CN107482978A - A kind of permagnetic synchronous motor on-line parameter discrimination method based on finite time algorithm - Google Patents

A kind of permagnetic synchronous motor on-line parameter discrimination method based on finite time algorithm Download PDF

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CN107482978A
CN107482978A CN201710720891.1A CN201710720891A CN107482978A CN 107482978 A CN107482978 A CN 107482978A CN 201710720891 A CN201710720891 A CN 201710720891A CN 107482978 A CN107482978 A CN 107482978A
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mrow
mtd
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CN107482978B (en
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沈传文
邱东
唐千龙
杨文�
张立宇
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Xian Jiaotong University
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Xian Jiaotong University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/16—Estimation of constants, e.g. the rotor time constant
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • H02P25/024—Synchronous motors controlled by supply frequency
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/07—Doubly fed machines receiving two supplies both on the stator only wherein the power supply is fed to different sets of stator windings or to rotor and stator windings
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2209/00—Indexing scheme relating to controlling arrangements characterised by the waveform of the supplied voltage or current
    • H02P2209/11—Sinusoidal waveform

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Control Of Ac Motors In General (AREA)
  • Other Investigation Or Analysis Of Materials By Electrical Means (AREA)

Abstract

To realize the on-line identification of the parameters such as the stator resistance of permagnetic synchronous motor, inductance and rotor flux, the invention discloses a kind of permagnetic synchronous motor on-line parameter discrimination method based on finite time algorithm, parameter identification equation group full rank is made by d shaft current injection methods, the multi-parameter on-line identification of permagnetic synchronous motor is realized by finite time Identification of parameter；Permagnetic synchronous motor on-line parameter discrimination method can be not only used for IPM synchronous motor designed by the present invention, can be used for durface mounted permanent magnet synchronous motor again；The present invention can realize the on-line parameter identification of permagnetic synchronous motor in finite time, and the identification time is unrelated with sample frequency, therefore can be reached under relatively low sample frequency with less interative computation amount and same identification effect when higher sample frequency and more interative computation amount.

Description

A kind of permagnetic synchronous motor on-line parameter discrimination method based on finite time algorithm
Technical field
The invention belongs to motor control technology field, and in particular to a kind of permagnetic synchronous motor based on finite time algorithm On-line parameter discrimination method.
Background technology
Permagnetic synchronous motor (PMSM) is because with spies such as small volume, simple in construction, efficiency high, high power/torque densities Put and obtained more and more extensive application.And because in the control system of permagnetic synchronous motor, the parameter of controller is often Need the parameter of electric machine to carry out Computer Aided Design (such as senseless control, vector controlled optimal controller parameter designing), therefore control The quality of performance processed is somewhat dependent upon the order of accuarcy of the parameter of electric machine.But the stator resistance of permagnetic synchronous motor, The parameters such as stator inductance, rotor flux amplitude can produce change with temperature, load and the change of magnetic saturation degree, if Controller is designed according to motor nominal parameters under different running statuses, then it is difficult to ensure that the control performance of motor.Therefore, be According to the change on-line tuning controller parameter of the parameter of electric machine, optimization motor control performance, motor in motor normal course of operation On-line parameter discrimination method be studied much.
The content of the invention
Parameter, the purpose of the present invention such as stator resistance, inductance and rotor flux for on-line identification permagnetic synchronous motor exist In a kind of permagnetic synchronous motor on-line parameter discrimination method based on finite time algorithm of proposition.
To reach above-mentioned purpose, the technical solution adopted in the present invention is：
A kind of permagnetic synchronous motor on-line parameter discrimination method based on finite time algorithm, passes through d shaft current injection methods Make parameter identification equation group full rank, the multi-parameter for realizing permagnetic synchronous motor by finite time Identification of parameter is distinguished online Know；Specific method comprises the following steps：
Step 1：Permagnetic synchronous motor is made to be operated in idUnder the conditions of=0 vector controlled
Voltage equation of the permagnetic synchronous motor under d-q axis coordinate systems be：
U in formulad、uqRespectively d, q axis component of stator voltage；id、iqRespectively d, q axis component of stator current；R is Stator resistance；Ld、LqRespectively d, q axle stator inductance；ωeFor angular rate；ψfFor rotor flux amplitude；
The uneoupled control of excitation and torque can be realized using vector control method, there is permagnetic synchronous motor similar straight Flow the control performance of motor；Using id=0 control strategy, for durface mounted permanent magnet synchronous motor, maximum turn can be realized Square electric current reduces the loss of electric machine than control；For IPM synchronous motor, although effectively can not be turned using its magnetic resistance Square, be but advantageous to realize parameter identification by d shaft current injection methods；
Step 2：Voltage equation exponent number is increased by d shaft currents injection method
From formula (1), permagnetic synchronous motor voltage equation has two, and parameter to be identified has four, and equation group is not Full rank, it can not directly pick out all parameters；Therefore equation is increased using d shaft currents injection method (sinusoidal current or step current) Exponent number, to avoid parameter to be identified from converging to locally optimal solution；Sampled using permagnetic synchronous motor after d shaft current injection methods Moment k1And k2Voltage equation be expressed as
In formula, k when using sinusoidal current injection method1And k2During the difference being illustrated respectively in after d axles injection sinusoidal current Carve；K when using step current injection method1And k2The a certain moment after preflood a certain moment and injection is represented respectively；
If motor is durface mounted permanent magnet synchronous motor, stator inductance meets Ld=Lq=Ls, parameter to be identified is changed into three Individual, equation (2) is then changed into
Using equation (2) or equation (3), pass through the d-q shaft voltages in sample motor running, d-q shaft currents and electricity Machine rotating speed, it becomes possible to realize the multi-parameter of permagnetic synchronous motor while recognize.
Step 3：Permagnetic synchronous motor parameter is recognized using finite time Identification of parameter
It is y, coefficient matrix Γ to the output vector as shown in formula (4)T, systematic parameter is θ system, is designed with Between in limited time shown in Identification of parameter such as formula (5)
Y=ΓTθ (4)
In formula (4), yT=[ud(k1)uq(k1)ud(k2)uq(k2)], when motor is IPM synchronous motor,
When motor is durface mounted permanent magnet synchronous motor,
In formula (5),And | |γRepresent to make scalar fortune to each component of vector with sign () Calculate, γ ∈ [0,1)；K is symmetric positive definite square formation；TsFor sampling time interval；WithRespectively the kth -1 of parameter θ and Kth time identification result, Γ (k) T and y (k) are respectively the coefficient matrix Γ T and output vector y obtained by kth group sampled result；
(because inverter output voltage is pwm voltage, adopted using the electric moter voltage, electric current and rotary speed data of sampling Sample is more difficult, can export given voltage approximation real electrical machinery voltage with controller), calculated by such as formula (5), it becomes possible to realize permanent magnetism The on-line identification of parameter of synchronous machine.
The present invention has the special feature that as follows：
1) permagnetic synchronous motor on-line parameter discrimination method designed by the present invention can be not only used for IPM synchronous motor, It can be used for durface mounted permanent magnet synchronous motor again.
2) present invention can realize the on-line parameter identification of permagnetic synchronous motor in finite time, and recognize time and sampling Frequency is unrelated, therefore can be reached under relatively low sample frequency with less interative computation amount and higher sample frequency and more iteration Same identification effect during operand.
Brief description of the drawings
Fig. 1 is permagnetic synchronous motor on-line parameter identification system structure chart under vector controlled.
Fig. 2 is permagnetic synchronous motor on-line parameter identification program flow chart, wherein：Fig. 2 a are parameter when step current injects Flow chart is recognized, Fig. 2 b are parameter identification flow chart when sinusoidal current injects.
Fig. 3 is permagnetic synchronous motor parameter identification simulation result (sample frequency when step current injects：500Hz), wherein： Fig. 3 a are Stator resistance identification result, and Fig. 3 b are d axle inductance identification results, and Fig. 3 c are q axle inductance identification results, and Fig. 3 d are rotor Magnetic linkage identification result.
Fig. 4 is permagnetic synchronous motor parameter identification simulation result (sample frequency when step current injects：250Hz), wherein： Fig. 4 a are Stator resistance identification result, and Fig. 4 b are d axle inductance identification results, and Fig. 4 c are q axle inductance identification results, and Fig. 4 d are rotor Magnetic linkage identification result.
Fig. 5 is permagnetic synchronous motor parameter identification simulation result (sample frequency when sinusoidal current injects：500Hz), wherein： Fig. 5 a are Stator resistance identification result, and Fig. 5 b are d axle inductance identification results, and Fig. 5 c are q axle inductance identification results, and Fig. 5 d are rotor Magnetic linkage identification result.
Embodiment
The present invention is described in further detail with reference to the accompanying drawings and detailed description.
Being discussed in detail to the permagnetic synchronous motor on-line parameter discrimination method based on finite time algorithm more than, with Under illustrate the tool of the present invention so that the IPM synchronous motor as shown in table 1 to a parameter carries out on-line parameter identification as an example Body embodiment.
The emulation of table 1 uses permagnetic synchronous motor parameter
Parameter Numerical value
Number of pole-pairs 4
Stator resistance 2.35Ω
D axle inductances 10.0mH
Q axle inductances 13.4mH
Rotor flux 0.13Wb
Permagnetic synchronous motor vector is built in MATLAB/SIMULINK simulation softwares according to system shown in Figure 1 structure chart Control and on-line parameter identification and simulation model, when using step current injection method, injected according to the step current shown in Fig. 2 a When parameter identification Flow Chart Design simulation process：
Permagnetic synchronous motor is set to work in i firstdUnder conditions of=0, sample and preserve the d-q shaft voltages of motor, d-q axles The data such as electric current and angular speed.
Next, make d axle Injection Currents iin=-1A；Sample motor d-q shaft voltages, d-q shaft currents and angular speed, and tie Close idThe data preserved when=0, it is possible to call the finite time Identification of parameter as shown in formula (5) to permagnetic synchronous motor Carry out parameter identification.
After parameter identification result reaches the condition of convergence, it is possible to parameter identification result is stored, terminates the injection of d shaft currents, Motor is set to continue in idRun under conditions of=0.
Set iteration convergence condition is ε=0.01% in emulation, i.e., when the identification result rate of change of each parameter is all small Think that parameter identification result has restrained when 0.01%；Selected matrix K and parameter γ be respectively
Parameter identification result when sample frequency is 500Hz is as shown in Figure 3.It is initial value with 0, iteration 267 times is also It is that each parameter identification result has just restrained after 0.534s.The identification result of stator resistance, d-q axle inductances and rotor flux is respectively 2.343 Ω, 11.31mH, 13.4mH, 0.128Wb；The relative error of identification result is respectively 0.3%, 13.1%, 0%, 1.5%.
Parameter identification result when sample frequency is 250Hz is as shown in Figure 4.It is initial value with 0, iteration 134 times is also It is that each parameter identification result has just restrained after 0.536s.The identification result of stator resistance, d-q axle inductances and rotor flux is respectively 2.34 Ω, 9.86mH, 13.26mH, 0.128Wb；The relative error of identification result is respectively 0.4%, 1.4%, 1%, 1.5%.
Compare the parameter identification result in Fig. 3 and Fig. 4 it can be found that under different sample frequencys, the present invention can be with Parameter identification result is restrained within the almost identical time, and there is higher parameter identification precision.Therefore, using the present invention The on-line parameter of permagnetic synchronous motor can be realized in finite time with less interative computation amount under relatively low sample frequency Identification.
When using sinusoidal current injection method, parameter identification Flow Chart Design when being injected according to the sinusoidal current shown in Fig. 2 b Simulation process：
Permagnetic synchronous motor is set to work in i firstdUnder conditions of=0.
Next, make d axle Injection Currents iin=0.5sin (20 π) A；Sample motor d-q shaft voltages, d-q shaft currents and angle Speed, it is possible to call the finite time Identification of parameter as shown in formula (5) to carry out parameter identification to permagnetic synchronous motor.
After parameter identification result reaches the condition of convergence, it is possible to parameter identification result is stored, terminates the injection of d shaft currents, Motor is set to continue in idRun under conditions of=0.
Set iteration convergence condition is ε, selected matrix K and parameter γ with using step current method in emulation Carry out identical during parameter identification.
Parameter identification result when sample frequency is 500Hz is as shown in Figure 5.It is initial value with 0, iteration 259 times is also It is that each parameter identification result has just restrained after 0.518s.The identification result of stator resistance, d-q axle inductances and rotor flux is respectively 2.336 Ω, 11.29mH, 13.31mH, 0.128Wb；The relative error of identification result is respectively 0.6%, 12.9%, 0.67%, 1.5%.
Compare the parameter identification result in Fig. 5 and Fig. 3 it can be found that either using step current injection method or sine Current injection method, the present invention can restrain parameter identification result in finite time, and with higher parameter identification essence Degree.

Claims (1)

  1. A kind of 1. permagnetic synchronous motor on-line parameter discrimination method based on finite time algorithm, it is characterised in that：Pass through d axles electricity Stream injection method makes parameter identification equation group full rank, and the multi-parameter of permagnetic synchronous motor is realized by finite time Identification of parameter On-line identification；Specific method comprises the following steps：
    Step 1：Permagnetic synchronous motor is made to be operated in idUnder the conditions of=0 vector controlled
    Voltage equation of the permagnetic synchronous motor under d-q axis coordinate systems be：
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    U in formulad、uqRespectively d, q axis component of stator voltage；id、iqRespectively d, q axis component of stator current；R is stator electricity Resistance；Ld、LqRespectively d, q axle stator inductance；ωeFor angular rate；ψfFor rotor flux amplitude；
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    Step 2：Voltage equation exponent number is increased by d shaft currents injection method
    From formula (1), permagnetic synchronous motor voltage equation has two, and parameter to be identified has four, equation group not full rank, All parameters can not directly be picked out；Therefore order of equation is increased using d shaft currents injection method (sinusoidal current or step current) Number, to avoid parameter to be identified from converging to locally optimal solution；Using permagnetic synchronous motor after d shaft current injection methods in sampling instant k1And k2Voltage equation be expressed as
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    In formula, k when using sinusoidal current injection method1And k2It is illustrated respectively in after d axles injection sinusoidal current at different moments；When Using k during step current injection method1And k2The a certain moment after preflood a certain moment and injection is represented respectively；
    If motor is durface mounted permanent magnet synchronous motor, stator inductance meets Ld=Lq=Ls, parameter to be identified is changed into three, Equation (2) is then changed into
    <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mfrac> <mrow> <msub> <mi>di</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;omega;</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <msub> <mi>di</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;omega;</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mfrac> <mrow> <msub> <mi>di</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;omega;</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <msub> <mi>di</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;omega;</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>R</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi>L</mi> <mi>s</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;psi;</mi> <mi>f</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    Using equation (2) or equation (3), turned by the d-q shaft voltages in sample motor running, d-q shaft currents and motor Speed, it becomes possible to realize the multi-parameter of permagnetic synchronous motor while recognize.
    Step 3：Permagnetic synchronous motor parameter is recognized using finite time Identification of parameter
    It is y, coefficient matrix Γ to the output vector as shown in formula (4)T, systematic parameter is θ system, is designed with prescribing a time limit Between shown in Identification of parameter such as formula (5)
    Y=ΓTθ (4)
    In formula (4), yT=[ud(k1) uq(k1) ud(k2) uq(k2)], when motor is IPM synchronous motor,
    <mrow> <msup> <mi>&amp;Gamma;</mi> <mi>T</mi> </msup> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mfrac> <mrow> <msub> <mi>di</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;omega;</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mfrac> <mrow> <msub> <mi>di</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mtd> <mtd> <mrow> <msub> <mi>&amp;omega;</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mfrac> <mrow> <msub> <mi>di</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;omega;</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mfrac> <mrow> <msub> <mi>di</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mtd> <mtd> <mrow> <msub> <mi>&amp;omega;</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>&amp;theta;</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>R</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi>L</mi> <mi>d</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>L</mi> <mi>q</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;psi;</mi> <mi>f</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
    When motor is durface mounted permanent magnet synchronous motor,
    <mrow> <msup> <mi>&amp;Gamma;</mi> <mi>T</mi> </msup> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mfrac> <mrow> <msub> <mi>di</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;omega;</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <msub> <mi>di</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;omega;</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mfrac> <mrow> <msub> <mi>di</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;omega;</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <msub> <mi>di</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;omega;</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>&amp;theta;</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>R</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi>L</mi> <mi>s</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;psi;</mi> <mi>f</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
    In formula (5),And | |γRepresent to make scalar operation, γ to each component of vector with sign () ∈[0,1)；K is symmetric positive definite square formation；TsFor sampling time interval；WithThe respectively kth -1 of parameter θ and kth time Identification result, Γ (k)TThe coefficient matrix Γ respectively obtained with y (k) by kth group sampled resultTWith output vector y；
    Using the electric moter voltage, electric current and rotary speed data of sampling, calculated by such as formula (5), it becomes possible to realize permagnetic synchronous motor The on-line identification of parameter.
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