KR101861023B1 - Torque controlling apparatus and method of induction motors based on model predictive control - Google Patents

Abstract

Provided is an apparatus for controlling torque of an induction motor which comprises: a processor; a determination unit for determining a plurality of operation sections in accordance with the speed that the induction motor at least temporarily performed by the processor operates; and a control unit for controlling torque by differentially calculating a reference state operation section based on reference torque (T_e)* provided according to a control condition corresponding to each of the plurality of operation sections.

Description

TECHNICAL FIELD [0001] The present invention relates to a torque control apparatus and method for induction motors based on model predictive control,

And more particularly to a control apparatus and method for efficiently controlling an output torque of an induction motor in a plurality of operation periods.

Model Predictive Control (MPC) is a widely used method in the field of power control today. As the main control methods, there are a finite control set-based control method (FCS-MPC) and a continuous control set-based control method (CCS-MPC). Specifically, the finite control set based control method can be implemented by calculating the cost function according to the switching state of the inverter.

In the conventional control method, there is a method of controlling the operation of the induction motor by continuously using one of five predefined input control vectors within a fixed time period. The conventional method as described above can be implemented in such a manner that the optimal input voltage vector calculated during the sampling time is applied to the next sampling period. Such a method may cause a large ripple phenomenon of torque and current. Therefore, a shorter sampling time is required for more precise control, and thus a higher switching frequency is required.

 S.J. Qin and T.A. Badgwell "A survey of industrial model predictive control technology." Control Eng. Pract., Vol. 11, no. 7, pp. 733-764, Jul. 2003.  P. Cortes, M. Kazmierkowski, R. Kennel, D. Quevede, and J. Rodriguez, "Predictive control in power electronics and drives.", IEEE Tran, Ind. Election, vol. 55, no. 12, pp 4312-4324, Dec. 2008.

According to one aspect, a torque control device for an induction motor is provided. Wherein the torque control device includes a processor, the determination unit determining a plurality of operation periods according to a speed at which the induction motor is at least temporarily implemented by the processor; And a control unit for controlling the torque by calculating a reference state operation interval defined by Equation (12) differently based on a given reference torque T _e ^* according to each of the plurality of operation periods,

이고, x^*는 기준 토크 T_e ^* 및 기준 자속 λ^*로 정의되는 기준 상태이고, i^* _ds는 d축 고정자 전류의 기준값, i^* _qs는 q축 고정자 전류의 기준값, λ^* _dr은 d축 회전자 자속의 기준값 및 λ^* _qr은 q축 회전자 자속의 기준값, L_r은 회전자 인덕턴스, L_m은 유도 전동기의 상호 인덕턴스 및 P는 유도 전동기 내의 폴의 개수를 나타내는 것을 특징으로 하고,

And, x ^* is the reference torque T _e ^* and the reference magnetic flux and the reference state is defined as λ ^*, i ^* _ds is the reference value of the reference value, i ^* _qs is the q-axis stator currents of the d-axis stator currents, λ ^* _dr is the d-axis L _r is the rotor inductance, L _m is the mutual inductance of the induction motor, and P is the number of poles in the induction motor. The reference value of the rotor flux _,? ^* _Qr is the reference value of the q-axis rotor flux,

The controller calculates a corrected cost index J (k) defined by Equation (47) according to the reference state operation period, and Equation (47)

And the controller calculates a cost index by a formula relating to a control input u [k], where W represents a positive definite matrix with respect to a weight as shown in equation (48)

이고, u_uc ^*(k)를 상기 수학식 48에서 정의되는 코스트 인덱스 J(k)의 제한되지 않은 최적 값으로 정의하고, 상기 u_uc ^*(k)는

조건을 만족하는 수학식 49를 상기 제어 입력의 최적 값으로서 계산하고, 상기 수학식 49는,

And, _uc ^* u (k) to, and defined as above, but not limited to the optimum value of the cost index, J (k) defined in equation 48 above _uc ^* u (k) is

(49) satisfying the condition is calculated as the optimal value of the control input, and the equation (49)

.

의 조건으로서 단조 감소하도록 안정도가 보장되도록

의 조건을 만족하도록 설정될 수 있다.The fixed matrix W about the weights is a matrix in which the cost index

So that stability is ensured such that monotonous reduction is achieved.

As shown in FIG.

According to one embodiment, the controller increases the magnitude of the reference torque T _e ^* by increasing the magnitude of the reference magnetic flux? ^* Of the induction motor so as to be the maximum torque per ampere (MTPA) operation in the first operation period, In the second operation period, the slip speed of the induction motor is increased to increase the magnitude of the reference torque T _e ^* in order to avoid the input saturation phenomenon. In the third operation period, the maximum value of the current and voltage of the induction motor is It is possible to limit the maximum output size of the reference torque T _e ^* so that it is not exceeded.

According to another embodiment of the present invention, the controller controls the magnitude of the reference flux? ^* (K) in the first operation period according to Equation (20)

In Equation (20)

이고, η는 0 보다 크고 1보다 작거나 같은 설계변수 이며, 동작 영역에 따라 다르게 설정될 수 있다. 또한, 임의의 제어 상수, p는 상기 유도 전동기 내의 폴(pole)의 개수, L_r은 상기 유도 전동기의 회전자 인덕턴스의 크기, T_e ^*(k)는 기준 토크의 크기를 나타내고, K_MTPA는 상기 유도 전동기의 고정자에 관한 d축 전류 및 q축 전류의 비율을 나타낼 수 있다.

Is a design variable greater than 0 and less than or equal to 1, and may be set differently depending on the operating region. In addition, any of the control constants, p is the number of poles (pole) in the induction motor, L _r is the size of the rotor inductance of the induction motor, T _e ^* (k) denotes a size of a reference torque, K _MTPA is And the ratio of the d-axis current and the q-axis current with respect to the stator of the induction motor.

According to yet another embodiment, the control unit is set to eta = 1 to obtain maximum efficiency in the first operating period, determines K _MTPA according to equation (19)

In Equation (19)

이고, R_r은 상기 유도 전동기의 회전자 저항의 크기, R_S는 상기 유도 전동기의 고정자 저항의 크기, L_m은 상기 유도 전동기의 유도 인덕턴스의 크기를 나타낼 수 있다.

R _r is the magnitude of the rotor resistance of the induction motor, R _S is the magnitude of the stator resistance of the induction motor, and L _m is the magnitude of the induced inductance of the induction motor.

According to another embodiment, the control unit controls the magnitude of the slip speed? _Sl ^* in the second operation period according to Equation (22), and when the reference magnetic flux? ^* (K) is saturated, the magnitude of the target torque Lt; / RTI >

로 설정되고,Equation (22)

Lt; / RTI >

이고, τ_r는 회전자 시간 상수, p는 상기 유도 전동기 내의 폴(pole)의 개수, L_r은 상기 유도 전동기의 회전자 인덕턴스의 크기, T_e ^*(k)는 기준 토크의 크기를 나타낼 수 있다.

Where _r is the rotor time constant, p is the number of poles in the induction motor, L _r is the magnitude of the rotor inductance of the induction motor, and T _e ^* (k) have.

According to another embodiment, the control unit controls the maximum output magnitude T ^* _{e_max} of the target torque in the third operation _period according to the equation (36)

In Equation (36)

이고, p는 상기 유도 전동기 내의 폴(pole)의 개수, L_m은 상기 유도 전동기의 유도 인덕턴스의 크기, L_r은 상기 유도 전동기의 회전자 인덕턴스의 크기, i_ds ^*는 상기 유도 전동기의 회전자에 관한 d축 전류, i_qs ^*는 상기 유도 전동기의 고정자에 관한 q축 전류를 나타낼 수 있다. 상기 제3 동작 구간에서 사용되는 전류 설정치는 모터의 최대 전류치에 따라 제한될 수 있다.

And, p is the number of poles (pole) in the induction motor, L _m is the size of the induced inductance of the induction motor, L _r is the size, i _ds ^* of the rotor inductance of the induction motor rotor of the induction motor d-axis current on, i _qs ^* may represent a q-axis current on the stator of the induction motor. The current set value used in the third operation period may be limited according to the maximum current value of the motor.

According to another embodiment, the determination unit may include a first operation period in which the magnetic flux increases and the target torque is increased according to the speed at which the induction motor operates, a second operation period in which the slip speed increases and the target torque is increased, A plurality of operation sections can be separated into a third operation section in which the maximum torque output is limited so as to operate in the control region.

According to another aspect, a torque control method of an induction motor is provided. The torque control method includes: determining a plurality of operation periods according to a speed at which the induction motor operates; increasing a magnitude of a target torque by increasing a magnitude of a reference magnetic flux of the induction motor; slip speed to increase the magnitude of the target torque and limiting the maximum output magnitude of the target torque corresponding to the current and voltage of the induction motor.

1 is a flowchart showing a torque control method of an induction motor according to an embodiment.
2 is a flowchart showing the torque control method of the induction motor in more detail.
Figure 3A shows an exemplary diagram in which the input control voltage is selected within a limited area.
3B shows an example in which the input control voltage is selected in the unrestricted area.
4 is a control block diagram illustrating the induction motor and the torque control device according to one embodiment.
FIG. 5 shows a torque / speed characteristic graph of an induction motor to which a control method according to an embodiment is applied.

Specific structural or functional descriptions of embodiments are set forth for illustration purposes only and may be embodied with various changes and modifications. Accordingly, the embodiments are not intended to be limited to the particular forms disclosed, and the scope of the present disclosure includes changes, equivalents, or alternatives included in the technical idea.

The terms first or second, etc. may be used to describe various elements, but such terms should be interpreted solely for the purpose of distinguishing one element from another. For example, the first component may be referred to as a second component, and similarly, the second component may also be referred to as a first component.

It is to be understood that when an element is referred to as being "connected" to another element, it may be directly connected or connected to the other element, although other elements may be present in between.

The singular expressions include plural expressions unless the context clearly dictates otherwise. In this specification, the terms " comprises ", or " having ", and the like, are used to specify one or more of the described features, numbers, steps, operations, elements, But do not preclude the presence or addition of steps, operations, elements, parts, or combinations thereof.

Unless otherwise defined, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art. Terms such as those defined in commonly used dictionaries are to be interpreted as having a meaning consistent with the meaning of the context in the relevant art and, unless explicitly defined herein, are to be interpreted as ideal or overly formal Do not.

1 is a flowchart showing a torque control method of an induction motor according to an embodiment. Referring to FIG. 1, the torque control method includes a step 110 of determining a plurality of operation intervals according to a speed at which the induction motor operates, and a step 110 of calculating a reference state operation interval on the basis of the reference torque, (Step 120). The general equations for the voltages of the stator and the rotor included in the induction motor in the synchronous frame can be summarized as shown in the following equations (1) and (2).

Where R _s is the magnitude of the stator resistance of the induction motor, R _r is the magnitude of the rotor resistance of the induction motor, L _s is the stator inductance, L _r is the rotor inductance, and L _m is the inductance of the induction motor Mutual inductance, ω _e is the rotational speed of the stator current, ω _r is the angular velocity of the rotor current, and u _dqs is the control input for the stator, respectively. In addition, the flux linkage of the stator professor (flux linkage) flux linkage λ Professor _dqs and rotor _dqr λ can be expressed as equations (3) and (4) below.

Based on the equations (1) to (4) described above, the stator current and rotor flux corresponding to each of the d-axis and the q-axis are used as four internal variables, It is possible to indicate the operation of the electric motor. More specifically, the torque control device that is described in this embodiment is below using the flux linkage Professor λ _dqs and flux linkage, Professor of the rotor λ _dqr of the stator, which is defined by Equation (1) and Equation (2) as a state variable, (5) defined in the state space as shown in Equation (5).

In Equation 5 x (t) is a [i _ds i _qs λ _dr λ _qr] shows four internal variables are defined as ^T, u (t) is [v _ds v _qs] Two control input is defined as ^T Lt; / RTI > The matrixes A _c and B _c used in Equation (5) can be calculated as Equation (6) below.

In Equation (6), α is the transient inductance of the stator as L _{s -} L _m ² / L _r , and β is the coupling factor of the rotor, L _m / L _r . In the above equation (6), it can be seen that the matrix A _c depends on the instantaneous value of the mechanical angular velocity _r . Therefore, when a new angular velocity? _R is obtained in all the sampling intervals, the discrete time-varying model can be newly updated.

Using the Euler method, the discrete state space model of the induction motor obtained from Equation (5) according to the sampling period h can be summarized as Equation (7) below.

로 정의되는 4행 4열의 행렬로 정의될 수 있다. B는 B_ch로 정의되는 2행 1열의 행렬로 정의될 수 있다. 또한, 상기 수학식 7에서 x[k]는 [i_ds i_qs λ_dr λ_qr]^T로 정의되는 네 개의 내부 변수를 나타내고 u[k]는 [v_ds v_qs]^T로 정의되는 두 개의 제어 입력을 나타낼 수 있다. 또한, 토크 제어 장치는 고정자의 전류, 회전자의 자속 및 유도 전동기 내의 폴(pole)의 개수 P에 관하여 정의된 유도 전동기의 전자기적 토크(electromagnetic torque)의 크기를 아래의 수학식 8과 같이 정의할 수 있다.A is

And a matrix of 4 rows and 4 columns defined by the matrix. B can be defined as a matrix of two rows and one column defined by B _c h. In Equation (7), x [k] represents four internal variables defined by [i _ds i _qs λ _dr λ _qr ] ^T and u [k] represents two internal variables defined by [v _ds v _qs ] ^T Input. The torque control device also defines the magnitude of the electromagnetic torque of the induction motor defined with respect to the current of the stator, the flux of the rotor, and the number P of poles in the induction motor, can do.

The control input u [k] may be generated using a three-phase, two-level voltage source inverter using pulse width modulation (PWM) of the space vector. Further, the control input u [k] may be limited to a continuous signal as shown in Equation (9) below.

2 is a flowchart showing the torque control method of the induction motor in more detail. Referring to FIG. 2, the torque control method of the induction motor includes a step 210 of increasing the magnitude of the reference torque T _e ^* by increasing the magnitude of the reference magnetic flux? ^{* So} as to become the maximum torque per ampere (MTPA) operation of the induction motor (220) for increasing the slip speed of the induction motor to avoid an input saturation phenomenon and increasing the magnitude of the reference torque T _e ^*; and adjusting the reference torque T _e ^* so that the maximum value of the current and voltage of the induction motor is not exceeded limiting the maximum output size of _e ^* (step 230).

In step 210, when the reference torque T _e ^* (k) at each time step for torque control of the induction motor is given so as to be a maximum torque per ampere (MTPA) operation, the reference torque T _e ^* x ^* proper reference state corresponding to a (k) can be calculated (T _e ^* (k)). More specifically, the reference state x ^* for controlling the induction motor may include the stator current i _dqs and the rotor flux _{d dqr} . The rotor flux can rotate according to the synchronized angular velocity ω _e . Further, the rotation angle [theta] _e of the rotor can be changed corresponding to the synchronized angular velocity [omega] _e . The rotation of the d-axis and q-axis frames used in the equations (1) and (2) may be based on the flux of the rotor. In other words, the position of the rotor flux can be provided based on the d-axis. Based on the indirect field oriented control principle, the direct axis component of the rotor flux becomes the same direction (? ^* _Dr =? ^* ) As the reference rotor flux value, and the rotor flux The quadrature component of the reference rotor flux value will be 0. (λ ^* _qr = 0) The selection of the reference rotor flux value can be described with a torque per ampere ratio. For a steady state (steady state) of the induction motor, the stator current can be associated with the rotor flux. (Λ _dr = L _m i _ds) torque control device is below the reference value of the d-axis stator current at step 210 Can be calculated as shown in Equation (10).

Considering the indirect field oriented control principle, the reference value of the stator current in the q-axis direction can be calculated according to the following Equation 11 based on the reference torque and the reference magnetic flux.

Based on Equation (10) and Equation (11), the torque control device can calculate the reference state including the reference torque T _e ^* and the reference magnetic flux? ^{* As} Equation (12) below. More specifically, the reference torque T _e ^* may represent a value input for control of the induction motor. In addition, the reference flux? ^* Of the corresponding rotor flux can be obtained according to the Maximum Torque Per Ampere (MTPA), flux-limited and field weakening control (FWC) have. The reference torque T _e ^* and the reference flux? ^* Obtained as described above can be used as reference values of the torque control device of the present embodiment based on the model predictive control.

The torque control apparatus according to the present embodiment can calculate the reference state defined by Equation (12) on the basis of different conditions according to each of the plurality of operation modes related to the induction motor. More specifically, the torque control device can calculate the reference torque T _e ^* and the reference magnetic flux? ^* Included in the reference state differently according to each of the plurality of operation modes of the induction motor. In the following description, how the different reference torque T _e ^* or the reference magnetic flux [lambda] ^* is calculated according to each operation period of the induction motor will be described in detail.

As described above, in the steady state, the magnetic flux professor λ _r of the rotor can be aligned in the d-axis direction (λ _dr = λ _r , λ _qr = 0) _dr = L _m i _ds and rotor current can be respectively set as i _dr = 0. The resistance loss of the stator and the rotor, which are summarized with respect to the d-axis current and the q-axis current, can be calculated as shown in the following equation (13).

The condition for minimizing the resistance loss with respect to the magnetic flux of the rotor in the steady state in which the output torque T _e of the induction motor and the angular velocity ω _e of the rotor are limited can be calculated as shown in Equation 14 below.

Using Equation (14), the torque control device can calculate Equation (15) below.

를 계산해낼 수 있다. 그에 따라, 아래의 수학식 16과 같이 정의되는 전자기적 토크 T_e를 고정자의 d축 전류 i_ds로 미분하면 아래의 수학식 17이 획득될 수 있다.When the electromagnetic torque T _e is a constant value, the torque control device

Can be calculated. Accordingly, the following equation (17) can be obtained by differentiating the electromagnetic torque T _e defined by the following equation (16) by the d-axis current i _ds of the stator.

Based on the equations (15) and (17) calculated above, the torque control apparatus can calculate the condition related to the stator current that minimizes the resistance loss of the induction motor as shown in the following equation (18).

In Equation (18), K _MTPA can represent a ratio between current components. More specifically, in order to obtain maximum efficiency, the design parameter? Is set to 1, and K _MTPA can be summarized as shown in Equation 19 below.

Example torque control device of the present embodiment based on torque λ ^* (k) is the case previously, given the mathematical reference state of the d-axis direction and the q-axis stator currents included in the formula 12 i ^* _ds and i ^* _qs is the mathematical It is possible to determine the maximum torque output condition per ampere to be determined to satisfy Eq. 18. The flux reference value corresponding to the MTPA operation can be calculated according to the following equation (20) based on the maximum torque output condition per ampere given in Equation (18).

In the above equation (20),? Represents a design variable that is greater than 0 and less than or equal to 1, can be set differently depending on the operating region of the induction motor, and is a constant determined to implement the control algorithm based on the torque ratio per ampere Lt; / RTI > In step 210, the torque control device can calculate a reference state in which?

In step 220, the torque control device may increase the slip speed of the induction motor to avoid the input saturation phenomenon, thereby increasing the magnitude of the reference torque. More specifically, step 220 may represent a control method for a flux limited region in which the induction motor operates with a limited magnetic flux. In the magnetic flux limiting region, the torque control device can adjust the magnitude of? According to the magnetic flux level to prevent saturation of the target torque that may occur due to limited control input. In step 220, the torque control device may calculate the requested slip speed? _Sl ^* of the induction motor as shown in Equation 21 below.

In Equation 21, _r τ represents a time constant (time constant) of the rotor, can be defined as L _r / _{R r.} The torque control apparatus can calculate the magnetic flux reference value corresponding to the magnetic flux restriction region using Equation (21) and Equation (12) as Equation (22) below.

로 설정될 수 있다. 또한, 상기 수학식 20 및 상기 수학식 21을 비교하여, 토크 제어 장치는 η에 관한 수학식 23을 아래와 같이 계산해낼 수 있다.In Equation (22)

Lt; / RTI > Also, by comparing Equation (20) and Equation (21), the torque control apparatus can calculate Equation (23) regarding? As follows.

As described in step 210, eta may be set to one in the maximum torque condition per ampere. Accordingly, Equation 24 regarding the optimum slip speed can be summarized as follows by substituting? = 1 into Equation 23 above.

In this embodiment, the induction motor must operate at a fixed slip speed in order to keep the stator current to a minimum for a specific input torque. In other words, the fixed slip rate at the maximum torque condition per ampere can be defined as the inverse of the product of the time constant of the rotor and K _MTPA .

However, in the magnetic flux confined region, the torque control device can increase the slip speed as the reference torque T _e ^* increases. Likewise, as the slip speed increases, eta will decrease. If the slip speed is not increased as described above, the output torque will not be maintained to the desired magnitude due to the input limit on the voltage vector.

In the case where the desired slip speed is designated by the torque control device,? May be selected in the magnetic flux limiting region according to Equation (23) as shown in the following Equation (25).

을 나타내고, C는

을 나타낼 수 있다.In the above equation (25), L

, And C represents

Lt; / RTI >

In step 230, the torque control device may limit the maximum output magnitude of the reference torque so that the maximum value of the current and voltage of the induction motor is not exceeded. The rated torque of the induction motor in the field weakening region will not be output as it is. Therefore, there will also be a need to adjust the magnitude of the reference torque used by the torque control device in accordance with the maximum output torque corresponding to the drive speed of the induction motor. In the field weakening region, the torque control apparatus can perform vector control based torque control in such a manner that the current component i _ds ^e in the d-axis direction and the current component i _qs ^e in the q-axis direction are reduced and weakened.

As the drive speed of the induction motor increases, the voltage and current of the stator can also approach the rated voltage and the rated current, respectively. The maximum value V _smax of the stator voltage can be determined by the available direct current connection voltage V _dc . In this case, the two control voltage components v _ds and v _qs based on the pulse width modulation scheme can be determined based on the following equation (26).

로 제한될 수 있다. 토크 제어 장치는 고정자의 저항 값 R_s를 고려하여 상기 수학식 26의 정확성을 높일 수 있다. 정상 상태에서 고정자의 d축 전압은 아래의 수학식 27과 같이 정의될 수 있다.In the above equation (26), V _smax is

Lt; / RTI > Torque control apparatus can improve the accuracy of the equation 26 in consideration of the resistance value R _s of the stator. The d-axis voltage of the stator in the steady state can be defined as: < EMI ID = 27.0 >

In the vector control method, since the q-axis magnetic flux of the rotor is 0, the q-axis current of the rotor can be calculated as shown in Equation 28 below.

Further, by using Equation (28), the relational expression regarding the d-axis voltage of the stator can be summarized as Equation (29) below.

Similarly, in the vector control method, since the q-axis flux of the rotor and the d-axis current of the rotor are 0, the q-axis voltage of the stator can be summarized as shown in Equation 30 below.

The torque control apparatus can calculate the equation (26) as shown in the following equation (31) based on the equation (30).

In Equation (31),? Can represent L _s- (L _m ² / L _r ). The torque control device can calculate the following equation (32) by dividing both sides in the inequality shown in the above equation (31) by L _s ² ω _e ² .

In Equation 32, I _smax ² represents i _ds ² + i _qs ² , and σ represents the total leakage factor of the induction motor, and may be defined as 1-L _m ² / (L _s L _r ) . However, when the driving speed of the induction motor exceeds a predetermined threshold value, the rightmost term of Equation (32) may be omitted because it is proportional to the reciprocal of the driving speed. Since L _s- alpha converges to a very small value, the above equation (32) can be modified to an equation of an ellipse expressed by the following equation (33).

The ellipse defined by equation (33) may represent the maximum limit for the steady state currents i _ds and i _qs determined based on the voltage maximum value V _smax of the stator.

On the other hand, in the field weakening region, the current components in the d-axis direction and the q-axis direction of the stator need to satisfy the following expression (34).

The I _smax may represent the maximum value of the stator current determined by the current rating and mechanical thermal rating of the inverter. However, the state currents i _ds ^* and i _qs ^* determined on the basis of the reference flux? ^{* In the} field weakening region may not satisfy the condition of the above Expression (33) and (34). Thus, the torque control device determines the reference state values defined by Equation (12) at the intersection of the voltage-constrained ellipse defined by Equation (33) and the current constrained ellipse defined by Equation (34) at a given operating frequency . More specifically, in the field weakening region, the torque control apparatus can calculate four reference states as shown in the following Equation (35) and use it for torque control.

As determined in the above equation (35), the reference current i _ds ^* can be determined by the angular speed? _E of the induction motor regardless of the reference torque T _e ^* . On the other hand, the reference current i _qs ^* can be determined by the reference torque T _e ^* . Using the equation relating to the reference torque T _e ^* defined in Equation (8), in step 230, the torque control device calculates the maximum output value of the target torque satisfying both the current limiting condition and the voltage limiting condition by the following equation Can be calculated as follows.

The reference current i _ds ^* determined in Equation (35) can be used to determine the torque value at a specific driving speed of the induction motor. However, when the target torque outputted by the torque control device is controlled in the field weakening region, the reference torque T _e ^* can be limited by the maximum value according to the above-mentioned equation (36). In addition, the current set value may be limited according to the maximum current value of the motor. In this case, the corrected reference torque T _efw ^* can be controlled as shown in Equation 37 below.

The slip speed of the modified reference torque T _efw ^* defined in Equation (37) can be defined as Equation (38) below, and the angular velocity ω _e can be calculated as Equation (39) below.

Figure 3A shows an exemplary diagram in which the input control voltage is selected within a limited area. The torque control apparatus of the present embodiment can calculate an equation for tracking the state as shown in the following Equation 40 at a given reference state x ^* .

Equation (40) may be dependent on Equation (7) for the Euler method and Equation (9) for input constraints. The torque control apparatus in this embodiment can solve the state tracking problem based on minimizing the cost index without any other numerical calculation method in the discrete time system. For this purpose, the predicted error state one step ahead can be calculated as shown in Equation 41 below.

, Using the predicted error state e _x [k + 1 | k] defined in Equation 41 and based on the reference state x ^* (T _e ^* ,? ^* ) In Equation 11, The cost index for the control system proposed in the present embodiment can be calculated by Equation (42) below.

의 조건으로서 단조 감소하도록 안정도가 보장되도록

의 조건을 만족하도록 설정될 수 있다. 이러한 코스트는 다음 시간 단계에서의 예측된 상태 에러를 악화시킬 수 있을 것이다. 웨이트 함수 W를 선택하는 것은 상태 추적 성능 및 시스템의 안정성을 향상시키는데 중요한 인자가 될 수 있다. 선형 행렬 부등식(LMI: Linear Matrix Inequality)에 기반한 최적화 기술은 최적의 W를 결정하는데 이용될 수 있다. 토크 제어 장치는 아래의 수학식 43과 같이 입력이 제한된 최적화 문제에 관한 수식을 계산할 수 있다.Where W represents a positive definite matrix with respect to weight and x [k + 1 | k] represents a predicted value of x [k + 1] based on available data at time k . The fixed matrix W about the weights is a matrix in which the cost index

So that stability is ensured such that monotonous reduction is achieved.

As shown in FIG. Such a cost may worsen the predicted state error at the next time step. Selecting the weight function W may be an important factor in improving the state tracking performance and the stability of the system. Optimization techniques based on Linear Matrix Inequality (LMI) can be used to determine the optimal W. The torque control device can calculate the equation concerning the optimization problem whose input is limited as shown in the following equation (43).

Equation (43) may be dependent on Equation (7) for the Euler method and Equation (9) for input constraint. The control of u (k) included in equation (41) may be applied to the inverter at a time step of k to minimize the cost index J (k) for the predicted state tracking error at time step k + 1. However, in practical applications, there may be a time delay due to the calculation time or modulation mechanism of the torque control device. In other words, the control input calculated at the time step of k can be applied to the inverter substantially at time step k + 1. Such a time delay may be a factor deteriorating the control performance of the torque control device, and the torque control device needs to compensate for such an effect.

From the above Equation (7), the predicted state model x [k + 2 | k] can be calculated as Equation (44) below.

The torque controller can modify the cost index according to Equation (42) as shown in Equation (45) below.

There is a need to modify the reference state defined in Equation (11) because of the uncertainties causing the steady state tracking error. In order to prevent the steady state tracking error from occurring, the reference state can be calculated by integrating the tracking error as shown in Equation 46 below.

The tracking error e _s [k] in Equation 46 represents e _s [k-1] + (x ^* (T _e ^* , λ ^* ) - x [k]) and K _s is defined in the system of the induction motor Can be expressed as a gain value. The corrected reference state x _s ^* [k] calculated from the above equation (46) can replace the reference state included in the above equation (45). The torque control device can calculate the corrected cost index from the substitution as shown in Equation (47) below.

To implement optimization, the cost index defined in Equation (47) can be calculated in the form of an equation with respect to the control input u [k] as shown in Equation (48) below.

조건을 만족하는 값을 구하는 방식으로 최적화될 수 있다. 최적화된 u_uc ^*(k)는 아래의 수학식 49와 같이 계산될 수 있다.u _uc ^* (k) is defined as an unlimited optimal value of the cost index J (k) defined in Equation (48), u _uc ^*

Can be optimized in such a manner that a value satisfying the condition is obtained. The optimized u _uc ^* (k) can be calculated as shown in Equation 49 below.

의 제한 조건이 존재하는 경우에, 제한 없는(unconstraint) u_uc ^*(k)와 동일하게 계산될 수 있다. 제한 조건 내에서 계산된 최적값 u_uc ^*(k)는 도 3a의 실시예를 통해 도시된다.The optimal value u _uc ^* (k) calculated in the optimization problem defined by the above equation (49)

Can be computed the same as unconstraint u _uc ^* (k) if there is a constraint of u _uc ^* (k). The calculated optimal value u _uc ^* (k) within the constraint is illustrated through the embodiment of Figure 3a.

조건을 만족하는 경우에 대해 최적값을 계산할 수 있다. 상기 수학식 9를 만족하는 구현 가능한 입력 집합의 범위는 도 3a 및 도 3b에 도시되는 d축 및 q축 상의 원으로 도시될 수 있다.3B shows an example in which the input control voltage is selected in the unrestricted area. The torque control device is different from the embodiment described in FIG. 3A

The optimum value can be calculated for the case where the condition is satisfied. The range of the input set that can be implemented satisfying Equation (9) can be shown as a circle on the d-axis and the q-axis shown in Figs. 3A and 3B.

There may be a case where the static matrix W for the weight is selected to satisfy the following expression (50).

In this case, the level set of the control voltage for all values of the cost function can be shown in the circles shown in FIG. 3B. Thus u _c ^* (k) will be at the tangential point on the boundary of the circle with respect to the set of levels of J (k). Torque control device may determine a set of selected of u (k) = a, from 0 point u _uc ^* method to calculate the boundary crossing of the straight line and the possible implementation of the input area to connect ^{_{(k) u c * (k}} ) . Therefore, the model predictive control based torque control apparatus provided in the present embodiment can determine u _c ^* (k) as shown in the following equation (51).

4 is a control block diagram illustrating the induction motor and the torque control device according to one embodiment. Referring to FIG. 4, a block diagram of a torque control device 420 for controlling the output torque of an induction motor (IM) 410 is shown. The torque control device 420 according to the present embodiment increases the slip speed of the induction motor 410 in the first operation period in which the magnitude of the reference magnetic flux of the induction motor 410 is increased to increase the magnitude of the target torque, The target torque can be controlled according to the second operation period for increasing the magnitude of the torque and the third operation period for limiting the maximum output magnitude of the target torque to correspond to the limit current and voltage of the induction motor. With respect to the control process of the target torque corresponding to each operation period, the description of the torque control device described above can be applied as it is, and a duplicate description will be omitted.

Table 1 below shows an example of a plurality of parameters set in the torque control device 420 for controlling the induction motor 410. [

DC bus voltage [V] V _dc 500 Number of Poles P 4 Power Factor cosθ 0.875 Rated Voltage [V] Y / Δ 200/380 Rated current [A] 14.2 / 8.2 Stator Resistance [Ω] R _s 1.77 Rotor Resistance [Ω] R _r 1.275 Stator Inductance [H] L _s 0.157 Rotor Inductance [H] L _r 0.158 Mutual Inductance [H] L _m 0.15 Inertia Coefficient [Kg.m ² ] J 0.0056 Rated Motor Speed [rpm] ω _N 1740 Rated Motor Frequency [Hz] f _N 60 Rated Power (kW) P _N 3.7 Sampling Frequency [kHz] f _s 10

FIG. 5 shows a torque / speed characteristic graph of an induction motor to which a control method according to an embodiment is applied. Referring to FIG. 5, a first graph 510 illustrating the limits of maximum output torque and a first reference torque 521 and a second reference torque 522 defined according to the operating mode of the induction motor are shown.

The torque control device can separate the entire speed section of the induction motor into three areas 531, 532, and 533. More specifically, in the low speed section, the first area 531 in which the reference magnetic flux T _e ^* increases as the magnetic flux increases can be defined. In addition, when the speed of the induction motor increases beyond the first area 531, the magnetic flux confined area can be defined as the second area 532. [ Break-point torque bounds 550, which define the boundaries of the first region 531 and the second region 532, may be implemented based on pre-stored look-up tables. In addition, when the base speed of the induction motor exceeds 1740 rpm (560), the field weakening period may be defined as the third area 533. The induction motor can set the first input reference torque 521 to 15 Nm and increase the output speed to 3000 rpm. However, since the rated current of the connected rod is limited to 14.2 A and the maximum supply voltage is limited to 260 V (450 Vdc), the magnetic flux weakens and the induction motor resets the second input reference torque 522 to 10.5 Nm .

Also, the torque control device can separate the operation section from the fixed torque region 541 and the fixed power region 542 according to the driving speed of the induction motor.

The torque control apparatus according to the present embodiment can calculate three operation periods in advance based on the rated current and the rated voltage provided to the induction motor. Further, the torque control device can calculate the respective boundary values of the three operation sections in advance in accordance with the driving speed of the induction motor. Accordingly, it is possible to realize more stable and accurate control in the control of the induction motor.

Although the embodiments have been described with reference to the drawings, various technical modifications and variations may be applied to those skilled in the art. For example, it is to be understood that the techniques described may be performed in a different order than the described methods, and / or that components of the described systems, structures, devices, circuits, Lt; / RTI > or equivalents, even if it is replaced or replaced.

Claims (5)

A torque control apparatus for an induction motor,
A processor comprising: a determination unit implemented by the processor; and a control unit implemented by the processor,
Wherein the determination unit determines a plurality of operation periods according to a speed at which the induction motor operates,
The control unit calculates a reference state x ^* defined by Equation (12) on the basis of a given reference torque T _e ^* according to each of the plurality of operation periods on the basis of different conditions according to each operation period of the induction motor The target torque is controlled,
Equation (12)

And, x ^* is the reference torque T _e ^* and the reference magnetic flux and the reference state is defined as λ ^*, i ^* _ds is the reference value of the reference value, i ^* _qs is the q-axis stator currents of the d-axis stator currents, λ ^* _dr is the d-axis L _r is the inductance of the rotor, L _m is the mutual inductance of the induction motor, and P is the number of poles in the induction motor. The reference value of the rotor flux, λ ^* _qr is the reference value of the q-
The control unit, as the different condition,
The magnitude of the reference torque T _e ^* is increased by increasing the magnitude of the reference magnetic flux? ^* Of the induction motor so as to become the maximum torque per ampere (MTPA) operation in the first operation period,
The slip speed of the induction motor is increased to avoid the input saturation phenomenon in the second operation period to increase the magnitude of the reference torque T _e ^*
The maximum output size of the reference torque T _e ^* is limited so that the maximum value of the current and voltage of the induction motor is not exceeded in the third operation period,
The controller calculates a corrected cost index J (k) defined by Equation (47) according to the reference state, and Equation (47)

And the controller calculates a cost index by a formula relating to a control input u [k], where W represents a positive definite matrix with respect to a weight as shown in equation (48)

And, _uc ^* u (k) to, and to define the optimum values of cost index J (k) defined in equation 48 above _uc ^* u (k) is

(49) satisfying the condition is calculated as the optimal value of the control input, and the equation (49)

.
In the above equations (48) and (49), A represents

B is a matrix of 2 rows and 1 column defined by B _c h, h is a sampling period of the induction motor,
A _c and B _c are defined as shown in Equation (6)
Equation (6)

And wherein the stator of the R _s are an induction motor in the equation (6) resistance size, R _r is of the induction motor rotor resistance size, L _r is the rotor inductance, ω _e is the angular velocity (rotational speed), ω _r of the stator current, Α is the angular velocity of the rotor current, α is the transient inductance of the stator as L _s -L _m ² / L _r , β is the coupling factor of the rotor as L _m / L _r , L _s is the stator inductance, L _m is the mutual inductance of the induction motor,
The controller determines the control input u _c ^* (k) according to equation (51) using the calculated optimum value u _uc ^* (k)
In Equation (51)

V _smax represents the maximum value of the voltage of the stator,
The fixed matrix W about the weights is a matrix in which the cost index

So that stability is ensured such that monotonous reduction is achieved.

Is satisfied. ≪ / RTI > The method according to claim 1,
Wherein the control unit controls the magnitude of the reference flux? ^* (K) in the first operation period according to Equation (20)
In Equation (20)

Where p is the number of poles in the induction motor, L _r is the magnitude of the rotor inductance of the induction motor, < RTI ID = 0.0 > , T _e ^* (k) denotes the magnitude of the reference torque, and K _MTPA denotes the ratio of the d-axis current and the q-axis current with respect to the stator of the induction motor.
3. The method of claim 2,
The control unit sets k = 1 to obtain maximum efficiency in the first operation period and determines K _MTPA according to the equation (19)
In Equation (19)

And, R _r is the torque control unit indicating the amount of inductance of the induction rotor resistance size, R _S is the size of the stator resistance of the induction motor, L _m is the induction motor of the induction motor.
The method according to claim 1,
The control unit controls the magnitude of the slip speed? _Sl ^* in the second operation period according to Equation (22), increases the magnitude of the target torque when the reference flux? ^* (K) is saturated,
Equation (22)

Is set to

( _R) is the rotor time constant, p is the number of poles in the induction motor, L _r is the magnitude of the rotor inductance of the induction motor, T _e ^* (k) controller.
The method according to claim 1,
The control unit controls the maximum output size T ^* _{e_max} of the target torque in the third operation _period according to the equation (36)
In Equation (36)

And, p is the number of poles (pole) in the induction motor, L _m is the size of the induced inductance of the induction motor, L _r is the size, i _ds ^* of the rotor inductance of the induction motor rotor of the induction motor d-axis current, i ^* _qs is a torque control device that represents a q-axis current on the stator of the induction motor, limited by the maximum current value of the current value is set on the motor.

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