Abstract:
A control system for a brushless DC motor, preferably used in a power steering system in a vehicle. Presently delivered torque is computed without measuring currents in the motor. A demanded torque signal is received, and a torque error signal is produced. The torque error signal is modified by an inertial torque component, if the motor is accelerating. In response to the modified error signal, the control system first attempts to increase motor torque by increasing motor voltage, if that is possible, without increasing magnetic field which is parallel with the magnetic field of the rotor. If that is not possible, then motor voltage is held fixed, and the magnetic field just mentioned is increased.

Description:
[0001]     The invention concerns a control system for brushless DC motors, wherein torque is measured for purposes of controlling stator current, without direct measurement of the stator currents. The invention also provides a two-tier stratagem for increasing torque produced by the motor.  
       BACKGROUND OF THE INVENTION  
       [0002]      FIG. 1  illustrates schematically three stator coils  3 ,  6 , and  9 , which are contained in a three-phase synchronous motor (not shown).  FIG. 2  shows the coils, but with connecting wires W of  FIG. 1  omitted, to avoid clutter. In  FIG. 2 , currents I 3 , I 6 , and I 9  are generated in the respective coils. Each current produces a magnetic field B 3 , B 6 , and B 9 , as indicated.  
         [0003]     The coils  3 ,  6 , and  9  are physically positioned to be 120 degrees apart, as shown, so that the fields B 3 , B 6 , and B 9  are also positioned 120 degrees apart physically (as opposed to chronologically). This arrangement allows creation of a magnetic field which rotates in space at a constant speed, if proper currents are generated in the coils, as will now be explained.  
         [0004]      FIG. 3  illustrates three-phase currents. The vertical axis on the coordinates runs from negative unity to positive unity for simplicity. In practice, one would multiply the values of unity by the actual peak-to-peak values of the currents being used.  
         [0005]     The horizontal axis represents time, but measured in degrees. For example, if the frequency of the sine waves is 60 Hz, then 360 degrees represent 1/60 seconds, or 16.7 milliseconds. One degree represents 16.7/360, or 0.046 milliseconds.  
         [0006]     Currents in the form of sine waves SIN 3 , SIN 6 , and SIN 9  are created respectively in coils  3 ,  6 , and  9 , as indicated. The sine waves are separated by 120 chronological, or electrical, degrees. Coil  3  resides at zero physical degrees. SIN 3  begins at zero degrees on the time axis, as indicated on the plot.  
         [0007]     Similarly, coil  6  stands at 120 degrees from coil  3 . SIN 6  begins at 120 degrees, as indicated on the plot. Similarly, coil  9  stands at 240 degrees from coil  3 . Correspondingly, SIN 9  begins at 240 degrees, as indicated on the plot.  
         [0008]     Each coil  3 ,  6 , and  9  produces a magnetic field, as indicated. Those three magnetic fields add vectorially to produce a single magnetic field, which rotates at a constant angular velocity, if the sine waves SIN 3 , SIN 6 , and SIN 9  have the same peak-to-peak magnitudes, and are exactly 120 degrees apart in phase.  
         [0009]      FIG. 4  represents the vector sum B of magnetic fields B 3 , B 6 , and B 9  of  FIG. 2 . Vector B in  FIG. 4  rotates in the direction of arrow  30 .  
         [0010]      FIG. 5  shows the coils of  FIGS. 1-3  superimposed over the rotating vector B. In addition, the rotor ROT of the motor is shown. Rotor ROT contains an apparatus which generates a rotor magnetic field BR. The apparatus may take the form of a permanent magnet PM.  
         [0011]     The rotor field BR continually attempts to align itself with the rotating vector B, thus causing the rotor ROT to rotate. Controlling the speed of the rotating vector B, by controlling the individual vectors B 3 , B 6 , and B 9  in  FIG. 2 , by controlling the currents  13 ,  16 , and  19 , allows one to control speed of the motor.  
         [0012]      FIG. 6  illustrates one type of prior-art control system, termed a “field oriented” control system. The overall task is to compute the current needed to deliver the torque demanded by the input  79  to summer  80 . Then, modulator PWM generates the appropriate currents, analogous to those in  FIG. 3 , which are delivered to the three coils in the motor. However, to simplify computation, translator  64  converts measurement of the sinusoidal instantaneous phase currents I u  and I v  into two equivalent direct currents I d  and I q , which rotate in space along with the rotor. After intermediate computations are performed to produce voltages Vq and Vd, a reverse transformation is undertaken by translator  95 , to generate three equivalent sinusoidal voltages V u  and V v  and V w .  
         [0013]     Explaining this in greater detail, a Pulse Width Modulator PWM synthesizes three sinusoidal currents Iu, Iv, and Iw, which correspond in concept to currents I 3 , I 6 , and I 8  in  FIG. 2 . Sensors  50  and  52  measure currents Iu and Iv. This measurement of two currents allows computation of the third current, Iw, because the three currents must sum to zero, because the COILS are Y-connected.  
         [0014]     Image  60  illustrates the spatial orientations of the three currents. (It is perhaps more accurate to speak of spatial orientation of the magnetic fields which the currents produce, but it has become customary to refer to spatial orientation of the currents, since the magnetic fields and the currents are closely related.) Image  63  illustrates vector addition of the three currents, producing a vector sum, Isum.  
         [0015]     In one approach, Isum, or the individual currents Iu, Iv, and Iw directly, are used in later computations which derive parameters the PWM needs to compute the necessary currents to generate in each of the COILS. However, such computations require extensive computer power.  
         [0016]     Another approach which requires less computation is to transform the rotating vector Isum into a stationary reference frame. This is done by block  64 , together with encoder  65 . The latter measures the present angle theta of the rotor, shown above the encoder  65 .  
         [0017]     Image  68  represents the rotating current Isum, but enlarged compared with image  60 . Image  72  superimposes a conventional rotating coordinate system, with axes labeled “d” (direct) and “q” (quadrature). This coordinate system is rotated by the angle theta. The angle of the coordinate system, of course, will continually change, as theta changes.  
         [0018]     Block  64  computes two coordinates, Id (I-direct) and Iq (I-quadrature) in the rotating coordinate system. These currents Id and Iq add vectorially to the current Isum, as do currents Iu, Iv, and Iw. However, the currents Id and Iq possess the advantage of being in a coordinate system which is superimposed on the rotor, and is thus stationary with respect to the rotor.  
         [0019]     The d-axis is aligned with the magnetic field of the rotor. Maximum torque is obtained when the stator field is aligned 90 degrees with the rotor field, that is, along the q-axis. Thus, Iq indicates the current which provides maximum torque.  
         [0020]     The currents Id and Iq are fed to summers  80  and  83 . Demanded torque is fed to summer  80 , and the output of summer  80  is an error signal E 1 , indicating deviation (if any) of Iq from demanded torque. A signal of zero is fed to summer  83 , which produces an error signal E 2 , indicating deviation of Id from zero. That is, at this time, Id is demanded to be zero, and error signal E 2  indicates whether Id meets that demand.  
         [0021]     Proportional-Integral (PI) controllers  90  and  93  compute voltages Vd and Vq which must be generated to produce the hypothetical currents Id and Iq. Reference frame translator  95  performs the reverse of translator  64 . Translator  95  computes three needed voltages Vu, Vv, and Vw which are needed to produce the three currents Iu, Iv, and Iw.  
         [0022]     Stated another way, voltages Vq and Vd are two orthogonal voltage vectors which sum to a certain voltage sum vector. Translator  95  computes three voltage vectors Vu, Vv, and Vw, which are not orthogonal but separated by 120 degrees, which sum to the same voltage sum vector.  
         [0023]     Block PWM produces output voltages corresponding to Vu, Vv, and Vw resulting in currents Iu, Iv, and Iw.  
         [0024]     The present invention offers certain improvements to the control system of  FIG. 6 .  
       OBJECTS OF THE INVENTION  
       [0025]     An object of the invention is to provide an improved control system for a brushless DC motor wherein response of the control system is improved by inertial compensation.  
         [0026]     Another object of the invention is to provide an improved control system wherein field-oriented control is implemented, but without measuring stator currents.  
       SUMMARY OF THE INVENTION  
       [0027]     In one form of the invention, a demanded torque is received. The inertial torque is computed from the measured rotor acceleration and summed with the demand torque to produce a torque error signal. The torque error is reduced by correcting the voltage magnitude and phase angle. Indirect current sensing is used to estimate the actual motor current and torque so that the new voltage parameters can be computed. The indirect current sensing is based on known motor parameters along with rotor speed and position measurement. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0028]      FIG. 1  illustrates coils in a three-phase motor of the prior art.  
         [0029]      FIG. 2  illustrates magnetic field vectors generated by the three coils.  
         [0030]      FIG. 3  illustrates three-phase currents applied to the coils of  FIGS. 1 and 2 .  
         [0031]      FIG. 4  illustrates the rotating vector sum B of the three magnetic fields of  FIG. 2 .  
         [0032]      FIG. 5  illustrates the coils of  FIGS. 1-3  and the rotor of a motor superimposed over  FIG. 5 .  
         [0033]      FIG. 6  is a schematic of a field-oriented control system for a three-phase motor.  
         [0034]      FIG. 7  illustrates one form of the invention.  
         [0035]      FIG. 8  illustrates equations utilized by one form of the invention.  
         [0036]      FIG. 9  illustrates processes undertaken by one form of the invention.  
         [0037]      FIGS. 10 and 11  illustrate a two-phase electric motor having a permanent magnet rotor.  
         [0038]      FIG. 12  illustrates generally the phase relations among the voltage V in  FIG. 12 , and the components EMF and I.  
         [0039]      FIG. 13  illustrates the waveforms of  FIG. 12  in phasor format. It is observed in  FIGS. 12 and 13  that the magnitudes shown are arbitrary. Also, by convention, phasors in  FIG. 13  rotate counterclockwise. In addition, time in  FIG. 12  refers to elapsed time, from a time of zero. Thus, point P 2  occurred before P 1 , which occurred before P. Angles alpha and delta in  FIG. 12  correspond to the same angles in  FIG. 13 .  
         [0040]      FIG. 14  illustrates one form of the invention.  
         [0041]      FIG. 15  illustrates an alternate form of the invention using indirect current sensing and inertial torque feedback.  
         [0042]      FIG. 16  illustrates an alternative form of the invention using a proportional-integral controller to minimize torque error.  
         [0043]      FIG. 17  illustrates an alternative implementation of the voltage calculator utilizing rotationally transformed d and q current and voltage variables.  
         [0044]      FIG. 18  illustrates an alternative implementation of the torque calculator utilizing rotationally transformed d and q current and voltage variables. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0045]      FIG. 15  is a block diagram of one form of the invention. Motor  120  can be of the two-phase brushless DC type, and can be used in a power steering system in a vehicle  300  in  FIG. 14 . Block  125  in  FIG. 15  represents a detection apparatus, such as an encoder or resoIver and its associated computation circuitry. Position output is converted into velocity and acceleration signals by differentiators  127  and  128 .  
         [0046]      FIG. 15  represents an improvement over the prior art  FIG. 6  in two ways. First, the current sensors  50  are replaced by indirect current sensing by using calculator  131  to compute the d and q axis current components from voltage, speed, position, and known motor parameters. The indirect current sensing represents a steady state estimate of the actual current.  
         [0047]      FIG. 15  incorporates a second improvement over prior art  FIG. 6  in that it incorporates inertial compensation in the formation of the torque error signal by summer  80 . The torque error signal is comprised of a demand torque signal  79 , an estimate of the torque  142  computed from the calculation of Iq, and a calculation of the inertial acceleration torque  141 . The inclusion of the inertial torque term estimates torque produced by the motor which may not be included in the steady state estimate of the current in block  131  and thereby serves to improve stability of the system as explained below.  
         [0048]      FIG. 7  is a block diagram of another form of the invention. Motor  120  can be of the two-phase brushless DC type, and can be used in a power steering system in a vehicle  300  in  FIG. 14 . Block  125  in  FIG. 7  represents a detection apparatus, such as an encoder or resoIver and its associated computation circuitry, which computes angular position of the motor. Based on the first time-derivative of angular position, block  125  computes motor speed. Based on the second time-derivative, block  125  computes motor acceleration.  
         [0049]     Speed and velocity, together with the present voltages applied to the motor (angle and phase), are fed to block  130 , which computes torque presently delivered by the motor. Rather than direct measurement of current with sensors  50  of prior art  FIG. 6 , or indirect current sensing  131  of  FIG. 15 , Equation 1 in  FIG. 8  computes the torque directly from measured speed and motor parameters. Viewed another way, Equation 1 of  FIG. 8  incorporates indirect current sensing in the steady state motor equations to predict the torque from measured speed and velocity together with known motor parameters. This torque is modified by an inertial torque, if the motor is accelerating, as explained below.  
         [0050]     Ke is a constant, which depends on the characteristics of the motor in question, and Ke is known in the art. Ke, multiplied by rotor speed in radians per second, gives the EMF discussed below. Ke indicates the degree of magnetic coupling between the rotor magnet and a coil, as well as the number of turns of the coil, if the latter is considered distinct from degree of coupling.  
         [0051]     In equation 1, ωm refers to mechanical rotor speed.  
         [0052]     In  FIG. 7 , block  135  indicates a demanded torque signal is received. The demanded torque signal is produced by apparatus external to the invention. In the case of a power steering system, demanded torque would be derived in a manner known in the art, based on driver torque sensor output, steering wheel position and vehicle speed.  
         [0053]     Block  140  computes an inertial torque, based on present acceleration, if any, of the rotor in the motor. The inertial torque, if present, increases the amount of electrical energy required to be delivered to the motor, and is perhaps more easily explained in linear-motion terms, as opposed to a rotational system like the motor  120 .  
         [0054]     One horsepower equals 550 foot-pounds per second. If 550 pounds are being raised one foot every second, then one horsepower is being developed. The force of 550 pounds is analogous to torque in the motor  120 .  
         [0055]     If, over ten seconds, the speed of lifting is increased from one foot per second to ten feet per second, then at the end of ten seconds, ten horsepower are being developed. However, during that ten seconds, the velocity of the object has increased from one foot per second to ten feet per second. The kinetic energy of the object, (½)mass×square of velocity, has increased from 275 to 27,500 pound-feet-squared/second-squared. Additional energy must be added during the acceleration to provide for the increase in kinetic energy.  
         [0056]     The inertial torque of  FIG. 7  is similar to that additional energy, but in a rotating frame of reference.  
         [0057]     The three torque signals are added in summer  160 . The output of the summer  160  is an error signal. The summer computes the error between the torque command and a summation of inertial and estimated motor output torque. The negative sign on summer  160  indicates that the torque error is reduced when the inertial torque is positive, during acceleration. This effectively reduces the torque required from the motor during acceleration. A positive sign, adding the inertial torque to summer  160 , would likewise increase the torque required during acceleration.  
         [0058]     Of course, if the motor is decelerating, the inertial torque supplies energy, and reduces the amount of electrical energy which must be supplied to produce a given shaft torque. During a deceleration the negative sign on the input of the inertial torque to summer  160  adds additional torque to the torque command while during acceleration summer  160  subtracts additional torque from the torque command. This situation is inherently more stable than if torque was added during acceleration and subtracted during deceleration as would be the case if the sign on summer  160  were positive.  
         [0059]     The summation includes feedback from the torque calculator  130 . This calculator uses steady state relationships to provide an estimate of torque excluding any electrical transients. Of course, a torque error could be computed using only the torque command  135  and the torque calculator  130  while disregarding any input from inertial torque  140 . However, it has been found that the system is more stable when the inertial torque is included in summer  160 .  
         [0060]     From one point of view, the sum of (1) the torque calculated by block  130  and (2) the torque demanded by block  135  can be viewed as a preliminary error signal. That preliminary error signal is then modified by the value of the inertial torque, if any to provide an improved error signal.  
         [0061]     The error signal is delivered to block  170 , which computes the voltage needed to provide the demanded torque. That voltage is delivered to an inverter  175 , which is known in the art. The inverter is so-called because it “inverts” DC power, as from an automobile battery, into sinusoidal AC power. In the case of a two-phase motor  120 , the inverter  175  produces two sine waves, ninety degrees apart. In the case of a three-phase motor, the inverter  175  produces three sine waves, 120 degrees apart.  
         [0062]      FIG. 9  illustrates processes implemented by voltage calculator  170  of  FIG. 170 . As background, to explain symbology used in  FIG. 9 ,  FIGS. 10-13  will be explained first.  FIG. 10  illustrates two pairs of coils C 1  and C 2  present in a two-phase motor. A rotor R contains a permanent magnet, which produces a magnetic flux B. The rotor R rotates, as in  FIG. 11 .  
         [0063]     The rotating flux B induces a voltage EMF, Electro Motive Force, in coil C 1 , as well as C 2 . The total voltage across the ends of the coil C 1  can be said to contain the three components indicated: the EMF, the IR voltage drop, and the wLI term, wherein w is electrical frequency of the applied current, L is the inductance of the coil at that frequency, and I is the applied current. The IR term will be ignored in this context, because it is small.  
         [0064]     The three voltages, namely, (1) the total voltage across the coil, (2) the EMF, and ( 3 ) the wLI term are approximately sinusoidal, as indicated in  FIG. 12 . Their magnitudes as indicated are arbitrary, since  FIG. 12  is used to indicate that these terms can have different phases. EMF differs from V by phase delta. Current I differs from EMF by phase alpha.  
         [0065]     Since these terms are sinusoidal, they can be represented by phasor-vectors, as in  FIG. 13 . Phasor EMF is taken as a reference, at angle zero. The current, or wLI term, is taken as having an angle alpha with respect to EMF, as indicated. The voltage vector V is taken as having an angle delta with respect to EMF, as indicated.  
         [0066]     Now the processes of  FIG. 9  can be explained. Block  200  indicates that a voltage Vmag is first computed, which is the voltage needed to produce the presently desired torque. Equation 2 in  FIG. 8  can be used to compute this voltage.  
         [0067]     In  FIG. 9 , blocks  205  and  210  represent alternatives. In the case where the motor  120  in  FIG. 7  is used in a vehicle, the power for the motor  120  most likely originates in a lead-acid battery. That battery has a limited voltage, such as 12 volts. Thus, the peak-to-peak voltage which inverter  175  in  FIG. 7  can produce is limited.  
         [0068]     Thus, if the voltage computed in block  200  in  FIG. 9  falls below the available battery voltage, the alternative of block  205  is taken. In that alternative, the voltage magnitude computed in block  200  is used, or generated, by the inverter  175  in  FIG. 7 .  
         [0069]     In addition, a phase angle delta is computed for the computed voltage. That phase angle delta is shown in  FIG. 13 . The phase angle delta is computed using equation 4 in  FIG. 8  and, when so computed, has the property of reducing the phase angle alpha in  FIG. 13  to zero.  
         [0070]     That is, this phase angle delta, computed according to Equation 4 in  FIG. 8 , causes the current I to be in-phase with the induced EMF. Stated another way, the direct, d, component of the current shown in image  72  in  FIG. 6  is driven to zero. The only component of current now present is at 90 degrees to the rotor magnetic field.  
         [0071]     In the other alternative, if the voltage computed in block  200  in  FIG. 9 , that is, the voltage computed in Equation 2 in  FIG. 8 , exceeds the available battery voltage, then the process of block  210  in  FIG. 9  is implemented. The computed voltage Vmag is set at the battery voltage, Vmax, which is the maximum voltage available. In addition, the needed phase angle delta is computed which will produce the desired torque. Equation 3 in  FIG. 8  can be used for this purpose.  
         [0072]     Blocks  205  and  210  can be recapitulated. First, Vmag is computed, which is the voltage magnitude needed for the desired torque. If Vmag can be supplied by the local power supply, then block  205  in  FIG. 9  is implemented. Angle delta in  FIG. 13  is computed according to Equation 4 in  FIG. 8 . This value of delta drives angle alpha in  FIG. 13  to zero, making I in-phase with EMF.  
         [0073]     In effect, in most cases, block  205  obtains any increase in required torque from an increase in voltage, leaving alpha unchanged at zero.  
         [0074]     If Vmag cannot be supplied by the local power supply, then block  210  is implemented. Vmag is now set equal to the local power supply voltage. Angle delta in  FIG. 13  is computed using equation 3 in  FIG. 8 . This will give angle alpha in  FIG. 13  some value, thus producing a current on the d-axis in  FIG. 6 .  
         [0075]     Block  215  in  FIG. 9  imposes a limit. Current to be expected from the voltage applied is computed, as known in the art. If the current exceeds one or more limits, then the phase angle delta is further adjusted to keep the current within bounds.  
         [0076]     Once Vmag and delta have been computed, the phase voltages for the two-phase motor are computed in block  220 , and applied to the motor  120  in  FIG. 7 . It is repeated that, in block  220  in  FIG. 9 , Vmag has one of two values. If Vmag computed in Equation 2 in  FIG. 8  exceeds the local supply voltage, then Vmag in block  220  is set equal to that local supply voltage (or whatever relevant maximum voltage is present). If the local supply voltage is not exceeded, then the Vmag computed in Equation 2 is used in block  220  in  FIG. 9 .  
         [0077]     An alternative configuration for the control scheme is illustrated in  FIG. 16 . Gain  134  and  144  can be added in each of the feedback loops to improve stability. It is also possible to add a proportional-integral control  161  to facilitate minimization of the torque error.  
         [0078]     It is also possible to implement the voltage and torque calculation blocks using d and q rotationally transformed variables that allow the calculations to be made without the need for inverse trigonometric functions. The alternative voltage calculator  170 , shown in  FIG. 17 , computes the required q-axis current from the torque command in  171 . This current, together with the rotor velocity, current, and voltage constraints are used in  172  to compute the d and q axis voltage required to produce this current in steady state. In accordance with the algorithm of  FIG. 9 , the d-axis may need to be regulated if the voltage maximum is reached. The required voltages are transformed in  173  to the instantaneous values for a 2 phase or 3 phase inverter.  
         [0079]     The alternative torque calculator,  130 , is shown in  FIG. 18 . Knowing the d and q axis voltages from block  172  of  FIG. 17 , and the rotor velocity measured with a sensor, the q axis current are computed in  131 . The current is multiplied by a torque constant in  132  to compute a steady state estimate of the torque.  
         [0080]     Numerous substitutions and modifications can be undertaken without departing from the true spirit and scope of the invention. What is desired to be secured by Letters Patent is the invention as defined in the following claims.  
         [0081]     What is claimed is: