CN104579089A - Estimation method of rotating speed of permanent-magnet synchronous motor - Google Patents

Abstract

The invention aims at providing an estimation method of a rotating speed of a permanent-magnet synchronous motor. The method comprises the following steps of 1, acquiring d-q-axis components id, iq, ud and uq of stator current and voltage of the permanent-magnet synchronous motor, 2, obtaining a corresponding relational expression by respectively superposing direct current signals on the d-axis stator current id and the voltage ud and keeping the q-axis stator current iq and the voltage uq constant provided that d-q-axis equivalent inductance of the permanent-magnet synchronous motor is same, 3, establishing a stator current adjustable model containing the to-be-estimated rotating speed, and 4, estimating the rotating speed according to a fractional order estimation rule based on the stator current adjustable model and the acquired motor stator current and voltage. The estimation method of the rotating speed overcomes the defects of low accuracy and poor steady and dynamic performance of the existing technical scheme, and an estimated value of the rotating speed is more accurate, so that a sensorless control system of the motor can obtain higher dynamic and static speed tracking control performance, and the robustness of the system is improved.

Description

Permagnetic synchronous motor method for estimating rotating speed

Technical field

The present invention relates to electric drive and control field, be specifically related to a kind of permagnetic synchronous motor method for estimating rotating speed.

Background technology

Permagnetic synchronous motor (PMSM), because of it, there is volume and the plurality of advantages such as moment of inertia is little, efficiency is high, torque ratio of inertias is large, overload capacity is strong, speed-regulating range width, make PMSM governing system become a study hotspot in Prospect of AC Adjustable Speed Drive field.At present, PMSM control system utilizes the mechanical sensor such as photoelectric encoder, resolver to detect rotating speed and the rotor-position of motor usually, to realize high performance rotating speed and position feedback control.But the introducing of mechanical pick-up device not only increases equipment cost, and dynamic and static state performance and the functional reliability that electric machine control system exports response can be reduced.The sensorless strategy technology of PMSM, because eliminating the mechanical pick-up device for measuring position of magnetic pole and speed, therefore effectively can solve above-mentioned difficulties.In recent ten years, the sensorless strategy research of PMSM is flourish, receives much attention.

So far, for the speed estimate problem in PMSM sensorless control system, there has been proposed based on the open loop estimation methods of motor model, state observer method, model reference adaptive method, kalman filter method and High Frequency Injection etc.Wherein, based on the model reference adaptive method of estimation of reactive power or stator current, although have algorithm simple, be easy to the advantage that numerical control system realizes, estimated accuracy depends on the accuracy of the parameter of electric machine.Therefore, the Shi Bianhui of real electrical machinery parameter makes electric machine control system cannot obtain gratifying stable state accuracy of observation and dynamic response characteristic in wider speed range of operation, therefore, model reference adaptive method is only applicable to some low speed and the not high occasion of required precision.

Summary of the invention

The present invention aims to provide a kind of permagnetic synchronous motor self adaptation method for estimating rotating speed, this method for estimating rotating speed overcomes that prior art accuracy is low, the defect of stable state and bad dynamic performance, speed estimate value is more accurate, make motor sensorless control system obtain more excellent dynamic and static state speed tracking control performance, and improve the robustness of system.

Technical scheme of the present invention is as follows:

A kind of permagnetic synchronous motor method for estimating rotating speed, comprises the following steps:

Step 1, obtains the d-q axle component i of permanent-magnetic synchronous motor stator electric current and voltage _d, i _qand u _d, u _q;

Step 2, assuming that permagnetic synchronous motor d-q axle equivalent inductance is identical, i.e. L _d=L _q=L _s, to d axle stator current i _dwith voltage u _dsuperpose direct current signal respectively, and the current i of q axle stator _qwith voltage u _qconstant, make it meet following relation:

${\tilde{i}}_d=i_d+\frac{{\mathrm{\ψ}}_f}{L_s},{\tilde{i}}_q=i_q,{\tilde{u}}_d=u_d+\frac{R_s{\mathrm{\ψ}}_f}{L_s},{\tilde{u}}_q=u_q;$

Wherein: ψ _ffor the magnetic potential that permanent magnet on rotor produces; L _sfor equivalent inductance; R _sit is stator winding resistance;

Step 3, set up the stator current adjustable model containing rotating speed to be estimated:

$\frac{d}{\mathrm{dt}}\left[\begin{array}{c}{\hat{i}}_d\\ {\hat{i}}_q\end{array}\right]\left[\begin{array}{cc}-R_s/L_s& {\widehat{\mathrm{\ω}}}_e\\ -{\widehat{\mathrm{\ω}}}_e& {-R}_s/L_s\end{array}\right]\left[\begin{array}{c}{\hat{i}}_d\\ {\hat{i}}_q\end{array}\right]+\frac{1}{L_s}\left[\begin{array}{c}{\tilde{u}}_d\\ {\tilde{u}}_q\end{array}\right];$

In formula: with for the stator current output variable of adjustable model; for to real electrical machinery angular rate ω _eestimation;

Step 4, according to motor stator electric current and the voltage of stator current adjustable model and acquisition, estimate that rule is estimated rotating speed according to following fractional order:

${\widehat{\mathrm{\ω}}}_e=k_i{D}_t^{-\mathrm{\α}}({\tilde{i}}_d{\hat{i}}_q-{\tilde{i}}_q{\hat{i}}_d)+k_p({\tilde{i}}_d{\hat{i}}_q-{\tilde{i}}_q{\hat{i}}_d)+{\widehat{\mathrm{\ω}}}_e\left(0\right);$

In formula: represent fractional order integration computing, wherein fractional order differential order α ∈ (0,1], α value is determined by performance index function Optimizing Search; k _iand k _pbe respectively integration, the proportionality coefficient of estimating rule; it is initial speed estimated value.

The design process of described speed estimate rule is as follows:

For fractional calculus operator, may be defined as

$D_t^{\mathrm{\&alpha;}}{}_a=\left\{\begin{array}{cc}\frac{d^{\mathrm{\&alpha;}}}{{\mathrm{dt}}^{\mathrm{\&alpha;}}}& \mathrm{Re}\left[\mathrm{\&alpha;}\right]>0\\ 1& \mathrm{Re}\left[\mathrm{\&alpha;}\right]=0\\ {\&Integral;}_a^t{\left(\mathrm{d\&tau;}\right)}^{-\mathrm{\&alpha;}}& \mathrm{Re}\left[\mathrm{\&alpha;}\right]<0\end{array}\right.---\left(1\right);$

In formula: α is any plural number, a and t represents the bound that operator operation operates respectively; As a=0, conventional represent at present, although fractional calculus computing has multiple different form of Definition, in actual applications, Riemann-Liouville (R-L) definition is the most frequently used one;

For the α rank calculus of function of a single variable f (t), its R-L is defined as

$D_t^{\mathrm{\&alpha;}}{}_{a}f\left(t\right)=\frac{1}{\mathrm{\&Gamma;}(m-\mathrm{\&alpha;})}\frac{d^m}{{\mathrm{dt}}^m}\underset{a}{\overset{t}{\&Integral;}}\frac{f\left(\mathrm{\&tau;}\right)}{{(t-\mathrm{\&tau;})}^{1-(m-a)}}\mathrm{d\&tau;}---\left(2\right);$

(m-1) < α <m in formula, m is integer, and a is the initial time of f (t).Γ () is gamma function, and

The stator voltage equation of PMSM under d-q axle rotating coordinate system:

$\left\{\begin{array}{c}{u}_d=R_s{i}_d+L_d\frac{{\mathrm{di}}_d}{\mathrm{dt}}-{\mathrm{\&omega;}}_e{L}_d{i}_q\\ u_q=R_s{i}_q+L_q\frac{{\mathrm{di}}_q}{\mathrm{dt}}+{\mathrm{\&omega;}}_e{\mathrm{\&psi;}}_f+{\mathrm{\&omega;}}_e{i}_d{L}_q\end{array}\right.---\left(3\right);$

In formula: u _d, u _qbe respectively the stator voltage under d, q axis coordinate system; i _d, i _qbe respectively d, q axle component of stator current; ψ _ffor the magnetic potential that permanent magnet on rotor produces; L _d, L _qbe respectively d, q axle equivalent inductance; ω _erepresent rotor angular rate; R _sit is stator winding resistance;

Assuming that d, q axle equivalent inductance is identical, i.e. L _d=L _q=L _s, and define

${\tilde{i}}_d=i_d+\frac{{\mathrm{\&psi;}}_f}{L_s},{\tilde{i}}_q=i_q,{\tilde{u}}_d=u_d+\frac{R_s{\mathrm{\&psi;}}_f}{L_s},{\tilde{u}}_q=u_q---\left(4\right);$

Then formula (3) can be arranged the current equation for following form

$\frac{d}{\mathrm{dt}}\left[\begin{array}{c}{\tilde{i}}_d\\ {\tilde{i}}_q\end{array}\right]\left[\begin{array}{cc}-R_s/L_s& {\mathrm{\&omega;}}_e\\ {-\mathrm{\&omega;}}_e& {-R}_s/L_s\end{array}\right]\left[\begin{array}{c}{\tilde{i}}_d\\ {\tilde{i}}_q\end{array}\right]+\frac{1}{L_s}\left[\begin{array}{c}{\tilde{u}}_d\\ {\tilde{u}}_q\end{array}\right]---\left(5\right);$

Above formula can be write as standard type expression formula further

$\frac{d}{\mathrm{dt}}\tilde{i}=A\tilde{i}+B\tilde{u}---\left(6\right);$

In formula: $A=\left[\begin{array}{cc}{-R}_s/L_s& {\mathrm{\&omega;}}_e\\ {-\mathrm{\&omega;}}_e& -R_s/L_s\end{array}\right],B=\left[\begin{array}{cc}1/L_s& 0\\ 0& 1/L_s\end{array}\right],\tilde{i}=\left[\begin{array}{c}{\tilde{i}}_d\\ {\tilde{i}}_q\end{array}\right],\tilde{u}=\left[\begin{array}{c}{\tilde{u}}_d\\ {\tilde{u}}_q\end{array}\right];$

Power taking machine itself, as with reference to model, is set up according to formula (5) and is had input identical with reference model, and the stator current adjustable model containing rotating speed to be estimated:

$\frac{d}{\mathrm{dt}}\left[\begin{array}{c}{\hat{i}}_d\\ {\hat{i}}_q\end{array}\right]\left[\begin{array}{cc}-R_s/L_s& {\widehat{\mathrm{\&omega;}}}_e\\ -{\widehat{\mathrm{\&omega;}}}_e& {-R}_s/L_s\end{array}\right]\left[\begin{array}{c}{\hat{i}}_d\\ {\hat{i}}_q\end{array}\right]+\frac{1}{L_s}\left[\begin{array}{c}{\tilde{u}}_d\\ {\tilde{u}}_q\end{array}\right]---\left(7\right);$

Wherein: with for the stator current output variable of adjustable model; represent speed estimate, above formula is write as standard type and is:

$\frac{d}{\mathrm{dt}}\hat{i}=\hat{A}\hat{i}+B\tilde{u}---\left(8\right);$

In formula: $\hat{A}=\left[\begin{array}{cc}{-R}_s/L_s& {\widehat{\mathrm{\&omega;}}}_e\\ -{\widehat{\mathrm{\&omega;}}}_e& -R_s/L_s\end{array}\right],\hat{i}=\left[\begin{array}{c}{\hat{i}}_d\\ {\hat{i}}_q\end{array}\right];$

Current error vector between definition adjustable model and reference model utilize formula (5) and (7) that current error equation can be obtained:

$\frac{d}{\mathrm{dt}}\left[\begin{array}{c}{e}_d\\ e_q\end{array}\right]=\left[\begin{array}{cc}-R_s/L_s& {\mathrm{\&omega;}}_e\\ -{\mathrm{\&omega;}}_e& -R_s/L_s\end{array}\right]\left[\begin{array}{c}{e}_d\\ e_q\end{array}\right]-({\mathrm{\&omega;}}_e-{\widehat{\mathrm{\&omega;}}}_e)M\left[\begin{array}{c}{\hat{i}}_d\\ {\hat{i}}_q\end{array}\right]=\mathrm{Ae}-({\mathrm{\&omega;}}_e-{\widehat{\mathrm{\&omega;}}}_e)M\hat{i}---\left(9\right);$

Wherein $M=\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right];$

Definition error for rotating speed estimation and choose the Lyapunov versus time change rule of following form:

In formula: fractional order differential order α ∈ (0,1]; Coefficient ξ >0; Assuming that motor is in constant speed operating state, i.e. ω _efor constant, in conjunction with error equation (10), above formula becomes

In view of A has negative real part characteristic root λ _1,2=-R _s/ L _s± j ω _e, when

$\frac{d^{\mathrm{\&alpha;}}{\widehat{\mathrm{\&omega;}}}_e}{{\mathrm{dt}}^{\mathrm{\&alpha;}}}=-{\mathrm{\&xi;}}^{-1}{e}^{T}M\hat{i}={\mathrm{\&xi;}}^{-1}({\tilde{i}}_d{\hat{i}}_q-{\tilde{i}}_q{\hat{i}}_d)---\left(12\right);$

Namely get and estimate that rule is

${\widehat{\mathrm{\&omega;}}}_e={\mathrm{\&xi;}}^{-1}{D}_t^{-\mathrm{\&alpha;}}({\tilde{i}}_d{\hat{i}}_q-{\tilde{i}}_q{\hat{i}}_d)+{\widehat{\mathrm{\&omega;}}}_e\left(0\right)---\left(13\right);$

Can make

In conjunction with the Theory of Stability of new fractional-order system and Lyapunov function Theory of Stability known, under the fractional order integration of formula (13) estimates rule condition, the stator current error between reference model and adjustable model and error for rotating speed estimation asymptotically stability can be made to converge to zero;

For improving the response performance of speed estimate, introducing proportional component, making formula (13) be modified to fractional order proportional integral form:

${\widehat{\mathrm{\&omega;}}}_e=k_i{D}_t^{-\mathrm{\&alpha;}}({\tilde{i}}_d{\hat{i}}_q-{\tilde{i}}_q{\hat{i}}_d)+k_p({\tilde{i}}_d{\hat{i}}_q-{\tilde{i}}_q{\hat{i}}_d)+{\widehat{\mathrm{\&omega;}}}_e\left(0\right)---\left(15\right);$

In formula: k _i=ξ ^-1>0 is integral coefficient, k _p>0 is proportionality coefficient, for speed estimate initial value; When α=1, formula (15) then become conventional integer rank, based on stator current reference model self adaptation speed estimate rule, coefficient k in rule is estimated for fractional order of the present invention _p, k _iwith , the coefficient magnitude corresponding to the self adaptation speed estimate rule of conventional integer rank can be quoted;

In conjunction with electric system parameter, quote the coefficient in the self adaptation speed estimate rule of conventional integer rank: k _p, k _iwith , set up the following time and take advantage of Error Absolute Value integration (ITAE) performance index function:

$I\left(t\right)={\&Integral;}_0^{T}t\left(\right|e_d|+|e_q|+|e_{\mathrm{\&omega;}}\left|\right)\mathrm{dt}---\left(16\right);$

Based on formula (16) ITAE performance index function minimum criteria, setting is expected after rotating speed, to fractional-order α (0,1] carry out finding optimum α value in scope, namely complete the structure that speed estimate is restrained after determining α value.

Permagnetic synchronous motor method for estimating rotating speed of the present invention is by setting up real electrical machinery stator current reference model and the stator current adjustable model containing estimation rotating speed, and current error equation basis between two models builds a kind of rotating speed fractional order and estimate rule, than existing integer rank, this estimation rule estimates that rule precision is higher, convergence is stronger, this speed estimate rule meets Theory of Stability and the Lyapunov function Theory of Stability of new fractional-order system, and the stator current error between reference model and adjustable model and error for rotating speed estimation asymptotically stability can be made to converge to zero; Meanwhile, add proportionality coefficient in speed estimate rule, improve the response performance of method for estimating rotating speed; Further, fractional-order parameter alpha is carried out optimizing by ITAE performance index function minimum criteria and is determined, makes this method for estimating rotating speed obtain optimum estimated accuracy, and then improves the performance of permagnetic synchronous motor sensorless strategy rotating speed.

Accompanying drawing explanation

Fig. 1 is method for estimating rotating speed schematic flow sheet of the present invention

Fig. 2 is the change curve of embodiment 1 performance objective function with fractional-order α

Fig. 3 is the temporal evolution comparison diagram of embodiment 1 scheme and contrast scheme error for rotating speed estimation

Fig. 4 is the temporal evolution comparison diagram that embodiment 1 scheme and contrast scheme turn stator current error

Fig. 5 is the tracing control situation comparison diagram of embodiment 1 scheme and contrast scheme actual speed

Fig. 6 is that embodiment 1 scheme and contrast scheme estimate the transient response change curve comparison diagram of rotating speed at initial period

Fig. 7 is embodiment 1 scheme and the transient response change curve comparison diagram of contrast scheme actual speed at initial period

Fig. 8 is that embodiment 1 scheme and contrast scheme estimate speed error change curve comparison diagram when load torque saltus step

Fig. 9 is embodiment 1 scheme and contrast scheme actual speed response change comparison diagram when load torque saltus step

Figure 10 be embodiment 1 scheme and contrast scheme in parameter and expect that rotating speed changes time actual speed and estimate between rotating speed error change curve comparison figure

Figure 11 be embodiment 1 scheme and contrast scheme in parameter and expect that rotating speed changes time actual speed control evolution comparison diagram

Number in the figure implication is as follows:

(a): contrast scheme--integer rank (α=1) method for estimating rotating speed;

(b): embodiment 1--fractional order (α=0.93) method for estimating rotating speed.

Embodiment

The present invention is illustrated below in conjunction with drawings and Examples.

Embodiment 1

As shown in Figure 1, a kind of permagnetic synchronous motor method for estimating rotating speed of the present embodiment, comprises the following steps:

Step 1, obtains the d-q axle component i of permanent-magnetic synchronous motor stator electric current and voltage _d, i _qand u _d, u _q;

Step 2, assuming that permagnetic synchronous motor d-q axle equivalent inductance is identical, i.e. L _d=L _q=L _s, to d axle stator current i _dwith voltage u _dsuperpose direct current signal respectively, and the current i of q axle stator _qwith voltage u _qconstant, make it meet following relation:

${\tilde{i}}_d=i_d+\frac{{\mathrm{\&psi;}}_f}{L_s},{\tilde{i}}_q=i_q,{\tilde{u}}_d=u_d+\frac{R_s{\mathrm{\&psi;}}_f}{L_s},{\tilde{u}}_q=u_q;$

Wherein: ψ _ffor the magnetic potential that permanent magnet on rotor produces; L _sfor equivalent inductance; R _sit is stator winding resistance;

Step 3, set up the stator current adjustable model containing rotating speed to be estimated:

$\frac{d}{\mathrm{dt}}\left[\begin{array}{c}{\hat{i}}_d\\ {\hat{i}}_q\end{array}\right]\left[\begin{array}{cc}-R_s/L_s& {\widehat{\mathrm{\&omega;}}}_e\\ -{\widehat{\mathrm{\&omega;}}}_e& {-R}_s/L_s\end{array}\right]\left[\begin{array}{c}{\hat{i}}_d\\ {\hat{i}}_q\end{array}\right]+\frac{1}{L_s}\left[\begin{array}{c}{\tilde{u}}_d\\ {\tilde{u}}_q\end{array}\right];$

In formula: with for the stator current output variable of adjustable model; for to real electrical machinery angular rate ω _eestimation;

Step 4, according to motor stator electric current and the voltage of stator current adjustable model and acquisition, estimate that rule is estimated rotating speed according to following fractional order:

${\widehat{\mathrm{\&omega;}}}_e=k_i{D}_t^{-\mathrm{\&alpha;}}({\tilde{i}}_d{\hat{i}}_q-{\tilde{i}}_q{\hat{i}}_d)+k_p({\tilde{i}}_d{\hat{i}}_q-{\tilde{i}}_q{\hat{i}}_d)+{\widehat{\mathrm{\&omega;}}}_e\left(0\right);$

In formula: represent fractional order integration computing, wherein fractional order differential order α ∈ (0,1], α value is determined by performance index function Optimizing Search; k _iand k _pbe respectively integration, the proportionality coefficient of estimating rule; it is initial speed estimated value.

The design process of described speed estimate rule is as follows:

For fractional calculus operator, may be defined as

$D_t^{\mathrm{\&alpha;}}{}_a=\left\{\begin{array}{cc}\frac{d^{\mathrm{\&alpha;}}}{{\mathrm{dt}}^{\mathrm{\&alpha;}}}& \mathrm{Re}\left[\mathrm{\&alpha;}\right]>0\\ 1& \mathrm{Re}\left[\mathrm{\&alpha;}\right]=0\\ {\&Integral;}_a^t{\left(\mathrm{d\&tau;}\right)}^{-\mathrm{\&alpha;}}& \mathrm{Re}\left[\mathrm{\&alpha;}\right]<0\end{array}\right.---\left(1\right)$

In formula: α is any plural number, a and t represents the bound that operator operation operates respectively.As a=0, conventional represent at present, although fractional calculus computing has multiple different form of Definition, in actual applications, Riemann-Liouville (R-L) definition is the most frequently used one;

For the α rank calculus of function of a single variable f (t), its R-L is defined as

$D_t^{\mathrm{\&alpha;}}{}_{a}f\left(t\right)=\frac{1}{\mathrm{\&Gamma;}(m-\mathrm{\&alpha;})}\frac{d^m}{{\mathrm{dt}}^m}\underset{a}{\overset{t}{\&Integral;}}\frac{f\left(\mathrm{\&tau;}\right)}{{(t-\mathrm{\&tau;})}^{1-(m-a)}}\mathrm{d\&tau;}---\left(2\right);$

(m-1) < α <m in formula, m is integer, and a is the initial time of f (t).Γ () is gamma function, and

The stator voltage equation of PMSM under d-q axle rotating coordinate system:

$\left\{\begin{array}{c}{u}_d=R_s{i}_d+L_d\frac{{\mathrm{di}}_d}{\mathrm{dt}}-{\mathrm{\&omega;}}_e{L}_d{i}_q\\ u_q=R_s{i}_q+L_q\frac{{\mathrm{di}}_q}{\mathrm{dt}}+{\mathrm{\&omega;}}_e{\mathrm{\&psi;}}_f+{\mathrm{\&omega;}}_e{i}_d{L}_q\end{array}\right.---\left(3\right);$

In formula: u _d, u _qbe respectively the stator voltage under d, q axis coordinate system; i _d, i _qbe respectively d, q axle component of stator current; ψ _ffor the magnetic potential that permanent magnet on rotor produces; L _d, L _qbe respectively d, q axle equivalent inductance; ω _erepresent rotor angular rate; R _sit is stator winding resistance;

Assuming that d, q axle equivalent inductance is identical, i.e. L _d=L _q=L _s, and define

${\tilde{i}}_d=i_d+\frac{{\mathrm{\&psi;}}_f}{L_s},{\tilde{i}}_q=i_q,{\tilde{u}}_d=u_d+\frac{R_s{\mathrm{\&psi;}}_f}{L_s},{\tilde{u}}_q=u_q---\left(4\right);$

Then formula (3) can be arranged the current equation for following form

$\frac{d}{\mathrm{dt}}\left[\begin{array}{c}{\tilde{i}}_d\\ {\tilde{i}}_q\end{array}\right]\left[\begin{array}{cc}-R_s/L_s& {\mathrm{\&omega;}}_e\\ {-\mathrm{\&omega;}}_e& {-R}_s/L_s\end{array}\right]\left[\begin{array}{c}{\tilde{i}}_d\\ {\tilde{i}}_q\end{array}\right]+\frac{1}{L_s}\left[\begin{array}{c}{\tilde{u}}_d\\ {\tilde{u}}_q\end{array}\right]---\left(5\right);$

Above formula can be write as standard type expression formula further

$\frac{d}{\mathrm{dt}}\tilde{i}=A\tilde{i}+B\tilde{u}---\left(6\right);$

In formula: $A=\left[\begin{array}{cc}{-R}_s/L_s& {\mathrm{\&omega;}}_e\\ {-\mathrm{\&omega;}}_e& -R_s/L_s\end{array}\right],B=\left[\begin{array}{cc}1/L_s& 0\\ 0& 1/L_s\end{array}\right],\tilde{i}=\left[\begin{array}{c}{\tilde{i}}_d\\ {\tilde{i}}_q\end{array}\right],\tilde{u}=\left[\begin{array}{c}{\tilde{u}}_d\\ {\tilde{u}}_q\end{array}\right];$

Power taking machine itself, as with reference to model, is set up according to formula (5) and is had input identical with reference model, and the stator current adjustable model containing rotating speed to be estimated:

$\frac{d}{\mathrm{dt}}\left[\begin{array}{c}{\hat{i}}_d\\ {\hat{i}}_q\end{array}\right]\left[\begin{array}{cc}-R_s/L_s& {\widehat{\mathrm{\&omega;}}}_e\\ -{\widehat{\mathrm{\&omega;}}}_e& {-R}_s/L_s\end{array}\right]\left[\begin{array}{c}{\hat{i}}_d\\ {\hat{i}}_q\end{array}\right]+\frac{1}{L_s}\left[\begin{array}{c}{\tilde{u}}_d\\ {\tilde{u}}_q\end{array}\right]---\left(7\right);$

Wherein: with for the stator current output variable of adjustable model; represent speed estimate, above formula is write as standard type and is:

$\frac{d}{\mathrm{dt}}\hat{i}=\hat{A}\hat{i}+B\tilde{u}---\left(8\right);$

In formula: $\hat{A}=\left[\begin{array}{cc}{-R}_s/L_s& {\widehat{\mathrm{\&omega;}}}_e\\ -{\widehat{\mathrm{\&omega;}}}_e& -R_s/L_s\end{array}\right],\hat{i}=\left[\begin{array}{c}{\hat{i}}_d\\ {\hat{i}}_q\end{array}\right];$

Current error vector between definition adjustable model and reference model utilize formula (5) and (7) that current error equation can be obtained:

$\frac{d}{\mathrm{dt}}\left[\begin{array}{c}{e}_d\\ e_q\end{array}\right]=\left[\begin{array}{cc}-R_s/L_s& {\mathrm{\&omega;}}_e\\ -{\mathrm{\&omega;}}_e& -R_s/L_s\end{array}\right]\left[\begin{array}{c}{e}_d\\ e_q\end{array}\right]-({\mathrm{\&omega;}}_e-{\widehat{\mathrm{\&omega;}}}_e)M\left[\begin{array}{c}{\hat{i}}_d\\ {\hat{i}}_q\end{array}\right]=\mathrm{Ae}-({\mathrm{\&omega;}}_e-{\widehat{\mathrm{\&omega;}}}_e)M\hat{i}---\left(9\right);$

Wherein $M=\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right];$

Definition error for rotating speed estimation and choose the Lyapunov versus time change rule of following form

In formula: fractional order differential order α ∈ (0,1]; Coefficient ξ >0.Assuming that motor is in constant speed operating state, i.e. ω _efor constant, in conjunction with error equation (9), above formula becomes:

In view of A has negative real part characteristic root λ _1,2=-R _s/ L _s± j ω _e, when

$\frac{d^{\mathrm{\&alpha;}}{\widehat{\mathrm{\&omega;}}}_e}{{\mathrm{dt}}^{\mathrm{\&alpha;}}}=-{\mathrm{\&xi;}}^{-1}{e}^{T}M\hat{i}={\mathrm{\&xi;}}^{-1}({\tilde{i}}_d{\hat{i}}_q-{\tilde{i}}_q{\hat{i}}_d)---\left(12\right);$

Namely get and estimate that rule is

${\widehat{\mathrm{\&omega;}}}_e={\mathrm{\&xi;}}^{-1}{D}_t^{-\mathrm{\&alpha;}}({\tilde{i}}_d{\hat{i}}_q-{\tilde{i}}_q{\hat{i}}_d)+{\widehat{\mathrm{\&omega;}}}_e\left(0\right)---\left(13\right);$

Can make

In conjunction with the Theory of Stability of new fractional-order system and Lyapunov function Theory of Stability known, under the fractional order integration of formula (13) estimates rule condition, the stator current error between reference model and adjustable model and error for rotating speed estimation asymptotically stability can be made to converge to zero;

For improving the response performance of speed estimate, introducing proportional component, making formula (13) be modified to fractional order proportional integral form:

${\widehat{\mathrm{\&omega;}}}_e=k_i{D}_t^{-\mathrm{\&alpha;}}({\tilde{i}}_d{\hat{i}}_q-{\tilde{i}}_q{\hat{i}}_d)+k_p({\tilde{i}}_d{\hat{i}}_q-{\tilde{i}}_q{\hat{i}}_d)+{\widehat{\mathrm{\&omega;}}}_e\left(0\right)---\left(15\right);$

In formula: k _i=ξ ^-1>0 is integral coefficient, k _p>0 is proportionality coefficient, for speed estimate initial value; When α=1, formula (15) then become conventional integer rank, restrain based on stator current reference model self adaptation speed estimate; Coefficient k in rule is estimated for the present embodiment fractional order _p, k _iwith numerical value, the coefficient corresponding to conventional integer rank self adaptation speed estimate rule can be quoted;

The present embodiment electric system parameter is as shown in table 1:

Table 1 embodiment 1 electric system parameter

In conjunction with electric system parameter, quote the coefficient corresponding to the self adaptation speed estimate rule of integer rank: k _i=5.6, k _p=12.8 Hes building the following time takes advantage of Error Absolute Value integration (ITAE) performance index function:

$I\left(t\right)={\&Integral;}_0^{T}t\left(\right|e_d|+|e_q|+|e_{\mathrm{\&omega;}}\left|\right)\mathrm{dt}---\left(16\right);$

Based on formula (16) ITAE performance index function minimum criteria, setting expects that rotating speed is after 3500r/min, to fractional-order α (0,1] carry out finding optimum α value in scope, namely complete the structure that speed estimate is restrained after determining α value;

Be illustrated in figure 2 the change curve of performance objective function with fractional-order α, as seen from Figure 2, when getting α=0.93, I (t) has minimum value, therefore, and α=0.93;

Thus, the estimation rule of embodiment 1 method for estimating rotating speed is:

${\widehat{\mathrm{\&omega;}}}_e=5.6D_t^{-0.93}({\tilde{i}}_d{\hat{i}}_q-{\tilde{i}}_d{\hat{i}}_d)+12.8({\tilde{i}}_d{\hat{i}}_q-{\tilde{i}}_q{\hat{i}}_d)---\left(17\right).$

Integer rank (α=1) the speed estimate scheme that the speed estimate scheme of embodiment 1 and prior art are commonly used is carried out simulation comparison below:

Under Fig. 3, Fig. 4 respectively illustrate integer rank (α=1) and embodiment 1 fractional order (α=0.93) ART network condition, the temporal evolution figure of error for rotating speed estimation and stator current error.Found out by Fig. 3 and Fig. 4, two kinds of adaptive approachs all can make the asymptotically stability convergence near zero of error for rotating speed estimation and stator current error, but compare integer rank situation, and it is more accurate that embodiment 1 adopts fractional order ART network to restrain the speed estimate value obtained;

Fig. 5 reflects the tracing control situation of actual speed, Fig. 6, Fig. 7 respectively illustrate PMSM control system and estimate rotating speed and the actual speed transient response change curve at initial period, from Fig. 5 to Fig. 7, embodiment 1 fractional order ART network scheme has better estimated accuracy and convergence, thus realizes making motor obtain more excellent dynamic and static state speeds control performance;

Fig. 8 show load torque t=5s by 4N.m saltus step be 5N.m, t=10s by 5N.m saltus step to estimation speed error situation of change during 7N.m; Fig. 9 is corresponding motor actual speed response change figure.Obviously found out by Fig. 8 and Fig. 9, under the motor operating conditions that there is load jump, compare integer rank situation, embodiment 1 fractional order self adaptation method for estimating rotating speed still can be estimated actual speed comparatively accurately, and at jumping moment, the pulsation of evaluated error and actual speed is all less, and this also shows that the adaptive estimation method of employing embodiment 1 fractional order can improve the anti-loading changing capability without transducer PMSM speeds control further;

Real electrical machinery is often in comparatively wide range speed control and reversion running status, and is subject to the variable effect as factors such as temperature, external magnetic field, magnetic saturation degree, and therefore, this will cause the winding resistance R of PMSM _s, permanent flux ψ _f change etc. parameter, therefore often there is parameter differences between adjustable model and realistic model.In order to verify the superiority of embodiment 1 fractional order self adaptation method for estimating rotating speed, respectively to real electrical machinery ψ in emulation _fcarry out the change of-20% and+20% with the parameter value of Rs, and consider to expect that rotating speed gets the motor ruuning situation of 1000r/min, 3500r/min, 1000r/min ,-1000r/min respectively when time 0s, 4s, 8s, 12s;

Figure 10 is that the error change curve chart in above-mentioned situation between actual speed and estimation rotating speed contrasts, and Figure 11 shows the control evolution condition contrast of motor actual speed.From Figure 10 and 11, even if there is larger parameter differences between real system and adjustable model, two kinds of self adaptation method for estimating rotating speed all can realize the stability contorting of motor relative broad range rotating speed, but compare integer rank situation, embodiment 1 fractional order adaptive estimation method has speed estimate effect more accurately, and this makes PMSM obtain more excellent motor speed tracing control precision and robustness.

Claims (2)

1. a permagnetic synchronous motor method for estimating rotating speed, is characterized in that comprising the following steps:

Step 1, obtains the d-q axle component i of permanent-magnetic synchronous motor stator electric current and voltage _d, i _qand u _d, u _q;

Step 2, assuming that permagnetic synchronous motor d-q axle equivalent inductance is identical, i.e. L _d=L _q=L _s, to d axle stator current i _dwith voltage u _dsuperpose direct current signal respectively, and the current i of q axle stator _qwith voltage u _qconstant, make it meet following relation:

${\tilde{i}}_d=i_d+\frac{{\mathrm{\&psi;}}_f}{L_s},{\tilde{i}}_q=i_q,{\tilde{u}}_d=u_d+\frac{R_s{\mathrm{\&psi;}}_f}{L_s},{\tilde{u}}_q=u_q;$

Wherein: ψ _ffor the magnetic potential that permanent magnet on rotor produces; L _sfor equivalent inductance; R _sit is stator winding resistance;

Step 3, set up the stator current adjustable model containing rotating speed to be estimated:

$\frac{d}{\mathrm{dt}}\left[\begin{array}{c}{\hat{i}}_d\\ {\hat{i}}_q\end{array}\right]=\left[\begin{array}{cc}-R_s/L_s& {\widehat{\mathrm{\&omega;}}}_e\\ -{\widehat{\mathrm{\&omega;}}}_e& -R_s/L_s\end{array}\right]\left[\begin{array}{c}{\hat{i}}_d\\ {\hat{i}}_q\end{array}\right]+\frac{1}{L_s}\left[\begin{array}{c}{\tilde{u}}_d\\ {\tilde{u}}_q\end{array}\right];$

In formula: with for the stator current output variable of adjustable model; for to real electrical machinery angular rate ω _eestimation;

Step 4, according to motor stator electric current and the voltage of stator current adjustable model and acquisition, estimate that rule is estimated rotating speed according to following fractional order:

${\widehat{\mathrm{\&omega;}}}_e=k_i{D}_t^{-\mathrm{\&alpha;}}({\tilde{i}}_d{\hat{i}}_q-{\tilde{i}}_q{\hat{i}}_d)+k_p({\tilde{i}}_d{\hat{i}}_q-{\tilde{i}}_q{\hat{i}}_d)+{\widehat{\mathrm{\&omega;}}}_e\left(0\right);$

In formula: represent fractional order integration computing, wherein fractional order differential order α ∈ (0,1], α value is determined by performance index function Optimizing Search; k _iand k _pbe respectively integration, the proportionality coefficient of estimating rule; it is initial speed estimated value.

2. permagnetic synchronous motor method for estimating rotating speed as claimed in claim 1, is characterized in that described performance index function Optimizing Search is specific as follows:

Definition current error $e_d={\tilde{i}}_d-{\hat{i}}_d,e_q={\tilde{i}}_q-{\hat{i}}_q,$ And error for rotating speed estimation $e_{\mathrm{\&omega;}}={\mathrm{\&omega;}}_e-{\widehat{\mathrm{\&omega;}}}_e,$ Set up the following time and take advantage of Error Absolute Value integral performance target function:

$I\left(t\right)={\&Integral;}_0^{T}t\left(\right|e_d|+|e_q|+|e_{\mathrm{\&omega;}}\left|\right)\mathrm{dt};$

Find the α value making I (t) be minimum value, then this α value is the α value determined by Optimizing Search.