Method of and apparatus for controlling the operation of an induction motor using a model of the induction motor

The invention relates to induction motors. More particularly, the invention relates to a method and apparatus for controlling the operation of an induction motor using a model of the induction motor.

Various control schemes have been used to control the operation of induction motors. Nevertheless, an improved control scheme that provides straightforward, reliable operation, and that is simple and less expensive to manufacture would be welcomed by those in the art.

The methods and apparatus of the invention provide motor control through the utilization of a model of the motor. In one embodiment, a control circuit or controller is connected to the motor to provide the motor control. The controller acts as an “observer” of the motor to determine values of the motor variables necessary to provide motor control without directly measuring from the motor the values of the motor variable or other values necessary to calculate the values of the motor variables. Instead, the controller utilizes commanded values of excitation speed and motor voltage and measured values of bus voltage and bus current to determine such values. In one embodiment, an inverter includes the bus voltage and the bus current and supplies a voltage to the motor based on a command signal provided by the controller. In some embodiments, the controller may also utilize other values measured from the inverter to determine the values necessary to calculate the values of the motor variables.

The controller thus eliminates the need for sensing devices coupled to the motor and circuitry necessary to convert such sensed signals. Additionally, values necessary to calculate the values of the motor variables may be obtained from the inverter using fewer and/or less expensive components. Therefore, the controller can be implemented using fewer and less expensive circuitry components than previous control schemes.

The model utilized to provide motor control is a simplified model, thus allowing for utilization of less powerful processors. A less powerful processor in combination with an overall fewer number of circuitry components allows for the production of a less expensive controller.

Other features of the invention will become apparent by consideration of the detailed description and accompanying drawings.

FIG. 1 is a schematic diagram of an induction motor and a controller connected to the induction motor.

FIG. 2 is a schematic diagram of another embodiment of the controller shown in FIG. 1 .

FIG. 3 is a schematic diagram of a lumped parameter induction motor model of the motor shown in FIG. 1 .

FIG. 4 is a schematic diagram of an induction motor model that neglects the effects of core losses.

Before any embodiments of the invention are explained in detail, it is to be understood that the invention is not limited in its application to the details of construction and the arrangement of components set forth in the following description or illustrated in the following drawings. The invention is capable of other embodiments and of being practiced or of being carried out in various ways. Also, it is to be understood that the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of “including,” “comprising,” or “having” and variations thereof herein is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. Unless specified or limited otherwise, the terms “mounted,” “connected,” and “coupled” are used broadly and encompass both direct and indirect mountings, connections, and couplings. Further, “connected” and “coupled” are not restricted to physical or mechanical connections or couplings.

Shown in FIGS. 1 and 2 of the drawings are schematic views of an induction motor 10 and a controller 15 connected to the motor 10 . The details of the induction motor 10 are commonly known in the art. Accordingly, the induction motor is not described in detail. Aspects of the controller 15 may also be useful for the control of other types of motors (e.g., permanent magnet brushless DC motors, etc.).

In one embodiment, the controller 15 is implemented using a programmable device (e.g., a microprocessor, a microcontroller, a digital signal processor (DSP), etc.) that utilizes software stored in a memory and at least one discrete power component (e.g., an inverter, a measuring circuit, etc.). As will be apparent to those of ordinary skill in the art, some of the software may be implemented in hardware using mechanisms such as hardware descriptor language to create application specific or special purpose circuits. Accordingly, elements described herein should not necessarily or inevitably be limited to a software or hardware embodiment simply because examples given are set forth in hardware or software specific terms. Further, although the software is illustrated as a number of separate elements or modules, the functionality of such elements can be combined into fewer elements or separated into more elements.

As shown in FIG. 1 , the controller 15 includes controllers 15 A and 15 B. The controller 15 A provides individual control of any variable of the motor 10 (e.g., torque, speed, slip, efficiency, flux, etc.) that is described by a model of the motor 10 . To perform such control, the controller 15 A includes a first comparator 20 , a first regulator 25 , a frequency-to-voltage converter 30 , a modulator 35 , an inverter 40 , a measuring circuit 45 having a current sensor 47 and an analog-to-digital (A/D) converter 50 , a calculator 55 , a second comparator 60 , a second regulator 65 , and a motor model module 70 . The controller 15 A controls the operation of the motor 10 by controlling a first motor variable MV 1 of the motor 10 using a second motor variable MV 2 of the motor 10 .

The first comparator 20 compares a commanded value of the first motor variable MV 1 CMD and a modeled value of the first motor variable MV 1 MODEL . The first comparator 20 outputs an error E MV1 that represents the difference between the commanded value MV 1 CMD and the modeled value MV 1 MODEL . In one embodiment, the commanded value MV 1 CMD is provided based at least in part on a user input to the environment of the motor 10 and the controller 15 (e.g., adjustment of a thermostat of an heating, ventilation, and air conditioning (HVAC) system where the motor 10 is used to drive a blower of the HVAC system and the controller 15 controls such operation). The modeled value MV 1 MODEL is determined by the motor model module 70 as discussed below. The error E MV1 is supplied to the first regulator 25 . If the commanded and modeled values MV 1 CMD and MV 1 MODEL , respectively, are the same value, the value of the error E MV1 is equal to zero.

The first regulator 25 receives the error E MV1 as an input and generates an output of a commanded value of excitation speed ω E-CMD . The first regulator 25 increments or decrements the previous value of the commanded value of excitation speed ω E-CMD based on the value of the error E MV1 , thereby generating a new value for the commanded value of excitation speed ω E-CMD . When the value of the error E MV1 is equal to zero, the first regulator 25 is in a steady-state condition and the value of the commanded value of excitation speed ω E-CMD does not change. When the value of the error E MV1 is positive or negative, the value of the commanded value of excitation speed ω E-CMD is ramped up or down, respectively. The new commanded value of the excitation speed ω E-CMD is supplied to the frequency-to-voltage converter 30 and to the modulator 35 .

In one embodiment, the first regulator 25 uses proportional-integral (PI) control, where the relationship between the input and the output is explained by the following equation:

ω E - CMD = K 1 ⁢ τ 1 ⁢ s + 1 s · E MV ⁢   ⁢ 1 [ e ⁢   ⁢ 1 ]

where the constant K 1 represents the gain of the first regulator 25 and the time constant τ 1 represents the time constant of the zero of the first regulator 25 . The values of the constant K 1 and time constant τ 1 determine how quickly the first regulator 25 reaches a steady-state condition. The rate at which the first regulator 25 adapts toward the steady-state condition can be varied based on the requirements of the application in which the motor 10 is utilized. In one embodiment, the values of the constant K 1 and time constant τ 1 are determined empirically based on the rated conditions of the motor 10 . Other embodiments of the first regulator 25 utilize other techniques for establishing the values of the constant K 1 and time constant τ 1 . Other embodiments of the first regulator 25 use a proportional-integral-derivative (PID) control, or other type of control capable of generating an output based on an input of the error E MV1 .

The frequency-to-voltage converter 30 receives the commanded value of excitation speed ω E-CMD as an input and generates an output of a commanded value of motor voltage V 1-CMD . In one embodiment, the relationship between the commanded value of excitation speed ω E-CMD and the commanded value of motor voltage V 1-CMD is based on the flux of the motor 10 . Other embodiments of the frequency-to-voltage converter 30 utilize other relationships between the commanded value of excitation speed ω E-CMD and the commanded value of motor voltage V 1-CMD . The commanded value of the motor voltage V 1-CMD is supplied to the modulator 35 .

The modulator 35 receives the commanded value of excitation speed ω E-CMD and the commanded value of motor voltage V 1-CMD as inputs and generates a modulated output. In one embodiment, the modulated output includes at least one command signal CS. Each command signal CS may include a duty cycle that is determined based at least in part on a ratio of the commanded value of motor voltage V 1-CMD to a DC bus voltage V DC of the inverter 40 . The amplitude of each command signals CS may be a nominal value (e.g., 5 volts DC, 15 volts DC, etc.). The number of command signals CS generated depends on the number of switches in the inverter 40 that need to be controlled and the method of control utilized (e.g., a three-phase power inverter may include six switches, a top switch and a bottom switch for each phase, where each phase is controlled by a separate command signal CS (i.e., three command signals CS), or where each switch is controlled by a separate command signal CS (i.e., six command signals CS)). In one embodiment, the modulator 35 includes a sine-triangle modulation scheme having a carrier frequency of 20 KHz. Other embodiments include other modulation schemes.

The inverter 40 receives each command signal CS as an input and generates an output of a motor voltage V 1 (e.g., a three-phase alternating current (AC) voltage) that is then fed to the motor 10 . The motor voltage V 1 continuously energizes the motor 10 until the value of the motor voltage V 1 is updated. In one embodiment, the inverter 40 includes a power inverter having a bridge circuit for generating a three-phase voltage for use by a three-phase induction motor. Other embodiments of the inverter 40 include other types of inverters (e.g., a current sourced inverter, other voltage sourced inverters, etc.) that energize the motor 10 based on an input of at least one command signal CS.

The inverter 40 includes a top node or DC voltage bus and a bottom node or DC current bus. A DC voltage signal is delivered to the DC voltage bus for use in generating the motor voltage V 1 . In one embodiment, the DC voltage signal is 300 volts DC and is obtained by rectifying an AC line voltage. Other embodiments of the DC voltage bus may include other values of DC voltage signals.

The measuring circuit 45 measures a value of DC bus voltage V DC and a value of DC bus current I DC . The DC bus voltage V DC is measured “directly” (after stepping down the voltage), and the DC bus current I DC is measured using the current sensor 47 (e.g., a small resistor connected to the bottom node of the inverter 40 ) that allows for measurement of a voltage that corresponds to the DC bus current I DC . In one embodiment, the current sensor 47 is sized such that the power drop in the inverter 40 is minimized. In some embodiments, an amplifier may be utilized to amplify the measured value of the voltage that corresponds to the DC bus current I DC . An analog-to-digital (A/D) converter can be utilized to convert the measured analog signals to digital signals. The values of the DC bus voltage and current V DC and I DC , respectively, are supplied to the calculator 55 .

The calculator 55 receives the values of the DC bus voltage V DC and the DC bus current I DC as inputs and calculates an estimated value of a second motor variable MV 2 EST based at least in part on the values of DC bus voltage and DC bus current. The estimated value MV 2 EST is supplied to the second comparator 60 .

The second comparator 60 compares the estimated value of the second motor variable MV 2 EST and a modeled value of the second motor variable MV 2 MODEL . The second comparator 60 outputs an error E MV2 that represents the difference between the estimated value MV 2 EST and the modeled value MV 2 MODEL . The modeled value MV 2 MODEL is determined by the motor model module 70 as discussed below. The error E MV2 is supplied to the second regulator 65 . If the estimated and modeled values MV 2 EST and MV 2 MODEL , respectively, are the same value, the value of the error E MV2 is equal to zero.

The second regulator 65 receives the error E MV2 as an input and generates an output of an estimated value of slip S EST . The second regulator 65 increments or decrements the previous value of the estimated value of slip S EST based on the value of the error E MV2 , thereby generating a new value for the estimated value of slip S EST . When the value of the error E MV2 is equal to zero, the second regulator 65 is in a steady-state condition and the value of the estimated value of slip S EST does not change. When the value of the error E MV2 is positive or negative, the value of the estimated value of slip S EST is ramped up or down, respectively. The new estimated value of the slip S EST is supplied to the motor model module 70 .

In one embodiment, the second regulator 65 uses PI control, where the relationship between the input and the output is explained by the following equation:

S EST = K 2 ⁢ τ 2 ⁢ s + 1 s · E MV ⁢   ⁢ 2 [ e ⁢   ⁢ 2 ]

where the constant K 2 represents the gain of the second regulator 65 and the time constant τ 2 represents the time constant of the zero of the second regulator 65 . The values of the constant K 2 and time constant τ 2 determine how quickly the second regulator 65 reaches a steady-state condition. The rate at which the second regulator 65 adapts toward the steady-state condition can be varied based on the requirements of the application in which the motor 10 is utilized. In one embodiment, the values of the constant K 2 and time constant τ 2 are determined empirically based on the rated conditions of the motor 10 . Other embodiments of the second regulator 65 utilize other techniques for establishing the values of the constant K 2 and time constant τ 2 . Other embodiments of the second regulator 65 use a proportional-integral-derivative (PID) control, or other type of control capable of generating an output based on an input of the error E MV2 .

The motor model module 70 receives the estimated value of slip S EST and a number of motor parameter values as inputs, and generates the modeled values of the first and second motor variable MV 1 MODEL and MV 2 MODEL , respectively, based at least in part on the estimated value of slip S EST . In one embodiment, the values of the motor parameters are based on the rated conditions of the motor. The modeled values MV 1 MODEL and MV 2 MODEL are utilized as feedback inputs that adjust the commanded value MV 1 CMD and the estimated value MV 2 EST , respectively, to control the first motor variable MV 1 of the motor 10 . In one embodiment, initial condition of the second regulator 65 are utilized to provide an estimated value of slip S EST that is utilized to generate the modeled values MV 1 MODEL and MV 2 MODEL for the first iteration of the controller 15 loop. Other embodiments of the motor model module 70 utilize other techniques (e.g., an initial condition for the modeled values MV 1 MODEL and MV 2 MODEL , use of a zero value for the modeled values MV 1 MODEL and MV 2 MODEL , etc.).

The controller 15 B provides control of a combination of the variables of the motor 10 discussed above. To perform such control, the controller 15 B includes the components of the controller 15 A and a second calculator 75 , a third comparator 80 , and a third regulator 85 . The controller 15 B controls the operation of the motor 10 by controlling the first motor variable MV 1 of the motor 10 and a third motor variable MV 3 of the motor 10 using the second motor variable MV 2 of the motor 10 .

The second calculator 75 receives the estimated value of slip S EST as an input and calculates an estimated value of the third motor variable MV 3 EST . The estimated value MV 3 EST is supplied to the third comparator 80 . Similar to the modeled values MV 1 MODEL and MV 2 MODEL , the initial value of the estimated value MV 3 EST can be determined using a number of techniques.

The third comparator 80 compares a commanded value of the third motor variable MV 3 CMD and the estimated value of the third motor variable MV 3 EST . The third comparator 80 outputs an error E MV3 that represents the difference between the commanded value MV 3 CMD and the estimated value MV 3 EST . In one embodiment, the commanded value MV 3 CMD is provided based at least in part on a user input to the environment of the motor 10 and the controller 15 . The error E MV3 is supplied to the third regulator 85 . If the commanded and estimated values MV 3 CMD and MV 3 EST , respectively, are the same value, the value of the error E MV3 is equal to zero.

The third regulator 85 receives the error E MV3 as an input and generates an output of the commanded value of the first motor variable MV 1 CMD . The third regulator 85 increments or decrements the previous value of the commanded value of the first motor variable MV 1 CMD based on the value of the error E MV3 , thereby generating a new value for the commanded value of the first motor variable MV 1 CMD . When the value of the error E MV3 is equal to zero, the third comparator 85 is in a steady-state condition and the value of the commanded value of the first motor variable MV 1 CMD does not change. When the value of the error E MV3 is positive or negative, the value of the commanded value of the first motor variable MV 1 CMD is ramped up or down, respectively. The new commanded value of the first motor variable MV 1 CMD is supplied to first comparator 20 as discussed above. In this embodiment, the commanded value MV 1 CMD is not directly based on a user input, but indirectly based on a user input.

In one embodiment, the third regulator 85 uses a PI control, where the relationship between the input and the output is explained by the following equation:

MV ⁢   ⁢ 1 CMD = K 3 ⁢ τ 3 ⁢ s + 1 s · E MV ⁢   ⁢ 3 [ e ⁢   ⁢ 3 ]

where the constant K 3 represents the gain of the third regulator 85 and the time constant τ 3 represents the time constant of the zero of the third regulator 85 . The values of the constant K 3 and time constant τ 3 determine how quickly the third regulator 85 reaches a steady-state condition. The rate at which the third regulator 85 adapts toward the steady-state condition can be varied based on the requirements of the application in which the motor 10 is utilized. In one embodiment, the values of the constant K 3 and time constant τ 3 are determined empirically based on the rated conditions of the motor 10 . Other embodiments of the third regulator 85 utilize other techniques for establishing the values of the constant K 3 and time constant τ 3 . Other embodiments of the third regulator 85 use a proportional-integral-derivative (PID) control, or other type of control capable of generating an output based on an input of the error E MV3 .

FIG. 2 schematically illustrates the motor 10 connected to the controller 15 where the controller includes controllers 15 AT and 15 BST. The controller 15 AT effects torque control of the motor 10 , and the controller 15 BST effects speed and torque control of the motor 10 . Control of the speed and/or torque variables of the motor 10 may be useful in a number of applications (e.g., CFM control on the blower of an HVAC system). As discussed above, the controller 15 provides control of an individual variable or a combination of variables of the motor 10 . The controllers 15 AT and 15 BST are two such examples.

The controller 15 AT includes the same components as discussed above with respect to the controller 15 A. The controller 15 AT controls the torque T of the motor 10 using the real part of the current or the torque producing current I T of the motor 10 .

The first comparator 20 compares a commanded value of torque T CMD and a modeled value of torque T MODEL . The commanded value of torque T CMD can be provided directly, or indirectly via the third regulator 85 . The first comparator 20 outputs an error E T that represents the difference between the commanded value T CMD and the modeled value T MODEL . The first regulator 25 receives the error E T as an input and generates an output of a commanded value of excitation speed ω E-CMD . The commanded value of excitation speed ω E-CMD is utilized along with the commanded value of motor voltage V 1-CMD to generate the motor voltage V 1 that energizes the motor 10 .

In addition to the values of DC bus voltage V DC and DC bus current I DC , the first calculator 55 also receives the commanded value of motor voltage V 1-CMD as an input. The first calculator 55 calculates an estimated value of the torque producing current I T-EST using the following equation:

I T - EST = K 4 ⁢ Eff INVERTER ⁢ V D ⁢   ⁢ C ⁢ I D ⁢   ⁢ C V 1 - CMD [ e4 ]

where the constant K 4 represents a scaling factor (e.g., a scaling factor based on the type of motor voltage V 1 utilized (e.g., a single phase motor voltage, a three phase motor voltage, etc.)), and the efficiency of the inverter EFF INVERTER represents the power loss in the inverter 40 .

The estimated value of torque producing current I T-EST equation (e4) is obtained using the interrelationships of power entering and exiting the inverter 40 and the motor 10 . The power input P MOTOR-IN of the motor 10 is described by the following equation:

P MOTOR — IN =V 1 I 1 cos(θ)= V 1 I T   [e5]

where V 1 represents the motor voltage, I 1 represents the motor current (i.e., the current through the stator of the motor) (see motor model 100 below), cos(θ) represents the power factor of the motor, and I 1 cos(θ) represents the torque producing current I T (i.e., the real part of the current). The power input P MOTOR-IN of the motor 10 is equal to the power output P INVERTER-OUT of the inverter 40 as shown in the following equation:

P MOTOR-IN =P INVERTER-OUT   [e6]

Based on the conversation of energy, the power output P INVERTER-OUT of the inverter 40 , and therefore the power input P MOTOR-IN of the motor 10 , is equal to the power input P INVERTER-IN of the inverter 40 times the efficiency of the inverter EFF INVERTER as shown in the following equation:

P INVERTER-OUT =P INVERTER-IN EFF INVERTER =P MOTOR-IN   [e7]

The power input P INVERTER-IN of the inverter 40 is equal to the DC bus voltage V DC times the DC bus current I DC as shown in the following equation:

P INVERTER-IN =V DC I DC   [e8]

By substituting the power input P INVERTER-IN of the inverter 40 equation (e8) and the power output P INVERTER-OUT of the inverter 40 equation (e7) into the power input P MOTOR-IN of the motor 10 equation (e5), solving for the real part of the current or the torque producing current I T , and substituting the variables of the controller 15 for the corresponding variables of the model 200 (e.g., I T-EST =I T , V 1-CMD =V 1 ) the estimated value of torque producing current I T-EST equation (e4) is obtained.

The second comparator 60 compares the estimated value of the torque producing current I T-EST and a modeled value of the torque producing current I T-MODEL . The second comparator 60 outputs an error E T that represents the difference between the estimated and modeled values I T-EST and I T-MODEL , respectively. The second regulator 65 receives the error E T as an input and generates an output of an estimated value of slip S EST .

In addition to the estimated value of slip S EST , the motor model module 70 receives the commanded values of excitation speed and motor voltage ω E-CMD and V 1-CMD , respectively, and based on a model of the motor 10 , generates the modeled values of torque and torque producing current T MODEL and I T-MODEL .

FIG. 3 illustrates a lumped parameter induction motor model 100 of the motor 10 where, for each phase of the motor 10 , R 1 represents the resistance of the stator, X 1 represents the reactance of the stator, R 2 represents the resistance of the rotor that corresponds to the resistance R 1 , X 2 represents the reactance of the rotor that corresponds to the reactance X 1 , R M represents the resistance associated with core losses, X M represents the magnetizing reactance, V 1 represents the motor voltage that energizes the stator of the motor 10 , and S is the slip of the motor. Values of the resistances R 1 and R 2P and the reactances X 1P and X MP are based on the rated motor parameter values. A rated value of slip S is also available, although slip S varies during the operation of the motor 10 based on the load and speed of the motor 10 .

The lumped parameter model 100 is simplified to the induction motor model 200 shown in FIG. 4 by neglecting the affects of core loss and using the following equations:

X S =X 1 +X M   [e9]

X R =X 2 +X M   [e10] X MP = X M 2 X R [ e11 ] X 1 ⁢ P = ( X s - X M 2 X R ) [ e ⁢   ⁢ 12 ] R 2 ⁢ P = ( X M X R ) 2 [ e ⁢   ⁢ 13 ]

The input impedance Z IN of the model 200 is represented by the following equation:

Z IN = R 1 + j ⁢   ⁢ ω E ⁢ X 1 ⁢ P + jω E ⁢ X MP ⁡ ( R 2 ⁢ P S ) j ⁢   ⁢ ω E ⁢ X MP + ( R 2 ⁢ P S ) [ e14 ]

Further, the motor current I 1 of the model 200 is represented by the following equation:

I 1 = V 1 Z IN [ e15 ]

By substituting the input impedance Z IN equation (e14) the motor current I 1 equation (e15), solving for the real part of the current or the torque producing current I T , and substituting the variables of the controller 15 for the corresponding variables of the model 200 (e g., I T-MODEL =I T , ω E-CMD =ω E , S EST =S, V 1-CMD =V 1 ), the following equation is obtained:

I T - MODEL = A B + C [ e16 ]

where

A=V 1-CMD ( R 1 R 2P 2 +R 1 ω E-CMD 2 X MP 2 S CALC 2 +ω E-CMD 2 X MP 2 R 2P S CALC )  [e17]

B=S CALC 2 X MP 2 X 1P 2 ω E-CMD 4 +S CALC 2 X MP 2 R 1 2 ω E-CMD 2 +2 R 1 R 2P ω E-CMD 2 X MP 2 S CALC   [e18]

C =( R 2P 2 X MP 2 +2 X 1P 2 R 2P 2 X MP +X 1P 2 R 2P 2 )ω E-CMD 2 +R 1 2 R 2P 2   [e19]

In one embodiment of the motor model module 70 , the modeled value of torque producing current I T-MODEL is generated based on the model 200 of the motor 10 that includes the above modeled value of torque producing current I T-MODEL equation (e16).

Based on the model 200 , the power developed P DEV by the motor 10 is represented by the following equation:

P DEV = I 2 ⁢ P 2 ⁢ R 2 ⁢ P S [ e20 ]

Further, the torque T of the motor 10 is represented by the following equation:

T = P DEV ( 1 - S ) ⁢ ω E [ e21 ]

By substituting the power developed P DEV equation (e20) into the torque T equation (e21), utilizing only the portion of the resulting equation that represents the real part of the current based on the interrelationship between the motor current I 1 and the current I 2P , and substituting the variables of the controller 15 for the corresponding variable of the model 200 (e.g., T MODEL =T, ω E-CMD =ω E , S CALC =S, V 1-CMD =V 1 ), the following equation is obtained:

T MODEL = E B + C [ e22 ]

where

E=V 1-CMD 2 X MP 2 ω E-CMD R 2P   [e23]

and B and C are defined in eqs. 18 and 19. Utilization of the equations (e16 and e22) having the same denominator reduces the amount of processing power necessary to control the operation of the motor 10 .

In one embodiment of the motor model module 70 , the modeled value of torque T MODEL is generated based on the model 200 of the motor 10 that includes the above modeled value of torque T MODEL equation (e22).

Other embodiments of the motor model module 70 include other equations based on the model 200 , equations based on other models of the motor 10 , look-up tables having values based on the model 200 or other models, etc.

The controller 15 BST includes the same components as discussed above with respect to the controller 15 B. The controller 15 BST controls the torque T and the output speed ω R of the motor 10 using the torque producing current I T of the motor 10 .

The second calculator 75 receives the estimated value of slip S EST and the commanded value of excitation speed ω E-CMD as inputs and calculates an estimated value of output speed ω R-EST based on the following equation:

ω R-MODEL =(1 −S EST )ω E-CMD   [e24]

The third comparator 80 compares a commanded value of the output speed ω R-CMD and the estimated value of the output speed ω R-EST . The third comparator 80 outputs an error E ωR that represents the difference between the commanded value ω R-CMD and the estimated value ω R-EST . The third regulator 85 receives the error E ωR as an input and generates an output of the commanded value of torque T CMD which is utilized as discussed above.

In an alternative embodiment, the controller 15 AT controls the torque T and the controller 15 BST controls the torque T and the output speed ω R of the motor 10 using the motor current I 1 instead of the torque producing current I T of the motor 10 . The control is similar to that discussed above with respect to the use of torque producing current I T except that motor current I 1 is the second motor variable MV 2 instead of torque producing current I T . The first calculator 55 calculates an estimated value of motor current I 1-EST using the following equation:

I 1 - EST = K 4 ⁢ Eff INVERTER ⁢ V DC ⁢ I DC V 1 - CMD ⁢ cos ⁢   ⁢ θ [ e25 ]

The estimated value of motor current I 1 equation (e25) is obtained by substituting the power input P INVERTER-IN of the inverter 40 equation (e8) and the power output P INVERTER-OUT of the inverter 40 equation (e7) into the power input P MOTOR-IN of the motor 10 equation (e5), solving for the motor current I 1 , and substituting the variables of the controller 15 for the corresponding variables of the model 200 (e.g., I 1-EST =I 1 , V 1-CMD =V 1 ). A modeled value of motor current I 1-MODEL is generated based on the model 200 of the motor 10 that includes a modeled value of motor current equation developed in a fashion similar to the above modeled value of torque producing current I T-MODEL equation (e16). A value of the power factor cos θ for use in calculating the estimated and modeled values of motor current I 1-EST and I 1-MODEL can be obtained in a number of ways. In one embodiment, a value of the power factor cos θ is obtained by determining the zero crossing of the motor current I 1 waveform at the output of the inverter 40 , and comparing that zero crossing to the waveform of the commanded voltage V 1-CMD .

In another alternative embodiment, the controller 15 AT controls the torque T and the controller 15 BST controls the torque T and the output speed ω R of the motor 10 using the power factor cos θ instead of the torque producing current I T of the motor 10 . The control is similar to that discussed above with respect to the use of torque producing current I T except that power factor cos θ is the second motor variable MV 2 . The first calculator 55 calculates an estimated value of power factor cos θ EST using the following equation:

cos ⁢   ⁢ θ EST = K 4 ⁢ Eff INVERTER ⁢ V DC ⁢ I DC V 1 - CMD ⁢ I 1 ⁢   [ e26 ]

The estimated value of power factor cos θ EST equation (e26) is obtained by substituting the power input P INVERTER-IN of the inverter 40 equation (e8) and the power output P INVERTER-OUT of the inverter 40 equation (e7) into the power input P MOTOR-IN of the motor 10 equation (e5), solving for the power factor cos θ, and substituting the variables of the controller 15 for the corresponding variables of the model 200 (e.g., V 1-CMD =V 1 ). A modeled value of power factor cos θ MODEL is generated based on the model 200 of the motor 10 that includes a modeled value of power factor equation developed in a fashion similar to the above modeled value of torque producing current I T-MODEL equation (e16). A value of the motor current I 1 for use in calculating the estimated and modeled values of power factor cos θ EST and cos θ MODEL can be obtained in a number of ways. In one embodiment, a value of the motor current I 1 is obtained by rectifying the motor current I 1 at the output of the inverter 40 to obtain an RMS value of the motor current I 1 .

Thus, the invention provides, among other things, a new and useful method of and apparatus for controlling the operation of an induction motor using a model of the induction motor. Various features of the invention are set forth in the following claims.