WO2009154491A1

WO2009154491A1 - A method for the estimation of the disturbances in a speed observer of an induction motor

Info

Publication number: WO2009154491A1
Application number: PCT/PL2009/000067
Authority: WO
Inventors: Zbigniew Krzeminski
Original assignee: Politechnika Gdanska
Priority date: 2008-06-18
Filing date: 2009-06-15
Publication date: 2009-12-23
Also published as: PL385465A1

Abstract

A method for the estimation of the disturbances in an observer of a speed of an induction motor consisting in measuring of components x and y of vectors of voltage and of stator current determined in Cartesian coordinate system fixed to the stator, estimating the values of the components x and y of a stator current vector and comparing with actual, measured values of the components of a stator current, estimating of the components x and y of a rotor flux vector, estimating the angular speed of the rotor is characterized according to the present invention by estimating the components x and y of the disturbances (zx, zy) in a system realizing the following relation: (I) (II) on the basis of measured components of a stator current vector (i_sx, i_sy), estimated components of a stator current vector ( i_sx, i_sy ),estimated angular speed of a rotor (ω_r),estimated components of a rotor flux vector (ψ_rx,ψ_ry ) and the value of the increment of the estimated angular speed (Δω ) in time (T_s) between two succesive measurements of components of a stator current (i_sx, i_sy).

Description

A method for the estimation of the disturbances in a speed observer of an induction motor

The subject of the invention is a method for the estimation of the disturbances in an observer of a speed of an induction motor. The invention is applicable in sensorless control systems of induction motors.

A direct measurement by means of a suitable speed sensor is a known method of acquiring a rotational speed signal of an induction motor in purpose of drive control. The inconvenience of this method lays in a long wire connection between the sensor and the inverter, which is sensitive to a mechanical damage. Additionaly measurement systems with speed sensors are sensitive to electromagnetic disturbances causing errors in signal transmission. The inconvenience of this method is also the fact, that when a rotational speed of an induction motor raises, speed sensors require additional systems to compensate the errors of quantization of measurement. The cost of the sensor may be higher than the cost of the motor.

Another known method for acquiring a rotational speed signal of an induction motor in drive system is estimation of a speed in systems called observers [Krzeminski Z. "Digital control of asynchronous machines", Politechnika Gdanska, 2001; Orlowska- Kowalska T. "Sensorless power transmission systems with induction motors", Politechnika Wroclawska, 2003]. The observers don't require long wire connections, so there are no transmission errors.

The increase of the precision in speed control is one of the users of the drive systems more often ocurring demands. Many applications require the control range of motor rotational speed starting from near zero to doubled or more value of the rated speed. Such situation creates the need to search new, better methods for estimation of a rotational speed of an induction motor.

The mathematical model of the motor is called vectorial model [Krzeminski Z. "Digital control of asynchronous machines", Politechnika Gdanska, 2001; Orlowska- Kowalska T. "Sensorless power transmission systems with induction motors", Politechnika Wroclawska, 2003]. The interdependences of state variable signals are non-linear.

From the publication Krzeminski Z. "Digital control of asynchronous machines", Politechnika Gdanska 2001, a method for transformation of the non-linear model of the motor to the linear form by replacing the products of the state variables, which are nonlinear, by z_x, Zy signals, conventionally called disturbances, is known. From the M. Adamowicz, Z. Krzeminski "Induction motor control in a wide range of angular speed of a shaft", Przeglad Elektrotechniczny, No. 12/2007, the observer of the speed and a method for estimation of a rotational speed of an induction motor ώ_r based on estimated components of a rotor flux vector ψ^, ψ^, and estimated components x and y of disturbances Z_x, z_y in a system realizing the following relation:

. ^zxΨrx + ^zyΨry

«r = — -₂ -₂

is known.

The precision in estimation of the disturbances has a clue meaning in the precision in estimation of the speed in the speed observer of of the induction motor.

From the publication Krzeminski Z. "Digital control of asynchronous machines",

Politechnika Gdanska 2001, and the patent description No. PL 187881 a method for reproduction of the components of a disturbance vector in integrators according to the following relation:

where:

Z_x, z_y - estimated components of a disturbance vector, i_x,i_y, i_x,i_y - measured and estimated components of a stator current vector, ki - gain factor is known.

The inconvenience of this method is in limited range of estimation of the rotational speed of the induction motor. The speed can be satisfactory estimated in the observer only to the value not more than rated speed because of the increase of errors in estimation of stator current and instability of the observer in higher rotational speed conditions.

Another method is known from the patent application No. PL375767 especially for high rotational speed. According to this method the disturbances are estimated using the estimated signal of a rotor flux pulsation and measured and estimated signal of stator current amplitude. However the limitation in appliance of this method to high rotational speed of the motor is its inconvenience.

From the patent application No. PL379574 yet another method for estimation of the disturbances in speed observer is known and is suitable for wide range of the estimation . According to it the pulsation of a rotor flux, which is used for the estimation of the disturbances, is estimated on the basis of filtered signal of the estimated angular speed of a rotor. The inconvenience of this method is neccesity of the estimation of an additional variable, which is the pulsation of a rotor flux and which is not regulated in drive system. Additionaly this method requires the filtration of the angular speed of a rotor, what complying with duration of the intermediate states on the level of milliseconds may cause the defect of the estimation .

A method for the estimation of the disturbances in the observer of the speed of the induction motor basing on measuring of components x and y of vectors of voltage and of stator current determined in Cartesian coordinate system fixed to the stator, estimating the values of the components x and y of a stator current vector and comparing with actual, measured values of the components of a stator current, estimating of the components x and y of a rotor flux vector, estimating the angular speed of the rotor is characterized according to the present invention by estimating the components x and y of the disturbances in a system realizing the following relation: dz_{x Λ} ? _Λ Δω , /. Ϊ \

-jp = ^⁰W + ^a6^zx - ^ωr^zy + Ψrx γ^~ + ^k6 (¹Sy ^{" 1}Sy J

dzy -> ? _* Δω . /. ? \

-^- = a₅ω_ri_sy + a₆z_y + ω_rz_x + ψ-y - — k₆ ^i_sx - i_sx J

where: i_sx, i_sy - measured components of a current vector, '_sxΛ_y " estimated components of a current vector, Ψ_rx»Ψ_ry " estimated components of a rotor flux vector, ω_r - estimated angular speed of a rotor, Δω_r - the increment of the reproducted angular speed, z_x, Zy - estimated components of disturbances vector, Ic₆ - gain factor,

T_s - time between two succesive measurements of components of a current vector _ R_rL_m _ R_r

Rr - rotor resistance,

L_r, L_m - rotor inductance and mutual inductance on the basis of measured components of a stator current vector, estimated components of a stator current vector, estimated angular speed of the rotor, estimated components of a rotor flux vector and the value of the increment of the estimated angular speed in time between two succesive measurements of components of the stator current.

The usage of the method according to the present invention enables estimation of the disturbances and the rotational speed of the induction motor practically within unlimited range of the rotational speed of the induction motor. The usage of the method according to the present invention enables estimation of every speed which can be phisically achieved by the induction motor. From the practical point of view it means that the range of a speed can vary from zero to the trippled value of rated speed. This advantage of the method according to the present invention comes out of the compliance of impact of every variables of the induction motor state on the disturbances signals courses. The usage of a method according to the present invention doesn't require the estimation of pulsation of a rotor flux, which is an additional variable and is neither regulated nor stabilized in drive system. Another advantage of a method according to the present invention is that it doesn't require the usage of filtration of the estimated rotational speed of then induction motor, that could result in a phase lag of estimated disturbances.

The invention has been explained in more details in an example of its application and in the figure schematically presenting the procedure. A method for the estimation of the disturbances in the speed observer of the induction motor consists in measuring the currents and the phase voltages of a stator, in systems equipped in analog-to-digital converters, the measured components of voltage and current stator vectors U_8x, u_sy, i_sx, i_sy are converted to digital form. The measured components of the stator current vector i_sx, i_sy and the estimated components of the rotor flux vector ψ,^ , ψ_^, and estimated components of stator current vector i_sx , i_sy obtained from the current and flux estimating element Ul and estimated rotational speed ω_r obtained from the speed estimating element U2 and the increment of the estimated angular speed Δω in time T₈ between two succesive measurements of components of the stator current vector, obtained from the speed increment measuring element T are converted in disturbances estimating element U4 according to the following relations: dz_{x Λ} ? _Λ Δω . /. ? \

-J^ = ^a5°Vsx + ^a6^zx - ^ωr^zy + Ψrx y + ^k6 (¹Sy ^{" 1}Sy J

S d^zy _Λ T ~ Δω , /. c \ -£- = *S<°τhy + ^a6^zy + ^ωr^zx + Ψry ^ ^k6 (¹Sx ^{" 1}SX J

as a result the signals of estimated components of disturbances vector z_x , z_y are received.

The estimated components of disturbances vector Z_x , z_y obtained from the estimating element U4 and estimated components of a rotor flux vector ψ,^ , ψ^ obtained from the current and flux estimating element Ul are converted in the speed estimating element U2 according to the following relation:

and the signals of estimated rotational speed of a rotor ω_r are received as a result. Estimated rotational speed of a rotor ώ_r obtained from the speed estimating element U2 is converted and compared in the speed increment measuring element T to the estimated rotational speed of a rotor ω_r obtained from the speed estimating element U2 in the moment earlier lasting T₅ that results in receiving the increment of the speed Δω . The estimated components of disturbances vector z_x , z_y obtained from the estimating element U4 and estimated components of a rotor flux vector ψ,^ , ψ^, obtained from the current and flux estimating element Ul are converted in the corrective impulse calculating element U3 according to the following relation:

^V = ^zxΨiy - ^zyΨπc that results in receiving a corrective impulse of the observer V.

The measured components of voltage and stator current vectors u_sx, u_sy, i_sx, i_sy and estimated components of disturbances vector Z_x , z_y obtained from the estimating element U4 and the calculated corrective impulse V received in the corrective impulse calculating element U3 are converted in the current and flux estimating element Ul according to the following relations:

-^- = a,ϊ_sx + a₂y_τx + a₃z_y + a₄u_sx + Ic₁ (i_sx - ϊ_sx ) + Ic₂Vy_1x - IC₃VMZ₀,

-^- = *i V + a₂ψry - a₃z_x + a₄u_sy + Ic₁ (i_sy - ϊ_sy ) + k₂ Vψ^y + Ic₃Vy_1x

-^- = a₅i_sx + a₆ψ_ra - Zy + k₄V_Ψrx - k₅ Vψ,y

dψ_jy

-^- = a₅i_sy + agψ_jy + Z_x + k₄ Vψ^ + k₅ Vψ^

As a result the estimated components of a rotor flux vector ψ^ , ψ^, and the estimated components of stator current vectors i_sx, i_sy are received, where: ki, k₂, k₃, Ic₄, k₅, Ic₆- gain factors, a_l5 a₂, a₃, a^ a₅, a₆ - factors related to the motor parameters, a₌ R_sL² _r +R_rL² _m _ R_rL_m _ L_{m =} L_r

^{1 "} w_sL_r ' ^{a2 ~} ^Λ ' ^{&3 "} ^7 ' "⁴ w_σ '

a₅ = ^-, a₆ = A , w_σ = L_sL_r -L² _m ,

R_s,R_r - stator, rotor resistance;

L_s,L_r,L_m - stator, rotor and mutual inductances.

Claims

Claim

A method for the estimation of the disturbances in an observer of a speed of an induction motor by measuring of the components x and y of vectors of voltage and of stator current determined in Cartesian coordinate system fixed to the stator, estimating the values of the components x and y of a stator current vector and comparing with actual, measured values of the components of a stator current, estimating of the components x and y of a rotor flux vector, estimating an angular speed of a rotor consisting of, on the basis of measured components of a stator current vector (i_sx, i_sy), estimated components of a stator current vector ( i_sx,i_sy), estimated angular speed of a rotor (ω_r), estimated components of a rotor flux vector (ψ_rxjψ_ry ) and the value of the increment of the estimated angular speed ( Δω ) in time (T_s) between two succesive measurements of components of a stator current (i_sx, i_sy), estimating the components x and y of the disturbances (z_x, z_y) in a system realizing the following relation: dz_{x Λ} ? _Λ Δω , /. Ϊ \

-J^- = ^a5°Vsx + ^a6^zx - ^ωr^zy + Ψrx y + ^k6 (¹Sy ^{" 1}Sy J

S d^zy _Λ 7 _Λ Δω . /. ? \

— = a₅ω_ri_sy + a₆z_y + ω_rz_x + ψ^ - — k₆ ^i_sx - I_8x J

where: i_sxj i_sy — measured components of a current vector, i_sx, i_gy - estimated components of a current vector,

Ψ_rx'Ψi_y " estimated components of a rotor flux vector, ώ_r - estimated angular speed of a rotor,

Δω_r - the increment of the estimated angular speed,

Z_x, Z_y - estimated components of disturbances vector, kβ - gain factor,

T_s - time between two succesive measurements of components of a current vector

J-._r L,_t

R_r - rotor resistance,

L_r, L_n, - rotor inductance and mutual inductance.