KR102017806B1 - Extended Luenberger-Sliding Mode Observer Capable of Estimating Rotor flux and Rotor Resistance for Three Phase Induction Motor - Google Patents

Abstract

The control precision of a three-phase induction motor depends largely on obtaining and estimating undetectable motor parameter values such as rotor resistance and rotor plus. The present invention proposes an Extended Luenberger-Sliding Mode Observer (ELSMO) that compensates for errors caused by motor parameter mismatch in a controller model by estimating rotor flux and rotor resistance according to an adaptation method. . Motor parameter mismatches are mainly caused by resistance changes due to temperature changes in operation and must be corrected in real time. Rotor resistance estimation is based on the Lyapunov stability theory and fed back to the ELSMO for more accurate current / flux / resistance estimation.

Description

Extended Luenberger-Sliding Mode Observer Capable of Estimating Rotor flux and Rotor Resistance for Three Phase Induction Motor}

The present invention relates to three-phase induction motor control, and more particularly, to an Extended Luenberger-Sliding Mode Observer (ELSMO) capable of estimating rotor flux and rotor resistance for three-phase induction motors.

Three-phase induction motors are applied in a wide range of industries in terms of price, simplicity, efficiency and reliability.

In general, vector control is widely adopted in the industry as one method for controlling the output torque of an induction motor at high speed.

Vector control is an orthogonal biaxial rotational coordinate system in which the power supply rotates synchronously and is a vector of a coordinate system called dq coordinate system taken in one of the secondary continuous directions. Independently control secondary flux.

Recently, applications for electric vehicles require precise control of three-phase induction motors, and parameter values such as rotor flux and rotor resistance must be measured accurately. If not, the stator current and rotor magnetic flux component are incorrectly measured, and as a result, in most cases the three-phase induction motor is subjected to speed drive control.

In particular, incorrectly measured rotor resistance causes four important phenomena:

1) More stator current is required.

2) The flux level is incorrect.

3) The steady state current / flux value differs from the commanded value.

4) The torque response is not immediate.

Therefore, these problems must be solved by measuring the rotor resistance as accurately as possible in real time and adapting it to the controller unit.

: Korean Laid-Open Patent Publication No. 10-2012-0041794

An object of the present invention is to provide an Extended Luenberger-Sliding Mode Observer (ELSMO) capable of estimating rotor flux and rotor resistance for three-phase induction motors.

Another object of the present invention is to provide an ELSMO having a parameter adaptation unit for compensating the stator current and rotor magnetic flux components estimated according to parameter varying conditions when driving a three-phase induction motor.

It is still another object of the present invention to provide an ELSMO that compensates for errors caused by motor parameter mismatch in a controller model by estimating rotor flux and rotor resistance according to an adaptation method.

In order to achieve the above object, the present invention provides an input variable ( An extended Luenberger-sliding mode observer (ELSMO) for obtaining rotor resistance estimates in an induction motor model driven and controlled by a vector controller that generates a PWM drive signal in response to An input matrix calculation unit for performing multiplication of the input matrix B with < RTI ID = 0.0 > The stator current measured from the induction motor model ) And stator current estimates ( ) To compare the state estimation error ( A comparator unit for calculating; State variable estimates ( ) And the state estimation error ( ) And the rotor resistance estimate ( A rotor resistance compensation / adaptation unit for calculating; The state variable estimate ( ) And rotor resistance estimates ( ) And the system matrix estimate ( A system estimate matrix calculation unit of a Luenberger observer that performs multiplication with < RTI ID = 0.0 > The state estimation error ( ) To compensate for the Luenberger gain matrix (L) and the sliding-mode gain matrix (K). Sliding-mode term on) A L matrix computation unit of a Luenberger observer to generate an output to which < RTI ID = 0.0 > Add the outputs of the input matrix calculation unit, the system estimate matrix calculation unit and the L matrix calculation unit to obtain the derivative of the state variable estimate ( An adder unit for calculating; Derivative of the state variable estimate ( ) To integrate the state variable estimates ( An integrator unit for calculating; And the state variable estimate ( ) And multiply by the output matrix (C) to estimate the stator current ( And an output matrix calculation unit of a Luenberger observer (LO) for calculating , B, C and Provides an extended Luenberger-sliding mode observer defined as follows.

,

,

,

,

Where R _s and R _r are stator and rotor resistances, L _s , L _r and L _m are stator inductance, rotor inductance and mutual inductance, respectively. , Is the rotor angular velocity, u _sd and u _sq are the stator voltage (d-axis) and stator voltage (q-axis), respectively, and χ is the state variable as

I _sd , i _sq , λ _rd and λ _rq are the stator current (d-axis), stator current (q-axis), rotor magnetic flux (d-axis) and rotor magnetic flux (q-axis), respectively.

The control precision of a three-phase induction motor depends largely on obtaining and estimating undetectable motor parameter values such as rotor resistance and rotor plus. In the present invention, the rotor flux and the rotor resistance may be estimated according to an adaptation method to compensate for an error caused by motor parameter mismatch in the controller model.

Motor parameter mismatches are mainly caused by resistance changes due to temperature changes in operation and must be corrected in real time. Rotor resistance estimation is based on the Lyapunov stability theory and fed back to the ELSMO for more accurate current / flux / resistance estimation.

The present invention has a parameter adaptation unit for compensating the stator current and rotor magnetic flux components estimated according to parameter variable conditions when driving a three-phase induction motor.

In the present invention, the three-phase induction motor control requiring high speed dynamic response with high efficiency can be satisfied by compensating for the stator current, flux, and speed caused by the parameter change.

The Luenberger gain matrix is optimized with trial and error method of pole placement and the sliding gain matrix is set so that the controller is robust to the parametric variations of the present invention. ELSMO uses an appropriate gain matrix to provide accurate rotor flux and rotor resistance estimates.

1 is a schematic block diagram showing an LSMO model used in a three-phase induction motor control apparatus according to an embodiment of the present invention.
Fig. 2 is a schematic block diagram showing a state estimation error model with a Luenberger observer (LO) used in the ELSMO model of the present invention.
3 is a schematic block diagram illustrating an Extended Luenberger-Sliding Mode Observer (ELSMO) with an adaptive rotor resistor in accordance with the present invention.
4 is a timing diagram illustrating a response time when the poles are -1000, -300, -300, and -1000.
5 is a timing diagram illustrating an error between the measured stator current and the estimated stator current when the sampling time is longer than the response time.
6 is a timing diagram showing the measured stator current and the estimated stator current d-axis.
7 is a timing diagram showing the measured stator current and the estimated stator current q-axis.
8 is a timing diagram illustrating a given rotor flux and estimated rotor flux d-axis.
9 is a timing diagram illustrating a given rotor flux and estimated rotor flux q-axis.
FIG. 10 shows a dynamic speed reference including ultra low speed and zero speed applied to an induction motor model to show the effect on rotor resistance estimation.
FIG. 11 shows the rotor resistance estimate as a function of time according to the dynamic speed reference given in FIG. 10.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. In this process, the size or shape of the components shown in the drawings may be exaggerated for clarity and convenience of description. In addition, terms that are specifically defined in consideration of the configuration and operation of the present invention may vary depending on the intention or custom of the user or operator. Definitions of these terms should be made based on the contents throughout the specification.

Observers are used to observe the state of a linear system. In a typical control system, it is not easy to know all the states of the system. In most cases, an algorithm that measures only part of a state directly or indirectly and observes the entire state from that part is called an observer. The most common observers are the Kalman Filter (KF) and the Luenberger Observer (LO).

The Luenberger Observer is for linear systems and nonlinear systems use Extended Luenberger Observer (ELO). The basic idea of an extended Luoenberger observer (ELO) used in a nonlinear system is to linearize the nonlinear system and then apply the Luuenberger observer's algorithm to the linearization system.

I. General Induction Motor Model

First, a state-space model of a three-phase induction motor is derived as follows.

Induction motors can be represented by the following equations (1) to (4):

Where i _sd , i _sq , λ _rd , λ _rq , u _sd and u _sq are the stator current (d-axis), stator current (q-axis), rotor flux (d-axis), rotor flux (q- Axis), stator voltage (d-axis) and stator voltage (q-axis). R _s and R _r are the stator and rotor resistances. In stator coordinates, Equations 1 and 2 are stator vector differential equations, and Equations 3 and 4 are rotor vector differential equations.

The stator current and rotor flux will be considered as the main state-space variable in the state-space model of a three-phase induction motor.

Here, λ _s , λ _r , L _s , L _r and L _m are stator flux, rotor flux, stator inductance, rotor inductance and mutual inductance, respectively. Based on Equations 5 and 6, the rotor current and stator flux may be rearranged as shown in Equations 7 and 8 below.

here, ego, to be.

Substituting Equations 7 and 8 into Equations 1 through 4, respectively, the following Equations 9 to 11 are obtained.

here, Is the rotor angular velocity. Substituting the equations (10) and (11) into equations (9), the equations (12) to (15) are shown.

Equations 12 to 15 represent state-space models of the three-phase induction motor.

Ⅱ. Extended Luenberger Observer (ELO)

Various kinds of algorithms have been published and developed to estimate the parameters of induction motors. Among them, the Extended Kalman Filter (EKF) and the Luenberger Observer (LO) are widely used algorithms for simplicity and precision. However, these two algorithms must consider a trial and error process to obtain accurate results.

In view of the above, the present invention proposes an Extended Luenberger-Sliding Mode Observer (ELSMO) shown in FIG. 3. ELSMO is a linearized form of the Luenberger-Sliding mode observer in a non-linearized form.

The general design of the Luenberger-Sliding Mode Observer (LSMO) is based on the state-space model of three-phase induction motors. The Luenberger-Sliding Mode Observer (LSMO) is a closed-loop observer in which an estimate is compared with a measurement to obtain an error between two estimates and a measurement.

Since the measurement variable is the basis of this algorithm, this error is multiplied by the Luenberger gain and sliding mode gain to correct the feedback to better show the performance which is greatly affected by the accuracy of the measurement variable. Moreover, closed-loop observers such as LO and ELSMO have a wide range of operating speeds, including zero speed.

In the fixed reference coordinate system, the state equation of the induction motor is expressed by Equation 16 below.

here, If,

, ,

,

to be.

Here, the A and B matrices are provided from the equations of the induction motor models (12) to (15), where x, u _s and y _s are state variables, input variables and output variables, respectively. In this case, the output variable y _s is the measurable stator current.

The Luenberger-Sliding Mode Observer (LSMO) is designed to estimate the stator current and rotor flux as shown in Equation 17 below.

here, ego,

Here, Λ represents an estimated value. The Luenberger-Sliding Mode Observer (LSMO) may be represented by Simulink, as shown in FIG. 1.

Referring to Figure 1, the induction motor model 15 is an input variable ( Drive control by the vector controller 13 which generates a PWM drive signal in response to " 11 ".

The Luenberger-Sliding Mode Observer (LSMO) is an input variable ( An input matrix calculation unit 21 for performing multiplication of 11 with the input matrix B; The stator current measured from the induction motor model 15 ( ) And stator current estimates ( ) To compare the state estimation error ( A comparator unit 25 for calculating); The state variable estimate ( A system matrix calculation unit 26 of a Luenberger observer for receiving multiplication with the system matrix A; The state estimation error ( ) To compensate for the Luenberger gain matrix (L) and the sliding-mode gain matrix (K). Sliding-mode term on) A L matrix calculation unit 27 of a Luenberger observer for generating an output with < RTI ID = 0.0 > By adding the outputs of the input matrix calculation unit 21, the system matrix calculation unit 26 and the L matrix calculation unit 27, the derivative value of the state variable estimate ( An adder unit 22 for calculating; Derivative of the state variable estimate ( ) To integrate the state variable estimates ( An integrator unit 23 that calculates. And the state variable estimate ( ) And multiply by the output matrix (C) to estimate the stator current ( It includes; output matrix calculation unit 24 of the Luenberger observer to calculate a).

Rouenburger Observer ) And sliding-mode terms ( ) Is added, where L and K are the Luenberger gain matrix and the sliding-mode gain matrix. The Luenberger observer terms correct the estimate by compensation and the sliding-mode terms control the robustness of the observer.

III. Extended Luenberger-Sliding Mode Observer (ELSMO)

A linear discretized induction motor model in which A _d , B _d , and C _d are time-invariant may be represented by Equations 18 and 19 below.

here, , , And T is the sampling time.

But, Due to the nonlinearity of the induction motor is a nonlinear system can be expressed as shown in Equation 20 below.

The Extended Luenberger Observer (ELO) provides an approximation of the best estimate. The nonlinear induction motor model can be approximated by linearizing the nonlinear induction motor model around the last state estimate. In order to validate these approximations, these linearizations should be very close to nonlinear models. The transformation to the linear induction motor model of the nonlinear induction motor model can be made as follows.

in The linearization of the surrounding nonlinear system dynamics is expressed by Equation 21 below.

In the case of linearization, system dynamics may be written as Equation 22 below.

The condensed form of Equation 22 may be expressed as Equation 23 below.

here, to be.

Since Equation 18 and Equation 23 should be identical to each other, as a result to be.

Ⅳ. Luenberger Gain Design

The Luenberger observer LO is designed as in Equation 24 and Equation 25 below so that the error decreases to "0" over time with respect to the initial value of the state variable x (0).

Subtracting Equation 24 from Equation 25, the error equation may be represented by the state equations of Equations 26 to 31 below.

The dynamics of the state estimation error can be expressed as Equation 32 below.

here, to be.

In this case, Matlab's Lsim command is used to check whether the initial error converges to "0". If so, convergence time can be obtained. Note that the input variables do not affect this decision. The command in Lsim is expressed as follows:

here, Initial error value.

The initial value used in the Lsim command is assumed to be a constant DC. However, the output variable measured during actual motor operation is considered constant only during the sampling time. The error between the measured output variable and the estimated output variable should reach "0" for a given sampling. The maximum response time for which the error approaches "0" is the sampling time and can be checked using the Lsim command. Therefore, select the Luenberger gain (L) and use the Lsim command to verify that the response time is at the sampling time. Otherwise the error will not be "0".

Laplace transform of Equation 21 is represented by Equations 33 and 34 below.

here,

to be.

The eigenvalue of A-L * C can be found as det [Is- (A-LC)] and must be equal to the selected pole. Therefore, the Luenberger gain matrix L is calculated by the above equation.

The Luenberger gain matrix L is designed by pole placement and the number of poles should be equal to the number of state variables. In this case, the four poles must be placed in different positions. One simple way to determine the L matrix is to use the 'PLACE' command in Matlab as follows:

Wherein p1, p2, p3 and p4 are four arranged poles.

In this case, since the two stator current components are measured, the observer gain matrix is expressed as follows and has a size of 4 × 2:

The pole is arranged by trial and error to obtain the observer gain matrix L such that (A-LC) is asymptotically stable.

Ⅴ. Adaptive Rotor Resistance Estimation

The present invention focused on the rotor resistance estimation. During the operation of a three-phase induction motor, a change in temperature can cause the rotor resistance to vary. In this case, the rotor resistance is treated as an unknown parameter of the observer whose estimated rotor resistance is fed back to the state-space model equation of the three-phase induction motor.

The estimated stator current and rotor flux are used to estimate rotor resistance. In order to find the conditions for estimating the rotor resistance, an error between the measured stator current and the estimated stator current is required. This may be calculated by subtracting Equation 17 from Equation 16 as follows.

here, , , , to be.

The rotor resistance estimate is expressed using the function of Lyapunov, shown in equation 39 below.

Where α is a positive constant. The estimated rotor resistance is equal to the actual rotor resistance Rr and the error e becomes zero so that the function is equal to zero. The time derivative of V is obtained by the following equations (40) and (41).

here,

It may be represented by the following equation (42).

here, to be.

Is obtained by the following equation (43) as above.

The derivative of the Lyapunov function can be expressed as Equation 44 by substituting Equation 42 and Equation 43 into Equation 41.

If the error is not "0", V must be reduced for asymptotic stability. The first term in Equation 44 always has a negative value, and the derivative of the Lyapunov function has a negative value, so the sum of the second term and the third term is "0" to satisfy the above condition. Under the conditions given above, the rotor resistance estimation equation is derived as in Equation 45 below.

3 is a schematic block diagram showing an Extended Luenberger-Sliding Mode Observer (ELSMO) with an adaptive rotor resistance in a three-phase induction motor according to the present invention.

Referring to FIG. 3, the induction motor model 15 has an input variable ( Drive control by the vector controller 13 which generates a PWM drive signal in response to " 11 ".

The extended luanger-sliding mode observer (ELSMO) of the present invention is an extended luenberger-sliding mode observer (ELSMO) for obtaining a rotor resistance estimate in an induction motor model 15. An input matrix calculation unit 21 for performing multiplication of 11) with the input matrix B; The stator current measured from the induction motor model 15 ( ) And stator current estimates ( ) To compare the state estimation error ( A comparator unit 25 for calculating); State variable estimates ( ) And the state estimation error ( ) And the rotor resistance estimate ( A rotor resistance compensation / adaptation unit 28 that yields The state variable estimate ( ) And rotor resistance estimates ( ) And the system matrix estimate ( A system estimate matrix calculation unit 29 of the Luenberger observer which performs multiplication with < RTI ID = 0.0 > The state estimation error ( ) To compensate for the Luenberger gain matrix (L) and the sliding-mode gain matrix (K). Sliding-mode term on) A L matrix calculation unit 27 of a Luenberger observer for generating an output to which i) is added; The derivatives of the state variable estimates are added by adding the outputs of the input matrix calculation unit 21, the system estimate matrix calculation unit 29 and the L matrix calculation unit 27. An adder unit 22 for calculating; Derivative of the state variable estimate ( ) To integrate the state variable estimates ( An integrator unit 23 that calculates. And the state variable estimate ( ) And multiply by the output matrix (C) to estimate the stator current ( It includes ;; output matrix calculation unit 24 of the Luenberger observer (LO) for calculating a).

The present invention proposes an Extended Luenberger-Sliding Mode Observer (ELSMO). ELSMO is a linearized form of the Luenberger-Sliding mode observer in a non-linearized form.

In the Extended Luenberger-Sliding Mode Observer (ELSMO), the estimated stator current (dq axis) should be compared with the measured stator current (dq axis), and the error between them is fed back and the Luenberger gain and Multiply by the sliding gain matrix.

Based on Lyapunov's theory and equation (45), three state variables, stator currents ( ), The rotor magnetic flux λ _r and the rotor resistance Rr are correlated with each other. Estimated rotor resistance ( ), Especially the rotor flux (λ _r ) and stator current ( Depends heavily on the exact estimation of the state variable In addition, the estimated state variable ( Accuracy of the rotor Depends on Therefore, rotor resistance (Rr), rotor magnetic flux (λ _r ) and stator current ( Accurate estimates of) must be obtained simultaneously.

To achieve this, the rotor resistance compensation / adaptation unit 28 is applied in real time to the " A " and " L " matrix calculation units 29 and 27 of the Luenberger observer.

Thus, a proposed Extended Luenberger-Sliding Mode Observer (ELSMO) with estimated rotor resistance adaptation is obtained. The Luenberger gain matrix is optimized with the trial and error method of pole placement and the sliding gain matrix is set so that the controller is robust to the parametric variations of the present invention. ELSMO uses an appropriate gain matrix to provide accurate rotor flux and rotor resistance estimates.

In order to confirm the performance of the ELSMO controller algorithm according to the present invention shown in Figure 3 below, the simulation of the ELSMO controller algorithm based on the motor parameters shown in Table 1.

Parameters of Three Phase Induction Motor Models sign parameter value Rs Stator Resistance (Ω) 0.087 Rr Rotor Resistance (Ω) 0.228 Ls Stator Inductance (H) 0.03827 Lr Rotor inductance (H) 0.03827 Lm Mutual inductance (H) 0.03747 P Pole double 2

4 is a timing diagram illustrating a response time when the poles are -1000, -300, -300, and -1000.

Using the Lsim command, the response time for an error between the measured value and the estimated value converges to "0". However, the response time is highly dependent on the pole placement. In FIG. 4, when the poles are -1000, -300, -300, and -1000, the time required for the error to reach "0" is 0.02 seconds. The pole should be placed on the left and the size should be sufficient to reduce the response time.

5 is a timing diagram illustrating an error between the measured stator current and the estimated stator current when the sampling time is longer than the response time.

Only for sampling times greater than the response time, the error between the measured stator current and the estimated stator current becomes "0", otherwise diverges and never reaches "0". Therefore, the sampling time must be larger than the response time. The response time is defined as the period during which the initial error reaches "0". Therefore, in this experiment, a sampling time of 0.02 seconds is selected based on the response time of FIG. In FIG. 5, the error between the measured stator current and the estimated stator current when the sampling time is longer than the response time is indicated.

In the Extended Luenberger-Sliding Mode Observer (ELSMO), the estimated stator current (dq axis) should be compared with the measured stator current (dq axis), and the error between them is fed back and the Luenberger gain and Multiply by the sliding gain matrix.

FIG. 6 is a timing diagram showing the measured stator current and the estimated stator current (d-axis), and FIG. 7 is a timing diagram showing the measured stator current and the estimated stator current (q-axis).

6 and 7 show a comparison of the estimated and measured stator current (d-q axis) waveforms. After 2.7 seconds, the error is reduced to almost zero. Since the error value between the measured and estimated stator currents shown in FIG. 5 is small compared to the stator current itself, the measured and estimated stator currents (d-q axis) are shown overlapping each other in FIGS. 6 and 7.

FIG. 8 is a timing diagram showing the determined rotor flux and the estimated rotor flux (d-axis), and FIG. 9 is a timing diagram showing the determined rotor flux and the estimated rotor flux (q-axis).

8 and 9 the estimated rotor flux (dq axis) waveforms are shown in comparison with the rotor flux (dq axis) waveforms provided by the Simulink induction motor model. The Simulink induction motor model is based on the state-space induction motor model and the estimation of the present invention is based on ELSMO. After 2.7 seconds the error is observed to be negligible. Accurate estimation of rotor flux (dq axis) is very important for estimating rotor resistance.

Based on Lyapunov's theory and equation 45, three state variables, stator current, rotor flux and rotor resistance, are interrelated. The accuracy of the estimated rotor resistance depends in particular on the accurate estimation of the state variables of the rotor flux and the stator current. On the other hand, the accuracy of the estimated state variable depends on the correct estimated rotor resistance. Therefore, accurate estimates of rotor resistance, flux and stator current must be obtained simultaneously.

In order to achieve the above, the rotor resistance compensation / adaptation unit 28 is applied in real time to the "A" and "L" matrix calculation units 29 and 27 of the Luenberger observer.

FIG. 10 shows a dynamic speed reference including ultra-low speed and zero speed applied to an induction motor model to show the effect on rotor resistance estimation.

FIG. 11 shows the rotor resistance estimate (if rotor resistance = 0.228Ω) as a function of time according to the dynamic speed reference given in FIG. 10.

The estimated rotor resistance is stabilized by catching the rotor resistance set in the Simulink induction motor model even at varying speeds. However, there is a slight difference in the magnitude of the estimated rotor resistance. When the speed reaches zero speed, the estimated rotor resistance tends to fall slightly.

The extended Luanger-Sliding Mode Observer (ELSMO), which is capable of estimating rotor flux and rotor resistance of the present invention, is applied to the control of a three-phase induction motor.

11: input variable 13: vector controller
15: induction motor model 21: input matrix calculation unit
22: adder unit 23; Integrator Unit
24: output matrix calculation unit 25: comparator unit
26: system matrix calculation unit 27: L matrix calculation unit
28: rotor resistance compensation / adaptation unit 29: system estimate matrix calculation unit

Claims (5)

Input variable ( Is an extended Luenberger-sliding mode observer (ELSMO) capable of obtaining rotor resistance estimates from an induction motor model driven and controlled by a vector controller that generates a PWM drive signal in response to
The input variable ( An input matrix calculation unit for performing multiplication of the input matrix B with < RTI ID = 0.0 >
The stator current measured from the induction motor model ) And stator current estimates ( ) To compare the state estimation error ( A comparator unit for calculating;
State variable estimates ( ) And the state estimation error ( ) And the rotor resistance estimate ( A rotor resistance compensation / adaptation unit for calculating;
The state variable estimate ( ) And rotor resistance estimates ( ) And the system matrix estimate ( A system estimate matrix calculation unit of the Luenberger observer that performs multiplication with < RTI ID = 0.0 >
The state estimation error ( ) To compensate for the Luenberger gain matrix (L) and the sliding-mode gain matrix (K). Sliding-mode term on) A L matrix computation unit of a Luenberger observer to generate an output to which < RTI ID = 0.0 >
By adding the outputs of the input matrix calculation unit, the system estimate matrix calculation unit and the L matrix calculation unit, the derivative of the state variable estimate ( An adder unit for calculating;
Derivative of the state variable estimate ( ) To integrate the state variable estimates ( An integrator unit for calculating; And
The state variable estimate ( ) And multiply by the output matrix (C) to estimate the stator current ( It includes; output matrix calculation unit of the Luenberger observer (LO) to calculate
remind , B, C and Is an extended Luenberger-sliding mode observer defined as follows.
,
,
,
,
Where R _s and R _r are stator and rotor resistances, L _s , L _r and L _m are stator inductance, rotor inductance and mutual inductance, respectively. , Is the rotor angular velocity, u _sd and u _sq are the stator voltage (d-axis) and stator voltage (q-axis), respectively, and χ is the state variable as

I _sd , i _sq , λ _rd and λ _rq are the stator current (d-axis), stator current (q-axis), rotor magnetic flux (d-axis) and rotor magnetic flux (q-axis), respectively. delete The method of claim 1,
The rotor resistance estimate ( ) Is an extended Luenberger-sliding mode observer obtained from the following equation.

Where α is a positive constant, , to be. The method of claim 1,
The Luenberger Observer term ( ) Corrects the estimate by compensation, and the sliding-mode term ( ) Is an extended Luenberger-sliding mode observer that controls the robustness of the observer. The method of claim 1,
The Luenberger gain matrix (L) is optimized with a trial and error method of pole placement, and the sliding gain matrix (K) is set such that the controller is robust to parameter deformation.