CN104617850A - Double-closed-loop controller and double-closed-loop control method of permanent magnet synchronous motor - Google Patents

Abstract

The invention provides a double-closed-loop control method of a permanent magnet synchronous motor. The double-closed-loop control method includes the steps: A, detecting three-phase current, actual rotating speed and a rotor position angle of the permanent magnet synchronous motor, and transforming the three-phase current to obtain stator current in a d-q axis coordinate system; B, controlling the actual rotating speed of the motor and expectation rotating speed by a rotating speed loop fractional order controller to obtain q axis reference current, controlling d axis current and d axis reference current by a current loop fractional order controller to obtain d axis voltage, and controlling q axis current and q axis reference current by the current loop fractional order controller to obtain q axis voltage; C, performing a series of transformations for d-q axis voltage and the rotor position angle, then outputting three-phase voltage, and controlling the permanent magnet synchronous motor. The invention further provides a double-closed-loop controller of the permanent magnet synchronous motor. The controller overcomes the shortcomings of poor applicability and weak anti-jamming capability when a current loop is controlled by the aid of an integer order, so that the motor has better dynamic rotating speed performance and anti-load jumping capability, and the efficiency of a motor system is improved.

Description

The double-closed-loop control device of permagnetic synchronous motor and control method

Technical field

The present invention relates to permagnetic synchronous motor control field, be specifically related to a kind of double-closed-loop control method of permagnetic synchronous motor.

Background technology

Permagnetic synchronous motor has a wide range of applications in fields such as industrial production, Digit Control Machine Tool, Aero-Space and new forms of energy pure electric automobiles.Permagnetic synchronous motor is the non linear system of a close coupling, inevitably external interference is subject to during real work, and under working environment complicated and changeable, system parameters and load etc. easily change, this is deteriorated causing the control performance of permagnetic synchronous motor, and then the rotating speed of direct influential system exports.Therefore, control strategy realizes Permanent-magnet Synchronous-motor Speed Servo System to obtain satisfactory performance output and improve the important guarantee of system robustness.

At present, people are for the rotating speed control problem of permagnetic synchronous motor, adopt double-closed-loop control structure, and based on vector control technology, propose the control methods such as such as proportion integration differentiation (PID) control, adaptive control, robust control, sliding formwork control, fuzzy control.Recent years, the advantage such as system control performance and robustness is significantly improved in view of fractional order control has, scholar is had to start to pay close attention to the fractional order control research of permagnetic synchronous motor, there is document respectively the integer rank PI of der Geschwindigkeitkreis and PID controller to be extended to fractional order form, and provide the setting method of fractional order control device parameter; The employing mixing difference artificial bee colony algorithm also had carries out self-adaptative adjustment to the controling parameters of fractional order PI controller respectively, further increases the adaptivity of Permanent-magnet Synchronous-motor Speed Servo System, dynamic and static state performance and anti-external interference ability.But, prior art is all for loop design fractional order adjuster, electric current loop still adopts traditional integer rank control form, in view of the key that electric current loop is in PMSM Speed servo system, it is to raising Systematical control precision and response speed, and improve control performance aspect important role, the fractional order control therefore for electric current loop is quite necessary.

Summary of the invention

The present invention aims to provide a kind of double-closed-loop control method of permagnetic synchronous motor, this control method overcomes defect poor for applicability when prior art adopts integer rank to control to electric current loop, antijamming capability is weak, adopt the scheme of der Geschwindigkeitkreis and electric current loop two close cycles fractional order control, motor is made to obtain more excellent speed dynamic performance and anti-loading saltus step ability, and obviously improve motor power factor, improve system effectiveness.

Technical scheme of the present invention is as follows: a kind of double-closed-loop control device of permagnetic synchronous motor, is characterized in that: difference and art methods, electric current, the rotating speed two close cycles of permagnetic synchronous motor all have employed fractional order control device.

Wherein propose electric current loop, the fractional order control device expression formula of der Geschwindigkeitkreis is respectively

$C_i\left(s\right)=K_i\left(\frac{1+{\mathrm{\τ}}_{i}s}{{\mathrm{\τ}}_i{s}^{\mathrm{\α}}}\right)---\left(1\right);$

With

$C_v\left(s\right)=K_v\left(\frac{1+{\mathrm{\τ}}_v{s}^{\mathrm{\λ}}}{{\mathrm{\τ}}_v{s}^{\mathrm{\λ}}}\right)---\left(2\right);$

In formula: α ∈ (0,1) is the fractional order integration order parameter of current loop controller, λ ∈ (0,1) is the fractional order integration order parameter of der Geschwindigkeitkreis controller, K _iand τ _ibe respectively electric current loop fractional order control device multiplication factor and the time of integration coefficient; K _v, and τ _vbe respectively der Geschwindigkeitkreis fractional order control device multiplication factor and the time of integration coefficient.

The present invention also provides a kind of method for controlling permanent magnet synchronous motor to comprise the following steps:

The three-phase current i of A, detection permagnetic synchronous motor _a, i _band i _c, detect actual speed ω, the rotor position angle of permagnetic synchronous motor three-phase current i _a, i _band i _ccurrent i under Clarke conversion obtains α, β coordinate system _α, i _β, by i _α, i _βbound site angle setting and the stator current i under Park conversion draws d-q axis coordinate system _d, i _q;

B, by motor actual speed ω with expect rotational speed omega _rcompare and draw speed error signal, speed error signal obtains q axle reference stator current value i after the process of der Geschwindigkeitkreis fractional order control device _qr; By d axle stator current i _dwith the d axle reference current i being preset as 0 _drcompare and obtain d axle stator current error signal, d axle stator current error signal obtains d axle stator voltage u after the process of electric current loop fractional order control device _d, by q axle stator current i _qwith its reference current i _qrcompare and obtain the error signal of q axle stator current, q axle stator current error signal obtains q axle stator voltage u after the process of electric current loop fractional order control device _q;

C, in conjunction with d axle stator voltage u _d, q axle stator voltage u _qand rotor position angle voltage u under utilizing Park inverse transformation to obtain α, β coordinate system _α, u _β; By u _α, u _βthreephase stator winding voltage u is exported through inverter again after SVPWM algorithm process _a, u _band u _crealize the drived control to permagnetic synchronous motor motor.

The present invention also provides a kind of permagnetic synchronous motor, utilizes the double-closed-loop control device of above-mentioned permagnetic synchronous motor.

The design process of the double-closed-loop control device of permagnetic synchronous motor of the present invention comprises following step:

A, set up electric current loop open-loop transfer function, obtain electric current loop closed loop transfer function, electric current loop closed loop transfer function, is processed and then obtain der Geschwindigkeitkreis open-loop transfer function and frequency characteristic mathematic(al) representation thereof;

B, design current ring integer rank pi controller, and obtain electric current loop integer rank pi controller multiplication factor and the time of integration coefficient;

C, phase margin criterion, robustness criterion and amplitude criterion in conjunction with control system Domain Design, to the frequency characteristic of der Geschwindigkeitkreis open-loop transfer function calculate the fractional-order parameter of der Geschwindigkeitkreis controller, multiplication factor and the time of integration coefficient, generate the expression of der Geschwindigkeitkreis fractional order control device;

D, using the multiplication factor of electric current loop integer rank controller and the time of integration coefficient as electric current loop fractional order integration derivative controller multiplication factor and the time of integration coefficient, preset the expectation rotating speed of motor, using motor power factor as performance index function, by the control imitation to motor two close cycles Fractional-order Control Systems model, obtain the change curve of electric system power factor with current loop controller fractional-order parameter, based on the maximum principle of power factor, determine the fractional order order value that corresponding power factor is maximum, then the expression of electric current loop fractional order control device is drawn, control imitation described in this step be by the fractional order order parameter alpha in fractional order current loop controller (0,1] travel through in scope, motor power factor size corresponding under realizing calculating different α value situation.

Steps A concrete steps are as follows:

Consider that d axle reference stator electric current is the vector control mode of zero, definition K ₁and τ ₁gain and the time constant filter of q axle stator current feedback filtering link respectively, and definition K ₂and τ ₂gain and the lag time constant of three-phase PWM inverter respectively, due to τ ₁and τ ₂numerical value very little, the open-loop transfer function of current loop control object can be set up:

$G_{\mathrm{io}}\left(s\right)=\frac{K_1{K}_2{K}_R}{(T_{i}s+1)\·(T_{m}s+1)}---\left(1\right);$

In formula: K _r=1/R, T _i=τ ₁+ τ ₂, T _m=L/R, T _mbe the electromagnetic time constant in armature loop, L is the equivalent inductance of motor d-q shaft, and R is stator winding resistance.

Electric current loop of the present invention, der Geschwindigkeitkreis fractional order control device expression formula are respectively

$C_i\left(s\right)=K_i\left(\frac{1+{\mathrm{\τ}}_{i}s}{{\mathrm{\τ}}_i{s}^{\mathrm{\α}}}\right)---\left(2\right);$

With

$C_v\left(s\right)=K_v\left(\frac{1+{\mathrm{\τ}}_v{s}^{\mathrm{\λ}}}{{\mathrm{\τ}}_v{s}^{\mathrm{\λ}}}\right)---\left(3\right);$

In formula: α ∈ (0,1) is the fractional order integration order parameter of current loop controller, λ ∈ (0,1) is the fractional order integration order parameter of der Geschwindigkeitkreis controller, K _iand τ _ibe respectively electric current loop fractional order control device multiplication factor and the time of integration coefficient; K _v, and τ _vbe respectively der Geschwindigkeitkreis fractional order control device multiplication factor and the time of integration coefficient.

Can derive electric current loop closed loop transfer function, in conjunction with (1) and (2) is

$G_{\mathrm{iB}}=\frac{K_1{K}_2{K}_R{K}_i\·(1+{\mathrm{\τ}}_{i}s)}{(T_{i}s+1)\·(T_{m}s+1){\mathrm{\τ}}_i{s}^{\mathrm{\α}}+K_1{K}_2{K}_R{K}_i(1+{\mathrm{\τ}}_{i}s)}---\left(4\right);$

For making the time constant limit offseting controlled device the zero point of current loop controller, get τ _i=T _m, and definition of T=τ _i/ (K ₁k ₂k _rk _i), then formula (4) becomes

$G_{\mathrm{ic}}\left(s\right)=\frac{1/T}{(T_{i}s+1)s^{\mathrm{\α}}+1/T}---\left(5\right);$

In view of the cut-off frequency of der Geschwindigkeitkreis is lower, and T _i<< τ _i<<1s, is treated to above formula depression of order

$G_{\mathrm{iB}}\left(s\right)=\frac{1}{T{s}^{\mathrm{\&alpha;}}+1}---\left(6\right);$

The equivalent model of der Geschwindigkeitkreis controlled device is:

$P\left(s\right)=\frac{K}{s(T{s}^{\mathrm{\&alpha;}}+1)}---\left(7\right);$

Wherein K=K _c/ J, moment coefficient, P _nfor magnetic pole of the stator logarithm, for the magnetic potential that permanent magnet produces, J is rotor moment of inertia;

The frequency characteristic of formula (7) is:

$\left|P\left(\mathrm{j\&Omega;}\right)\right|=K/\sqrt{A_0^2+B_0^2}---\left(8\right);$

Arg(P(jΩ))＝-arctan(B ₀/A ₀)(9)；

In formula: $A_0=-T{\mathrm{\&Omega;}}^{1+\mathrm{\&alpha;}}\sin \left(\frac{\mathrm{\&alpha;\&pi;}}{2}\right),B_0=\mathrm{\&Omega;}+T{\mathrm{\&Omega;}}^{1+\mathrm{\&alpha;}}\cos \left(\frac{\mathrm{\&alpha;\&pi;}}{2}\right);$

Convolution (3) and formula (7) can draw der Geschwindigkeitkreis open-loop transfer function and frequency characteristic thereof

$G\left(s\right)=C_v\left(s\right)P\left(s\right)=\frac{{\mathrm{KK}}_v({\mathrm{\&tau;}}_v{s}^{\mathrm{\&lambda;}}+1)}{{\mathrm{\&tau;}}_v{s}^{1+\mathrm{\&lambda;}}(s^{\mathrm{\&alpha;}}+1)}---\left(10\right);$

$\left|G\left(\mathrm{j\&Omega;}\right)\right|=K\sqrt{(A_1^2+B_1^2)/(A_0^2+B_0^2)}---\left(11\right);$

Arg(G(jΩ))＝arctan(B ₁/A ₁)-arctan(B ₀/A ₀)(12)；

In formula: $A_1=K_v[1+{\mathrm{\&Omega;}}^{-\mathrm{\&lambda;}}\cos \left(\frac{\mathrm{\&pi;\&lambda;}}{2}\right)/{\mathrm{\&tau;}}_v],B_1=-K_v{\mathrm{\&Omega;}}^{-\mathrm{\&lambda;}}\sin \left(\frac{\mathrm{\&pi;\&lambda;}}{2}\right)/{\mathrm{\&tau;}}_v.$

Step B concrete steps are as follows:

Convolution (5), according to classical control theory, when α=1, requires overshoot≤5%, and getting damping ratio is 0.707, T=2T _i, and in conjunction with τ _i=T _m=L/R, can obtain

K _i＝τ _i/(K ₁K ₂K _RT)＝0.5L/[K ₁K ₂(τ ₁+τ ₂)] (13)；

According to the system parameters of motor, by τ _i=T _m=L/R calculates τ _i, calculate K by formula (13) _i,

Step C concrete steps are as follows:

According to control system Domain Design theory, as the cut-off frequency Ω of initialization system _cand phase margin under the stability of a system and robustness requirement condition, the phase place of open-loop transfer function G (s) and amplitude should meet following design criterion:

(1) phase margin criterion

(2) the robustness criterion of system gain change

$\frac{d\left(\mathrm{Arg}\left(C\left(\mathrm{j\&Omega;}\right)P\left(\mathrm{j\&Omega;}\right)\right)\right)}{\mathrm{d\&Omega;}}{|}_{\mathrm{\&Omega;}={\mathrm{\&Omega;}}_c}=0---\left(15\right);$

(3) amplitude criterion

|G(jΩ _c)|＝|C(jΩ _c)P(jΩ _c)|＝1 (16)；

Choose cut-off frequency Ω _cand phase margin according to criterion (1), can be obtained by formula (12):

In formula:

According to criterion (2), can be obtained by formula (12):

${\mathrm{\&tau;}}_v=\frac{2B{\mathrm{\&Omega;}}_c^{-2\mathrm{\&lambda;}}}{-D\&PlusMinus;\sqrt{D^2-4B^2{\mathrm{\&Omega;}}_c^{-2\mathrm{\&lambda;}}}}---\left(18\right);$

Wherein: $B=\frac{T}{1+{\left(T{\mathrm{\&Omega;}}_c\right)}^2},D={\mathrm{\&Omega;}}_c^{-\mathrm{\&lambda;}}[2B\cos \left(\frac{\mathrm{\&lambda;\&pi;}}{2}\right)-{\mathrm{\&lambda;\&Omega;}}_c^{-1}\sin \left(\frac{\mathrm{\&lambda;\&pi;}}{2}\right)];$

According to criterion (3), can be obtained by formula (11):

$K_v=\frac{{\mathrm{\&Omega;}}_c\sqrt{1+{\left({\mathrm{\&Omega;}}_{c}T\right)}^2}}{\sqrt{{(1+{\mathrm{\&Omega;}}_c^{-\mathrm{\&lambda;}}\cos \frac{\mathrm{\&lambda;\&pi;}}{2}/{\mathrm{\&tau;}}_v)}^2+{({\mathrm{\&Omega;}}_c^{-\mathrm{\&lambda;}}\cos \frac{\mathrm{\&lambda;\&pi;}}{2}/{\mathrm{\&tau;}}_v)}^2}}---\left(19\right);$

According to formula (17) and (18), in conjunction with the τ of electric system parameter, electric current loop integer rank controller _iand K _i, the method for being got intersection point by mapping solves τ _vwith λ, substitute into formula (19) and obtain K _v, by τ _v, λ and K _vbring formula (3) into, der Geschwindigkeitkreis fractional order control implement body expression formula can be obtained.

Meanwhile, the integer rank for λ=1 control situation, for taking into account phase margin and the robustness requirement of control system, τ _vthe mean value of retrievable (17) and (18) two Directly solution, then adopts (19) to obtain K _v, therefore can draw the integer rank controller expression that der Geschwindigkeitkreis is traditional.

Step D concrete steps are as follows:

By electric current loop integer rank controller according to formula (2) fractional order, using motor power factor as performance index function, wherein, power factor

In formula: θ represents power-factor angle; Preset the expectation rotating speed of motor, by the control imitation to motor two close cycles Fractional-order Control Systems model, according to power factor maximal criterion to the fractional-order α of current loop controller (0,1] search is optimized in scope, namely by the fractional-order parameter alpha of current loop controller (0,1] traversal in scope, measures motor d, q axle stator current i simultaneously _dand i _q, calculate the value of corresponding electric system power factor, obtain the fractional-order α value when power factor is maximum; According to τ _i,k _isubstitute into formula (2) with α, draw the expression of electric current loop fractional order control device.

The two close cycles fractional order control device of permagnetic synchronous motor of the present invention have employed the combination of electric current loop FO-ID (fractional order integration differential) controller and der Geschwindigkeitkreis FO-PI (fractional order proportional integral) controller, above-mentioned controller is under the requirement meeting the stability of a system and robustness, design according to the design criterion that phase place and amplitude should meet, motor can not only be made to obtain more excellent speed dynamic performance and anti-loading saltus step ability, and obviously improve motor power factor, improve system effectiveness; Wherein electric current loop FO-ID (fractional order integration differential) controller, can not only improve the current follow-up control ability of electric current loop further, and q axle stator current is less, copper wastage is reduced, further increases system effectiveness.

Accompanying drawing explanation

Fig. 1 is the two close cycles fractional order control device design flow diagram of permagnetic synchronous motor of the present invention

Fig. 2 is the permagnetic synchronous motor two close cycles Fractional-order Control Systems fundamental diagram in embodiment 1

Fig. 3 is τ in embodiment 1 _iwith the graph of relation of λ

Fig. 4 be in embodiment 1 power-factor cos θ with the change curve of α

Fig. 5 is the baud comparison diagram of double-closed-loop control method and two kinds of compared with control methods in embodiment 1

Fig. 6 is the rotation speed change curve comparison figure of embodiment 1 double-closed-loop control method and two kinds of compared with control methods

Fig. 7 is the q shaft current change curve of embodiment 1 double-closed-loop control method and two kinds of compared with control methods

Fig. 8 is the motor power factor change curve of embodiment 1 double-closed-loop control method and two kinds of compared with control methods

Motor speed change curve when Fig. 9 is the load jump of embodiment 1 double-closed-loop control method and two kinds of compared with control methods

Power factor change curve chart when Figure 10 is the load jump of embodiment 1 double-closed-loop control method and two kinds of compared with control methods

Figure 11 is the motor speed change curve in embodiment 1 speed Control situation

Figure 12 is the motor power factor change curve in embodiment 1 speed Control situation

In Fig. 5-12 curve title and label as follows:

A () is the curve of traditional double closed loop integer rank proportional plus integral control method (λ=α=1);

B () is der Geschwindigkeitkreis fractional order pi controller, the curve on electric current loop integer rank proportional integral method (λ=0.72, α=1);

C () is the curve of the present embodiment 1 two close cycles two close cycles fractional order control method (λ=0.72, α=0.65).

Embodiment

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

The double-closed-loop control device of the present embodiment permagnetic synchronous motor, comprise electric current loop fractional order control device and der Geschwindigkeitkreis fractional order control device, their controller mathematic(al) representation is respectively:

$C_i\left(s\right)=K_i\left(\frac{1+{\mathrm{\&tau;}}_{i}s}{{\mathrm{\&tau;}}_i{s}^{\mathrm{\&alpha;}}}\right)---\left(1\right);$

With

$C_v\left(s\right)=K_v\left(\frac{1+{\mathrm{\&tau;}}_v{s}^{\mathrm{\&lambda;}}}{{\mathrm{\&tau;}}_v{s}^{\mathrm{\&lambda;}}}\right)---\left(2\right);$

In formula: α ∈ (0,1) is the fractional order integration order parameter of current loop controller, λ ∈ (0,1) is the fractional order integration order parameter of der Geschwindigkeitkreis controller, K _iand τ _ibe respectively electric current loop fractional order control device multiplication factor and the time of integration coefficient; K _v, and τ _vbe respectively der Geschwindigkeitkreis fractional order control device multiplication factor and the time of integration coefficient.

As shown in Figure 1, the double-closed-loop control method of permagnetic synchronous motor, comprises the following steps:

The three-phase current i of A, detection permagnetic synchronous motor _a, i _band i _c, detect actual speed ω, the rotor position angle of permagnetic synchronous motor three-phase current i _a, i _band i _ccurrent i under Clarke conversion obtains α, β coordinate system _α, i _β, by i _α, i _βbound site angle setting and the stator current i under Park conversion draws d-q axis coordinate system _d, i _q;

B, by motor actual speed ω with expect rotational speed omega _rcompare and draw speed error signal, speed error signal obtains q axle reference stator current value i after the process of der Geschwindigkeitkreis fractional order control device _qr; By d axle stator current i _dwith the d axle reference current i being preset as 0 _drcompare and obtain d axle stator current error signal, d axle stator current error signal obtains d axle stator voltage u after the process of electric current loop fractional order control device _d, by q axle stator current i _qwith its reference current i _qrcompare and obtain the error signal of q axle stator current, q axle stator current error signal obtains q axle stator voltage u after the process of electric current loop fractional order control device _q;

C, in conjunction with d axle stator voltage u _d, q axle stator voltage u _qand rotor position angle voltage u under utilizing Park inverse transformation to obtain α, β coordinate system _α, u _β; By u _α, u _βthreephase stator winding voltage u is exported through inverter again after SVPWM algorithm process _a, u _band u _crealize the drived control to permagnetic synchronous motor motor.

The double-closed-loop control device method for designing of the present embodiment permagnetic synchronous motor, comprises following step:

A, set up electric current loop open-loop transfer function, obtain electric current loop closed loop transfer function, electric current loop closed loop transfer function, is processed and then obtain der Geschwindigkeitkreis open-loop transfer function and frequency characteristic mathematic(al) representation thereof;

Concrete steps are as follows:

Consider that d axle reference stator electric current is the vector control mode of zero, definition K ₁and τ ₁gain and the time constant filter of q axle stator current feedback filtering link respectively, and definition K ₂and τ ₂gain and the lag time constant of three-phase PWM inverter respectively, due to τ ₁and τ ₂numerical value very little, the open-loop transfer function of current loop control object can be set up:

$G_{\mathrm{io}}\left(s\right)=\frac{K_1{K}_2{K}_R}{(T_{i}s+1)\&CenterDot;(T_{m}s+1)}---\left(1\right);$

In formula: K _r=1/R, T _i=τ ₁+ τ ₂, T _m=L/R, T _mbe the electromagnetic time constant in armature loop, L is the equivalent inductance of motor d-q shaft, and R is stator winding resistance.

Electric current loop of the present invention, der Geschwindigkeitkreis fractional order control device expression formula are respectively

$C_i\left(s\right)=K_i\left(\frac{1+{\mathrm{\&tau;}}_{i}s}{{\mathrm{\&tau;}}_i{s}^{\mathrm{\&alpha;}}}\right)---\left(2\right);$

With

$C_v\left(s\right)=K_v\left(\frac{1+{\mathrm{\&tau;}}_v{s}^{\mathrm{\&lambda;}}}{{\mathrm{\&tau;}}_v{s}^{\mathrm{\&lambda;}}}\right)---\left(3\right);$

In formula: α ∈ (0,1) is the fractional order integration order parameter of current loop controller, λ ∈ (0,1) is the fractional order integration order parameter of der Geschwindigkeitkreis controller, K _iand τ _ibe respectively electric current loop fractional order control device multiplication factor and the time of integration coefficient; K _v, and τ _vbe respectively der Geschwindigkeitkreis fractional order control device multiplication factor and the time of integration coefficient.

Can derive electric current loop closed loop transfer function, in conjunction with (1) and (2) is

$G_{\mathrm{iB}}=\frac{K_1{K}_2{K}_R{K}_i\&CenterDot;(1+{\mathrm{\&tau;}}_{i}s)}{(T_{i}s+1)\&CenterDot;(T_{m}s+1){\mathrm{\&tau;}}_i{s}^{\mathrm{\&alpha;}}+K_1{K}_2{K}_R{K}_i(1+{\mathrm{\&tau;}}_{i}s)}---\left(4\right);$

For making the time constant limit offseting controlled device the zero point of current loop controller, get τ _i=T _m, and definition of T=τ _i/ (K ₁k ₂k _rk _i), then formula (4) becomes

$G_{\mathrm{ic}}\left(s\right)=\frac{1/T}{(T_{i}s+1)s^{\mathrm{\&alpha;}}+1/T}---\left(5\right);$

In view of the cut-off frequency of der Geschwindigkeitkreis is lower, and T _i<< τ _i<<1s, is treated to above formula depression of order

$G_{\mathrm{iB}}\left(s\right)=\frac{1}{T{s}^{\mathrm{\&alpha;}}+1}---\left(6\right);$

The equivalent model of der Geschwindigkeitkreis controlled device is:

$P\left(s\right)=\frac{K}{s(T{s}^{\mathrm{\&alpha;}}+1)}---\left(7\right);$

Wherein K=K _c/ J, moment coefficient, P _nfor magnetic pole of the stator logarithm, for the magnetic potential that permanent magnet produces, J is rotor moment of inertia;

The frequency characteristic of formula (7) is:

$\left|P\left(\mathrm{j\&Omega;}\right)\right|=K/\sqrt{A_0^2+B_0^2}---\left(8\right);$

Arg(P(jΩ))＝-arctan(B ₀/A ₀) (9)；

In formula: $A_0=-T{\mathrm{\&Omega;}}^{1+\mathrm{\&alpha;}}\sin \left(\frac{\mathrm{\&alpha;\&pi;}}{2}\right),B_0=\mathrm{\&Omega;}+T{\mathrm{\&Omega;}}^{1+\mathrm{\&alpha;}}\cos \left(\frac{\mathrm{\&alpha;\&pi;}}{2}\right);$

Convolution (3) and formula (7) can draw der Geschwindigkeitkreis open-loop transfer function and frequency characteristic thereof

$G\left(s\right)=C_v\left(s\right)P\left(s\right)=\frac{{\mathrm{KK}}_v({\mathrm{\&tau;}}_v{s}^{\mathrm{\&lambda;}}+1)}{{\mathrm{\&tau;}}_v{s}^{1+\mathrm{\&lambda;}}(s^{\mathrm{\&alpha;}}+1)}---\left(10\right);$

$\left|G\left(\mathrm{j\&Omega;}\right)\right|=K\sqrt{(A_1^2+B_1^2)/(A_0^2+B_0^2)}---\left(11\right);$

Arg(G(jΩ))＝arctan(B ₁/A ₁)-arctan(B ₀/A ₀) (12)

In formula: $A_1=K_v[1+{\mathrm{\&Omega;}}^{-\mathrm{\&lambda;}}\cos \left(\frac{\mathrm{\&pi;\&lambda;}}{2}\right)/{\mathrm{\&tau;}}_v],B_1=-K_v{\mathrm{\&Omega;}}^{-\mathrm{\&lambda;}}\sin \left(\frac{\mathrm{\&pi;\&lambda;}}{2}\right)/{\mathrm{\&tau;}}_v.$

B, design current ring integer rank pi controller, and obtain electric current loop integer rank pi controller multiplication factor and the time of integration coefficient;

Concrete steps are as follows:

Convolution (5), when α=1, requires overshoot≤5%, and getting damping ratio is 0.707, T=2T _i, and in conjunction with τ _i=T _m=L/R, can obtain

K _i＝τ _i/(K ₁K ₂K _RT)＝0.5L/[K ₁K ₂(τ ₁+τ ₂)] (13)；

The present embodiment selects the parameter of electric machine as shown in table 1:

Table 1 embodiment 1 parameter of electric machine

According to the system parameters of motor, by τ _i=T _m=L/R calculates τ _i=0.004, calculate K by formula (13) _i=4.789;

C, phase margin criterion, robustness criterion and amplitude criterion in conjunction with control system Domain Design, to the frequency characteristic of der Geschwindigkeitkreis open-loop transfer function calculate the fractional-order parameter of der Geschwindigkeitkreis controller, multiplication factor and the time of integration coefficient, generate the expression of der Geschwindigkeitkreis fractional order control device;

Concrete steps are as follows:

According to control system Domain Design theory, as the cut-off frequency Ω of initialization system _cand phase margin under the stability of a system and robustness requirement condition, the phase place of open-loop transfer function G (s) and amplitude should meet following design criterion:

(1) phase margin criterion

(2) the robustness criterion of system gain change

$\frac{d\left(\mathrm{Arg}\left(C\left(\mathrm{j\&Omega;}\right)P\left(\mathrm{j\&Omega;}\right)\right)\right)}{\mathrm{d\&Omega;}}{|}_{\mathrm{\&Omega;}={\mathrm{\&Omega;}}_c}=0---\left(15\right);$

(3) amplitude criterion

G(jΩ _c)|＝|C(jΩ _c)P(jΩ _c)|＝1 (16)；

The present embodiment chooses cut-off frequency Ω _c=1000rad/s, phase margin

According to criterion (1), can be obtained by formula (12):

In formula:

According to criterion (2), can be obtained by formula (12):

${\mathrm{\&tau;}}_v=\frac{2B{\mathrm{\&Omega;}}_c^{-2\mathrm{\&lambda;}}}{-D\&PlusMinus;\sqrt{D^2-4B^2{\mathrm{\&Omega;}}_c^{-2\mathrm{\&lambda;}}}}---\left(18\right);$

Wherein: $B=\frac{T}{1+{\left(T{\mathrm{\&Omega;}}_c\right)}^2},D={\mathrm{\&Omega;}}_c^{-\mathrm{\&lambda;}}[2B\cos \left(\frac{\mathrm{\&lambda;\&pi;}}{2}\right)-{\mathrm{\&lambda;\&Omega;}}_c^{-1}\sin \left(\frac{\mathrm{\&lambda;\&pi;}}{2}\right)];$

According to criterion (3), can be obtained by formula (11):

$K_v=\frac{{\mathrm{\&Omega;}}_c\sqrt{1+{\left({\mathrm{\&Omega;}}_{c}T\right)}^2}}{\sqrt{{(1+{\mathrm{\&Omega;}}_c^{-\mathrm{\&lambda;}}\cos \frac{\mathrm{\&lambda;\&pi;}}{2}/{\mathrm{\&tau;}}_v)}^2+{({\mathrm{\&Omega;}}_c^{-\mathrm{\&lambda;}}\cos \frac{\mathrm{\&lambda;\&pi;}}{2}/{\mathrm{\&tau;}}_v)}^2}}---\left(19\right);$

According to formula (17) and (18), as shown in Figure 2, τ is solved by the method for getting intersection point of mapping _v=0.0276, λ=0.72, substitutes into formula (19) and obtains K _v=0.4617; By τ _v, λ and K _vbring formula (3) into, namely obtain der Geschwindigkeitkreis fractional order control implement body expression formula:

$C_v\left(s\right)=0.4617\left(\frac{1+0.0276s^{0.72}}{{0.0276s}^{0.72}}\right);$

Meanwhile, the integer rank for λ=1 control situation, for taking into account phase margin and the robustness requirement of control system, τ _vthe mean value of retrievable (17) and (18) two Directly solution, utilizes (19) simultaneously, also can obtain the integer rank controller expression formula that der Geschwindigkeitkreis is traditional:

$C_v\left(s\right)=0.5049\left(\frac{1+0.00375s}{0.00375s}\right);$

D, using the multiplication factor of electric current loop integer rank controller and the time of integration coefficient as electric current loop fractional order integration derivative controller multiplication factor and the time of integration coefficient, preset the expectation rotating speed of motor, using motor power factor as performance index function, by the control imitation to motor two close cycles Fractional-order Control Systems model, obtain the change curve of electric system power factor with current loop controller fractional-order parameter, based on the maximum principle of power factor, determine the fractional order order value that corresponding power factor is maximum, then the expression of electric current loop fractional order control device is drawn,

Concrete steps are:

By electric current loop integer rank controller according to formula (2) fractional order, using motor power factor as performance index function,

Wherein, power factor:

Wherein θ represents power-factor angle;

The expectation rotating speed that the present embodiment presets motor is 3500r/min, according to power factor maximal criterion to the fractional-order α of current loop controller (0,1] search is optimized in scope, namely by the fractional-order parameter alpha of current loop controller (0,1] traversal in scope, measures motor d, q axle stator current i simultaneously _dand i _q, calculate the value of corresponding electric system power factor, as shown in Figure 4, obtain fractional-order α=0.65 when power factor is maximum;

According to τ _i,k _ibring formula (2) into α, obtain electric current loop fractional order control implement body expression formula:

$C_i\left(s\right)=4.789\left(\frac{1+0.004s}{{0.004s}^{0.65}}\right).$

Therefore, the electric current loop of the double-closed-loop control device of the present embodiment permagnetic synchronous motor, der Geschwindigkeitkreis fractional order control device expression formula are respectively:

$C_i\left(s\right)=4.789\left(\frac{1+0.004s}{{0.004s}^{0.65}}\right);$

$C_v\left(s\right)=0.4617\left(\frac{1+0.0276s^{0.72}}{{0.0276s}^{0.72}}\right).$

The present embodiment sets up PMSM two close cycles Fractional-order Control Systems simulation model under MATLAB/Simulink environment, and wherein the numerical computations of fractional calculus utilizes Oustaloup filtering method to realize.

By checking herein the validity of proposition two close cycles fractional order control method and advance, give also two close cycles integer rank in emulation and control (λ=1, α=1), and der Geschwindigkeitkreis FO-PI controls, electric current loop IO-PI controls (λ=0.72, α=1) with the Comparative result of the present embodiment two close cycles fractional order control (λ=0.72, α=0.65):

Fig. 5 is the baud comparison diagram of the present embodiment double-closed-loop control method and two kinds of compared with control methods; As seen from Figure 5, compare traditional two close cycles IO-PI and control (λ=1, α=1) and der Geschwindigkeitkreis FO-PI, electric current loop IO-PI control situation (λ=0.72, α=1), the Ω of the present embodiment PMSM two close cycles fractional order control (λ=0.72, α=0.65) _cwith all meet designing requirement, and phase curve is at Ω _cthe flat extent at place is wider, and this also shows that two close cycles Fractional-order Control Systems meets Robustness Design criterion calls;

Under expectation rotating speed is the condition of 3500r/min, Fig. 6 shows the rotation speed change curve of the PMSM (permagnetic synchronous motor) under three kinds of different control method effects.As can be seen from Figure 6, three kinds of different control methods all can realize PMSM and expect that the tenacious tracking of rotating speed controls and non-overshoot, but the present embodiment two close cycles fractional order control (λ=0.72, α=0.65) but can make PMSM obtain more excellent speed dynamic performance;

Fig. 7 and 8 is the change curve of q shaft current and motor power factor respectively, from Fig. 7 and Fig. 8 relatively, under the effect of the present embodiment two close cycles fractional order control, q axle stator current amplitude is minimum and stable state accuracy is better, power factor obtains and significantly improves, and this shows that the electric current loop FO-ID controller in double closed-loop control system can not only improve the current follow-up control ability of electric current loop further, and q axle stator current is less, copper wastage is reduced, thus improves system effectiveness;

When Fig. 9 and Figure 10 sets forth load jump, the change curve of motor speed and power factor works as load torque, wherein load is 4N.m at t=0.1s by 2N.m saltus step, is obviously found out, at jumping moment the present embodiment by Fig. 9, two close cycles fractional order control, the PMSM fluctuation of speed is minimum; Figure 10 reflects when load torque increases, although the power factor of three kinds of control methods all decreases, but it is minimum that the permagnetic synchronous motor power factor under the effect of the present embodiment two close cycles fractional order control reduces amplitude, this shows, the present embodiment two close cycles fractional order control strategy can make permagnetic synchronous motor have good anti-loading changing capability;

Provide the control performance of the present embodiment two close cycles fractional order control method in speed Control situation below, consider to expect that at 0.2s place rotating speed accelerates to 4000r/min by 2000r/min, then carry the speed Control situation being decelerated to 3000r/min by 4000r/min at 0.4s place; Found out by Figure 11, three kinds of different control methods all can realize the tracing control to expectation rotating speed, but the present embodiment two close cycles fractional order control scheme all has starts to control speed faster, and under High-speed Control condition, over control is also minimum, this shows in large-scale speed governing situation, and compared to traditional integer rank control program, two close cycles fractional order control method has better dynamic control performance;

Figure 12 is the motor power factor change curve in above-mentioned speed Control situation, and as seen from Figure 12, even if under speed governing operating mode on a large scale, the present embodiment two close cycles fractional order control method still has higher power factor, significantly improves electric system efficiency.

Claims (3)

1. a double-closed-loop control device for permagnetic synchronous motor, is characterized in that:

This controller is electric current loop and der Geschwindigkeitkreis fractional order double-closed-loop control, wherein

The expression formula of the fractional order control device of electric current loop is

$C_i\left(s\right)=K_i\left(\frac{1+{\mathrm{\&tau;}}_{i}s}{{\mathrm{\&tau;}}_i{s}^{\mathrm{\&alpha;}}}\right)---\left(1\right);$

The fractional order control device expression formula of der Geschwindigkeitkreis is

$C_v\left(s\right)=K_v\left(\frac{1+{\mathrm{\&tau;}}_v{s}^{\mathrm{\&lambda;}}}{{\mathrm{\&tau;}}_v{s}^{\mathrm{\&lambda;}}}\right)---\left(2\right);$

In formula: α ∈ (0,1) is the fractional order integration order parameter of current loop controller, λ ∈ (0,1) is the fractional order integration order parameter of der Geschwindigkeitkreis controller, K _iand τ _ibe respectively electric current loop fractional order control device multiplication factor and the time of integration coefficient; K _v, and τ _vbe respectively der Geschwindigkeitkreis fractional order control device multiplication factor and the time of integration coefficient.

2. the double-closed-loop control device of permagnetic synchronous motor as claimed in claim 1, is characterized in that: apply its method for controlling permanent magnet synchronous motor carried out and comprise the following steps:

The three-phase current i of A, detection permagnetic synchronous motor _a, i _band i _c, detect actual speed ω, the rotor position angle θ of permagnetic synchronous motor, three-phase current i _a, i _band i _ccurrent i under Clarke conversion obtains α, β coordinate system _α, i _β, by i _α, i _βbound site angle setting θ also draws the stator current i under d-q axis coordinate system through Park conversion _d, i _q;

B, by motor actual speed ω with expect rotational speed omega _rcompare and draw speed error signal, speed error signal obtains q axle reference stator current value i after the process of der Geschwindigkeitkreis fractional order control device _qr; By d axle stator current i _dwith the d axle reference current i being preset as 0 _drcompare and obtain d axle stator current error signal, d axle stator current error signal obtains d axle stator voltage u after the process of electric current loop fractional order control device _d, by q axle stator current i _qwith its reference current i _qrcompare and obtain the error signal of q axle stator current, q axle stator current error signal obtains q axle stator voltage u after the process of electric current loop fractional order control device _q;

C, in conjunction with d axle stator voltage u _d, q axle stator voltage u _qwith rotor position angle θ, the voltage u under utilizing Park inverse transformation to obtain α, β coordinate system _α, u _β; By u _α, u _βthreephase stator winding voltage u is exported through inverter again after SVPWM algorithm process _a, u _band u _crealize the drived control to permagnetic synchronous motor motor.

3. a permagnetic synchronous motor, is characterized in that applying double-closed-loop control device as claimed in claim 1.