supplied to the rotating device by means of imposing an electromagnetic field onto a field generated by a permanent magnet rotor. To control an AC permanent magnet machine, the absolute position of the magnetic field produced by the rotor permanent magnets (PM) needs to be known at all times. The magnet's position is important for determining the stator current magnitude of the machine necessary to produce the desired torque. This operation is known as the stator current commutation. Since magnets are rotating with respect to the stator, the magnet position can be calculated by measuring the rotor absolute angular position. Absolute position sensors such as resolvers and optical encoders are typically used to measure the absolute angular position of the machine rotor.
H-bridge topologies are commonly used to drive open delta permanent magnet machines, as well as other types of machines. An H-bridge is an electronic circuit which enables a voltage to be applied across a load in either direction. The term “H-bridge” is derived from the typical graphical representation of such a circuit as seen in FIG. 1A. An H-bridge is built with four switches, which may be solid-state or mechanical. As seen in FIG. 1B, when switches S1 and S4 are closed, and switches S2 and S3 are open, a positive voltage will be applied across the motor. However, by opening switches S1 and S4, and closing switches S2 and S3 (FIG. 1C), this voltage is reversed allowing reverse operation of the motor. An H-bridge arrangement may be used to reverse the polarity of the motor, but may also be used to stop the motor if the motor's terminals are shorted.
One of the main benefits for using an H-bridge to drive a PM machine is that it lowers the ripple current in the motor windings that results from the pulsating voltage waveforms of the pulse modulated power stage. Ripple current is a small unwanted residual periodic variation of the direct current output of a power supply which has been derived from an alternating power source. Another benefit garnered from driving a PM machine with an H-bridge is that the H-bridge allows a greater level of flexibility to shape the current waveform beyond the 120-degree limitation imposed by a conventional 3-phase inverter.
To properly control the currents and to minimize the harmonic content in the current waveforms, robust control must be performed. One of the issues with H-bridge control is that in order to reduce the machine ripple current, unipolar pulse width modulation (PWM) must be employed. With unipolar PWM, a 50% reduction in ripple current is achieved when compared to bipolar PWM. When using unipolar PWM during transition periods where the machine emf voltage has a different polarity from the terminal voltage, a combination of unipolar and bipolar PWM must be employed; otherwise, current distortion will result. The existing prior art merely selects unipolar verses bipolar PWM based upon the sign of the current waveform. This conventional approach leads to additional harmonics in the current waveform that will lead to increased heating in the machine.
SUMMARY OF THE DISCLOSURE
The present method and system optimizes the pulse width modulation generation by appropriately determining when unipolar or bipolar PWM should be used, by exploiting the machine temperature measurements, machine parameters, operation conditions, and the dynamic model of the machine windings.
Embodiments of the present disclosure relate to a computer-implemented method for determining a predictive duty cycle that is able to determine the magnitude and pulse width of an H-bridge pulse width modulation that is used to drive a machine motor, including determining machine parameters, inputting the machine parameters into a predicted duty cycle module, determining the optimum polarity of the pulse width modulation for a predicted duty cycle based on a pulse width modulation generation algorithm, and determining the optimum type of the pulse width modulation for a predicted duty cycle based on the pulse width modulation generation algorithm.
The embodiments of the present disclosure relate to a system for determining a predictive duty cycle that is able to determine the magnitude and pulse width of an H-bridge pulse width modulation that is used to drive a machine motor, including means for determining machine parameters, means for inputting the machine parameters into a predicted duty cycle module, means for determining the optimum polarity of the pulse width modulation for a predicted duty cycle based on a pulse width modulation generation algorithm; and means for determining the optimum type of the pulse width modulation for a predicted duty cycle based on the pulse width modulation generation algorithm.
The embodiments of the present disclosure further relate to a computer-readable medium for determining a predictive duty cycle that is able to determine the magnitude and pulse width of an H-bridge pulse width modulation that is used to drive a machine motor, including means for determining machine parameters, means for inputting the machine parameters into a predicted duty cycle module, means for determining the optimum polarity of the pulse width modulation for a predicted duty cycle based on a pulse width modulation generation algorithm; and means for determining the optimum type of the pulse width modulation for a predicted duty cycle based on the pulse width modulation generation algorithm.
The method for determining a predictive duty cycle that is able to determine the magnitude and pulse width of an H-bridge pulse width modulation that is used to drive a machine motor may include that the type of the predicted duty cycle is one of unipolar or bipolar, and the pulse width modulation generation algorithm is




  
    
      d
      prediction
    
    ⁡
    
      (
      
        θ
        elect
      
      )
    
  
  =
  
    
      (
      
        
          
            
              
                
                  
                    E
                    emf
                  
                  ⁡
                  
                    (
                    
                      
                        T
                        magnet
                      
                      ,
                      rpm
                    
                    )
                  
                
                ·
                
                  sin
                  ⁡
                  
                    (
                    
                      θ
                      elect
                    
                    )
                  
                
              
              +
            
          
        
        
          
            
              
                
                  
                    i
                    ref
                  
                  ⁡
                  
                    (
                    
                      θ
                      elect
                    
                    )
                  
                
                ⁢
                
                  
                    R
                    s
                  
                  ⁡
                  
                    (
                    
                      T
                      winding
                    
                    )
                  
                
              
              +
              
                L
                ·
                
                  
                    d
                    
                      i
                      ref
                    
                  
                  
                    d
                    t
                  
                
              
            
          
        
      
      )
    
    Vbus
  




wherein Eemf(Tmagnet,rpm) is the back emf of the machine as a function of the magnet temperature and speed, θelect is the electrical angle for the machine during that particular duty cycle, Iref is an input quantity of reference current, i.e., the amount of current that the processor wants to get out of that particular duty cycle, Rs is the phase resistance of the machine and is a known input parameter, Twinding is the temperature of the windings in the coil, and is also a known input parameter, L is the inductance of the inductor and is also an input parameter, and Vbus is the supply voltage of the inverter, and is a quantity that is measured by an analog-to-digital converter.

The system for determining a predictive duty cycle that is able to determine the magnitude and pulse width of an H-bridge pulse width modulation that is used to drive a machine motor may further include that the type of the predicted duty cycle is one of unipolar or bipolar, and the pulse width modulation generation algorithm is




  
    
      d
      prediction
    
    ⁡
    
      (
      
        θ
        elect
      
      )
    
  
  =
  
    
      (
      
        
          
            
              
                
                  
                    E
                    emf
                  
                  ⁡
                  
                    (
                    
                      
                        T
                        magnet
                      
                      ,
                      rpm
                    
                    )
                  
                
                ·
                
                  sin
                  ⁡
                  
                    (
                    
                      θ
                      elect
                    
                    )
                  
                
              
              +
            
          
        
        
          
            
              
                
                  
                    i
                    ref
                  
                  ⁡
                  
                    (
                    
                      θ
                      elect
                    
                    )
                  
                
                ⁢
                
                  
                    R
                    s
                  
                  ⁡
                  
                    (
                    
                      T
                      winding
                    
                    )
                  
                
              
              +
              
                L
                ·
                
                  
                    d
                    
                      i
                      ref
                    
                  
                  
                    d
                    t
                  
                
              
            
          
        
      
      )
    
    Vbus
  




wherein Eemf(Tmagnet,rpm) is the back emf of the machine as a function of the magnet temperature and speed, θelect is the electrical angle for the machine during that particular duty cycle, Iref is an input quantity of reference current, i.e., the amount of current that the processor wants to get out of that particular duty cycle, Rs is the phase resistance of the machine and is a known input parameter, Twinding is the temperature of the windings in the coil, and is also a known input parameter, L is the inductance of the inductor and is also an input parameter, and Vbus is the supply voltage of the inverter, and is a quantity that is measured by an analog-to-digital converter.

The computer-readable medium for determining a predictive duty cycle that is able to determine the magnitude and pulse width of an H-bridge pulse width modulation that is used to drive a machine motor may further include that the type of the predicted duty cycle is one of unipolar or bipolar, and the pulse width modulation generation algorithm is




  
    
      d
      prediction
    
    ⁡
    
      (
      
        θ
        elect
      
      )
    
  
  =
  
    
      (
      
        
          
            
              
                
                  
                    E
                    emf
                  
                  ⁡
                  
                    (
                    
                      
                        T
                        magnet
                      
                      ,
                      rpm
                    
                    )
                  
                
                ·
                
                  sin
                  ⁡
                  
                    (
                    
                      θ
                      elect
                    
                    )
                  
                
              
              +
            
          
        
        
          
            
              
                
                  
                    i
                    ref
                  
                  ⁡
                  
                    (
                    
                      θ
                      elect
                    
                    )
                  
                
                ⁢
                
                  
                    R
                    s
                  
                  ⁡
                  
                    (
                    
                      T
                      winding
                    
                    )
                  
                
              
              +
              
                L
                ·
                
                  
                    d
                    
                      i
                      ref
                    
                  
                  
                    d
                    t
                  
                
              
            
          
        
      
      )
    
    Vbus
  




wherein Eemf(Tmagnet,rpm) is the back emf of the machine as a function of the magnet temperature and speed, θelect is the electrical angle for the machine during that particular duty cycle, Iref is an input quantity of reference current, i.e., the amount of current that the processor wants to get out of that particular duty cycle, Rs is the phase resistance of the machine and is a known input parameter, Twinding is the temperature of the windings in the coil, and is also a known input parameter, L is the inductance of the inductor and is also an input parameter, and Vbus is the supply voltage of the inverter, and is a quantity that is measured by an analog-to-digital converter.




BRIEF DESCRIPTION OF THE DRAWINGS
The disclosure is described through a preferred embodiment and the attached drawings in which:
FIG. 1A is a schematic representation of the general structure of an H-bridge;
FIG. 1B is a schematic representation of an H-bridge in one basic state;
FIG. 1C is schematic representation of an H-bridge in another basic state;
FIG. 2 is a schematic representation of the magnets used in the motor in accordance with one embodiment of the present disclosure;
FIG. 3 is a block diagram of the arrangement of the system in one embodiment of the present invention;
FIG. 4 is a graphical representation of the of a duty cycle with respect to one embodiment of the present disclosure;
FIG. 5A is a schematic diagram of a 3-phase open delta machine model;
FIG. 5B is an expanded view of a terminal of the machine;
FIG. 6 is a block diagram for determining the sign and type of the predicted duty cycle; and
FIG. 7 is a flowchart for determining the optimum pulse width modulation for a duty cycle.



DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
Applicants have discovered a method and system to optimize the pulse width modulation generation by appropriately determining when a unipolar verses a bipolar pulse width modulation should be used. Moreover, the present method and system uses a predictive method to determine when bipolar verses unipolar PWM should be used, and this prediction is based on factors such as machine temperature measurements, machine parameters, operation conditions, and the dynamic model of the machine windings.
A preferred embodiment of the motor/generator used in the present method and system is illustrated in FIG. 2. The motor/generator of the present method and system includes, among other things, ironless rotor magnets 202, 204, as well as a stator 206.
FIG. 3 illustrates a block diagram of one embodiment of the present invention, including a processor 302 with a duty cycle prediction module 304 which sends information to a pulse width modulator 306. The pulse width modulator 306 switches the pulse for a permanent magnet machine 308.
FIG. 4 illustrates a graphical representation of a duty cycle with respect to one embodiment of the present method and system. FIG. 4 depicts, by way of example, when a duty cycle is unipolar and how the machine and processor determines when unipolar positive pulses verses unipolar negative pulses are used in the duty cycle. This graphical representation also shows the transition periods when the machine emf voltage has a different polarity from the terminal voltage, and a combination of unipolar and bipolar pulse width modulation must be should be applied to avoid current distortion.
FIG. 5A illustrates a 3-phase open delta configuration machine model that includes schematic representations for three power sources Ea, Eb, and Ec, three resistors Ra, Rb, and Rc, and three inductors La, Lb, and Le, although other configurations are contemplated. The currents ia, ib, and ic of each of the phases are also depicted in the machine model seen in FIG. 5A. The machine model is considered an open delta configuration since the three windings are not all connected to one point. The machine is able to receive digital-signals which dictate the motor's movement. For instance, in the case of a permanent magnet machine, the motor is started spinning by the motor setting the current vector to a very high DC magnitude. Setting the current vector to a high constant value enables the magnetic field vector of the motor to align itself with the current vector. At this initial time, the torque angle of the motor is near zero.
FIG. 5B is an expanded view of a terminal of the machine, depicting a terminal being driven by an H-bridge at a power stage 504. The power stage 504 includes the four switches S1, S2, S3, S4 of the H-bridge. Thus, the machine is said to have 6-switching poles since the motor has 3 phases. FIG. 4B also depicts the supply voltage Vbus and a capacitor C.
FIG. 6 depicts a flow diagram for determining which of the switching poles needs to be switched based on the sign and polarity of the of duty cycle. This is accomplished by a processor by solving the algorithm:




  
    
      d
      prediction
    
    ⁡
    
      (
      
        θ
        elect
      
      )
    
  
  =
  
    
      
        (
        
          
            
              
                
                  
                    
                      E
                      emf
                    
                    ⁡
                    
                      (
                      
                        
                          T
                          magnet
                        
                        ,
                        rpm
                      
                      )
                    
                  
                  ·
                  
                    sin
                    ⁡
                    
                      (
                      
                        θ
                        elect
                      
                      )
                    
                  
                
                +
              
            
          
          
            
              
                
                  
                    
                      i
                      ref
                    
                    ⁡
                    
                      (
                      
                        θ
                        elect
                      
                      )
                    
                  
                  ⁢
                  
                    
                      R
                      s
                    
                    ⁡
                    
                      (
                      
                        T
                        winding
                      
                      )
                    
                  
                
                +
                
                  L
                  ·
                  
                    
                      d
                      
                        i
                        ref
                      
                    
                    
                      d
                      t
                    
                  
                
              
            
          
        
        )
      
      Vbus
    
    .
  




Where:
Eemf(Tmagnet,rpm) is the back emf of the machine as a function of the magnet temperature and speed;
θelect is the electrical angle for the machine during that particular duty cycle;
Iref is an input quantity of reference current, i.e., the amount of current that the processor wants to get out of that particular duty cycle;
Rs is the phase resistance of the machine and is a known input parameter;
Twinding is the temperature of the windings in the coil, and is also a known input parameter;
L is the inductance of the inductor and is also an input parameter; and
Vbus is the supply voltage of the inverter, and is a quantity that is measured by an analog-to-digital converter. Some or all of the input parameters/quantities do not have to be measured during the operation of the machine, but rather can be known prior to operation. Parameters that are unknown prior to the operation of the machine may be measured during operation.
The sign (+ or −) of the output of the algorithm, dpredictive, delineated above will determine which of the switching poles needs to be switched. When dpredictive is a positive value then the pulse width modulation is unipolar positive, thus switching S1 and S2 on while maintaining S4 on and S3 off will drive a current in the positive direction. When dpredictive is a negative value, the pulse width modulation is unipolar negative, thus switching S3 and S4 on while maintaining S2 on and S1 off will drive a current in the negative direction.
As illustrated in FIG. 6, once the processor inputs parameters 602 into the predictive duty cycle 604, the algorithm is able to determine the sign 606 of the predictive duty cycle, as well as the value of dpredictive 608, which determines the polarity of the duty cycle. Moreover, the processor determines a predicted duty cycle such that the PI regulator 610 is limited in the amount of current correction that it implements, i.e., such that the actual current 614 in the motor is close to the reference current 612 that the processor wants to get out of that particular duty cycle. This reduces the ripple current of the machine and consequently the machine motor runs more efficiently.
FIG. 7 illustrates a flowchart for optimizing the torque of a permanent magnet machine in one embodiment of the present method and system. In step 702, machine parameters are determined. These parameters may be values known prior to the operation of the machine, and/or they may be parameters that are measured during the operation of the machine. Next, in step 704, the machine parameters are input into a duty cycle prediction module. Then, the optimum polarity of the pulse width modulation is determined for a predicted duty cycle based on a pulse width modulation generation algorithm, which is the equation described above, in step 706. Finally, in step 708, the optimum type of pulse width modulation is determined for a predicted duty cycle based on a pulse width modulation generation algorithm.
Although, the above recited method and system is described for implementation in a permanent magnet machine, this system, method, and computer-readable medium could be used in any type of motor that has a back emf that is proportional to speed.
Thus, the above described method, system, and computer-readable medium in accordance with the embodiments of the present method and system, as can now be fully appreciated, provides a very effective method for determining the optimum selection of pulse width modulation polarity and type.
The method and system has been described through a preferred embodiment. However, various modifications can be made without departing from the scope of the method and system as defined by the appended claims and legal equivalents.

## Claims

1. A method for determining a predictive duty cycle that is able to determine the magnitude and pulse width of an H-bridge pulse width modulation that is used to drive a machine motor, comprising:
determining one or more machine parameters;
inputting the machine parameters into a predicted duty cycle module;
determining the optimum polarity of the pulse width modulation for a predicted duty cycle based on a pulse width modulation generation algorithm; and
determining whether the pulse width modulation is unipolar or bipolar for a predicted duty cycle based on the pulse width modulation generation algorithm,
wherein the pulse width modulation generation algorithm is





  
    
      
        d
        prediction
      
      ⁡
      
        (
        
          θ
          elect
        
        )
      
    
    =
    
      
        (
        
          
            
              
                
                  
                    
                      E
                      emf
                    
                    ⁡
                    
                      (
                      
                        
                          T
                          magnet
                        
                        ,
                        rpm
                      
                      )
                    
                  
                  ·
                  
                    sin
                    ⁡
                    
                      (
                      
                        θ
                        elect
                      
                      )
                    
                  
                
                +
              
            
          
          
            
              
                
                  
                    
                      i
                      ref
                    
                    ⁡
                    
                      (
                      
                        θ
                        elect
                      
                      )
                    
                  
                  ⁢
                  
                    
                      R
                      s
                    
                    ⁡
                    
                      (
                      
                        T
                        winding
                      
                      )
                    
                  
                
                +
                
                  L
                  ·
                  
                    
                      d
                      
                        i
                        ref
                      
                    
                    
                      d
                      t
                    
                  
                
              
            
          
        
        )
      
      Vbus
    
  
  ,



 wherein Eemf(Tmagnet,rpm) is the back emf of the machine as a function of the magnet temperature and speed, θelect is the electrical angle for the machine during that particular duty cycle, Iref is an input quantity of reference current, i.e., the amount of current that the processor wants to get out of that particular duty cycle, Rs is the phase resistance of the machine and is a known input parameter, Twinding is the temperature of the windings in the coil, and is also a known input parameter, L is the inductance of the inductor and is also an input parameter, and Vbus is the supply voltage of the inverter, and is a quantity that is measured by an analog-to-digital converter.

2. A system for determining a predictive duty cycle that is able to determine the magnitude and pulse width of an H-bridge pulse width modulation that is used to drive a machine motor, comprising:
means for determining one or more machine parameters;
means for inputting the machine parameters into a predicted duty cycle module;
means for determining the optimum polarity of the pulse width modulation for a predicted duty cycle based on a pulse width modulation generation algorithm; and
means for determining whether the pulse width modulation is unipolar or bipolar for a predicted duty cycle based on the pulse width modulation generation algorithm,

wherein the pulse width modulation generation algorithm is




  
    
      
        d
        prediction
      
      ⁡
      
        (
        
          θ
          elect
        
        )
      
    
    =
    
      
        (
        
          
            
              
                
                  
                    
                      E
                      emf
                    
                    ⁡
                    
                      (
                      
                        
                          T
                          magnet
                        
                        ,
                        rpm
                      
                      )
                    
                  
                  ·
                  
                    sin
                    ⁡
                    
                      (
                      
                        θ
                        elect
                      
                      )
                    
                  
                
                +
              
            
          
          
            
              
                
                  
                    
                      i
                      ref
                    
                    ⁡
                    
                      (
                      
                        θ
                        elect
                      
                      )
                    
                  
                  ⁢
                  
                    
                      R
                      s
                    
                    ⁡
                    
                      (
                      
                        T
                        winding
                      
                      )
                    
                  
                
                +
                
                  L
                  ·
                  
                    
                      d
                      
                        i
                        ref
                      
                    
                    
                      d
                      t
                    
                  
                
              
            
          
        
        )
      
      Vbus
    
  
  ,




wherein Eemf(Tmagnet,rpm) is the back emf of the machine as a function of the magnet temperature and speed, θelect is the electrical angle for the machine during that particular duty cycle, Iref is an input quantity of reference current, i.e., the amount of current that the processor wants to get out of that particular duty cycle, Rs is the phase resistance of the machine and is a known input parameter, Twinding is the temperature of the windings in the coil, and is also a known input parameter, L is the inductance of the inductor and is also an input parameter, and Vbus is the supply voltage of the inverter, and is a quantity that is measured by an analog-to-digital converter.

3. A computer-readable medium for determining a predictive duty cycle that is able to determine the magnitude and pulse width of an H-bridge pulse width modulation that is used to drive a machine motor, comprising:
means for determining one or more machine parameters;
means for inputting the machine parameters into a predicted duty cycle module; and
means for determining the optimum polarity of the pulse width modulation for a predicted duty cycle based on a pulse width modulation generation algorithm; and
means for determining whether the pulse width modulation is unipolar or bipolar for a predicted duty cycle based on the pulse width modulation generation algorithm,

wherein the pulse width modulation generation algorithm is




  
    
      
        d
        prediction
      
      ⁡
      
        (
        
          θ
          elect
        
        )
      
    
    =
    
      
        (
        
          
            
              
                
                  
                    
                      E
                      emf
                    
                    ⁡
                    
                      (
                      
                        
                          T
                          magnet
                        
                        ,
                        rpm
                      
                      )
                    
                  
                  ·
                  
                    sin
                    ⁡
                    
                      (
                      
                        θ
                        elect
                      
                      )
                    
                  
                
                +
              
            
          
          
            
              
                
                  
                    
                      i
                      ref
                    
                    ⁡
                    
                      (
                      
                        θ
                        elect
                      
                      )
                    
                  
                  ⁢
                  
                    
                      R
                      s
                    
                    ⁡
                    
                      (
                      
                        T
                        winding
                      
                      )
                    
                  
                
                +
                
                  L
                  ·
                  
                    
                      d
                      
                        i
                        ref
                      
                    
                    
                      d
                      t
                    
                  
                
              
            
          
        
        )
      
      Vbus
    
  
  ,




wherein Eemf(Tmagnet,rpm) is the back emf of the machine as a function of the magnet temperature and speed, θelect is the electrical angle for the machine during that particular duty cycle, Iref is an input quantity of reference current, i.e., the amount of current that the processor wants to get out of that particular duty cycle, Rs is the phase resistance of the machine and is a known input parameter, Twinding is the temperature of the windings in the coil, and is also a known input parameter, L is the inductance of the inductor and is also an input parameter, and Vbus is the supply voltage of the inverter, and is a quantity that is measured by an analog-to-digital converter.