KR20240008190A - System for controlling torque of induction motor - Google Patents

Abstract

This technology discloses a torque control system for an induction motor. According to a specific implementation example of the present technology, the state behavior of the induction motor is tracked through continuous control and the coefficient factor of the gain G of the discrete state time domain is determined by adjusting the knob according to the tracking results. By adjusting, the pole conversion for the estimated rotor speed is small and the number of poles that are unstable operating points at low speeds can be reduced, so the rotor speed can be estimated quickly and overshoot in transient response can be reduced. , from the perspective of the observer, the number of unstable operating points at low speeds can be reduced, and from the aspect of the torque controller, a stable gain G can be derived.

Description

Speed sensorless torque control system for induction motor {SYSTEM FOR CONTROLLING TORQUE OF INDUCTION MOTOR}

The present invention relates to a speed sensorless torque control system for an induction motor, and more specifically, to a technology that reduces the number of unstable operating points of a speed sensorless induction motor.

Recently, as interest in electric vehicles has grown and commercialization of electric vehicles has occurred, electric vehicle technology is making a significant contribution to alleviating concerns about energy consumption and carbon dioxide emissions in the transportation sector.

One important advantage of electric vehicles is that the vehicle's kinetic energy can be converted into electrical energy through regenerative braking and stored.

Because regenerative braking can increase the driving range of electric vehicles by 8 to 25%, it is one of the ways to improve the driving range of electric vehicles.

Accordingly, a variety of research on regenerative braking of electric motors is in progress. Regenerative braking is based on the basic principle of making the motor's torque negative and transferring mechanical energy to the battery.

When using an induction motor, various methods have been proposed to control the charging current flowing into the battery using a robust control method.

Accordingly, the induction motor considers the dynamics of the vehicle in order to create a negative torque setting value that produces optimal efficiency, but when a change in dynamics occurs, the speed sensorless induction motor improves the convergence speed with two tuning parameters.

However, in a typical speed sensorless induction motor, the gain oscillates in a low-speed unstable state, and a large overshoot occurs in the transient response.

Patent Registration No. 10-1005432 (December 27, 2010)

The purpose of the present invention is to eliminate overshoot of transient response without gain oscillation by reducing the unstable operating point of a speed sensorless induction motor to a predetermined number at low speed by using one parameter.

Accordingly, the present invention is intended to reduce computational complexity and perform precise control of a speed sensorless induction motor.

The object of the present invention is not limited to the object mentioned above, and other objects and advantages of the present invention that are not mentioned can be understood through the following description and will be more clearly understood through examples of the present invention. In addition, it will be readily apparent that the objects and advantages of the present invention can be realized by means and combinations thereof as indicated in the claims.

The speed sensorless torque control system for the induction motor of the present invention to achieve this technical task is,

In a speed sensorless torque control system for an induction motor that controls the rotor speed using a continuous control element model predictive control technique,

It includes an observer that converts the measured stator current of the induction motor into the dq axis and then derives rotor flux estimation and rotor speed estimation by inputting the converted dq stator current.

The observer,

The coefficient factor included in the gain by designing the gain for the discrete time state estimator of the induction motor By adjusting , the number of poles, which are unstable operating points of the continuous-time state estimator converted to a continuous-time model, is reduced to a predetermined number to perform stable speed estimation and torque control accordingly.

Preferably, the observer is:

a discrete state estimation unit that derives a discrete state estimation from the state equation of the induction motor;

a gain derivation unit that derives a gain in the time domain for the discrete state estimation;

A rotor speed estimation unit that derives a rotor speed estimate by applying an adaptation law to the induction motor speed derived from the characteristic equation of the induction motor and performs proportional integral control on the derived rotor speed estimate;

arbitrary operating point A state analysis unit that determines whether the proportional integrally controlled rotor speed estimation is an unstable operating point; and

Coefficient factor of the derived gain G in case of unstable operating point It may include a state adjuster that controls the convergence speed of the estimated speed and torque control for the rotor speed by adjusting .

Preferably, the state analysis unit,

The arbitrary operating point Based on the state and speed dynamics of the induction motor, the state and rotor speed are derived, and then the state error derivative is derived,

If the Jacobian matrix included in the derived state error derivative has an eigenvalue, it can be determined as an unstable operating point.

Preferably, the state adjusting unit,

The coefficient factor of one parameter of the gain G at the unstable arbitrary operating point It can be provided to reduce the number of unstable poles for the estimated rotor speed by adjusting the pole to be moved to a position where the imaginary part of the gain G is not increased.

Preferably, the observer is:

Coefficient factor adjusted for each sampling time It may further include a state determination unit for deriving a rotor speed estimate with a gain G including , determining whether the Jacobian matrix included in the derived rotor speed estimate has an eigenvalue, and determining a stable state of the gain G.

According to the present invention as described above, the state behavior of the induction motor is tracked through continuous control and the coefficient factor of the gain G of the discrete state time domain is determined by adjusting the knob according to the tracking result. By adjusting, the pole conversion for the estimated rotor speed is small and the number of poles that are unstable operating points at low speeds can be reduced, so the rotor speed can be estimated quickly and overshoot in transient response can be reduced. , from the perspective of the observer, the number of unstable operating points at low speeds can be reduced, and from the aspect of the torque controller, a stable gain G can be derived.

The following drawings attached to this specification illustrate preferred embodiments of the present invention, and serve to further understand the technical idea of the present invention together with the detailed description of the invention described later. Therefore, the present invention includes the matters described in such drawings. It should not be interpreted as limited to only .
1 is a configuration diagram of an induction motor control system according to an embodiment.
Figure 2 is a detailed configuration diagram of the observer of Figure 1.
Figure 3 is an exemplary diagram showing a motor and an observer pole in one embodiment.
Figure 4 is an example diagram showing an unstable operating point of one embodiment.
Figure 5 is an example diagram showing unstable operating points for each load torque in one embodiment.
6 shows the adjusted coefficient factor of one embodiment. These are examples that showed stellar torque.
Figure 7 is a waveform diagram of the output of each part of the observer according to an embodiment.
Figure 8 is a torque waveform diagram in low-speed and high-speed regions of one embodiment.
Figure 9 shows output waveforms of a torque controller according to one embodiment.
Figure 10 is an example diagram showing speed estimation error in no-load torque in one embodiment.
Figure 11 is an output waveform diagram of an induction motor in one embodiment.
Figure 12 is an output waveform diagram in a regenerative mode of an induction motor according to an embodiment.
Figure 13 is an output waveform diagram of an induction motor at speed 0 according to one embodiment.
Figure 14 is a comparative waveform diagram showing the observer gain of one embodiment and the existing gain.
Figure 15 is a waveform diagram comparing the convergence speed of the observer in one embodiment and the existing convergence speed.

The advantages and features of the present invention and methods for achieving them will become clear with reference to the embodiments described below along with the accompanying drawings. However, the present invention is not limited to the embodiments disclosed below and may be implemented in various different forms. The present embodiments are merely provided to ensure that the disclosure of the present invention is complete and to be understood by those skilled in the art. It is provided to fully inform those who have the scope of the invention, and the present invention is only defined by the scope of the claims.

The terms used in this specification will be briefly explained, and the present invention will be described in detail.

The terms used in the present invention are general terms that are currently widely used as much as possible while considering the function in the present invention, but this may vary depending on the intention or precedent of a person working in the art, the emergence of new technology, etc. In addition, in certain cases, there are terms arbitrarily selected by the applicant, and in this case, the meaning will be described in detail in the description of the relevant invention. Therefore, the terms used in the present invention should be defined based on the meaning of the term and the overall content of the present invention, rather than simply the name of the term.

When it is said that a part "includes" a certain element throughout the specification, this means that, unless specifically stated to the contrary, it does not exclude other elements but may further include other elements.

Accordingly, the functionality provided within the components and “parts” may be combined into a smaller number of components and “parts” or may be further separated into additional components and “parts”.

Below, with reference to the attached drawings, embodiments of the present invention will be described in detail so that those skilled in the art can easily implement the present invention. In order to clearly explain the present invention in the drawings, parts unrelated to the description are omitted.

An embodiment may include any number of each component to which it applies, in any suitable configuration. In general, computing and communication systems come in a wide range of configurations, and the drawings do not limit the scope of the disclosure to any particular configuration. Although the drawings illustrate one operating environment in which the various features disclosed in this patent document may be used, such features may be used in any other suitable system.

Before explaining the specification, some terms used in the specification will be clarified. In this specification, an adaptive full orders observer (AFO) refers to an observer in a discrete state, and thus the terms state observer, adaptive full orders observer, observer, or AFO will be used interchangeably.

In the description in the specification, the subject performing the operation may be a processor that controls an induction motor (IM), and as another example, it may be a recording medium on which a program for performing measurement and control processes is recorded or a device containing the same. there is.

FIG. 1 is a configuration diagram of a torque control system of a speed sensorless induction motor according to an embodiment. Referring to FIG. 1, the torque control system of a speed sensorless induction motor according to an embodiment is an induction motor (hereinafter abbreviated as IM: Induction Motor). includes a drive system (1) and an IM control system (2). The IM control system (2) includes a current converter (21), an observer (22), a PI controller (23), a slip angular velocity deriver (24), an adder (25), an integrator (26), a torque controller (27), and a voltage converter. (28), and may include at least one of space vector PWM (29).

The induction motor (IM) is a speed sensorless motor, so the stator current of each phase of the induction motor (IM) is provided to the IM control system (2).

Accordingly, the current converter 21 of the IM control system 2 converts the stator current of each phase of the received IM into the stator current of the dq axis. Convert it to and then pass it to the AFO (22).

FIG. 2 is a diagram showing the processing algorithm of the observer 22 of FIG. 1. Referring to FIG. 2, the observer 22 calculates the measured dc link voltage and the converted stator current of the dq axis. Estimation of rotor flux based on and rotor angular velocity estimation. Derive .

Accordingly, the observer 22 detects the converted stator current of the dq axis. and a discrete state estimation deriving unit 221 that derives a discrete state estimation equation through Euler approximation performed with a predetermined state equation of the induction motor.

In other words, the state equation of an induction motor (IM: Induction Motor) can be expressed as Equation 1 below.

[Equation 1]

here, , and are the stator current and rotor flux, is the stator input voltage supplied from the outside, where the matrix can be summarized in Equation 2 below.

[Equation 2]

Here, each matrix , and Each can be represented by Equations 3 to 5 below.

[Equation 3]

[Equation 4]

[Equation 5]

here, are stator resistance, rotor resistance, stator inductance, rotor inductance, and mutual inductance between the stator and rotor.

also, is the time constant of the rotor, is the synchronous angular velocity of the induction motor, is the rotor angular velocity, is the slip angular velocity, where, the slip angular velocity Can be determined by Equation 6 below.

[Equation 6]

Here, supplied from outside is the current command value of the stator, is an estimate of the magnetic flux of the d-axis rotor.

That is, the observer 22 discretizes the state equation of the induction motor (IM) in Equation 1 through Euler approximation to derive the discrete state x(k+1), and the derived discrete state equation of the induction motor x(k +1) can be expressed in equation 7 below.

[Equation 7]

Here, A _d = I+T _s ; B _d = T _s XB _c and T _s are the sampling times. Accordingly, the matrices A _d and B _d in complex form can be expressed as Equation 8 and Equation 9 below, respectively.

[Equation 8]

[Equation 9]

here,

am.

Additionally, the observer (AFO) estimates the discrete state of the induction motor (IM) at the current sampling period k . Derive and estimate the discrete state of the derived current sampling period k Based on the current sampling period k , the next consecutive sampling period k+1 Discrete state estimation of induction motor (IM) The discrete state estimation equation for the following sampling period k+1 is derived by deriving can be expressed in equation 10 below.

[Equation 10]

here, is the estimate of the rotor angular velocity.

The observer 22 includes a gain derivation unit 222 that derives g1 to g4 of the gain G in the form of a complex number included in the discrete state estimation equation using a predetermined characteristic equation of the induction motor.

The characteristic equation for a complex induction motor can be expressed as Equation 11 below.

[Equation 11]

The characteristic equation for the induction motor is the coefficient factor There is a root proportional to the poles of the induction motor.

[Equation 12]

Comparing the coefficients of Equations 11 and 12, each matrix value ( g ₁ to g ₄ ) of the gain G of the observer (AFO) is as shown in Equations 13 to 16 below.

[Equation 13]

[Equation 14]

[Equation 15]

[Equation 16]

here, is the coefficient factor of the observer (AFO) am.

Additionally, the observer 22 includes a rotor angular velocity estimation unit 223 that derives a rotor angular velocity estimate based on the derived gain G.

The rotor angular velocity estimation unit 223 uses the gain G having the matrix values of Equations 13 to 16 to calculate the discrete state estimation equation for the next sampling period. , and the discrete state estimation equation for the following sampling period determined: Can be expressed as the following equations 17 and 18.

[Equation 17]

[Equation 18]

here, am.

And the discrete state estimation equation for the next sampling period constant of is derived as the ratio of gain G and sampling period Ts . in other words, am.

At this time, the gain G of the observer 22 is designed so that the eigenvalue of A _c -GC is located within the unit circle.

In addition, the discrete state observer 22 is the state equation of the induction motor in Equation 1 In Equation 17, the following discrete state estimation equation By subtracting the state error equation and the derived state error equation can be expressed as Equation 19 below.

[Equation 19]

here, is the rotor angular velocity measurement value and rotor angular velocity estimates It is derived by car.

Afterwards, the rotor speed estimation unit 223 applies the Lyapunov function to derive the speed V ₁ of the induction motor, and the derived speed V ₁ of the induction motor is designed as Equation 20 below.

[Equation 20]

here, am.

rotor speed fluctuation If is close to 0, that is, If, then the state error equation Substitute into the derivative of the induction motor speed V ₁ , and then the derivative of the induction motor speed V ₁ can be expressed as the following equation 21.

[Equation 21]

Rotor angular velocity estimate To implement the adaptation law for , the derivative of the induction motor speed in Equation 21 The second and third terms of should be removed. Therefore, estimating the rotor speed from the second and third terms of Equation 21 derivative for Derive and estimate the derived rotor angular velocity satisfies the following equation 22:

[Equation 22]

here, am.

Accordingly, the observer (AFO) estimates the rotor speed in Equation 22. derivative for is the derivative of the induction motor speed. Apply to and derivative of induction motor speed can be expressed in equation 23 below.

[Equation 23]

Here, the derivative of the rotor speed estimate decreases as the induction motor speed changes rapidly. To improve the responsiveness of the derivative of the rotor speed estimate as shown in Equation 24 below: Proportional and integral control are performed for .

[Equation 24]

here, , class are the proportionality and integration constants.

and the derivative of the rotor speed estimate in Equation 24. Estimation of discrete rotor speed by discretization with Tustine algorithm satisfies Equation 25 below.

[Equation 25]

And, synchronous angular velocity estimation and flux angle estimation of a discrete rotor. can be obtained from Equation 26 and Equation 27 below, respectively.

[Equation 26]

[Equation 27]

Synchronous angular velocity estimate and an estimate of the magnetic flux angle of the rotor. is converted to the dq axis.

And the observer 22 estimates the rotor speed. It includes a state analysis unit 224 that determines the state of.

That is, the state analysis unit 224 determines whether it is an unstable operating point, and if it is an unstable operating point as a result of the determination, the adjustment knob value of the gain G By compensating, the number of unstable operating points is reduced.

Accordingly, the state derivatives for each state and speed dynamics of the induction motor are and rotor angular velocity derivative Each satisfies Equation 28 below.

[Equation 28]

State derivative of equation 28 The discrete state estimation equation in Equation 17 and the derivative of the speed estimate of the proportionally controlled rotor in Equation 24. By subtracting the state error derivative The state error derivative derived by deriving is derived based on Equation 29 below.

[Equation 29]

here, , stator current error converted to dq axis , rotor flux error , and rotor speed fluctuation value Includes.

Also the operating point The state error derivative of Equation 29 in By linearizing , the following equation 30 can be derived.

[Equation 30]

here, Is is the steady state value of, where is the Jacobian matrix silver

is derived.

The state analysis unit 224 is a matrix The operating point with one eigenvalue of is judged to be an unstable operating point.

In addition, the observer 22 determines the coefficient factor of the gain G when the analysis result of the state analysis unit 224 indicates an unstable operating point. It includes a state adjustment unit 225 that adjusts to reduce the unstable operating point to a predetermined number or less. where the coefficient factor Correction of is performed with the shift angle selected through adjustment of the knob.

The state adjusting unit 225 uses the derivative for the estimation of the rotor angular velocity in Equation 24 variable of To summarize, the variable can be expressed in equation 31 below.

[Equation 31]

here, is the flux shift angle of the rotor. The unstable state adjusting unit 225 uses the derivative for estimating the speed of the rotor in Equation 24. of a variable in equation 31. As the linearization of the induction motor control system of equations 28 to 30 is performed by replacing with, the matrix can be derived. For example When, matrix The value of the 5th column is as follows.

here,

is the operating point is the synchronous angular velocity at, Each is rotor angular velocity, slip angular velocity, d-axis rotor flux command value, and steady-state control input.

Here, the matrix The operating point with this eigenvalue is defined as the unstable operating point.

Figure 3 is an exemplary diagram showing the real part and the imaginary part with a positive rated slip angular velocity at rotor angular speeds from -1000 rpm to 1000 r/min, where the eigenvalues of Ac (indicated in blue), Ac-LC of Prior Document 1 This diagram shows the eigenvalues of (indicated in red) and the eigenvalues of Ac-GC/Ts using the gain (indicated in green) of one embodiment.

Referring to FIG. 3, when the pole of the observer 22 in one embodiment is moved to the left of the pole of the induction motor, it can be seen that the imaginary part does not increase, as indicated in green, and at this time, the state equation converges. The speed is increased by the observer's virtual pole being moved to the left of the induction motor's pole.

Accordingly, the observer 22 of one embodiment has a convergence speed faster than the pole of an induction motor without large vibration in an unstable state, and can reduce overshoot in transient response.

Figure 4 is a diagram showing the load torque (Torque) for each angular speed of the rotor. (a) is a diagram showing the unstable operating point for the adaptation law of the derivative of the rotor angular velocity estimate in Equation 24, and (b) is a diagram showing the unstable operating point in Equation 31. A diagram showing the unstable operating point for the adaptation law of the Jacobian matrix, (c) is a diagram showing the unstable operating point of the adaptation law for the Jacobian matrix of Equation 31 of Prior Document 2, and (d) is a diagram showing the unstable operating point of the adaptation law for the Jacobian matrix in Equation 31 of Prior Document 2. This diagram shows the unstable operating point of the observer. Here, ZSF (Zero Synchronous Frequency) is indicated by a red line, and (+) is the unstable operating point.

Referring to (a) of FIG. 4, it can be seen that the existing observer exhibits multiple unstable operating points, and referring to (b) and (c), the observer 22 using the adaptation law of Equation 31 has a gain G If is 0, the number of unstable operating points can be reduced, but it can be seen that the unstable operating points still exist in the low-speed region. And referring to (d) of FIG. 4, the derivative for estimating the angular velocity of the rotor in Equation 24 It can be seen that the unstable operating point of the observer 22 of one embodiment using is reduced in the ZSF line.

Meanwhile, the observer 22 determines the coefficient factor by adjusting the knob. A matrix derived from the discrete state estimation equation containing the gain G derived according to It may further include a state determination unit 226 that determines whether it is in a stable state based on .

The state determination unit 226 performs linearization of the induction motor control system of Equation 31 according to Lyapunov stabilization theory and determines whether the stable state condition of Equation 32 below is satisfied.

[Equation 32]

Uncertainties in stator and rotor resistance and mutual inductance can be expressed by Equations 33 to 35 below, respectively.

[Equation 33]

[Equation 34]

[Equation 35]

here, is the percentage of parameter uncertainty of the induction motor.

Here, the steady state condition in Equation 32 can be derived from the uncertainty of the state of the induction motor. Considering the boundaries of Equations 33 to 35, the Jacobian matrix is the polyhedral uncertainty set of equation 36: belongs to

[Equation 36]

where the many-sided uncertainty set The number of boundaries is determined by the uncertainty bounds of the parameters of the rotor speed estimate. For example, the boundary of the uncertainty set of a 3-body surface is 8.

Therefore, the operating point If there is a matrix P _A > 0 that satisfies the linear matrix inequality (LMI) of Equation 37 below, operating point for is in a stable state.

[Equation 37]

The linear matrix inequality in Equation 37 can be confirmed with a MATLAB program. For example, if the torque δ is high, the number of uncertainty boundaries in the polyhedral surface increases.

Figure 5 is a diagram showing the unstable operating point of various load torques δ for rotor speed. Referring to Figure 4, (a) no uncertainty, (b) δ = 0.1, (c) δ = 0.17, (d) δ = 0.18 Indicates the results of the robustness analysis based on each load torque, and + indicates the unsafe operating point.

Referring to Figure 4, it can be seen that as the uncertainty boundary of the parameter increases, the instability area of the observer increases. Referring to (d) of FIG. 4, it can be seen that many unstable operating points appear at high load torque when δ = 0.18.

As a result of the determination of the status determination unit 226, the coefficient factor of the gain G set by adjusting the knob In this stable state, the rotor angular velocity estimation unit 223 uses the knob adjusted coefficient factor. Estimation of the angular velocity of the rotor based on the gain G including Derive .

Knob Adjusted Coefficient Factor Estimation of the angular velocity of the rotor based on the gain G including and d-axis rotor flux estimation is transmitted to the IM control system (2).

That is, estimation of the angular velocity of the rotor is transmitted to the PI controller (23).

The PI controller (23) sets the rotor angular velocity setpoint PI control is performed for the torque setpoint. Derive the torque command value derived from is transmitted to the slip angular velocity deriver 24.

The slip angular velocity deriver 24 derives the torque command value Based on this, the slip speed is derived according to Equation 6, and the derived slip speed is Derive and the derived slip speed is transmitted to the adder 25.

Accordingly, the adder 25 estimates the rotor speed of the observer 22 according to Equation 26. and slip speed Estimating synchronous speed by adding Derive . Derived synchronous speed estimate is transmitted to the integrator 26.

The integrator 26 estimates the magnetic flux angle of the rotor according to Equation 26. Derive and estimate the magnetic flux angle of the derived rotor is converted to the dq axis.

Meanwhile, the torque command value derived from the PI controller (23) , estimation of the d-axis magnetic flux of the rotor derived from the observer (22) , dq-axis current of the stator of the current converter 21 , is transmitted to the torque controller 27.

The torque controller 27 is a torque controller based on model estimation, and the derived torque command value , estimation of the d-axis magnetic flux of the rotor derived from the observer (22) , dq-axis current of the stator of the current converter 21 , The dq-axis voltage of the stator as a minimization solution to the cost function derived from , Derive .

In other words, considering the dynamics of the induction motor control system of the discrete state equation Equation 7, the torque controller 27 uses a torque reference can be converted from status commands.

Stator d-axis current command , d-axis magnetic flux command of the rotor , and stator q-axis current command Each is defined by the following formulas 38 to 40.

[Equation 38]

[Equation 39]

[Equation 40]

here, is the torque command, is the maximum torque of the induction motor, ; p is the number of pole pairs of the induction motor; ; ; and Each is defined by the minimum and maximum values of the rotor flux. Using the FOC (Field oriented Control) technique, the q-axis rotor magnetic flux command is 0 and is a status command is reduced to Equation 41 below.

[Equation 41]

In other words, the model prediction-based torque controller (MPTC: Model Predictive Torque Control) is a possible state command when the induction motor is unstable, and the coefficient factor of the gain G is Quickly adjust and state command equation under steady-state conditions satisfies Equation 42 below.

[Equation 42]

is the state reference equation in the steady state is the control input of is the reduced matrix of the discrete state equation in Equation 7. Additionally, the synchronous speed estimation in Equation 26 Control input in steady state using can be derived according to Equation 43 below.

[Equation 43]

All parameters in equation 43 are nominal values. Discrete state equation x(k+1) in Equation 7 and state command equation in Equation 42 From this, the error dynamics can be derived as Equation 44 below.

[Equation 44]

here, is the control error, am.

Parameter uncertainty of induction motors is inevitable, and in order to eliminate steady-state errors, an integral term is added to the new state variable z(k) for torque control, and a new state variable z(k) for torque control is created and generated. The new state variable z(k) can be expressed as Equation 45 below.

[Equation 45]

here, is the integral term of the stator current error, am. The dynamics of the state variable z(k) for such torque control is expressed in Equation 46 below.

[Equation 46]

here, am.

Additionally, a single cost function can be derived using the gain g ₃ of the observer in Equation 15, and the single cost function can be derived from Equation 47 below.

[Equation 47]

here, am. Here, W is the specific gravity matrix.

cost function The optimal solution can be obtained according to Equation 48 below.

[Equation 48]

here, , and V _dc is the DC link voltage. The control input u(k) is designed as Equation 49 below.

[Equation 49]

Here, K , which should be designed so that the cost function decreases monotonically, is the control gain.

Accordingly, if the cost function in Equation 47 is summarized, it can be expressed as Equation 50 below.

[Equation 50]

The selection conditions for the control gain K can be derived based on the analysis results, and the difference in the cost function can be derived using Equation 51 below.

[Equation 51]

here, If , the torque controller 27 is in a stable state. The right side of equation 51 is negative definite. Therefore, in order to make the difference in the cost function negative, the matrix of the first quadratic term in Equation 51 must satisfy the conditions in Equation 52 below.

[Equation 52]

On both sides of equation 52 By multiplying, the following equation 53 can be derived.

[Equation 53]

here, am. If the convergence rate ρ of the gain G of Equations 13 to 16 derived based on the characteristic equation of Equation 12 is inserted into Equation 53 and organized, Equation 53 can be expressed as Equation 54 below.

[Equation 54]

Here, the convergence rate ρ must be optimized to the maximum, and due to the quadratic term on the left side of Equation 54, the convergence rate ρ is must be satisfied.

here, If there is a matrix P ₀ that satisfies , the linear matrix inequality in Equation 54 satisfies Equation 55 below.

[Equation 55]

If the inequality in Equation 55 is rearranged to be the same as the Linear Matrix Inequality (LMI) using Schur decomposition, Equation 56 below is derived.

[Equation 56]

Here, the operating point Let us assume that the matrix P that satisfies the linear matrix inequality in belongs to the polyhedral uncertainty set of Equation 57 below.

[Equation 57]

All matrices by linear matrix inequality If is satisfied, Equation 56 satisfies the conditions of Equation 57 below.

[Equation 56]

also, By substituting , the cost function in Equation 48 can be summarized as Equation 59 below under the constraints of Equation 52.

[Equation 59]

The solution to minimizing the cost function in Equation 59 can be derived based on the MATLAB program, and the control gain K can be determined from the matrices Po , P , and Y.

The optimal stator dq-axis voltage at which the cost function of the torque controller 27 is minimized. , is converted into a voltage vector for each phase by the power converter 28, and then the converted voltage vector for each phase is transferred to the space vector PWM 29.

The space vector PWM (29) determines the duty ratio and switching state and transmits the PWM signal of the duty ratio to the induction motor through the inverter switching of the IM driving system (1).

Therefore, the coefficient factor of the gain G determined by adjusting the knob The convergence rate of torque control is adjusted using , and the control gain K derived at this time is derived based on Equation 60 below.

[Equation 60]

In one embodiment, the state behavior of the induction motor is tracked using a continuous control element model, and according to the tracking results, the number of unstable operating points according to the load torque is determined by adjusting the knob. As the convergence rate of torque control ρ using By adjusting it, the convergence speed can be controlled without significant vibration in unstable conditions, and overshoot in transient response can be reduced.

6 shows various coefficient factors As an example diagram showing the convergence speed according to , as shown in FIG. 6, the torque convergence speed ρ of the MPTC in one embodiment is a coefficient factor. You can see that as this increases, it becomes slower. coefficient factor If this is small, Since it causes large vibrations in the steady state or causes large overshoot in transient response, the coefficient factor is set to an adjacent value of r=1e13. It can be seen that this has been decided.

FIG. 7 is an exemplary diagram showing speed control of the rotor in the regenerative mode of an induction motor of one embodiment. Referring to FIG. 7, the observer 22 of one embodiment can stably operate at 60 r/min in the regenerative mode. can confirm. Also, referring to * in FIG. 6, it can be seen that when the gain G of the observer 22 is 0, the speed estimation error of the rotor increases rapidly.

Figure 8 is an example diagram showing the speed for stable operation of an induction motor. Referring to Figure 8, it can be seen that the speed estimation error is derived in a low-speed regenerative mode, and it can be confirmed that it operates stably at multiple operating points. .

FIG. 9 is an exemplary diagram showing estimation of rotor speed, load torque, and rotor magnetic flux based on the torque controller 27 of one embodiment. As shown in (c) of FIG. 8, one embodiment has no load torque It can be seen that the minimum estimated magnetic flux is λmim=0.05W. Additionally, from 10s to 15s, the load torque increases from 0 to 5 Nm, but the minimum estimated magnetic flux is maintained at 0.05Wb because the result of I _d is smaller than I _{d_min} . When the load torque increases from 5 to 10N.m, I _d is greater than I _{d_min} , so it can be seen that it varies higher than 0.05Wb.

Figure 10 is an example diagram showing the speed estimation error between 0 rpm and 1500 rpm at no-load torque. Referring to (a) of Figure 10, it can be seen that the speed control of the induction motor is stable between 0 rpm and 1500 rpm. Referring to (b) of FIG. 10, it can be seen that the steady-state error of speed estimation is less than 50r.min, and the red line in (a) of FIG. 10 is the measured speed based on speed control of the induction motor in one embodiment. .

Figure 11 is an example diagram showing the rotor speed, load torque, and phase current based on the observer 22 of the induction motor at step loads of 5 and 10 N.m. Referring to Figure 11, with step loads of 20 s and 25 s. As a result of monitoring the rotor speed, load torque, and phase current of the induction motor, it can be seen that it operates at 200 r/min. That is, referring to (c) of FIG. 11, it can be seen that when a step-type load torque is applied, the speed decreases and converges to the command value of 200 r/min after 05 seconds.

Figure 12 is an example diagram showing the rotor speed, load torque estimate, and shift angle in a regenerative mode according to an embodiment. Referring to Figure 11, it can be seen that the rotor speed increases and quickly converges to the standard, As shown in (c), the shift angle changes depending on the slip frequency, so it can be seen that it changes when different load torques are applied. Referring to Figures 11 and 12, it can be seen that the torque control system of the induction motor of one embodiment is stable in motoring and regenerative modes at medium speed.

FIG. 13 is an exemplary diagram showing rotor speed and load torque estimates at zero speed with step loads of 5 and 10 N.m based on an induction motor of one embodiment. Referring to FIG. 13, one embodiment is a step load It can be seen that the rotor speed at zero speed is stable when applied at 20 and 25 seconds.

Figure 14 is an example diagram comparing the gain of the observer 22 in one embodiment. Referring to Figure 14, one coefficient factor It can be confirmed that the gain of one embodiment derived from force adjustment is stable even at a load torque of 5 N·m or more.

FIG. 15 is an example diagram comparing the convergence speed when the gain G = 0 of the observer 22 in one embodiment. Referring to FIG. 15, the convergence speed of speed control is improved at low speed according to the observer 22 in one embodiment. can be seen.

Accordingly, in one embodiment, one coefficient factor By adjusting 1, a stable gain G can be derived and the unstable operating point can be reduced in the low-speed region.

Although the preferred embodiments have been described and illustrated above to illustrate the technical idea of the present invention, the present invention is not limited to the configuration and operation as shown and described, and does not deviate from the scope of the technical idea. Those skilled in the art will appreciate that numerous changes and modifications can be made to the present invention without any modification. Accordingly, all such appropriate changes, modifications and equivalents shall be considered to fall within the scope of the present invention.

1: IM driving system
2: IM control system
21: current transducer
22: Horizontal measuring instrument
221: Discrete state estimation derivation unit
222: gain derivation unit
223: Rotor speed estimation unit
224: State analysis unit
225: Status adjustment unit
226: Status judgment unit
23: PI controller
24: slip speed derivation device
25: adder
26: integrator
27: Torque controller
28: Voltage converter
29: Space vector PWM

Claims (5)

In a speed sensorless torque control system for an induction motor that controls the rotor speed using a continuous control element model predictive control technique,
It includes an observer that converts the measured stator current of the induction motor into the dq axis and then derives rotor flux estimation and rotor speed estimation by inputting the converted dq stator current.
The observer,
The coefficient factor included in the gain by designing the gain for the discrete time state estimator of the induction motor By adjusting , the number of poles, which are unstable operating points of the continuous-time state estimator converted to a continuous-time model, is reduced to a predetermined number to perform stable speed estimation and corresponding torque control. Torque control system. The method of claim 1, wherein the observer:
A discrete state estimation unit that derives a discrete state estimate at each sampling time from the state equation of the induction motor;
a gain derivation unit that derives a gain in the time domain for the discrete state estimation;
A rotor speed estimation unit that derives a rotor speed estimate by applying an adaptation law to the induction motor speed derived from the characteristic equation of the induction motor and performs proportional integral control on the derived rotor speed estimate;
arbitrary operating point A state analysis unit that determines whether the proportional integrally controlled rotor speed estimation is an unstable operating point; and
Coefficient factor of the derived gain G in case of unstable operating point A speed sensorless torque control system for an induction motor, comprising a state adjustment unit that controls the convergence speed of the estimated speed and torque control for the rotor speed by adjusting . The method of claim 2, wherein the state analysis unit,
The arbitrary operating point Based on the state and speed dynamics of the induction motor, the state and rotor speed are derived, and then the state error derivative is derived,
A speed sensorless torque control system for an induction motor, characterized in that it is provided to determine an unstable operating point when the Jacobian matrix included in the derived state error derivative has an eigenvalue. The method of claim 3, wherein the state adjusting unit,
The coefficient factor of one parameter of the gain G at the unstable arbitrary operating point A speed sensorless torque control system for an induction motor, characterized in that it is provided to reduce the number of unstable poles for the estimated rotor speed by adjusting the pole to be moved to a position where the imaginary part of the gain G is not increased. The method of claim 4, wherein the observer:
Coefficient factor adjusted for each sampling time Characterized by further comprising a state determination unit for deriving a rotor speed estimate with a gain G including A speed sensorless torque control system for induction motors.