WO2006000901A2

WO2006000901A2 - Method and device for sensorless control of position and speed of a reluctance synchronous motor

Info

Publication number: WO2006000901A2
Application number: PCT/IB2005/001843
Authority: WO
Inventors: Roberto Berto
Original assignee: Earp S.P.A.
Priority date: 2004-06-29
Filing date: 2005-06-29
Publication date: 2006-01-05
Also published as: ITVI20040156A1; WO2006000901A3

Abstract

A method for controlling the position and speed of a synchronous reluctance motor (M) having a stator and a rotor, which method provides the steps of: measuring the supply voltage (Vdc, Vα, Vβ) and current (Iu, Iv, iα, iβ, id, iq) to the motor (M); estimating the magnetic flux (λd' , λq') of the motor (M) by using a mathematical model of the magnetic behavior of the motor (M); combining the estimated magnetic flux (λd' , λq') and an ideal magnetic flux, obtained by integrating in time the supply voltage (Vα, Vβ) decreased by the resistive losses in the stator, to obtain an observed magnetic flux (λd', λq') ; calculating as first error signal (eHS) from an estimation (θ') of the angular position of the rotor and from an angular position feedback value (θ) ; introducing a high frequency flux component and calculating a second error signal (eLS) by determining the difference (Δλq) between the observed flux (λd', λq') and the estimated flux (λd', λq'); introducing a combination of the error signals (eHS, eLS) in a controller (8) having a pair of integrators, to determine the angular position (θ) of the rotor and ensure a regular behavior aver the full range of rotation speeds (ω) of the rotor; using the angular position (θ) as determined to the previous step to control the motor (M).

Description

METHOD AND DEVICE FOR SENSORLESS CONTROL OF POSITION AND SPEED OF A RELUCTANCE SYNCHRONOUS MOTOR

Field of the Invention

This invention is generally directed to the field of electric drives and particularly relates to a method and an apparatus for controlling the position and speed of a synchronous reluctance motor.

Background art

A number of methods are known for sensorless position or speed control of various motors, and particularly for synchronous reluctance motors.

More in detail, certain methods of sensorless control of synchronous reluctance motors are known to determine the angular position of the rotor to perform their control operations. Infact, by means of trigonometric relations, the angular position of the rotor may be determined from the observed magnetic flux in a stator fixed reference system, and from the estimated magnetic flux in a moving reference system solid with the rotor. The flux estimation method requires the knowledge of a magnetic model of the motor. The flux observation method requires the knowledge of the magnetic flux estimated by using the magnetic model of the motor and is based on the combination thereof with an ideal flux obtained by integration of the supply voltage decreased by resistive losses. Furthermore, the determination of the estimated flux and the observed flux also requires the knowledge of the angular position of the rotor, as the relationship between the magnetic flux and the current is defined in the moving coordinate system.

An apparent drawback of this solution is the unsatisfactory behavior and poor accuracy that may be obtained at low speeds and in steady-state conditions. Furthermore, particular adaptation processes are required when starting.

A further known method for sensorless control of a synchronous reluctance method provides the use of the above method at rotor speeds above a predetermined value, and addition of a closed loop control algorithm to improve low-speed performances. Particularly, a high frequency signal, at about 800 Hz, is added along a rotor rotating direction. The flux observation method as described above provides the observed value λ", whereas the magnetic model of the motor provides the estimated value λ' . The difference Δλ between the high frequency components of λ' and λ" along a rotating direction orthogonal to the high frequency signal introduction direction, is proved to represent the error between the estimated and actual positions. Therefore, the difference Δλ, after being suitably demodulated to obtain an error-proportional signal, is introduced as a feedback in a position observer that updates the estimated position.

Thus, the process for determining the rotation angle of the rotor provides the use of both the high frequency signal and the flux observation method as described above. Particularly, the latter acts as a feedforward contribution, and is added to the action of the feedback loop downstream from the PI controller, to remove the position error.

An apparent drawback of this solution is that the shift from high speed to low speed operation causes perturbations in rotor motion, particularly during deceleration. This drawback is particularly felt in industrial applications, which generally have a wide speed range with any speed change causing perturbations in processing operations.

Summary of the invention

A primary object of this invention is to obviate the above drawbacks, by providing a control method and a control apparatus that are cost-effective to such an extent as to allow extensive circulation thereof in the market.

A particular object is to provide a control method and a control apparatus that allow regular operation even in the transition from high speed operation to low speed operation.

Another object is to provide a control method and apparatus that can assure a relatively high torque availability, both at high rotation speeds, low rotation speeds and intermediate speeds.

A further object of the invention is to provide a control method and apparatus that assure a high positioning accuracy over the full operating range. Another particular object is to provide a control method and apparatus that are reliable, and have a high noise rejection capability.

These objects, as well as other objects that will be more apparent hereafter, are fulfilled, according to claim 1, by a method for controlling the position and speed of a synchronous reluctance motor having a stator and a rotor, wherein the method provides the steps of: a) measuring the DC voltage of the inverter and the supply current to the motor; b) providing a mathematical model of the magnetic behavior of the motor to estimate the magnetic flux of the motor from the supply currents thereto; c) estimating the magnetic flux of the motor by using the magnetic model; d) calculating an ideal magnetic flux by integrating in time the supply voltage decreased by the resistive losses in the stator; e) combining the ideal magnetic flux and the estimated magnetic flux to obtain an observed magnetic flux; f) calculating a first error signal from an estimation of the angular position of the rotor and from an angular position feedback value; g) introducing a high frequency flux component and calculating a second error signal by determining the difference between the observed flux and the estimated flux; h) combining the first and the second error signals as a function of the rotation speed of the rotor to obtain a single error signal; i) introducing the single error signal in a controller having a pair of integrators, to determine the angular position of the rotor and ensure a regular behavior over the full range of rotation speeds of the rotor; 1) using the angular position as determined in step i) to control the motor without using position and speed sensors.

Thanks to this particular configuration, the motion of the rotor may be controlled in an accurate and regular manner, over a wide range of rotation speeds.

Brief Description of the Drawings

Further characteristics and advantages of the invention will be more apparent from the detailed description of a few preferred, non-exclusive embodiments of a method and an apparatus according to the invention, which are described as non-limiting examples with the help of the annexed drawings, in which: FIG. 1 is a schematic view of a method according to the invention; FIG. 2 is a schematic view of certain steps of the method of FIG. 1; FIG. 3 shows the coordinate systems used in the method of FIG. 1; FIGURES 4 to 10 are schematic views of certain steps of the method of FIG. 1.

Detailed description of a preferred embodiment

Particularly referring to the above figures, a method and an apparatus according to the invention are described, which apparatus is collectively designated with numeral 1, for controlling the position and speed of a synchronous reluctance motor M. Particularly, the motor M may be of the type that comprises a stator, a rotor and a power circuit (not shown in the annexed drawings) . Suitably, the power circuit may comprise an inverter I with IGBT switches to power the motor M with a voltage having an appropriate duty cycle.

More in detail, the method provides the following steps.

In a first step a) the supply voltage Vdc_r V_α, Vp and current I₁₁, I_v, i_α, ip, i_d, i_q to the motor M are directly or indirectly measured. Particularly, the DC voltage V_dc of the inverter and the supply currents to the motor I_u and I_v are measured directly, whereas the other voltages V_α, Vp and the other currents i_α, ip, id, i_q are determined as described hereafter.

Current values I_u and I_v are measured in the three-phase power system of the motor and may be then expressed as i_α and ip in a two-phase stator coordinate system by the Clark transform 2, which is schematically shown in FIG. 4, and may be synthesized by the following general expressions: Y_α = X_u and Yp = X_u/3^1/2 + X_v 2/3^1/2 , where X_u, X_v represent the input and Y_α, Yp represent the output.

The measurement of DC voltage V_dc, as well as the knowledge of the duty cycle of the inverter I allow to determine the components V_α and Vp of the supply voltage to the motor M in the fixed coordinate system. The voltages V_α e Vp may be also determined by using the Clark transform 2.

Then, currents i_α and ip, as expressed in the fixed coordinate system, are transformed into a rotor moving coordinate system, and expressed by the components i_d and i_q. The components i_d and i_q may be determined from i_α and i_β by using the Park transform 3, which is shown in FIG.5 and may be synthesized by the following general expressions: Y_d = X_α cos (θ) + Xβ sin(θ) and Y_q = -X_α sin(θ) + X_β cos (θ) . This transform 3 uses a feedback value of the θ position angle of the rotor with respect to the stator, to be determined in a later step i) .

In a second step b) , a mathematical model is provided for the magnetic behavior of the motor M, to estimate the magnetic flux λ_d' and λ_q' of the motor from the supply currents i_d and i_q thereto. More in detail, the magnetic model may be of various types, either a linear or nonlinear model, and will be preferably expressed by nonlinear functions λ_d' (i_d, i_q) and λ_q' (i_d, i_q) of current components i_d, i_q and of the rotation angle θ of the rotor. Once again, the calculation is performed by using a feedback value of the angle θ, which is determined in a later step i) .

In a third step c) , the magnetic flux λ_d' and λ_q' of the motor M is estimated by using the magnetic model. Particularly, as shown in FIG. 8, such calculation may be performed in a suitable flux estimator 4, by using a look up table, in which each pair of values i_d and i_q is associated to a pair of flux values λ_d' and λ_q' in the moving coordinate system. Then, the estimated flux λ_d' , λ_q' in the moving coordinate system may be expressed by the components λ_α' and λp' in the fixed coordinate system, by using an inverse Park transform 3' .

In a fourth step d) , an ideal magnetic flux is determined, which is obtained by integrating in time the supply voltage V_α and Vp decreased by the resistive losses in the stator. A fifth step e) provides the combination of the ideal magnetic flux and the estimated magnetic flux λ_α' and λp' to obtain an observed magnetic flux λ_α" and λp". Step d) and step e) may be carried out together by a single flux observer 5, as shown in FIG. 6.

As shown in FIGS. 2 and 7, in the next step f) , a first error signal e_Hs is determined from an estimation θ' of the angular position of the rotor and from an angular position feedback value θ to be determined in a later step i) . The estimated angul'ar position value θ' may be obtained by using appropriate trigonometric relations from the observed flux λ_α", λp" in the fixed coordinate system and by the estimated flux λ_d' , λ_q' in the rotor moving coordinate system. Referring to FIG. 3, if the magnetic flux has an absolute value λ, its components in the fixed coordinate system may be expressed by λ_α = λcos (θ+δ) , λp = λsin(θ+δ), whereas the components in the moving coordinate system may be expressed by λ_d = λcos (δ) and λ_q = λsin(δ) . The following expressions result therefrom: cos (θ) = cos ( (θ+δ) -δ) = cos (θ+δ) cos (δ) +sin (θ+δ) sin (δ) , as well as sin(θ) = sin ( (θ+δ) -δ) = sin (θ+δ) cos (δ) -cos (θ+δ) sin (δ) . By using in these expressions the calculated flux values and vector notation with con λ_dq' = [λ_d' λ_q' ] e λ_αβ" = [λ_α" λp"], the following expressions are obtained: cos(θ') = (λ_dq' x λ_αβ")/λ² and sin(θ') = (λ_dq' Λ λ_αβ")/λ².

Once the cos (θ' ) and sin(θ') values have been estimated, the first error signal e_Hs may be determined by suitably filtering, by a low-pass filter, the difference Δθ between the value θ obtained by a feedback branch and the estimated value θ' as schematically shown in FIG. 7. Furthermore, the difference Δθ may be calculated by the following trigomonetric expression: Δθ = θ - θ' « sin(θ - θ' ) = =sin(θ)cos (θ' ) - cos (θ)sin(θ' ) . The feedback value θ may be derived from a feedback branch which receives the angular position θ of the rotor, as determined in a later step i) .

In the same manner as described above, the observed flux λ_α ^λX, λ_β" may be also converted from the fixed coordinate system to the moving coordinate system by using the Park transform as shown in FIG. 5, and be thus expressed by the components λ_d", λ_q".

In a step g) a high frequency flux component is introduced and a second error signal e_Ls is calculated, as shown in FIG. 9, by determining the difference Δλ between the observed flux λ_d", λ_q" and the estimated flux λ_d' , λ_q' and by demodulating the high frequency component in the difference Δλ. More in detail, the high frequency flux component may be introduced along a first coordinate axis d of the rotor moving coordinate system, whereas the difference between the observed flux Xd.", λ_q" and the estimated flux Xd.' , Xq may be only determined between the respective components λ_q" and λ_q' along a second coordinate axis q of the moving coordinate system. Particularly, the coordinate axes d, q may be substantially in quadrature and the d axis may be disposed along the minimum reluctance direction of the rotor Hence, the difference Δλ_q is obtained, which is proportional to [sin2 (θ - θ')]/2.

Advantageously, the high frequency component introduced in the flux may have a frequency of 300 Hz to 800 Hz and preferably of 400 Hz. The use of a relatively low frequency, such as 400 Hz, allows to limit the inductance values in the power circuit of the motor M and, as a result, to reduce voltage drops. This particular arrangement further provides a motor M with a higher torque availability and a higher capability to address sudden changes of the mechanical load thereon, even at intermediate rotation speeds ω of the rotor.

As shown in FIG. 9, the calculation of the second error signal e_LS may sequentially involve filtering of the difference Δλ_q by a high-pass filter, demodulation of the high frequency component by using a heterodyne demodulator 6, and further filtering by a low-pass filter.

In a next step h) the first and second error signals e_Hs, e_LS are combined in a suitable mixer 7, to obtain a single error signal e₀. As shown in FIG.10, the two error signals e_ΑSr e_LS may be combined by multiplying each error e_Hs, e_LS by a corresponding multiplication coefficient k_Hsfi (^ω) r k_Lsf₂ (ω) . The latter may be composed of respective constant coefficients k_Hs, k_LS and respective coefficients fi(ω), f2(ω) variable as a function of the rotation speeds ω of the rotor. The variable coefficients fi(ω), f₂ (ω) may increase the first error signal e_Hs with respect to the second error signal e_LΞ for relatively high rotation speeds ω and increase the second error signal e_LS with respect to the first error signal e_Hs for relatively low speeds, near zero.

The rotation speed co of the rotor, which is used to determine the variable coefficients fi(ω), f₂ (ω) is determined from the observed flux λ_α", λp" in the fixed coordinate system and from the estimated flux λ_d' , λ_q' in the moving coordinate system. In more detail, in the same manner as described above and shown in FIG. 7, the difference Δθ is determined, and later filtered to obtain the rotation speed ω of the rotor.

In a next step i) a single error signal e_α is introduced in a controller 8, as shown in FIG. 10, which has a pair of integrators. This the angular position θ of the rotor is obtained at the output of the controller 8, and is used as a feedback signal in all the previous steps when the angular position value θ is required. The position feedback value θ allows to form a closed loop, which may be repeatedly executed with a predetermined cycle frequency. Particularly, at each repeated cycle, the calculations in the steps a) to i) may be performed by using the value θ obtained at the end of step i) of the previous cycle.

The feature of combining the first and second error signals e_Hs_/ e_LS upstream from a double integration provides a regular behavior over the full range of rotation speeds ω of the rotor.

Conveniently, the controller 8 may include a proportional and integral (PI) control block, which is connected in series with an integrator, as shown in FIG. 10.

Finally, in a last step 1) of the control method, the angular position θ determined in step i) is used, in a manner known per se, to control the motor without the assistance of position and speed sensors.

Conveniently, the IGBT switches may be controlled at a switching freguency of 3 KHz to 8 KHz, and preferably of 4 KHz.

The above control method may be implemented by using an apparatus 1 for controlling the position and speed of a synchronous reluctance motor M.

One feature of the apparatus 1 consists in that it comprises at least one control unit (not shown in the accompanying drawings) , for carrying out all the steps a to 1) of the above method. Particularly, the control unit may be a fixed-point unit and comprise a single microcontroller to carry out all the steps a) to 1) . Thus a cost-effective control unit may be obtained, which has a relatively low manufacturing cost. In certain preferred embodiments, the control unit may comprise a DSP.

The above disclosure clearly shows that the inventive method and apparatus fulfill the proposed objects and particularly the method allows a stable and regular sensorless control of a synchronous reluctance motor and the apparatus allows to reduce manufacturing costs.

The method and apparatus of this invention are susceptible to a number of changes or variants, within the inventive concept disclosed in the annexed claims. All the details thereof may be replaced by other technically equivalent parts, and the materials may vary depending on different needs, without departure from the scope of the invention.

While the method and apparatus have been described with particular reference to the accompanying figures, the numerals referred to in the disclosure and claims are only used for the sake of a better intelligibility of the invention and shall not be intended to limit the claimed scope in any manner.

Claims

1. A method for controlling the position and speed of a synchronous reluctance motor (M) having a stator and a rotor, which method provides the follow steps: a) measuring the supply voltage (Vd_C, V_α, Vp) and current (I_u, I_v, i_α, ip, i_d, i_q) to the motor (M) ; b) providing a mathematical model for the magnetic behavior of the motor (M) , to estimate the magnetic flux (λ_d' , λ_q' , λ_α' , λp' ) of the motor (M) from the supply currents (id, iq) thereto; c) estimating the magnetic flux (λd' , λ_q' ) of the motor (M) by using said magnetic model; d) determining an ideal magnetic flux, by integrating in time said supply voltage (V_α, Vp) decreased by the resistive losses in the stator; e) combining said ideal magnetic flux and the estimated magnetic flux (λ_d' , λ_q' , λ_</ , λp' ) to obtain an observed magnetic flux (λ_α", λp", λ_d", λ_q") ; f) calculating a first error signal (e_Hs) from an estimation (θ' ) of the angular position of the rotor and from an angular position feedback value (θ) ; g) introducing a high frequency flux component and calculating a second error signal (e_LS) by determining the difference (Δλ, Δλ_q) between said observed flux (λ_α", λp", λ_d", λ_q") and said estimated flux (λd' , λ_q' , λ_α' , λp' ) and by demodulating the high frequency component induced in said observed and estimated fluxes; h) combining said first and the second error signals (e_Hs, e_LS) as a function of the rotation speed (ω) of the rotor to obtain a single error signal (e_D); i) introducing said single error signal (e₀) in a controller (8) having a pair of integrators, to determine the angular position (θ) of the rotor and ensure a regular behavior over the full range of rotation speeds (ω) of the rotor; 1) using the angular position (θ) as determined in said step i) to control the motor (M) without using position and speed sensors.

2. Method as claimed in claim 1, characterized in that said estimation of the angular position ( (θ' ) to determine said first error signal (e_Hs) is performed by using appropriate trigonometric relations, from said observed flux (λ_α", λ_β", λ_d", λ_q") in said fixed coordinate system and from said estimated flux (λ_d' , λ_q' , λ_α' , λp' ) in a rotor moving coordinate system, said feedback value being derived from a feedback branch, which receives the angular position (θ) of the rotor as determined in step i) .

3. Method as claimed in claim 2, characterized in that the introduction • of a high frequency flux component in said step g) occurs along a first coordinate axis (d) of a rotor moving coordinate system.

4. Method as claimed in claim 3, characterized in that said difference (Δλ_q) between said observed flux (λ_q") and said estimated flux (λ_q' ) to obtain said second error signal (e_Ls) is determined between the components of said fluxes along a second coordinate axis (q) of said moving coordinate system, which is in quadrature with the first coordinate axis (d) .

5. Method as claimed in claim 1, characterized in that said high frequency component introduced in the flux has a frequency of 300 Hz to 800 Hz and preferably of 400 Hz.

6. Method as claimed in claim 1, characterized in that said supply voltage (V_α, Vp) is generated by an inverter (I) with IGBT switches to obtain an appropriate duty cycle.

7. Method as claimed in claim 6, characterized in that said switches are controlled at a switching frequency of 3 KHz to 8 KHz, and preferably of 4 KHz.

8. Method as claimed in any of the preceding claims, characterized in that said controller (8) having a pair of integrators comprises a proportional and integral (PI) block, which is connected in series with an integrator.

9. Method as claimed in any of the preceding claims, characterized in that said step c) of estimation of the magnetic flux (λ_d' , λ_q' , λ_α' , λp' ) involves the conversion of said supply current from the fixed coordinate system (i_α, ip) to the moving coordinate system (i_d, i_q) by using the Park transform.

10. Method as claimed in claim 9, characterized in that said step c) of estimation of the magnetic flux (λ_d' , λ_q' , λ_</ , λp' ) involves the determination of said flux in the moving coordinate system (λ_d' , λ_q' ) from the magnetic model of the motor (M) and from said current (i_d, i_q) in the moving coordinate system.

11. Method as claimed in claim 10, characterized in that said step c) of estimation of the magnetic flux (λ_d' , λ_q' , λ_α' , λp' ) involves the conversion of said estimated flux from the moving coordinate system (λ_d' , λ_q' ) to the fixed coordinate system (λ_α' , λ_β' ) by using the inverse Park transform.

12. Method as claimed in claim 11 characterized in that said magnetic model is nonlinear.

13. Method as claimed in any of the preceding claims, characterized in that said combination step h) involves the multiplication of each of said first and second error signals (e_Hs, e_Ls) by a respective variable coefficient (fi(ω), f2(ω)) as a function of the rotation speed (ω) of the rotor.

14. Method as claimed in claim 13, characterized in that said variable coefficients (fχ(ω), £₂(0)) increase said first error signal (e_Hs) with respect to the second error signal (e_Ls) for relatively high rotation speeds and increase said second error signal (e_Ls) with respect to said first error signal (e_Hs) for relatively low speeds, near zero.

15. Method as claimed in claim 13, characterized in that the rotation speed (ω) of the rotor, which is used in said step h) is determined from said observed flux (λ_α", λ_β") in the fixed coordinate system and from said estimated flux in the moving coordinate system (λ_d' , λ_q' ) .

16. Method as claimed in any of the preceding claims, characterized in that said step g) of determination of a second error signal (e_LS) involves the conversion of said observed flux from the fixed coordinate system (λ_α", λp") to the moving coordinate system (λ_d", λ_q") by using the Park transform.

17. An apparatus for control of position and speed of a synchronous reluctance motor (M) , for carrying out a method according to one or more of the preceding claims, characterized in that it comprises at least one control unit for carrying out all of said steps a) to 1) •

18. Apparatus as claimed in claim 17, characterized in that said control unit comprises a single microcontroller for carrying out all of said steps a) to 1) .

19. Apparatus as claimed in claim 17 characterized said control unit comprises a DSP.

20. Apparatus as claimed in claim 17 characterized said control unit is a fixed-point unit.