Patent Publication Number: US-6667597-B2

Title: Method of extending the operating speed range of a rotor flux based MRAS speed observer in a three phase AC induction motor

Description:
This application claims priority under 35 USC §119(e)(1) of Provisional Application No. 60/343,515, filed Dec. 20, 2001. 
    
    
     TECHNICAL FIELD OF THE INVENTION 
     The technical field of this invention is motor speed control and particularly using rotor flux based MRAS (Model Reference Adaptive System) speed observers. 
     BACKGROUND OF THE INVENTION 
     Electronic speed control of AC induction motors is well known in the art. Such AC induction motors are typically driven by selectively switching a DC voltage formed by rectifying an AC power source across the motor phase windings. An electronic controller including a microcontroller or digital signal processor (DSP) controls three phase switching of the DC voltage to produce a pulse width modulated three-phase AC input to the motor. It is feasible to employ speed feedback in these systems. Thus the electronic controller would compare an actual motor speed from a sensor with the command speed. This electronic controller would then continuously modify the drive to the AC induction motor to minimize any difference between the actual motor speed and the commanded motor speed. 
     A modification of this technique is the subject of this invention. Sensors that generate an electrical indication of motor speed such as tachometers are expensive and unreliable when compared with sensors for measuring electrical quantities such as voltage and current. Thus, speed observers such as rotor flux based model reference adaptive system speed observers are widely used. Rotor flux based model reference adaptive system speed observers employ electrical measurements of currents and voltages in the stator windings of the AC induction motor. The electronic controller employs these measures in a rotor flux estimator. The rotor flux estimate is employed both in generation of the motor drive control signals and in the rotor flux estimation. 
     A typical prior art system is illustrated in FIGS. 1 and 2. FIG. 1 illustrates the typical AC induction motor drive hardware  100  in block diagram form. AC induction motor drive hardware  100  includes high voltage module  110 , electronic control module  120 , AC induction motor  130  coupled to high voltage module  110  via three phase AC lines  135  and load  140  coupled to AC induction motor  130 . High voltage module  110  includes all electronic parts that must handle high voltages. Alternating current (AC) line power supplied to rectifier/doubler  111  enables production of a direct current (DC) voltage used for induction motor drive. Switching module  113  is shown schematically in FIG.  1 . Switching module  113  includes six high voltage semiconductor switches connected in three series pairs between the DC voltage and ground. The junction between each pair of semiconductor switches drives one phase of the three phase inputs  135  to induction motor  130 . Predriver module  117  supplies switching signals to the six semiconductor switches. Current shunt module  115  includes a current shunt sensing resistor of resistance R sense  in the ground path of each series pair of semiconductor switches. Signal conditioning module  119  receives the voltage across each of these resistors. The voltage across these sensing resistors corresponds to the current to ground from the corresponding semiconductor switch pair. 
     Electronic control module  120  provides the control function for AC induction motor drive hardware  100 . Electronic control module  120  receives three analog input signals, ADC 1 , ADC 2  and ADC 3  from signal conditioning module  119 . These three signals correspond to the voltage across the respective current shunt sensing resistor. Electronic control module  120  employs these input signals together with a speed command or other command input (not shown) to produce six switching signals PWM 1 , PWM 2 , PWM 3 , PWM 4 , PWM 5  and PWM 6 . These six switching signals PWM 1 , PWM 2 , PWM 3 , PWM 4 , PWM 5  and PWM 6  are supplied to predriver module  117 . Each of the six switching signals PWM 1 , PWM 2 , PWM 3 , PWM 4 , PWM 5  and PWM 6  provides control of the ON/OFF state of one of the six semiconductor switches of switching module  113 . As known in the art, each of these signals provides a pulse width modulated drive to a corresponding one of the three phase drive lines  135  to induction motor  130 . 
     FIG. 2 illustrates speed estimator algorithm  200  typically used in such rotor flux based model reference adaptive system (MRAS) speed observers. Speed estimator algorithm  200  forms two rotor flux estimates. Reference rotor flux estimator  201  forms rotor flux reference estimate λ r  from stator voltage vector v s  and stator current vector i s . These two dimensional vectors having direct and quadrature components are derived from the stator voltages and currents of all three phases using the well-known Clarke transformation. It is understood that the rotor flux estimate is based upon the respective inputs for all three phases. Adaptive rotor flux estimator  202  forms adaptive rotor flux estimate λ a  from the stator current i s  and a motor speed estimate ω. Error calculator  203  determines the difference between the reference rotor flux estimate λ r  and the adaptive rotor flux estimate λ a . The error signal e supplies a proportional/integral controller  204  which forms the motor speed estimate ω. Motor speed estimate ω is compared with a commanded speed in a feedback loop. This drives a conventional pulse width modulation algorithm generating the six switching signals PWM 1 , PWM 2 , PWM 3 , PWM 4 , PWM 5  and PWM 6 . 
     This rotor flux estimator method offers many advantages over a classic open loop speed observers. It does not involve any open loop integrators or differentiators. It is computationally simple. It does not require a separate slip speed calculation. However, this rotor flux estimator method is prone to stability problems, especially at high speeds. 
     FIG. 3 illustrates a typical adaptive rotor flux estimator algorithm  202 . Gain blocks  301  and  302  receive respective stator currents i sd  and i sq . The output of gain block  301  supplies an additive input of summing junction  305 . The output of summing junction  305  supplies low pass filter  309 , which produces rotor flux estimate λ ad . Similarly, the output of gain block  303  supplies an additive input of summing junction  307 . The output of summing junction  307  supplies low pass filter  311 , which produces rotor flux estimate λ aq . Adaptive rotor flux estimator  202  includes two feedback paths. The rotor flux estimate λ ad  supplies one input of multiplier  313 . The other input of multiplier  313  receives the motor speed estimate ω. The product output of multiplier  313  supplies a second, additive input of summing junction  307 . The rotor flux estimate λ aq  supplies one input of multiplier  315 . The other input of multiplier  315  receives the motor speed estimate ω. The product output of multiplier  315  supplies a second, subtractive input of summing junction  305 . 
     Adaptive rotor flux estimator  202  is stable at low speeds where the feedback is near zero. At higher speeds, the cross-coupling becomes significant. The estimator poles become more and more lightly damped at higher speeds. At a sufficiently high speed, the additional phase lag in a digital implementation due to zero order hold reconstruction and processor time delay will cause instability. 
     SUMMARY OF THE INVENTION 
     A method of AC induction motor control known as rotor flux based model reference adaptive system. Model reference adaptive systems develop two estimates of rotor flux. The reference flux estimate is based on the voltages and currents in the stator windings. The so-called adaptive estimate is based on the stator currents and the measured or estimated operating speed. These two estimates are compared by taking the cross product between the reference and adaptive rotor fluxes and the estimated speed is adjusted by a proportional-integral controller until the estimator outputs agree. In this invention, the upper speed range of the rotor flux-based MRAS speed observer is extended by discretely or continuously modifying the gain/bandwidth parameters of the low-pass filter in the adaptive flux estimator as a function of estimated speed to increase the stability margin. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     These and other aspects of this invention are illustrated in the drawings, in which: 
     FIG. 1 illustrates the hardware of a prior art motor control system; 
     FIG. 2 illustrates the algorithm of a rotor flux estimator portion of a prior art rotor flux based model reference adaptive speed observer; 
     FIG. 3 illustrates the algorithm of the adaptive rotor flux estimator portion of the algorithm of FIG. 2; 
     FIG. 4 illustrates a comparison of the gain/frequency characteristics of the prior art low pass filter and one example of an low pass filter of this invention; 
     FIG. 5 illustrates an aspect of this invention involving switching between low pass filter characteristics dependent upon estimated motor speed; 
     FIG. 6 illustrates the algorithm of a rotor flux based model reference adaptive speed observer of this invention employing continuously variable low pass filter characteristics based upon estimated motor speed; and 
     FIG. 7 illustrates the algorithm of the filter compensator generating filter gain from the estimated motor speed. 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     FIG. 4 illustrates a comparison of the gain/frequency characteristics of low pass filters  309  and  311  and one example of an low pass filter of this invention. This invention solves the high speed stability problem of the prior art by modifying the dynamics of low pass filters  309  and  311 . As shown in FIG. 3, low pass filters  309  and  311  of the prior art have a transfer function G(s) given by:          G        (   s   )       =     1     1   +       τ   r        s                         
     This transfer function has a DC gain G DC =1. This transfer function is shown at curve  401  of FIG.  4 . The modified transfer function illustrated in curve  402  has a lower DC gain and a higher cutoff frequency τ new . The new transfer function G new  (S) is given by:            G   new          (   s   )       =         τ   r     /     τ   new         1   +       τ   new        s                         
     This transfer function has a DC gain G DC =τ r /τ new . Note that these two changes to the transfer function result in that same filter characteristics in the region of the operating frequency which is higher than the original cutoff frequency τ r  and the new cutoff frequency τ new . This change preserves the original amplitude response in the region of the operating frequency. The higher cutoff frequency reduces the phase lag at the operating frequency corresponding to the estimated motor speed. This provides greater stability. 
     This solution comes at a price. The reduced gain and increased cutoff frequency creates amplitude and phase distortions at low frequencies corresponding to low motor speeds. These produce estimation errors at low frequencies. 
     FIG. 5 illustrates a switching system to combat this problem. This invention uses a series of modified low pass filter transfer functions based on estimated motor speed. Speed estimator algorithm  200  is illustrated in detail in FIG.  2 . Speed estimator algorithm  200  receives the stator voltage v s  and the stator current i s  and generates a motor speed estimate ω. In addition to its other uses, motor speed estimate ω supplies switching logic  501 . Switching logic  501  determines a frequency band for the received motor speed estimate ω. These frequency bands are preferably overlapping with hysteresis. This means that the upper limit frequency of one band is above the lower limit frequency of the next higher band. This hysteresis minimizes frequency band switching when near the frequency band boundaries. Switching logic  501  produces an index signal idx indicative of the current frequency band. 
     Switching logic  501  supplied this index signal idx to τ table  503 . This τ table  503  stores the constants needed to implement one filter function per frequency band. In particular, when the index signal idx changes, τ table  503  outputs τ next . This τ table  503  supplies constant τ next  to speed estimator  200  and to state re-initializer  505 . State re-initializer  505  also receives the rotor flux estimate λ n  and the current constant τ current  from speed estimator  200 . State re-initializer  505  generates a next rotor flux signal λ n+1 . This next rotor flux signal λ n+1  is supplied to speed estimator  200  to set λ n+1 =λ n . This avoids discontinuity in speed estimator  200 . Such discontinuities could cause oscillations. This reinitialization and the frequency band hysteresis preserve stability in speed estimator  200 . The low pass filter function switching enabled by switching logic  501  enables selection of low pass filter transfer characteristics selected for the current motor speed estimate ω. 
     FIGS. 6 and 7 illustrate another embodiment of this invention. FIGS. 6 and 7 show an algorithm employing a continuously variable gain in the adaptive rotor flux estimator  202  and proportional/integral controller  204 . FIG. 6 illustrates a modified version of adaptive rotor flux estimator  202 , together with error calculator  203  and proportional/integral controller  204 . Adaptive rotor flux estimator  202  illustrated in FIG. 6 is similar to that illustrated in FIG.  3 . Gain blocks  301  and  302  receive respective stator currents i sd  and i sq . The output of gain block  301  supplies an additive input of summing junction  605 . Summing junction  605  differs from summing junction  305  by including an additional term. This will be further described below. The output of summing junction  605  supplies gain block  608  and discrete time integrator  609 . These parts perform the function of low pass filter  309 . Similarly, the output of gain block  303  supplies an additive input of summing junction  607 . Summing junction  607  includes another term not provided by summing junction  307 . The output of summing junction  607  supplies gain block  610  and discrete time integrator  611 , which perform the function of low pass filter  311 . Adaptive rotor flux estimator  202  includes two feedback paths. The output of discrete time integrator  609  supplies one input of multiplier  313 . The other input of multiplier  313  receives the motor speed estimate ω from gain block  639 . The product output of multiplier  313  supplies a second, additive input of summing junction  607 . The output of discrete time integrator  611  supplies one input of multiplier  315 . The other input of multiplier  315  receives the motor speed estimate ω from gain block  639 . The product output of multiplier  315  supplies a second, subtractive input of summing junction  607 . 
     Error calculator  203  includes multipliers  621  and  623  and summing junction  625 . Multiplier  621  receives the output of discrete time integrator  609  corresponding to rotor flux estimate λ ad . Multiplier  621  receives a similar reference rotor flux estimate λ rd  from reference rotor flux estimator  201  (FIG.  3 ). The product output supplies an additive input of summing junction  625 . Multiplier  623  similarly multiplies rotor flux estimate λ aq  from discrete time integrator  611  and reference rotor flux estimate λ rq  from reference rotor flux estimator  201  (FIG.  3 ). The product output supplies a subtractive input of summing junction  625 . The output of summing junction  625  is the error e shown in FIG.  2 . 
     Proportional/integral controller  204  includes gain blocks  631  and  633 , integrator  635  and summing junction  637 . Gain block  631  receives the output of summing junction  625 , which is the output of error calculator  203  and forms the proportional control term. The output of gain block  631  supplies one input to summing junction  637 . Gain block  633  also receives the output of summing junction  625 , which is the output of error calculator  203 . Gain block  633  drives the input of integrator  635 . Gain block  633  and integrator  635  form the integral control term. The output of integrator  635  supplies the second input of summing junction  637 . The output of summing junction  637  corresponds to motor speed estimate ω. As previously described, motor speed estimate ω is coupled to one input of multipliers  313  and  315  via gain block  639 . 
     FIG. 6 illustrates addition feedback of the motor speed estimate ω. Motor speed estimate ω is supplied to the input of filter compensator  640 . Filter compensator  640  generates a filter gain output. This filter gain output supplies one input to multipliers  604  and  606 . Multiplier  604  receives the output of discrete time integrator  609  at its second input. The product output of multiplier  604  supplies a subtractive input of summing junction  605 . Multiplier  606  receives the output of discrete time integrator  611  at its second input. The product output of multiplier  606  supplies a subtractive input of summing junction  607 . Thus the algorithm of FIG. 6 provides feedback in the adaptive rotor flux estimate dependent upon the motor speed estimate ω. 
     FIG. 7 illustrates the preferred embodiment of filter compensator  640 . Filter compensator  640  includes gain block  701 , function block  703  and saturation block  705 . Filter block  703  preferably implements a quadratic function of the form: 
     
       
           f ( u )= av   2   +bv+c    
       
     
     where: v is the input; a, b and c are constants with a=0.0000577, b=0.0000547 and b=0.9221. Saturation block  705  limits the magnitude of the function gain introduced through multipliers  604  and  606  by limiting the filter gain output. 
     The system illustrated in FIGS. 6 and 7 is of a type commonly known as quadratic gain scheduling. This system implements the adjustments described in conjunction with FIG. 4 in continuous adjustments of the amplitude and cutoff frequency. This system avoids transients that could occur in switching between frequency bands. 
     In the preferred embodiment the control functions illustrated in FIGS. 2 to  7  are implemented in a programmed digital signal processor. This implementation is not the only manner of practicing the control functions of this invention. It is feasible to embody these control functions in an application specific integrated circuit (ASIC) employing either digital logic or analog elements. Those skilled in the control art would understand how to implement the disclosed control functions of this invention in any of these forms.