Abstract:
A novel method is proposed for controlling the torque of a PM brushless motor with sinusoidal back-emfs without current sensors by computing the required input phase voltages with measured rotor position and speed and known machine parameters. These voltages are fed to the machine at an angle computed in terms of input parameters and the phase voltage with respect to their back-emfs so that phase currents are aligned with their back-emfs to exactly mimic the performance of the current mode controller.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is based upon, and claims the benefit of, U.S. Provisional Patent Application No. 60/154,613, filed Sep. 17, 1999; No. 60/154,681, filed Sep. 17, 1999; and No. 60/183,301, filed Feb. 17, 2000, the disclosures of all three of which are incorporated by reference herein in their entirety. 
    
    
     TECHNICAL FIELD 
     This invention relates to torque control in automotive permanent magnet (PM) brushless electric motors. 
     BACKGROUND OF THE INVENTION 
     It is known in the art of permanent magnet brushless electric motors to control torque by aligning phase currents with back-emf. The torque delivered by the electric motor is then directly proportional to the phase current and is therefore easily controlled by simply controlling the aligned phase currents. This is commonly referred to as “current mode control.” The drawback is that current sensors are required to determine what the currents are. The sensors necessarily have a finite, though small, dc voltage drops that induce torque ripple into the motor. 
     SUMMARY OF THE INVENTION 
     An exemplary embodiment is a method of controlling torque in electric motors that is analogous to traditional current mode control methods, but which requires no current sensors to determine what the current is in any particular phase. Instead, phase current information is calculated from knowledge of the rotor&#39;s position and rate of rotation. The information is used to calculate a required voltage and electrical angle offset needed to obtain a user-specified torque. The calculated voltage and offset is added to the input power of the electric motor by known means, usually an inverter. 
    
    
     DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a phasor diagram for a permanent magnet motor. 
     FIG. 2 is a schematic representation of a system for controlling the torque of a sinusoidally excited permanent magnet motor. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     A description of the preferred embodiment of the present invention will now be had with reference to FIGS. 1 and 2 of the drawings. 
     Referring to FIG. 1 there is shown a phasor diagram. In permanent magnet (PM) synchronous machines with sinusoidal back-emfs, torque control is accomplished by regulating the phase currents and aligning them with respective back-emfs, typically by adding a phase voltage to the motor input at a load angle δ. Under these conditions, the torque is directly proportional to the phase current. This is shown in the phasor diagram of FIG. 1, wherein: 
     E=stator phase back-emf, 
     V=stator phase terminal voltage, 
     I=stator phase current, 
     R=stator phase resistance, 
     X=ω e ·L a =stator phase reactance, 
     ω e =electrical angular frequency, rad/sec, 
     L a =stator phase inductance, 
     δ=load angle between back-emf and stator phase terminal voltage, and 
     Ψ f =magnet flux linkage. 
     The electromagnetic torque of the machine is given by 
     
       
           T   e =3 E·I/ω   m   (1) 
       
     
     where ω m =P·ω e =mechanical angular frequency in rad/sec, and P=number of pole pairs. Equation (1) may be written in terms of a back-emf constant, K e  as 
     
       
           T   e =3 K   e   ·I   (2) 
       
     
     Where K e =E/ω m , V/(mech rad/s). Because torque is directly proportional to the phase current in current mode controller, it requires two current sensors for measuring phase currents. 
     The drawback of current mode control is the production of low frequency torque ripple caused by dc offset in the current measurements of the current sensors. This is undesirable in the case of column-assisted electric power steering where the sinusoidal PM motor is coupled directly into the steering column to provide torque assistance. 
     The phasor diagram of FIG. 1 is used to compute required phase voltages for a given torque command, T cmd : 
     
       
           V =( E+I·R )+ j·I·X   (3) 
       
     
     where j is the imaginary square root of −1, therefore 
     
       
           V   2 =( E+I·R ) 2 +( I·X ) 2   (4) 
       
     
     From Equation (2), 
     
       
           I=T   cmd /3 K   e   (5) 
       
     
     Substituting Equation (5) into Equation (4) gives 
     
       
           v   2   =[E +( T   cmd   ·R/ 3 K   e )] 2   +[T   cmd   ·P·L   a ·ω m 3 K   e ] 2   (6) 
       
     
     Equation (6) can then be simplified as 
     
       
           V =[( K   e ·ω m   +K   1   ·T   cmd ) 2   +K   2 ( T   cmd ·ω m ) 2 ] ½   (7) 
       
     
     where K 1 =R/3K e  and K 2 =(P·L a /3K e ) 2 . The phase voltages can also be obtained from a V 2  vs. V look-up table to reduce computational time. 
     From FIG. 1, the load angle, δ, is obtained in terms of known parameters as 
     
       
           V ·sinδ= T   cmd ·ω m   ·K   3   (8) 
       
     
     and therefore, 
     
       
         δ=sin −1 ( T   cmd ·ω m   ·K   3   /V )  (9) 
       
     
     where K 3 =P·L a /3K e    
     The load angle, δ, can be calculated from a V·sin δ vs δ look-up table and V −1  can be obtained from a V 2  vs V −1  look-up table to reduce computational time. Therefore, the input phase voltages are 
     
       
           V   a   =V ·sin(δ+θ)  (10) 
       
     
     
       
           V   b   =V ·sin(δ+θ+120°)  (11) 
       
     
     
       
           V   c   =V ·sin(δ+θ+240°)  (12) 
       
     
     Referring to FIG. 2, the system in an exemplary embodiment includes a rotor position encoder  110  coupled to a PM motor  108 . The encoder  110  is operative to measure the angular position, θ, of the rotor of the motor and provides as output a position signal  112  indicative thereof. A speed measuring circuit  114  is connected to the position encoder  110  for determining the angular speed, dθ/dt=ω m  and providing as output therefrom a speed signal  116  indicative thereof. The position and angular speed signals  112 ,  116  as well as a torque command signal, T cmd ,  118 , indicative of a desired motor torque, are applied to a controller  200 . The controller  200  generates the input phase voltages  214  and motor voltage command signals  218  in response to the position and angular speed signals  112 ,  116  and the torque command signal  118 . Blocks  202 ,  208 .  212 , and  216  indicate processing performed by controller  200 . An inverter  104  is coupled between a power source  102  and the controller  200  for applying phase voltages  106  across the motor  108  in response to the motor voltage command signals  218  in order to develop the desired motor torque. In order to generate phase voltages  106  with an average sinusoidal shape, switching devices indigenous to the inverter  104 , must be turned on and off for specific durations at specific rotor angular positions, θ. Control of the inverter  104  to generate phase voltages  106  with an average sinusoidal shape can be implemented by way of any appropriate pulse width modulation (PWM) scheme  216 . Because space vector modulation (SVM) has advantages in higher output voltage, low harmonic distortion, low switching power loses and easy microprocessor implementation, SVM-based control may be preferred. 
     An exemplary method includes sensing the angular position, θ, of the rotor and determining the angular speed, dθ/dt=ω m , thereof. In response to the angular position, θ, and angular speed, ω m , of the rotor and to the torque command signal, T cmd ,  118 , the controller  200  generates motor voltage command signals  218  indicative of the voltage required to produce the desired motor torque. Phase voltages  106  are applied across the motor windings in response to the motor voltage command signals  218  to develop the desired motor torque. In particular, in response to the torque command signal, T cmd ,  118 , the angular speed signal  116  and known parameters, at  202  the controller  200  calculates V according to Equation (7) above. Alternatively, V may be determined by using V 2  vs V or V 2  vs V −1  look-up tables. Based upon the calculated value for V and known parameters, at  208  the controller  200  calculates δ according to Equation (9) above. Alternatively, δ may be determined by using a sin δ vs δ look-up tables. Based upon the calculated value for V, the calculated value for δ and the angular position, θ, at  212  the controller  200  calculates the input phase voltages, V a , V b , and V c ,  214 . At  216 , input phase voltages, V a , V b , and V c ,  214  are subject to a pulse width modulation (PWM) scheme. Motor voltage command signals  218 , indicative of the voltage required to produce the desired motor torque and in the form of pulse width modulated signals having an average sinusoidal shape, are applied to the inverter  104  wherein the necessary switching is performed for application to the motor  108 . By controlling torque without using current sensors, torque ripple is reduced resulting in smoother application of torque. 
     While the invention has been described by reference to a preferred embodiment, it should be understood that numerous modifications can be made thereto. Accordingly it is intended that the invention not be limited to the disclosed embodiment, but that it retain the full scope and spirit permitted by the language of the appended claims.