CN103296959B - Permagnetic synchronous motor senseless control system and method - Google Patents

Abstract

The invention provides a kind of permagnetic synchronous motor senseless control system and method, this system comprises motor body unit, inverter unit, SVPWM unit, first, second comparator, first, second PI controller, first, second, third coordinate transformation unit and sliding formwork extended Kalman filter; Sliding mode control law embeds in EKF state equation and output equation by the present invention, by linearisation and discretization, finally obtains digital extended Kalman filter, then obtains with reference to stator current through spreading kalman recursion with rotor speed ω _rstate estimation; Achieve the senseless control of control system for permanent-magnet synchronous motor, and to d under q coordinate with reference to stator current carry out real-time update.Effectively can realize the senseless control of permagnetic synchronous motor, the high frequency that inhibit independent application Sliding mode variable structure control to produce is buffeted, to spinner velocity and the more accurate measurement of position realization of motor.

Description

Permagnetic synchronous motor senseless control system and method

Technical field

The invention belongs to AC electrical drive technology field, particularly a kind of permagnetic synchronous motor senseless control system and method.

Technical background

Permagnetic synchronous motor has that volume is little, lightweight, efficiency high, is widely used in various high-performance drive system.Because permagnetic synchronous motor has the features such as multivariable, non-linear, close coupling, the factor such as the Parameters variation in permagnetic synchronous motor system and external loading disturbance is made to affect the performance of control system.High-precision servo drive system needs rotating speed and the position of detecting rotor, but the installation of traditional mechanical pick-up device adds volume and the cost of system, reduces the reliability of system, also limit the application of permagnetic synchronous motor at some special occasions.

What sliding formwork control technology had becomes and the strong robustness of external disturbance during system parameters, have quick response, to Parameters variation and disturbance is insensitive, without the need to System Discrimination, the advantages such as physics realization is simple.But sliding formwork control technology can produce the buffeting of high frequency, limit sliding-mode control application in systems in practice.

Summary of the invention

The object of the present invention is to provide a kind of permagnetic synchronous motor senseless control system and method, realize the high accuracy position Sensorless Control of permagnetic synchronous motor, the high frequency of further suppression Sliding mode variable structure control is buffeted, to improve the dynamic property of system, robustness and stability.

To achieve these goals, the present invention adopts following technical scheme:

Permagnetic synchronous motor senseless control system, comprises motor body unit, inverter unit, SVPWM unit, the first comparator, the second comparator, a PI controller, the 2nd PI controller, the first coordinate transformation unit, the second coordinate transformation unit, three-dimensional converter unit and sliding formwork extended Kalman filter;

First coordinate transformation unit, for the three-phase windings current i by drive motors body unit _a, i _b, i _ctransform to the stator current i under alpha-beta coordinate system _α, i _β;

Sliding formwork extended Kalman filter, for by the stator current under alpha-beta coordinate system and voltage i _α, i _β, u _α, u _βand given rotor speed as the input of sliding formwork Kalman filter, after spreading kalman recursive operation, obtain rotor speed ω _r, corner with d ?reference stator current under q coordinate system

Second coordinate transformation unit, for by stator current i _α, i _βtransform to the stator current i under d-q coordinate system _q, i _d;

First comparator, for obtaining with reference to stator current with stator current i _qdifference relatively;

Second comparator, for obtaining stator current i _dwith reference stator current difference relatively;

One PI controller, for reference to stator current with stator current i _qdifference relatively carries out ratio, integral operation obtains q shaft voltage component instruction

2nd PI controller, for stator current i _dwith reference stator current difference relatively carries out ratio, integral operation obtains d shaft voltage component instruction

Three-dimensional converter unit, for by d shaft voltage component instruction transform to the stator voltage u under alpha-beta coordinate system _α, u _β;

SVPWM unit, for according to stator voltage u _α, u _β, adopt Using dSPACE of SVPWM algorithm to generate pulse width signal input inverter;

Inverter, the pulse width signal for exporting according to SVPWM unit generates three-phase windings current drives motor body unit.

The present invention further improves and is: sliding formwork extended Kalman filter according to state equation and output equation, according to five recursion steps of Kalman filtering carry out d ?reference stator current under q coordinate system with rotor speed ω _rstate estimation;

Described state equation and output equation are:

$\left\{\begin{array}{c}x\left(k\right)=F\left(k\right)x(k-1)+B\left(k\right)u\left(k\right)+w\left(k\right)\\ y\left(k\right)=\mathrm{Hx}\left(k\right)+v\left(k\right)\end{array}\right.$

Wherein, w (t) is system noise function, and v (t) is measurement noises function, R _sfor stator resistance, λ _rfor stator magnetic linkage, L _sfor stator equivalent inductance, θ _rfor electrical degree, ρ is negative constant,

$\left\{\begin{array}{c}\frac{{\mathrm{di}}_{\mathrm{\α}}}{\mathrm{dt}}=-\frac{R_s}{L_s}{i}_{\mathrm{\α}}+\frac{{\mathrm{\λ}}_r}{L_s}{\mathrm{\ω}}_r\sin {\mathrm{\θ}}_r+\frac{1}{L_s}{u}_{\mathrm{\α}}\\ \frac{{\mathrm{di}}_{\mathrm{\β}}}{\mathrm{dt}}=-\frac{R_s}{L_s}{i}_{\mathrm{\α}}-\frac{{\mathrm{\λ}}_r}{L_s}{\mathrm{\ω}}_r\sin {\mathrm{\θ}}_r+\frac{1}{L_s}{u}_{\mathrm{\β}}\end{array}\right.,$

$A={\left[\begin{array}{cccccc}0& 1/L_s& 0& 0& 0& 0\\ 0& 0& 1/L_s& 0& 0& 0\end{array}\right]}^T,$

$H=\left[\begin{array}{cccccc}0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right],$

$B=\frac{\mathrm{\ρ}}{b}[\frac{(b+\mathrm{\Δb})\mathrm{\ρ}}{b}-(a+\mathrm{\Δa})],$

$C=-\frac{\mathrm{\ρ}-a}{b}\frac{\∂\stackrel{\·}{{\mathrm{\ω}}_r^{*}}}{\∂{\mathrm{\ω}}_r^{*}}+\frac{1}{b}\frac{\∂\stackrel{\·\·}{{\mathrm{\ω}}_r^{*}}}{\∂{\mathrm{\ω}}_r^{*}},$

$D=\frac{\∂\stackrel{\·}{{\mathrm{\ω}}_r^{*}}}{\∂{\mathrm{\ω}}_r^{*}},$

$H\left(x\left(t\right)\right)=\frac{\∂y}{\∂x}{|}_{x=x\left(t\right)}=\left[\begin{array}{cccccc}0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right],$

$F\left(k\right)=e^{F\left(x\right)T}\≈I+F\left(x\right)T$

$=\left[\begin{array}{cccccc}1& 0& 0& \mathrm{AT}& 0& \mathrm{BT}\\ 0& 1-\frac{R_s}{L_s}T& 0& \frac{{\mathrm{\λ}}_r}{L_s}\sin {\mathrm{\θ}}_r& \frac{{\mathrm{\λ}}_r{\mathrm{\ω}}_r}{L_s}\cos {\mathrm{\θ}}_r& 0\\ 0& 0& 1-\frac{R_s}{L_s}T& -\frac{{\mathrm{\λ}}_r}{L_s}\cos {\mathrm{\θ}}_r& \frac{{\mathrm{\λ}}_r{\mathrm{\ω}}_r}{L_s}\sin {\mathrm{\θ}}_r& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& T& 1& 0\\ 0& 0& 0& 0& 0& 1+\mathrm{CT}\end{array}\right],$

$B\left(k\right)={\∫}_0^T{e}^{F\left(x\right)T}\mathrm{dBt}\≈\mathrm{BT}={\left[\begin{array}{cccccc}0& T/L_s& 0& 0& 0& 0\\ 0& 0& T/L_s& 0& 0& 0\end{array}\right]}^T.$

The present invention further improves and is:

The control method of permagnetic synchronous motor senseless control system, comprising:

1), whole control system powers on and initialization; SVPWM unit sends initial pulse width signal to inverter; Inverter generates three-phase windings electric current according to this initial pulse width signal and exports to PMSM, drives PMSM to rotate;

2), initialization terminates, and whole control system is run; Three-phase windings current i _a, i _b, i _cexport the first coordinate transformation unit to, the first coordinate transformation unit is by three-phase windings current i _a, i _b, i _ctransform to the stator current i under alpha-beta coordinate system _α, i _β; Stator current i _α, i _βinput sliding formwork extended Kalman filter and the second coordinate transformation unit, stator current i _α, i _βthe stator current i under d-q coordinate system is transformed in the second coordinate transformation unit _q, i _d; Sliding formwork extended Kalman filter unit is by the stator current i under alpha-beta coordinate system _α, i _β, stator voltage u _α, u _βand given rotor speed as the input of sliding formwork Kalman filter, after spreading kalman recursive operation, obtain rotor speed ω _r, corner with d ?reference stator current under q coordinate system with reference to stator current input the first comparator and stator current i _qdifference input the one PI controller relatively, a PI controller carries out ratio to difference, integral operation obtains q shaft voltage component instruction input three-dimensional converter unit; Stator current i _dinput the second comparator and reference stator current difference input the 2nd PI controller compared, the 2nd PI controller carries out ratio to difference, integral operation obtains d shaft voltage component instruction input three-dimensional converter unit; Corner signal inputs the second coordinate transformation unit and three-dimensional converter unit; D shaft voltage component instruction input in three-dimensional converter unit the stator voltage u transformed under alpha-beta coordinate system _α, u _β; Stator voltage u _α, u _βsend into SVPWM unit, SVPWM unit is according to stator voltage u _α, u _β, adopt Using dSPACE of SVPWM algorithm generating power device pulse width signal input inverter; Inverter generates three-phase windings electric current according to this pulse width signal and sends to motor body unit;

3), repeat step (2) and carry out loop control.

The present invention further improves and is: step 2) in sliding formwork extended Kalman filter unit by the stator current i under alpha-beta coordinate system _α, i _β, stator voltage u _α, u _βand given rotor speed as the input of sliding formwork Kalman filter, after spreading kalman recursive operation, obtain rotor speed ω _r, corner with d ?reference stator current under q coordinate system specifically comprise:

(1) according to permagnetic synchronous motor PMSM kinetic model and in conjunction with coordinate transform, the motor status equation under alpha-beta coordinate system is obtained:

$\left\{\begin{array}{c}\frac{{\mathrm{di}}_{\mathrm{\α}}}{\mathrm{dt}}=-\frac{R_s}{L_s}{i}_{\mathrm{\α}}+\frac{{\mathrm{\λ}}_r}{L_s}{\mathrm{\ω}}_r\sin {\mathrm{\θ}}_r+\frac{1}{L_s}{u}_{\mathrm{\α}}\\ \frac{{\mathrm{di}}_{\mathrm{\β}}}{\mathrm{dt}}=-\frac{R_s}{L_s}{i}_{\mathrm{\α}}-\frac{{\mathrm{\λ}}_r}{L_s}{\mathrm{\ω}}_r\sin {\mathrm{\θ}}_r+\frac{1}{L_s}{u}_{\mathrm{\β}}\end{array}\right.$

In formula, R _sfor stator resistance, λ _rfor stator magnetic linkage, L _sfor stator equivalent inductance, θ _rfor electrical degree;

(2) further, by Sliding mode variable structure control strategy determine d ?reference stator current under q coordinate system its process is as follows:

A) designing Integral Sliding Mode face is: $S=e\left(t\right)-\underset{0}{\overset{t}{\∫}}(\mathrm{\ρ}-a)e\left(\mathrm{\τ}\right)\mathrm{d\τ},$ Sliding mode control law is: μ=ρ e (t)-β sign (s), and wherein ρ is negative constant, and β is sliding formwork handoff gain coefficient,

$\mathrm{sign}\left(s\right)=\left\{\begin{array}{cc}1,& s>0\\ 0,& s=0\\ -1,& s<0\end{array}\right.$ For sign function;

B) Lyapunov function is selected thus make system can reach sliding formwork state in any initial condition, thus can obtain $\mathrm{\&mu;}=\mathrm{\&rho;e}\left(t\right)-\mathrm{\&beta;sign}\left(s\right)={\mathrm{bi}}_q^{*}-{\mathrm{a\&omega;}}_r^{*}-\stackrel{\&CenterDot;}{{\mathrm{\&omega;}}^{*}};$

C) push away: $i_q^{*}=\frac{1}{b}[\mathrm{\&rho;}({\mathrm{\&omega;}}_r-{\mathrm{\&omega;}}_r^{*})-\mathrm{\&beta;sign}\left(s\right)+a{\mathrm{\&omega;}}_r^{*}+\stackrel{\&CenterDot;}{{\mathrm{\&omega;}}^{*}}];$

(3) Sliding mode variable structure control is embedded in EKF, from extended Kalman filter, by rotor speed ω _r, given rotor speed electrical degree θ _r, the stator current i under alpha-beta coordinate system _α, i _βand d ?reference stator current under q coordinate system as state variable, state equation and the output equation that can obtain system are as follows:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{X}\left(t\right)=f\left(x\right)+\mathrm{Au}\left(t\right)+w\left(t\right)\\ y\left(t\right)=\mathrm{Hx}\left(t\right)+v\left(t\right)\end{array}\right.$

Wherein, in the system mode of t $X={\left[\begin{array}{cccccc}{i}_q^{*}& i_{\mathrm{\&alpha;}}& i_{\mathrm{\&beta;}}& {\mathrm{\&omega;}}_r& {\mathrm{\&theta;}}_r& {\mathrm{\&omega;}}_r^{*}\end{array}\right]}^T,$ System control amount

U=[V _αv _β] ^t, measured value ${y=\left[\begin{array}{ccc}{i}_{\mathrm{\&alpha;}}& i_{\mathrm{\&beta;}}& {\mathrm{\&omega;}}_r^{*}\end{array}\right]}^T,$ W (t) is system noise function, and v (t) is measurement noises function, $f\left(x\right)=\left[\begin{array}{c}{f}_1\\ f_2\\ f_3\\ f_4\\ f_5\\ f_6\end{array}\right]=\left[\begin{array}{c}\frac{{\mathrm{di}}_q^{*}}{\mathrm{dt}}\\ \frac{{\mathrm{di}}_{\mathrm{\&alpha;}}}{\mathrm{dt}}\\ \frac{{\mathrm{di}}_{\mathrm{\&beta;}}}{\mathrm{dt}}\\ \frac{{\mathrm{d\&omega;}}_r}{\mathrm{dt}}\\ \frac{{\mathrm{d\&theta;}}_r}{\mathrm{dt}}\\ \frac{{\mathrm{d\&omega;}}_r^{*}}{\mathrm{dt}}\end{array}\right]=\left[\begin{array}{c}\frac{b}{1}[\mathrm{\&rho;}\stackrel{\&CenterDot;}{{\mathrm{\&omega;}}_r}-(\mathrm{\&rho;}-a)\stackrel{\&CenterDot;}{{\mathrm{\&omega;}}^{*}}+\stackrel{\&CenterDot;\&CenterDot;}{{\mathrm{\&omega;}}_r^{*}}]\\ -\frac{R_S}{L_S}{i}_{\mathrm{\&alpha;}}+\frac{{\mathrm{\&lambda;}}_r}{L_S}{\mathrm{\&omega;}}_r\sin {\mathrm{\&theta;}}_r\\ -\frac{R_S}{L_S}{i}_{\mathrm{\&alpha;}}+\frac{{\mathrm{\&lambda;}}_r}{L_S}{\mathrm{\&omega;}}_r\sin {\mathrm{\&theta;}}_r\\ 0\\ {\mathrm{\&omega;}}_r\\ {\mathrm{\&omega;}}_r^{*}\end{array}\right],$

Sliding mode variable structure control equation is comprised in f (x): $i_q^{*}=\frac{1}{b}[\mathrm{\&rho;}({\mathrm{\&omega;}}_r-{\mathrm{\&omega;}}_r^{*})-\mathrm{\&beta;sign}\left(s\right)+a{\mathrm{\&omega;}}_r^{*}+\stackrel{\&CenterDot;}{{\mathrm{\&omega;}}^{*}}],$

System parameters matrix: $A={\left[\begin{array}{cccccc}0& 1/L_s& 0& 0& 0& 0\\ 0& 0& 1/L_s& 0& 0& 0\end{array}\right]}^T,$

The parameter matrix of measuring system: $H=\left[\begin{array}{cccccc}0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right];$

(4) for mating the non-linear of permagnetic synchronous motor, by extended Kalman filter digitlization, first need to carry out linearization process to f (x), its Jacobian matrix is:

$F\left(x\left(t\right)\right)=\frac{\&PartialD;f}{\&PartialD;x}{|}_{x=x\left(t\right)}=\left[\begin{array}{cccccc}0& 0& 0& B& 0& C\\ 0& -R_s/L_s& 0& \frac{{\mathrm{\&lambda;}}_r}{L_s}\sin {\mathrm{\&theta;}}_r& \frac{{\mathrm{\&lambda;}}_r{\mathrm{\&omega;}}_r}{L_s}\cos {\mathrm{\&theta;}}_r& 0\\ 0& 0& -R_s/L_s& -\frac{{\mathrm{\&lambda;}}_r}{L_s}\cos {\mathrm{\&theta;}}_r& \frac{{\mathrm{\&lambda;}}_r{\mathrm{\&omega;}}_r}{L_s}\sin {\mathrm{\&theta;}}_r& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& D\end{array}\right]$

Wherein: $B=\frac{\mathrm{\&rho;}}{b}[\frac{(b+\mathrm{\&Delta;b})\mathrm{\&rho;}}{b}-(a+\mathrm{\&Delta;a})],$ $C=-\frac{\mathrm{\&rho;}-a}{b}\frac{\&PartialD;\stackrel{\&CenterDot;}{{\mathrm{\&omega;}}_r^{*}}}{\&PartialD;{\mathrm{\&omega;}}_r^{*}}+\frac{1}{b}\frac{\&PartialD;\stackrel{\&CenterDot;\&CenterDot;}{{\mathrm{\&omega;}}_r^{*}}}{\&PartialD;{\mathrm{\&omega;}}_r^{*}},$ $D=\frac{\&PartialD;\stackrel{\&CenterDot;}{{\mathrm{\&omega;}}_r^{*}}}{\&PartialD;{\mathrm{\&omega;}}_r^{*}},$

$H\left(x\left(t\right)\right)=\frac{\&PartialD;y}{\&PartialD;x}{|}_{x=x\left(t\right)}=\left[\begin{array}{cccccc}0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right];$

(5) matrix after step (4) neutral line is carried out discretization, process is as follows:

$F\left(k\right)=e^{F\left(x\right)T}\&ap;I+F\left(x\right)T$

$=\left[\begin{array}{cccccc}1& 0& 0& \mathrm{AT}& 0& \mathrm{BT}\\ 0& 1-\frac{R_s}{L_s}T& 0& \frac{{\mathrm{\&lambda;}}_r}{L_s}\sin {\mathrm{\&theta;}}_r& \frac{{\mathrm{\&lambda;}}_r{\mathrm{\&omega;}}_r}{L_s}\cos {\mathrm{\&theta;}}_r& 0\\ 0& 0& 1-\frac{R_s}{L_s}T& -\frac{{\mathrm{\&lambda;}}_r}{L_s}\cos {\mathrm{\&theta;}}_r& \frac{{\mathrm{\&lambda;}}_r{\mathrm{\&omega;}}_r}{L_s}\sin {\mathrm{\&theta;}}_r& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& T& 1& 0\\ 0& 0& 0& 0& 0& 1+\mathrm{CT}\end{array}\right]$

$B\left(k\right)={\&Integral;}_0^T{e}^{F\left(x\right)T}\mathrm{dBt}\&ap;\mathrm{BT}={\left[\begin{array}{cccccc}0& T/L_s& 0& 0& 0& 0\\ 0& 0& T/L_s& 0& 0& 0\end{array}\right]}^T$

According to above formula, thus obtain the system mode after discretization and output equation:

$\left\{\begin{array}{c}x\left(k\right)=F\left(k\right)x(k-1)+B\left(k\right)u\left(k\right)+w\left(k\right)\\ y\left(k\right)=\mathrm{Hx}\left(k\right)+v\left(k\right)\end{array}\right.$

(6) after the state equation obtaining the sliding formwork embedded type extended Kalman filter in step (5) after digitlization and output equation, according to five recursion steps of Kalman filtering carry out d ?reference stator current under q coordinate system with rotor speed ω _rstate estimation.

A kind of based in the permagnetic synchronous motor senseless control system of sliding formwork embedded type EKF, sliding formwork extended Kalman filter unit is by the stator current under alpha-beta coordinate system and voltage i _α, i _β, u _α, u _βand given rotor speed as the input of sliding formwork Kalman filter, after spreading kalman recursive operation, obtain rotor speed ω _rwith d ?reference stator current under q coordinate system rotor speed ω after renewal _rwith reference stator current be re-used as the input of recursive operation next time, and then with this recursive operation repeatedly.

The present invention selects rotor speed ω _r, given rotor speed electrical degree θ _r, the stator current i under alpha-beta coordinate system _α, i _βand d ?reference stator current under q coordinate system as state variable, by sliding mode control law $i_q^{*}=\frac{1}{b}[\mathrm{\&rho;}({\mathrm{\&omega;}}_r-{\mathrm{\&omega;}}_r^{*})-\mathrm{\&beta;sign}\left(s\right)+a{\mathrm{\&omega;}}_r^{*}+\stackrel{\&CenterDot;}{{\mathrm{\&omega;}}^{*}}]$ Embed EKF state equation and output equation $\left\{\begin{array}{c}\stackrel{\&CenterDot;}{X}\left(t\right)=f\left(x\right)+\mathrm{Au}\left(t\right)+w\left(t\right)\\ y\left(t\right)=\mathrm{Hx}\left(t\right)+v\left(t\right)\end{array}\right.$ In, by linearisation and discretization, finally obtain digital extended Kalman filter, then obtain through spreading kalman recursion with ω _rstate estimation.

Relative to prior art, permagnetic synchronous motor senseless control system and method for the present invention at least has the following advantages:

(1) the present invention is based on the permagnetic synchronous motor senseless control system of sliding formwork embedded type EKF, achieve the high accuracy senseless control of permagnetic synchronous motor, instead of traditional mechanical pick-up device, decrease volume and the cost of system, add the reliability of system, and expand the range of application of permagnetic synchronous motor.

(2) the present invention is based on the permagnetic synchronous motor senseless control system of sliding formwork embedded type EKF, the high frequency that can effectively suppress synovial membrane variable-structure control to be introduced is buffeted, have concurrently simultaneously Sliding mode variable structure control response rapidly, without the need to the advantages such as System Discrimination and the anti-random disturbances of EKF and noise immune is strong, can the advantage such as real-time parameter renewal.

(3) the present invention is not high to the required precision of the Mathematical Modeling of control system for permanent-magnet synchronous motor, and, external disturbance uncertain to system parameters has adaptivity and stronger robustness, in controlling permagnetic synchronous motor, have excellent dynamic and static characteristic.

Accompanying drawing explanation

Fig. 1 is the theory diagram of the permagnetic synchronous motor senseless control system that the present invention is based on sliding formwork embedded type EKF;

Fig. 2 is the internal model figure of sliding formwork embedded type EKF module;

Fig. 3 is sliding formwork embedded type EKF control system state convergence trajectory diagram.

Embodiment

Describe the present invention below in conjunction with accompanying drawing, it is a kind of preferred embodiment in various embodiments mode of the present invention.

Refer to shown in Fig. 1, a kind of permagnetic synchronous motor senseless control system based on sliding formwork embedded type EKF of the present invention, comprises motor body unit, inverter unit, SVPWM unit, coordinate transformation unit and sliding formwork extended Kalman filter in order to replace traditional velocity location detecting unit.The three-phase windings current i of motor body unit _a, i _b, i _cinput the first coordinate transformation unit transform to alpha-beta coordinate system under stator current i _α, i _β, stator current i _α, i _βinput sliding formwork extended Kalman filter and the second coordinate transformation unit, stator current i _α, i _βthe stator current i under d-q coordinate system is transformed in the second coordinate transformation unit _q, i _d; Sliding formwork extended Kalman filter unit is by the stator current under alpha-beta coordinate system and voltage i _α, i _β, u _α, u _βand given rotor speed as the input of sliding formwork Kalman filter, after spreading kalman recursive operation, obtain rotor speed ω _r, corner with d ?reference stator current under q coordinate system with reference to stator current input the first comparator and stator current i _qdifference input the one PI controller relatively, a PI controller carries out ratio to difference, integral operation obtains q shaft voltage component instruction input three-dimensional converter unit; Stator current i _dinput the second comparator and reference stator current difference input the 2nd PI controller compared, the 2nd PI controller carries out ratio to difference, integral operation obtains d shaft voltage component instruction input three-dimensional converter unit; Corner signal inputs the second coordinate transformation unit and three-dimensional converter unit.D shaft voltage component instruction input in three-dimensional converter unit the stator voltage u transformed under alpha-beta coordinate system _α, u _β; Stator voltage u _α, u _βsend into SVPWM unit, SVPWM unit is according to stator voltage u _α, u _β, adopt Using dSPACE of SVPWM algorithm generating power device pulse width signal input inverter; Inverter, sends to motor body unit and the first coordinate transformation unit for generating three-phase windings electric current according to this pulse width signal.

Below the permagnetic synchronous motor Speed Sensorless Control Method that the present invention is based on sliding formwork embedded type EKF is described in detail:

Based on a permagnetic synchronous motor Speed Sensorless Control Method for sliding formwork EKF, comprise the following steps:

1), whole control system powers on and initialization; SVPWM unit sends initial pulse width signal to inverter; Inverter generates three-phase windings electric current according to this initial pulse width signal and exports to PMSM, drives PMSM to rotate;

2), initialization terminates, and whole control system is run; Three-phase windings current i _a, i _b, i _cexport the first coordinate transformation unit to, the first coordinate transformation unit is by three-phase windings current i _a, i _b, i _ctransform to the stator current i under alpha-beta coordinate system _α, i _β; Stator current i _α, i _βinput sliding formwork extended Kalman filter and the second coordinate transformation unit, stator current i _α, i _βthe stator current i under d-q coordinate system is transformed in the second coordinate transformation unit _q, i _d; Sliding formwork extended Kalman filter unit is by the stator current i under alpha-beta coordinate system _α, i _β, stator voltage u _α, u _βand given rotor speed as the input of sliding formwork Kalman filter, after spreading kalman recursive operation, obtain rotor speed ω _r, corner with d ?reference stator current under q coordinate system with reference to stator current input the first comparator and stator current i _qdifference input the one PI controller relatively, a PI controller carries out ratio to difference, integral operation obtains q shaft voltage component instruction input three-dimensional converter unit; Stator current i _dinput the second comparator and reference stator current difference input the 2nd PI controller compared, the 2nd PI controller carries out ratio to difference, integral operation obtains d shaft voltage component instruction input three-dimensional converter unit; Corner signal inputs the second coordinate transformation unit and three-dimensional converter unit; D shaft voltage component instruction input in three-dimensional converter unit the stator voltage u transformed under alpha-beta coordinate system _α, u _β; Stator voltage u _α, u _βsend into SVPWM unit, SVPWM unit is according to stator voltage u _α, u _β, adopt Using dSPACE of SVPWM algorithm generating power device pulse width signal input inverter; Inverter generates three-phase windings electric current according to this pulse width signal and sends to motor body unit;

3), repeat step (2) and carry out loop control.

Step 2) in sliding formwork extended Kalman filter unit by the stator current i under alpha-beta coordinate system _α, i _β, stator voltage u _α, u _βand given rotor speed as the input of sliding formwork Kalman filter, after spreading kalman recursive operation, obtain rotor speed ω _r, corner with d ?reference stator current under q coordinate system , specifically comprise:

(1) according to permagnetic synchronous motor PMSM kinetic model and in conjunction with coordinate transform, the motor status equation under alpha-beta coordinate system is obtained:

$\left\{\begin{array}{c}\frac{{\mathrm{di}}_{\mathrm{\&alpha;}}}{\mathrm{dt}}=-\frac{R_s}{L_s}{i}_{\mathrm{\&alpha;}}+\frac{{\mathrm{\&lambda;}}_r}{L_s}{\mathrm{\&omega;}}_r\sin {\mathrm{\&theta;}}_r+\frac{1}{L_s}{u}_{\mathrm{\&alpha;}}\\ \frac{{\mathrm{di}}_{\mathrm{\&beta;}}}{\mathrm{dt}}=-\frac{R_s}{L_s}{i}_{\mathrm{\&alpha;}}-\frac{{\mathrm{\&lambda;}}_r}{L_s}{\mathrm{\&omega;}}_r\sin {\mathrm{\&theta;}}_r+\frac{1}{L_s}{u}_{\mathrm{\&beta;}}\end{array}\right.$

In formula, R _sfor stator resistance, λ _rfor stator magnetic linkage, L _sfor stator equivalent inductance, θ _rfor electrical degree.

(2) further, by Sliding mode variable structure control strategy determine d ?reference stator current under q coordinate system , its process is as follows:

A) designing Integral Sliding Mode face is: $S=e\left(t\right)-\underset{0}{\overset{t}{\&Integral;}}(\mathrm{\&rho;}-a)e\left(\mathrm{\&tau;}\right)\mathrm{d\&tau;},$ Sliding mode control law is: μ=ρ e (t)-β sign (s), and wherein ρ is negative constant, and β is sliding formwork handoff gain coefficient,

$\mathrm{sign}\left(s\right)=\left\{\begin{array}{cc}1,& s>0\\ 0,& s=0\\ -1,& s<0\end{array}\right.$ For sign function.

B) Lyapunov function is selected thus make system can reach sliding formwork state in any initial condition, thus can obtain $\mathrm{\&mu;}=\mathrm{\&rho;e}\left(t\right)-\mathrm{\&beta;sign}\left(s\right)={\mathrm{bi}}_q^{*}-{\mathrm{a\&omega;}}_r^{*}-\stackrel{\&CenterDot;}{{\mathrm{\&omega;}}^{*}}.$

C) in sum, can be derived from: $i_q^{*}=\frac{1}{b}[\mathrm{\&rho;}({\mathrm{\&omega;}}_r-{\mathrm{\&omega;}}_r^{*})-\mathrm{\&beta;sign}\left(s\right)+a{\mathrm{\&omega;}}_r^{*}+\stackrel{\&CenterDot;}{{\mathrm{\&omega;}}^{*}}].$

(3) further, in order to eliminate in sliding moding structure after state trajectory arrives sliding-mode surface, be difficult to strictly slide towards balance point along sliding-mode surface, but passing through back and forth in sliding-mode surface both sides, thus the high frequency produced trembles shake, Sliding mode variable structure control is embedded in EKF.Figure 2 shows that the internal model figure of sliding formwork EKF module.From extended Kalman filter, by rotor speed ω _r, given rotor speed , electrical degree θ _r, the stator current i under alpha-beta coordinate system _α, i _βand d ?reference stator current under q coordinate system as state variable.State equation and the output equation that can obtain system are as follows:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{X}\left(t\right)=f\left(x\right)+\mathrm{Au}\left(t\right)+w\left(t\right)\\ y\left(t\right)=\mathrm{Hx}\left(t\right)+v\left(t\right)\end{array}\right.$

Wherein, in the system mode of t $X={\left[\begin{array}{cccccc}{i}_q^{*}& i_{\mathrm{\&alpha;}}& i_{\mathrm{\&beta;}}& {\mathrm{\&omega;}}_r& {\mathrm{\&theta;}}_r& {\mathrm{\&omega;}}_r^{*}\end{array}\right]}^T,$ System control amount u=[V _αv _β] ^t, measured value ${y=\left[\begin{array}{ccc}{i}_{\mathrm{\&alpha;}}& i_{\mathrm{\&beta;}}& {\mathrm{\&omega;}}_r^{*}\end{array}\right]}^T,$ W (t) is system noise function, and v (t) is measurement noises function, $f\left(x\right)=\left[\begin{array}{c}{f}_1\\ f_2\\ f_3\\ f_4\\ f_5\\ f_6\end{array}\right]=\left[\begin{array}{c}\frac{{\mathrm{di}}_q^{*}}{\mathrm{dt}}\\ \frac{{\mathrm{di}}_{\mathrm{\&alpha;}}}{\mathrm{dt}}\\ \frac{{\mathrm{di}}_{\mathrm{\&beta;}}}{\mathrm{dt}}\\ \frac{{\mathrm{d\&omega;}}_r}{\mathrm{dt}}\\ \frac{{\mathrm{d\&theta;}}_r}{\mathrm{dt}}\\ \frac{{\mathrm{d\&omega;}}_r^{*}}{\mathrm{dt}}\end{array}\right]=\left[\begin{array}{c}\frac{b}{1}[\mathrm{\&rho;}\stackrel{\&CenterDot;}{{\mathrm{\&omega;}}_r}-(\mathrm{\&rho;}-a)\stackrel{\&CenterDot;}{{\mathrm{\&omega;}}^{*}}+\stackrel{\&CenterDot;\&CenterDot;}{{\mathrm{\&omega;}}_r^{*}}]\\ -\frac{R_S}{L_S}{i}_{\mathrm{\&alpha;}}+\frac{{\mathrm{\&lambda;}}_r}{L_S}{\mathrm{\&omega;}}_r\sin {\mathrm{\&theta;}}_r\\ -\frac{R_S}{L_S}{i}_{\mathrm{\&alpha;}}+\frac{{\mathrm{\&lambda;}}_r}{L_S}{\mathrm{\&omega;}}_r\sin {\mathrm{\&theta;}}_r\\ 0\\ {\mathrm{\&omega;}}_r\\ {\mathrm{\&omega;}}_r^{*}\end{array}\right],$ Sliding mode variable structure control equation is comprised in f (x): $i_q^{*}=\frac{1}{b}[\mathrm{\&rho;}({\mathrm{\&omega;}}_r-{\mathrm{\&omega;}}_r^{*})-\mathrm{\&beta;sign}\left(s\right)+a{\mathrm{\&omega;}}_r^{*}+\stackrel{\&CenterDot;}{{\mathrm{\&omega;}}^{*}}],$ System parameters matrix: $A={\left[\begin{array}{cccccc}0& 1/L_s& 0& 0& 0& 0\\ 0& 0& 1/L_s& 0& 0& 0\end{array}\right]}^T,$ The parameter matrix of measuring system:

$H=\left[\begin{array}{cccccc}0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right].$

(4) for mating the non-linear of permagnetic synchronous motor, by extended Kalman filter digitlization, first need to carry out linearization process to f (x), its Jacobian matrix is:

$F\left(x\left(t\right)\right)=\frac{\&PartialD;f}{\&PartialD;x}{|}_{x=x\left(t\right)}=\left[\begin{array}{cccccc}0& 0& 0& B& 0& C\\ 0& -R_s/L_s& 0& \frac{{\mathrm{\&lambda;}}_r}{L_s}\sin {\mathrm{\&theta;}}_r& \frac{{\mathrm{\&lambda;}}_r{\mathrm{\&omega;}}_r}{L_s}\cos {\mathrm{\&theta;}}_r& 0\\ 0& 0& -R_s/L_s& -\frac{{\mathrm{\&lambda;}}_r}{L_s}\cos {\mathrm{\&theta;}}_r& \frac{{\mathrm{\&lambda;}}_r{\mathrm{\&omega;}}_r}{L_s}\sin {\mathrm{\&theta;}}_r& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& D\end{array}\right]$

Wherein: $B=\frac{\mathrm{\&rho;}}{b}[\frac{(b+\mathrm{\&Delta;b})\mathrm{\&rho;}}{b}-(a+\mathrm{\&Delta;a})],$ $C=-\frac{\mathrm{\&rho;}-a}{b}\frac{\&PartialD;\stackrel{\&CenterDot;}{{\mathrm{\&omega;}}_r^{*}}}{\&PartialD;{\mathrm{\&omega;}}_r^{*}}+\frac{1}{b}\frac{\&PartialD;\stackrel{\&CenterDot;\&CenterDot;}{{\mathrm{\&omega;}}_r^{*}}}{\&PartialD;{\mathrm{\&omega;}}_r^{*}},$ $D=\frac{\&PartialD;\stackrel{\&CenterDot;}{{\mathrm{\&omega;}}_r^{*}}}{\&PartialD;{\mathrm{\&omega;}}_r^{*}},$

$H\left(x\left(t\right)\right)=\frac{\&PartialD;y}{\&PartialD;x}{|}_{x=x\left(t\right)}=\left[\begin{array}{cccccc}0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right].$

(5) further, the matrix after step (4) neutral line is carried out discretization, and process is as follows:

$F\left(k\right)=e^{F\left(x\right)T}\&ap;I+F\left(x\right)T$

$=\left[\begin{array}{cccccc}1& 0& 0& \mathrm{AT}& 0& \mathrm{BT}\\ 0& 1-\frac{R_s}{L_s}T& 0& \frac{{\mathrm{\&lambda;}}_r}{L_s}\sin {\mathrm{\&theta;}}_r& \frac{{\mathrm{\&lambda;}}_r{\mathrm{\&omega;}}_r}{L_s}\cos {\mathrm{\&theta;}}_r& 0\\ 0& 0& 1-\frac{R_s}{L_s}T& -\frac{{\mathrm{\&lambda;}}_r}{L_s}\cos {\mathrm{\&theta;}}_r& \frac{{\mathrm{\&lambda;}}_r{\mathrm{\&omega;}}_r}{L_s}\sin {\mathrm{\&theta;}}_r& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& T& 1& 0\\ 0& 0& 0& 0& 0& 1+\mathrm{CT}\end{array}\right]$

$B\left(k\right)={\&Integral;}_0^T{e}^{F\left(x\right)T}\mathrm{dBt}\&ap;\mathrm{BT}={\left[\begin{array}{cccccc}0& T/L_s& 0& 0& 0& 0\\ 0& 0& T/L_s& 0& 0& 0\end{array}\right]}^T$

According to above formula, thus obtain the system mode after discretization and output equation:

$\left\{\begin{array}{c}x\left(k\right)=F\left(k\right)x(k-1)+B\left(k\right)u\left(k\right)+w\left(k\right)\\ y\left(k\right)=\mathrm{Hx}\left(k\right)+v\left(k\right)\end{array}\right.$

(6) after the state equation obtaining the sliding formwork embedded type extended Kalman filter in step (5) after digitlization and output equation, can according to five of a Kalman filtering recursion step carry out d ?reference stator current under q coordinate system with rotor speed ω _rstate estimation.

Fig. 3 is the state trajectory convergence graph as the preferred embodiments of the present invention, can find out that sliding formwork embedded type EKF has good inhibition to the high frequency buffeting that Sliding mode variable structure control produces.

Be exemplarily described type patent of the present invention by reference to the accompanying drawings above, obviously can not limit the scope of type of the present invention enforcement with this, all simple conversion done according to type claim description of the present invention, all should belong to the protection range of type of the present invention.

Claims (4)

1. permagnetic synchronous motor senseless control system, it is characterized in that, comprise motor body unit, inverter unit, SVPWM unit, the first comparator, the second comparator, a PI controller, the 2nd PI controller, the first coordinate transformation unit, the second coordinate transformation unit, three-dimensional converter unit and sliding formwork extended Kalman filter;

First coordinate transformation unit, for the three-phase windings current i by drive motors body unit _a, i _b, i _ctransform to the stator current i under alpha-beta coordinate system _α, i _β;

Sliding formwork extended Kalman filter, for by the stator current under alpha-beta coordinate system and voltage i _α, i _β, u _α, u _βand given rotor speed as the input of sliding formwork extended Kalman filter, after spreading kalman recursive operation, obtain rotor speed ω _r, corner with the reference stator current under d-q coordinate system

Second coordinate transformation unit, for by stator current i _α, i _βtransform to the stator current i under d-q coordinate system _q, i _d;

First comparator, for obtaining with reference to stator current with stator current i _qdifference relatively;

Second comparator, for obtaining stator current i _dwith reference stator current difference relatively;

One PI controller, for reference to stator current with stator current i _qdifference relatively carries out ratio, integral operation obtains q shaft voltage component instruction

2nd PI controller, for stator current i _dwith reference stator current difference relatively carries out ratio, integral operation obtains d shaft voltage component instruction

Three-dimensional converter unit, for by d shaft voltage component instruction q shaft voltage component instruction transform to the stator voltage u under alpha-beta coordinate system _α, u _β;

SVPWM unit, for according to stator voltage u _α, u _β, adopt Using dSPACE of SVPWM algorithm to generate pulse width signal input inverter;

Inverter, the pulse width signal for exporting according to SVPWM unit generates three-phase windings current drives motor body unit;

Sliding formwork extended Kalman filter is according to state equation and output equation, and five recursion steps according to Kalman filtering carry out the reference stator current under d-q coordinate system with rotor speed ω _rstate estimation;

Described state equation and output equation are:

$\left\{\begin{array}{c}x\left(k\right)=F\left(k\right)x(k-1)+B\left(k\right)u\left(k\right)+w\left(k\right)\\ y\left(k\right)=\mathrm{Hx}\left(k\right)+v\left(k\right)\end{array}\right.$

$\left\{\begin{array}{c}\frac{{\mathrm{di}}_{\mathrm{\&alpha;}}}{\mathrm{dt}}=-\frac{R_s}{L_s}{i}_{\mathrm{\&alpha;}}+\frac{{\mathrm{\&lambda;}}_r}{L_s}{\mathrm{\&omega;}}_r\sin {\mathrm{\&theta;}}_r+\frac{1}{L_s}{u}_{\mathrm{\&alpha;}}\\ \frac{{\mathrm{di}}_{\mathrm{\&beta;}}}{\mathrm{dt}}=-\frac{R_s}{L_s}{i}_{\mathrm{\&alpha;}}-\frac{{\mathrm{\&lambda;}}_r}{L_s}{\mathrm{\&omega;}}_r\sin {\mathrm{\&theta;}}_r+\frac{1}{L_s}{u}_{\mathrm{\&beta;}}\end{array}\right.,$

$A={\left[\begin{array}{cccccc}0& 1/L_s& 0& 0& 0& 0\\ 0& 0& 1/L_s& 0& 0& 0\end{array}\right]}^T,$

$H=\left[\begin{array}{cccccc}0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right],$

$B=\frac{\mathrm{\&rho;}}{b}[\frac{(b+\mathrm{\&Delta;b})\mathrm{\&rho;}}{b}-(a+\mathrm{\&Delta;a})],$

$C=-\frac{\mathrm{\&rho;}-a}{b}\frac{{\&PartialD;\stackrel{.}{\mathrm{\&omega;}}}_r^{*}}{\&PartialD;{\mathrm{\&omega;}}_r^{*}}+\frac{1}{b}\frac{\&PartialD;{\stackrel{..}{\mathrm{\&omega;}}}_r^{*}}{\&PartialD;{\mathrm{\&omega;}}_r^{*}},$

$D=\frac{\&PartialD;{\stackrel{.}{\mathrm{\&omega;}}}_r^{*}}{\&PartialD;{\mathrm{\&omega;}}_r^{*}},$

$H\left(x\left(t\right)\right)={\frac{\&PartialD;y}{\&PartialD;x}|}_{x=x\left(t\right)}=\left[\begin{array}{cccccc}0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right],$

$\begin{array}{c}F\left(k\right)=e^{F\left(x\right)T}\&ap;I+F\left(x\right)T\\ =\left[\begin{array}{cccccc}1& 0& 0& \mathrm{AT}& 0& \mathrm{BT}\\ 0& 1-\frac{R_s}{L_s}T& 0& \frac{{\mathrm{\&lambda;}}_r}{L_s}\sin {\mathrm{\&theta;}}_r& \frac{{\mathrm{\&lambda;}}_r{\mathrm{\&omega;}}_r}{L_s}\cos {\mathrm{\&theta;}}_r& 0\\ 0& 0& 1-\frac{R_s}{L_s}T& -\frac{{\mathrm{\&lambda;}}_r}{L_s}\cos {\mathrm{\&theta;}}_r& \frac{{\mathrm{\&lambda;}}_r{\mathrm{\&omega;}}_r}{L_s}\sin {\mathrm{\&theta;}}_r& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& T& 1& 0\\ 0& 0& 0& 0& 0& 1+\mathrm{CT}\end{array}\right]\end{array},$

$B\left(k\right)={\&Integral;}_0^T{e}^{F\left(x\right)T}\mathrm{dBt}\&ap;\mathrm{BT}={\left[\begin{array}{cccccc}0& T/L_s& 0& 0& 0& 0\\ 0& 0& T/L_s& 0& 0& 0\end{array}\right]}^T$

Wherein, the system noise function that w (k) is discretization, the measurement noises function that v (k) is discretization, R _sfor stator resistance, λ _rfor stator magnetic linkage, L _sfor stator equivalent inductance, θ _rfor electrical degree, ρ is negative constant; A, b are for setting characteristic procedure amount, and Δ b is that process error compensates; T representation feature matrix.

2. permagnetic synchronous motor senseless control system according to claim 1, is characterized in that, $i_d^{*}=0.$

3. the control method of permagnetic synchronous motor senseless control system according to claim 1, is characterized in that, comprising:

1), whole control system powers on and initialization; SVPWM unit sends initial pulse width signal to inverter; Inverter generates three-phase windings electric current according to this initial pulse width signal and exports to PMSM, drives PMSM to rotate;

2), initialization terminates, and whole control system is run; Three-phase windings current i _a, i _b, i _cexport the first coordinate transformation unit to, the first coordinate transformation unit is by three-phase windings current i _a, i _b, i _ctransform to the stator current i under alpha-beta coordinate system _α, i _β; Stator current i _α, i _βinput sliding formwork extended Kalman filter and the second coordinate transformation unit, stator current i _α, i _βthe stator current i under d-q coordinate system is transformed in the second coordinate transformation unit _q, i _d; Sliding formwork extended Kalman filter unit is by the stator current i under alpha-beta coordinate system _α, i _β, stator voltage u _α, u _βand given rotor speed as the input of sliding formwork extended Kalman filter, after spreading kalman recursive operation, obtain rotor speed ω _r, corner with the reference stator current under d-q coordinate system with reference to stator current input the first comparator and stator current i _qdifference input the one PI controller relatively, a PI controller carries out ratio to difference, integral operation obtains q shaft voltage component instruction input three-dimensional converter unit; Stator current i _dinput the second comparator and reference stator current difference input the 2nd PI controller compared, the 2nd PI controller carries out ratio to difference, integral operation obtains d shaft voltage component instruction input three-dimensional converter unit; Corner signal inputs the second coordinate transformation unit and three-dimensional converter unit; D shaft voltage component instruction input in three-dimensional converter unit the stator voltage u transformed under alpha-beta coordinate system _α, u _β; Stator voltage u _α, u _βsend into SVPWM unit, SVPWM unit is according to stator voltage u _α, u _β, adopt Using dSPACE of SVPWM algorithm generating power device pulse width signal input inverter; Inverter generates three-phase windings electric current according to this pulse width signal and sends to motor body unit;

3), repeat step (2) and carry out loop control.

4. control method according to claim 3, is characterized in that, step 2) in sliding formwork extended Kalman filter unit by the stator current i under alpha-beta coordinate system _α, i _β, stator voltage u _α, u _βand given rotor speed as the input of sliding formwork extended Kalman filter, after spreading kalman recursive operation, obtain rotor speed ω _r, corner with the reference stator current under d-q coordinate system specifically comprise:

(1) according to permagnetic synchronous motor PMSM kinetic model and in conjunction with coordinate transform, the motor status equation under alpha-beta coordinate system is obtained:

$\left\{\begin{array}{c}\frac{{\mathrm{di}}_{\mathrm{\&alpha;}}}{\mathrm{dt}}=-\frac{R_s}{L_s}{i}_{\mathrm{\&alpha;}}+\frac{{\mathrm{\&lambda;}}_r}{L_s}{\mathrm{\&omega;}}_r\sin {\mathrm{\&theta;}}_r+\frac{1}{L_s}{u}_{\mathrm{\&alpha;}}\\ \frac{{\mathrm{di}}_{\mathrm{\&beta;}}}{\mathrm{dt}}=-\frac{R_s}{L_s}{i}_{\mathrm{\&alpha;}}-\frac{{\mathrm{\&lambda;}}_r}{L_s}{\mathrm{\&omega;}}_r\sin {\mathrm{\&theta;}}_r+\frac{1}{L_s}{u}_{\mathrm{\&beta;}}\end{array}\right.$

In formula, R _sfor stator resistance, λ _rfor stator magnetic linkage, L _sfor stator equivalent inductance, θ _rfor electrical degree;

(2) further, the reference stator current under d-q coordinate system is determined by Sliding mode variable structure control strategy its process is as follows:

A) designing Integral Sliding Mode face is: sliding mode control law is: μ=ρ e (t)-β sign (s), and wherein ρ is negative constant, and β is sliding formwork handoff gain coefficient,

$\mathrm{sign}\left(s\right)=\left\{\begin{array}{cc}1,& s>0\\ 0,& s=0\\ -1,& s<0\end{array}\right.$ For sign function;

B) Lyapunov function is selected thus make system can reach sliding formwork state in any initial condition, thus can obtain $\mathrm{\&mu;}=\mathrm{\&rho;e}\left(t\right)-\mathrm{\&beta;sign}\left(s\right)={\mathrm{bi}}_q^{*}-a{\mathrm{\&omega;}}_r^{*}-{\stackrel{.}{\mathrm{\&omega;}}}^{*};$

C) push away: $i_q^{*}=\frac{1}{b}[\mathrm{\&rho;}({\mathrm{\&omega;}}_r-{\mathrm{\&omega;}}_r^{*})-\mathrm{\&beta;sign}\left(s\right)+a{\mathrm{\&omega;}}_r^{*}+{\stackrel{.}{\mathrm{\&omega;}}}^{*}];$

(3) Sliding mode variable structure control is embedded in EKF, from extended Kalman filter, by rotor speed ω _r, given rotor speed electrical degree θ _r, the stator current i under alpha-beta coordinate system _α, i _βand the reference stator current under d-q coordinate system as state variable, state equation and the output equation that can obtain system are as follows:

$\left\{\begin{array}{c}\stackrel{.}{X}\left(t\right)=f\left(x\right)+\mathrm{Au}\left(t\right)+w\left(t\right)\\ y\left(t\right)=\mathrm{Hx}\left(t\right)+v\left(t\right)\end{array}\right.$

Wherein, in the system mode of t $X={\left[\begin{array}{cccccc}{i}_q^{*}& i_{\mathrm{\&alpha;}}& i_{\mathrm{\&beta;}}& {\mathrm{\&omega;}}_r& {\mathrm{\&theta;}}_r& {\mathrm{\&omega;}}_r^{*}\end{array}\right]}^T,$ System control amount u=[V _αv _β] ^t, measured value $y={\left[\begin{array}{ccc}{i}_{\mathrm{\&alpha;}}& i_{\mathrm{\&beta;}}& {\mathrm{\&omega;}}_r^{*}\end{array}\right]}^T,$ W (t) is system noise function, and v (t) is measurement noises function, $f\left(x\right)=\left[\begin{array}{c}{f}_1\\ f_2\\ f_3\\ f_4\\ f_5\\ f_6\end{array}\right]=\left[\begin{array}{c}\frac{{\mathrm{di}}_q^{*}}{\mathrm{dt}}\\ \frac{{\mathrm{dt}}_{\mathrm{\&alpha;}}}{\mathrm{dt}}\\ \frac{{\mathrm{di}}_{\mathrm{\&beta;}}}{\mathrm{dt}}\\ \frac{d{\mathrm{\&omega;}}_r}{\mathrm{dt}}\\ \frac{d{\mathrm{\&theta;}}_r}{\mathrm{dt}}\\ \frac{d{\mathrm{\&omega;}}_r^{*}}{\mathrm{dt}}\end{array}\right]=\left[\begin{array}{c}\frac{1}{b}[\mathrm{\&rho;}{\stackrel{.}{\mathrm{\&omega;}}}_r-(\mathrm{\&rho;}-a){\stackrel{.}{\mathrm{\&omega;}}}^{*}+{\stackrel{..}{\mathrm{\&omega;}}}_r^{*}]\\ -\frac{R_S}{L_S}{i}_{\mathrm{\&alpha;}}+\frac{{\mathrm{\&lambda;}}_r}{L_S}{\mathrm{\&omega;}}_r\sin {\mathrm{\&theta;}}_r\\ -\frac{R_S}{L_S}{i}_{\mathrm{\&alpha;}}+\frac{{\mathrm{\&lambda;}}_r}{L_S}{\mathrm{\&omega;}}_r\sin {\mathrm{\&theta;}}_r\\ 0\\ {\mathrm{\&omega;}}_r\\ {\mathrm{\&omega;}}_r^{*}\end{array}\right],$

Sliding mode variable structure control equation is comprised in f (x): $i_q^{*}=\frac{1}{b}[\mathrm{\&rho;}({\mathrm{\&omega;}}_r-{\mathrm{\&omega;}}_r^{*})-\mathrm{\&beta;sign}\left(s\right)+a{\mathrm{\&omega;}}_r^{*}+{\stackrel{.}{\mathrm{\&omega;}}}^{*}],$

System parameters matrix: $A={\left[\begin{array}{cccccc}0& 1/L_s& 0& 0& 0& 0\\ 0& 0& 1/L_s& 0& 0& 0\end{array}\right]}^T,$

The parameter matrix of measuring system: $H=\left[\begin{array}{cccccc}0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right];$

(4) for mating the non-linear of permagnetic synchronous motor, by extended Kalman filter digitlization, first need to carry out linearization process to f (x), its Jacobian matrix is:

$F\left(x\left(t\right)\right)={\frac{\&PartialD;f}{\&PartialD;x}|}_{x=x\left(t\right)}=\left[\begin{array}{ccccccc}0& 0& 0& B& & 0& C\\ 0& -R_s/L_s& 0& \frac{{\mathrm{\&lambda;}}_r}{L_s}\sin {\mathrm{\&theta;}}_r& & \frac{{\mathrm{\&lambda;}}_r{\mathrm{\&omega;}}_r}{L_s}\cos {\mathrm{\&theta;}}_r& 0\\ 0& 0& -R_s/L_s& -\frac{{\mathrm{\&lambda;}}_r}{L_s}\cos {\mathrm{\&theta;}}_r& & \frac{{\mathrm{\&lambda;}}_r{\mathrm{\&omega;}}_r}{L_s}\sin {\mathrm{\&theta;}}_r& 0\\ 0& 0& 0& 0& & 0& 0\\ 0& 0& 0& 1& & 0& 0\\ 0& 0& 0& 0& & 0& D\end{array}\right]$

Wherein: $B=\frac{\mathrm{\&rho;}}{b}[\frac{(b+\mathrm{\&Delta;b})\mathrm{\&rho;}}{b}-(a+\mathrm{\&Delta;a})],$ $C=-\frac{\mathrm{\&rho;}-a}{b}\frac{{\&PartialD;\stackrel{.}{\mathrm{\&omega;}}}_r^{*}}{\&PartialD;{\mathrm{\&omega;}}_r^{*}}+\frac{1}{b}\frac{\&PartialD;{\stackrel{..}{\mathrm{\&omega;}}}_r^{*}}{\&PartialD;{\mathrm{\&omega;}}_r^{*}},$ $D=\frac{\&PartialD;{\stackrel{.}{\mathrm{\&omega;}}}_r^{*}}{\&PartialD;{\mathrm{\&omega;}}_r^{*}},$ $H\left(x\left(t\right)\right)={\frac{\&PartialD;y}{\&PartialD;x}|}_{x=x\left(t\right)}=\left[\begin{array}{cccccc}0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right];$

(5) matrix after step (4) neutral line is carried out discretization, process is as follows:

$\begin{array}{c}F\left(k\right)=e^{F\left(x\right)T}\&ap;I+F\left(x\right)T\\ =\left[\begin{array}{cccccc}1& 0& 0& \mathrm{AT}& 0& \mathrm{BT}\\ 0& 1-\frac{R_s}{L_s}T& 0& \frac{{\mathrm{\&lambda;}}_r}{L_s}\sin {\mathrm{\&theta;}}_r& \frac{{\mathrm{\&lambda;}}_r{\mathrm{\&omega;}}_r}{L_s}\cos {\mathrm{\&theta;}}_r& 0\\ 0& 0& 1-\frac{R_s}{L_s}T& -\frac{{\mathrm{\&lambda;}}_r}{L_s}\cos {\mathrm{\&theta;}}_r& \frac{{\mathrm{\&lambda;}}_r{\mathrm{\&omega;}}_r}{L_s}\sin {\mathrm{\&theta;}}_r& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& T& 1& 0\\ 0& 0& 0& 0& 0& 1+\mathrm{CT}\end{array}\right]\end{array}$

$B\left(k\right)={\&Integral;}_0^T{e}^{F\left(x\right)T}\mathrm{dBt}\&ap;\mathrm{BT}={\left[\begin{array}{cccccc}0& T/L_s& 0& 0& 0& 0\\ 0& 0& T/L_s& 0& 0& 0\end{array}\right]}^T$

According to above formula, thus obtain the system mode after discretization and output equation:

$\left\{\begin{array}{c}x\left(k\right)=F\left(k\right)x(k-1)+B\left(k\right)u\left(k\right)+w\left(k\right)\\ y\left(k\right)=\mathrm{Hx}\left(k\right)+v\left(k\right)\end{array}\right.$

(6), after the state equation obtaining the sliding formwork embedded type extended Kalman filter in step (5) after digitlization and output equation, the reference stator current under d-q coordinate system is carried out according to five recursion steps of Kalman filtering with rotor speed ω _rstate estimation.