Control system, observer, and control method for a speed-sensorless induction motor drive

Claim 2

A control system vector-controlling an induction motor that does not comprise at least either a speed sensor or a position sensor, and is represented by a following equation,  {   t  ( φ s φ r ) = ( - R s  L sg  I R s  L m   g  I R r  L m   g  I - R r  L rg  I + ω r  J ) · ( φ s φ r ) + ( I 0 ) · v s = Ax + Bu i s = ( L sg  I - L m   g  I ) · ( φ s φ r ) = Cx where φ s =[φ sα φ sβ ] T : space vectors associated with a stator flux; φ r =[φ rα φ rβ ] T : space vectors associated with a rotor flux; i s =[i sα i sβ ] T : space vectors associated with a stator current; i r =[i rα i rβ ] T : space vectors associated with a stator voltage; L sg = 1 σ · L s = L r L s · L r - L m 2 ; L rg = 1 σ · L r = L s L s · L r - L m 2 ; L m   g = 1 σ · L m = L m L s · L r - L m 2 ; I = [ 1 0 0 1 ] ;  J = [ 0 - 1 1 0 ] ;  0 = [ 0 0 0 0 ] ; R s , R r : Stator and rotor resistance; L s , L r , L m : Stator, rotor, and mutual inductance; σ=1−L m 2 /(L s ·L r ): Total leakage coefficient; ω r : Angular rotor speed said control system comprising: an observer unit determining a feedback gain K which stabilizes an equation of estimation error of an estimated stator current e i , e i =  Ce = C  ( s   I 4 - A - K   C ) - 1  ( 0 - I )   ( - ( ω ^ r - ω r )  J   φ ^ r ) =  G 1  ( s ) · ( - Δ   ω r  J   φ r ) where values below the symbol {circumflex over ( )} are observed values; C=[L sg I−L mg I]; A = [ A 11 A 12 A 21 A 22 ] ; A 11 =−R s L sg I; A 12 =R s L mg I; A 21 =R r L mg I; A 22 =−R r L rg I+ω r J; e i : estimated stator current; s: Laplace operator; G l (s): linear transfer function; and obtaining and outputting at least either of an observed flux and an estimated speed based on the feedback gain K; and a control unit controlling the induction motor based on an output of said observer unit.

Claim 3

The control system according to claim 1 , wherein said observer unit determines a value that satisfies lim ω → 0  ∠   G l  ( jω ) = ∞ where ω is primary frequency, and ∠ is a phase angle as a feedback gain K for a transfer function G l being a linear portion of a system of the estimation error of the stator current.

Claim 4

The control system according to claim 1 , wherein said observer unit determines the feedback gain K based on a following equation k 2  C = - L r · R s R r · ω r K = ( k 2  C  J 0 ) where L r is a rotor inductance, R s is a stator resistance, R r is a rotor resistance, ω r is an angular rotor speed, and k 2c is a parameter of the feedback gain K and J = [ 0 - 1 1 0 ] ;  0 = [ 0 0 0 0 ] .

Claim 5

The control system according to claim 1 , wherein said observer unit determines the feedback gain K a magnitude of which is within a predetermined range if a rotation speed of the induction motor is equal to or higher than a preset value.

Claim 6

The control system according to claim 4 , wherein said observer unit determines the feedback gain K by using a value of an angular rotor speed ω r , which is restricted to within a predetermined range.

Claim 7

The control system according to claim 1 , wherein said control unit comprises a vector rotating unit performing vector rotation based on the output of said observer unit, and a current regulating unit outputting a current command to the induction motor based on the output of said observer unit.

Claim 8

A control system vector-controlling an induction motor that does not comprise at least either a speed sensor or a position sensor, and is represented by a following equation,  {   t  ( φ s φ r ) = ( - R s  L sg  I R s  L m   g  I R r  L m   g  I - R r  L rg  I + ω r  J ) · ( φ s φ r ) + ( I 0 ) · v s = Ax + Bu i s = ( L sg  I - L m   g  I ) · ( φ s φ r ) = Cx where φ s =[φ sα φ sβ ] T : space vectors associated with a stator flux; φ r =[φ rα φ rβ ] T : space vectors associated with a rotor flux; i s =[i sα i sβ ] T : space vectors associated with a stator current; i r =[i rα i rβ ] T : space vectors associated with a stator voltage; L sg = 1 σ · L s = L r L s · L r - L m 2 ; L rg = 1 σ · L r = L s L s · L r - L m 2 ; L m   g = 1 σ · L m = L m L s · L r - L m 2 ; I = [ 1 0 0 1 ] ;  J = [ 0 - 1 1 0 ] ;  0 = [ 0 0 0 0 ] ; R s , R r : Stator and rotor resistance; L s , L r , L m : Stator, rotor, and mutual inductance; σ=1−L m 2 /(L s ·L r ): Total leakage coefficient; ω r : Angular rotor speed, said control system comprising: observer means for determining a feedback gain K which stabilizes an equation of estimation error of an estimated stator current e i , e i =  Ce = C  ( s   I 4 - A - K   C ) - 1  ( 0 - I )   ( - ( ω ^ r - ω r )  J   φ ^ r ) =  G 1  ( s ) · ( - Δ   ω r  J   φ r ) where values below the symbol {circumflex over ( )} are observed values; C=[L sg I−L mg I]; A = [ A 11 A 12 A 21 A 22 ] ; A 11 =−R s L sg I; A 12 =R s L mg I; A 21 =R r L mg I; A 22 =−R r L rg I+ω r J; e i : stator current; s: Laplace operator; G l (s): linear transfer function; and for obtaining and outputting at least either of an observed flux and an estimated speed based on the feedback gain K; and control means for controlling the induction motor based on an output of said observer means.

Claim 9

A control system vector-controlling an induction motor that does not comprise at least either a speed sensor or a position sensor, and is represented by a following equation,  {   t  ( φ s φ r ) = ( - R s  L sg  I R s  L m   g  I R r  L m   g  I - R r  L rg  I + ω r  J ) · ( φ s φ r ) + ( I 0 ) · v s = Ax + Bu i s = ( L sg  I - L m   g  I ) · ( φ s φ r ) = Cx where φ s =[φ sα φ sβ ] T : space vectors associated with a stator flux; φ r =[φ rα φ rβ ] T : space vectors associated with a rotor flux; i s =[i sα i sβ ] T : space vectors associated with a stator current; i r =[i rα i rβ ] T : space vectors associated with a stator voltage; L sg = 1 σ · L s = L r L s · L r - L m 2 ; L rg = 1 σ · L r = L s L s · L r - L m 2 ; L m   g = 1 σ · L m = L m L s · L r - L m 2 ; I = [ 1 0 0 1 ] ;  J = [ 0 - 1 1 0 ] ;  0 = [ 0 0 0 0 ] ; R s , R r : Stator and rotor resistance; L s , L r , L m : Stator, rotor, and mutual inductance; σ=1−L m 2 /(L s ·L r ): Total leakage coefficient; ω r : Angular rotor speed, said control system comprising: observer means for determining a feedback gain K which stabilizes an equation of estimation error of an estimated stator current e i , e i =  Ce = C  ( s   I 4 - A - K   C ) - 1  ( 0 - I )   ( - ( ω ^ r - ω r )  J   φ ^ r ) =  G 1  ( s ) · ( - Δ   ω r  J   φ r ) where values below the symbol {circumflex over ( )} are observed values; C=[L sg I−L mg I]; A = [ A 11 A 12 A 21 A 22 ] ; A 11 =−R s L sg I; A 12 =R s L mg I; A 21 =R r L mg I; A 22 =−R r L rg I+ω r J; e i : stator current; s: Laplace operator; G l (s): linear transfer function; and for obtaining and outputting at least either of an observed flux and an estimated speed based on the feedback gain K; and control means for controlling the induction motor based on an output of said observer means.

Claim 10

An observer used to vector-control an induction motor that does not comprise at least either a speed sensor or a position sensor, and is represented by a following equation,  {   t  ( φ s φ r ) = ( - R s  L sg  I R s  L m   g  I R r  L m   g  I - R r  L rg  I + ω r  J ) · ( φ s φ r ) + ( I 0 ) · v s = Ax + Bu i s = ( L sg  I - L m   g  I ) · ( φ s φ r ) = Cx where φ s =[φ sα φ sβ ] T : space vectors associated with a stator flux; φ r =[φ rα φ sβ ] T : space vectors associated with a rotor flux; i s =[i sα i sβ ] T : space vectors associated with a stator current; i r =[i rα i rβ ] T : space vectors associated with a stator voltage; L sg = 1 σ · L s = L r L s · L r - L m 2 ; L rg = 1 σ · L r = L s L s · L r - L m 2 ; L m   g = 1 σ · L m = L m L s · L r - L m 2 ; I = [ 1 0 0 1 ] ;  J = [ 0 - 1 1 0 ] ;  0 = [ 0 0 0 0 ] ; R s , R r : Stator and rotor resistance; L s , L r , L m : Stator, rotor, and mutual inductance; σ=1−L m 2 /(L s ·L r ): Total leakage coefficient; ω r : Angular rotor speed, said observer comprising: a feedback gain determining unit determining a feedback gain K which stabilizes an equation of estimation error of an estimated stator current e i , e i =  Ce = C  ( s   I 4 - A - K   C ) - 1  ( 0 - I )   ( - ( ω ^ r - ω r )  J   φ ^ r ) =  G 1  ( s ) · ( - Δ   ω r  J   φ r ) where values below the symbol {circumflex over ( )} are observed values; C=[L sg I−L mg I]; A = [ A 11 A 12 A 21 A 22 ] ; A 11 =−R s L sg I; A 12 =R s L mg I; A 21 =R r L mg I; A 22 =−R r L rg I+ω r J; e i : estimated stator current; s: Laplace operator; G l (s): linear transfer function; and an outputting unit obtaining and outputting at least either of an observed flux and an estimated speed based on the feedback gain K.

Claim 11

An observer used to vector-control an induction motor that does not comprise at least either a speed sensor or a position sensor, and is represented by a following equation,  {   t  ( φ s φ r ) = ( - R s  L sg  I R s  L m   g  I R r  L m   g  I - R r  L rg  I + ω r  J ) · ( φ s φ r ) + ( I 0 ) · v s = Ax + Bu i s = ( L sg  I - L m   g  I ) · ( φ s φ r ) = Cx where φ s =[φ sα φ sβ ] T : space vectors associated with a stator flux; φ r =[φ rα φ sβ ] T : space vectors associated with a rotor flux; i s =[i sα i sβ ] T : space vectors associated with a stator current; i r =[i rα i rβ ] T : space vectors associated with a stator voltage; L sg = 1 σ · L s = L r L s · L r - L m 2 ; L rg = 1 σ · L r = L s L s · L r - L m 2 ; L m   g = 1 σ · L m = L m L s · L r - L m 2 ; I = [ 1 0 0 1 ] ;  J = [ 0 - 1 1 0 ] ;  0 = [ 0 0 0 0 ] ; R s , R r : Stator and rotor resistance; L s , L r , L m : Stator, rotor, and mutual inductance; σ=1−L m 2 /(L s ·L r ): Total leakage coefficient; ω r : Angular rotor speed, said observer comprising: a feedback gain determining unit determining a feedback gain K which stabilizes an equation of estimation error of an estimated stator current e i , e i =  Ce = C  ( s   I 4 - A - K   C ) - 1  ( 0 - I )   ( - ( ω ^ r - ω r )  J   φ ^ r ) =  G 1  ( s ) · ( - Δ   ω r  J   φ r ) where values below the symbol {circumflex over ( )} are observed values; C=[L sg I−L mg I]; A = [ A 11 A 12 A 21 A 22 ] ; A 11 =−R s L sg I; A 12 =R s L mg I; A 21 =R r L mg I; A 22 =−R r L rg I+ω r J; e i : estimated stator current; s: Laplace operator; G l (s): linear transfer function; and an outputting unit obtaining and outputting at least either of an observed flux and an estimated speed based on the feedback gain K.

Claim 12

The observer according to claim 8 , wherein said feedback gain determining unit determines the feedback gain a magnitude of which is within a predetermined range if a rotation speed of the induction motor is equal to or higher than a preset value.

Claim 13

An observer used to vector-control an induction motor that does not comprise at least either a speed sensor or a position sensor, and is represented by a following equation,  {   t  ( φ s φ r ) = ( - R s  L sg  I R s  L m   g  I R r  L m   g  I - R r  L rg  I + ω r  J ) · ( φ s φ r ) + ( I 0 ) · v s = Ax + Bu i s = ( L sg  I - L m   g  I ) · ( φ s φ r ) = Cx where φ s =[φ sα φ sβ ] T : space vectors associated with a stator flux; φ r =[φ rα φ rβ ] T : space vectors associated with a rotor flux; i s =[i sα i sβ ] T : space vectors associated with a stator current; i r =[i rα i rβ ] T : space vectors associated with a stator voltage; L sg = 1 σ · L s = L r L s · L r - L m 2 ; L rg = 1 σ · L r = L s L s · L r - L m 2 ; L m   g = 1 σ · L m = L m L s · L r - L m 2 ; I = [ 1 0 0 1 ] ;  J = [ 0 - 1 1 0 ] ;  0 = [ 0 0 0 0 ] ; R s , R r : Stator and rotor resistance; L s , L r , L m : Stator, rotor, and mutual inductance; σ=1−L m 2 /(L s ·L r ): Total leakage coefficient; ω r : Angular rotor speed, said observer comprising: feedback gain determining means for determining a feedback gain K which stabilizes an equation of estimation error of an estimated stator current e i , e i =  Ce = C  ( s   I 4 - A - K   C ) - 1  ( 0 - I )   ( - ( ω ^ r - ω r )  J   φ ^ r ) =  G 1  ( s ) · ( - Δ   ω r  J   φ r ) where values below the symbol {circumflex over ( )} are observed values; C=[L sg I−L mg I]; A = [ A 11 A 12 A 21 A 22 ] ; A 11 =−R s L sg I; A 12 =R s L mg I; A 21 =R r L mg I; A 22 =−R r L rg I+ω r J; e i : stator current; s: Laplace operator; G l (s): linear transfer function; and outputting means for obtaining and outputting at least either of an observed flux and an estimated speed based on the feedback gain K.

Claim 14

An observer used to vector-control an induction motor that does not comprise at least either a speed sensor or a position sensor, and is represented by a following equation,  {   t  ( φ s φ r ) = ( - R s  L sg  I R s  L m   g  I R r  L m   g  I - R r  L rg  I + ω r  J ) · ( φ s φ r ) + ( I 0 ) · v s = Ax + Bu i s = ( L sg  I - L m   g  I ) · ( φ s φ r ) = Cx where φ s =[φ sα φ sβ ] T : space vectors associated with a stator flux; φ r =[φ rα φ rβ ] T : space vectors associated with a rotor flux; i s =[i sα i sβ ] T : space vectors associated with a stator current; i r =[i rα i rβ ] T : space vectors associated with a stator voltage; L sg = 1 σ · L s = L r L s · L r - L m 2 ; L rg = 1 σ · L r = L s L s · L r - L m 2 ; L m   g = 1 σ · L m = L m L s · L r - L m 2 ; I = [ 1 0 0 1 ] ;  J = [ 0 - 1 1 0 ] ;  0 = [ 0 0 0 0 ] ; R s , R r : Stator and rotor resistance; L s , L r , L m : Stator, rotor, and mutual inductance; σ=1−L m 2 /(L s ·L r ): Total leakage coefficient; ω r : Angular rotor speed, said observer comprising: feedback gain determining means for determining a feedback gain K which stabilizes an equation of estimation error of an estimated stator current e i , e i =  Ce = C  ( s   I 4 - A - K   C ) - 1  ( 0 - I )   ( - ( ω ^ r - ω r )  J   φ ^ r ) =  G 1  ( s ) · ( - Δ   ω r  J   φ r ) where values below the symbol {circumflex over ( )} are observed values; C=[L sg I−L mg I]; A = [ A 11 A 12 A 21 A 22 ] ; A 11 =−R s L sg I; A 12 =R s L mg I; A 21 =R r L mg I; A 22 =−R r L rg I+ω r J; e i : stator current; s: Laplace operator; G l (s): linear transfer function; and outputting means for obtaining and outputting at least either of an observed flux and an estimated speed based on the feedback gain K.

Claim 17

The method according to claim 11 , wherein the feedback gain a magnitude of which is within a predetermined range if a rotation speed of the induction motor is equal to or higher than a preset value.