CN1405973A - Method for directly controlling structure-change torque of inductive motor modulated by space vector - Google Patents

Abstract

The characters of the method are as follows. Based on the amplitude of the stator magnetic linkage and the quantity of each error, the stator voltage vector is calculated through the magnetic linkage of the various structures and the torque controller is order to control the convergence of the errors. Then, with space vector modulation type, the switch control signal of the voltage inverter is generated so as to control the torque of the induction-motor. Comparing with the directional control of the rotor magnetic field, the method provides the features of small calculating quantity, simple implemention and the robustness of the changed parameters. Comparing with the directive torque control, the invented method realizes constant switch cycle of the voltage inverter and overcomes the dithering issue in the directive torque control.

Description

The induction motor of space vector modulation becomes the direct control method of structure torque

Technical field

The induction motor of space vector modulation becomes the direct control method of structure torque and belongs to alternating current machine drive technology field.

Background technology

Induction motor is to exchange most widely used motor in the transmission, but because its complicated control characteristic, the high performance control of induction motor is one of main research difficult problem that exchanges drive technology.

Two rest frames (α, β) under, the dynamical equation of induction motor can followingly be represented in the formula _s=[ _{S α S β}] ^T _r=[ _{R α R β}] ^TRepresent stator magnetic linkage and rotor flux respectively, i _s=[i _{S α}i _{S β}] ^TThe expression stator current, R _s, R _rRepresent stator resistance and rotor resistance respectively, ω _rBe rotor speed, u _s=[u _{S α}u _{S β}] ^TBe stator voltage, $J=\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$ 。Stator current, magnetic linkage and rotor current, magnetic linkage satisfy following relation,

L in the formula _sBe stator self-induction, L _rBe the rotor self-induction, M is mutual inductance.Be without loss of generality and establish the number of pole-pairs n of induction motor _p=1, then torque equation is

The key problem of induction motor high performance control is torque control.

The seventies in 20th century, German engineer F.Blashke has proposed the rotor field-oriented control principle of induction motor, and promptly usually said principle of vector control makes ac speed control technology that a qualitative leap take place.It solved substantially theoretically induction motor be controlled on quiet, the dynamic characteristic can with suitable this problem of direct current machine.Vector control technology imitation control of DC adopts rotor field-oriented method, has realized the decoupling zero to induction motor rotating speed and rotor flux control.Selecting stator current and rotor flux in the vector control is state variable, and then the torque dynamical equation (3) in conjunction with equation (2) induction motor is rewritten as

For (4) formula, in that (M has on T) with rotor field-oriented synchronous rotating frame _RM=‖ _r‖, _RT=0, then the torque dynamical equation is

Wherein the rotor flux amplitude satisfies following dynamical equation

When the amplitude of rotor flux keeps constant, the torque component i of induction motor torque and stator current _STLinearly proportional, this moment, induction motor had the torque control characteristic identical with DC motor.But rotor flux is difficult for directly measuring again very difficult accurately observation, and the control characteristic of vector control is subjected to the variable effect of the parameter of electric machine very big, in analog DC Electric Machine Control process, to be rotated complex calculations such as coordinate transform in addition, make the working control effect of vector control be difficult to reach result of theoretic analysis.

German scholar M.Depenbrock had proposed direct torque control [US-4678248, July7,1987] first in 1985, for the high performance control of induction motor has been opened up brand-new direction.It has solved the vector control algorithm complexity in realization to a great extent, control performance is subject to shortcomings such as rotor side parameter variable effect, once proposing just to be subjected to extensive concern, becomes the focus of research.At present, international major company such as the ABB high-performance AC also endeavouring to develop based on direct torque control drives product.Compare with vector control, the direct torque control main characteristics is: 1, and the stator magnetic linkage that control is easily observed is also by direct FEEDBACK CONTROL torque; 2, do not need rotating coordinate transformation; 3, directly generate the inverter switching device signal drive motor by hysteresis comparator and the mode of looking into the space voltage vector option table.In direct torque control, the dynamical equation of torque (3) is expressed as

σ=1-M in the formula ²/ L _sL _r, θ _sWith θ _rRepresent the corner that stator, rotor flux vector are fastened in static coordinate respectively.When the amplitude of stator magnetic linkage and rotor flux keeps constant, the torque of induction motor and sin (θ _s-θ _r) proportional relation.The direct torque control of induction motor is come controlling torque by amplitude and the corner of adjusting the stator magnetic linkage vector.By dynamically satisfying of equation (1) stator magnetic linkage

Under the hypothesis of ignoring the pressure drop on the stator resistance, in control cycle Δ T to stator magnetic linkage dynamical equation integration

Different with vector control, direct torque control is in control cycle Δ T, and stator voltage is one of 6 of being generated by inverter (perhaps comprise zero vector 8) voltage vector, so for (8) formula, keeps constant at control cycle Δ T internal stator voltage.Control the dynamic principle of stator magnetic linkage as shown in Figure 1 by the space voltage vector that inverter generates.As seen at u _s(t _K) effect under, the amplitude of stator magnetic linkage vector and the variation of corner are respectively

Suppose in control cycle Δ T, when stator magnetic linkage changes, the amplitude ‖ of rotor flux _r‖ and corner _rDo not change, and regulation then can select space voltage vector to change the amplitude and the torque of stator magnetic linkage according to the position of stator magnetic linkage counterclockwise for the positive direction of stator magnetic linkage angle variation accordingly.For example shown in Figure 1, suppose corner-π/6＜θ at k moment induction motor stator magnetic linkage _sV in control cycle Δ T, is selected in≤π/6 ₃For deciding voltage vector, then at V ₃Effect under, satisfy ‖ constantly at k+1 _s(k+1) ‖＜‖ _s(k) ‖, T (k+1)＞T (k).Promptly at V ₃The effect amplitude of stator magnetic linkage down reduces, and torque increases.Can generate the space voltage vector option table of controlling stator magnetic linkage amplitude and torque according to Fig. 1 and (9) formula.Table 1 is the space voltage vector option table that adopts usually at present.

The space voltage vector option table of table 1 direct torque control

Direct torque control according to the plus or minus of magnetic linkage and torque error, selects in 6 (or 8) stator voltage vectors one to control the trend that magnetic linkage and torque increase or reduce by the mode of tabling look-up in a control cycle.Shortcomings such as direct torque control is the control of a kind of " qualitative " to magnetic linkage and torque on this meaning, thereby has caused the switch periods of inverter non-constant, and torque and magnetic linkage control shake are big.Trace it to its cause mainly is that the control of stator magnetic linkage amplitude and torque is lacked rigorous theoretical analysis.Though after direct torque control proposes, developed improving one's methods of some space voltage vector option tables at its shortcoming, but the shortage that is limited to the theory analysis of direct torque control own, these methods can not fundamentally overcome the shortcoming of direct torque control.

Vector control and direct torque control have promoted the development of induction motor high performance control respectively greatly aspect theory and practice, but because of its pluses and minuses that exist separately, make the two not replaced by one of them.Development structure is simple, strong robustness and control method with good dynamic and static state performance are the difficult problems of induction motor high performance control theory and practice, and this difficult problem still is not well solved so far.

Summary of the invention

The induction motor that the present invention proposes the space voltage vector modulation becomes the direct control method of structure torque.This method control is the stator magnetic linkage of observation easily, do not need field orientation to realize the decoupling zero of magnetic linkage and torque control, by direct feedback stator magnetic linkage amplitude and torque, adopt change structure magnetic linkage and torque controller control stator magnetic linkage amplitude and torque to converge to reference value.The control system theory diagram of the inventive method as shown in Figure 2.Magnetic linkage and torque observer calculate the measured value of stator magnetic linkage amplitude and torque, the error e between measured value and the reference value _ψAnd e _TeGenerate stator voltage component u by becoming structure magnetic linkage control device and becoming the structure torque controller respectively _SdAnd u _Sq, with u _Sd, u _SqConversion synthesizes space voltage vector and adopts space vector modulation (Space VectorModulation, the SVM) switching signal of generator generation voltage inverter, thereby driven induction motor.

The invention is characterized in: it be a kind of according to stator magnetic linkage amplitude and torque separately the size of error adopt and become the stator voltage vector that structure magnetic linkage and torque controller calculate these error convergences of control, send the switching signal of voltage inverter again in the mode of space vector modulation (SVM) generator, method with the control of induction torque, particularly, it contains following steps successively:

(1). set stator magnetic linkage amplitude reference value ψ _SREFWith torque reference value T _EREF, the input computer;

(2). the following parameter that is drawn by control system adjustment and controller parameter setting procedure is sent into computer: become structure magnetic linkage control device parameter: ε _ψ＞ε _{Δ ψ}, ${\mathrm{\&epsiv;}}_{\mathrm{\&Delta;\&psi;}}=R_s{\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="A0214865000231.png,A0214865000232.png"\; state="\{\{state\}\}">M</figure-callout>}}^2{\mathrm{\&psi;}}_{\mathrm{sREF}}/\mathrm{\&sigma;}{L}_s^2{L}_r,$ K _ψ＞0; Wherein, σ=1-(M ²/ L _sL _r), L _s: the stator self-induction; L _r: rotor self-induction, M: mutual inductance; R _s: stator resistance; The convergence time of stator magnetic linkage error: $t_{\mathrm{\&psi;}}\&le;\left|e_{\mathrm{\&psi;}}\left({\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="A0214865000231.png,A0214865000242.png"\; state="\{\{state\}\}">t</figure-callout>}}_0^{\mathrm{\&psi;}}\right)\right|/({\mathrm{\&epsiv;}}_{\mathrm{\&psi;}}-{\mathrm{\&epsiv;}}_{\mathrm{\&Delta;\&psi;}})$ Wherein, e _ψ=ψ _SREF-ψ _s, ψ _s: stator magnetic linkage amplitude, t ₀ ^ψBe stator magnetic linkage ψ _sThe initial time of control; Become structure torque controller parameter: ${\mathrm{\&epsiv;}}_{\mathrm{Te}}>\left|{\mathrm{\&psi;}}_{\mathrm{sREF}}{\stackrel{..}{\mathrm{\&theta;}}}_s\right|,$ K _Te＞0；

(3). magnetic linkage and torque observer calculate the stator magnetic linkage amplitude Measured value with torque

(3.1). computer records phase current i by the voltage and current measurement circuit from the inverter circuit of Alternating Current Power Supply _A, i _B, i _CAnd busbar voltage V _Dc, the on off state SA (t) of inverter in observation cycle, SB (t), SC (t);

(3.2). calculate the component that stator current, stator voltage are fastened in static coordinate by following formula: $i_{\mathrm{s\&alpha;}}=i_A-\frac{1}{2}(i_B+i_C),i_{\mathrm{s\&beta;}}=\frac{\sqrt{3}}{2}(i_B-i_C),$ ${\tilde{u}}_{\mathrm{s\&alpha;}}=\frac{V_{\mathrm{dc}}}{3}(2\mathrm{SA}-\mathrm{SB}-\mathrm{SC}),$ ${\tilde{u}}_{\mathrm{s\&beta;}}=\frac{V_{\mathrm{dc}}}{\sqrt{3}}(\mathrm{SB}-\mathrm{SC});$

(3.3). calculate by following formula

(3.4). calculate by following formula

(3.5). calculate by following formula

(4). become structure magnetic linkage and torque controller respectively according to e _ψ, e _TeCalculate stator voltage u _sComponent u on the stator magnetic linkage dynamic coordinate system _Sd, u _Sq:

Whether at first differentiate t＞t _ψIf: the stator magnetic linkage amplitude has entered stable state, t 〉=t constantly at t _ψ, then: $e_{\mathrm{\&psi;}}={\mathrm{\&psi;}}_{\mathrm{sREF}}-{\widehat{\mathrm{\&psi;}}}_s,e_{\mathrm{Te}}=T_{\mathrm{eREF}}-{\hat{T}}_e,$ So: $u_{\mathrm{sd}}=\frac{R_s}{\mathrm{\&sigma;}{L}_s}{\mathrm{\&psi;}}_s+K_{\mathrm{\&psi;}}{e}_{\mathrm{\&psi;}}+{\mathrm{\&epsiv;}}_{\mathrm{\&psi;}}\mathrm{sgn}{e}_{\mathrm{\&psi;}},$ $u_{\mathrm{sq}}=\frac{R_s}{{\mathrm{\&psi;}}_{\mathrm{sREF}}}{T}_{\mathrm{eREF}}+{\&Integral;}_{t_T^0}^t(K_{\mathrm{Te}}{e}_{\mathrm{Te}}+{\mathrm{\&epsiv;}}_{\mathrm{Te}}\mathrm{sgn}{e}_{\mathrm{Te}})\mathrm{d\&tau;};$ T wherein ₀ ^TInitial time for induction motor torque control; If: the stator magnetic linkage amplitude does not enter stable state, t＜t constantly at t _ψ, then: $e_{\mathrm{\&psi;}}={\mathrm{\&psi;}}_{\mathrm{sREF}}-{\widehat{\mathrm{\&psi;}}}_s,e_{\mathrm{Te}}=0-{\hat{T}}_e,$ So: $u_{\mathrm{sd}}=\frac{R_s}{\mathrm{\&sigma;}{L}_s}{\mathrm{\&psi;}}_s+K_{\mathrm{\&psi;}}{e}_{\mathrm{\&psi;}}+{\mathrm{\&epsiv;}}_{\mathrm{\&psi;}}\mathrm{sgn}{e}_{\mathrm{\&psi;}},$ $u_{\mathrm{sq}}=\frac{R_s}{{\mathrm{\&psi;}}_{\mathrm{sREF}}}{T}_{\mathrm{eREF}}+{\&Integral;}_{t_T^0}^t(K_{\mathrm{Te}}{e}_{\mathrm{Te}}+{\mathrm{\&epsiv;}}_{\mathrm{Te}}\mathrm{sgn}{e}_{\mathrm{Te}})\mathrm{d\&tau;};$

(5). synthetic space vector modulation (SVM) generator that reaches of voltage vector is according to u _Sd, u _Sq,

Calculate the needed threephase switch control signal of inverter SA, SB, SC:

(5.1). calculate u by following formula _{S α}, u _{S β}: $u_s=\left[\begin{array}{c}{u}_{\mathrm{s\&alpha;}}\\ u_{\mathrm{s\&beta;}}\end{array}\right]=\left[\begin{array}{cc}\cos {\mathrm{\&theta;}}_s& -\sin {\mathrm{\&theta;}}_s\\ \sin {\mathrm{\&theta;}}_s& \cos {\mathrm{\&theta;}}_s\end{array}\right]\left[\begin{array}{c}{u}_{\mathrm{sd}}\\ u_{\mathrm{sq}}\end{array}\right]$

(5.2). calculate the amplitude U of stator voltage vector by following formula _sAnd rotational angle theta _Us $U_s=\sqrt{u_{\mathrm{s\&alpha;}}^2+u_{\mathrm{s\&beta;}}^2},$

θ _us＝cos ^-1(u _sα/U _s)；

(5.3). pass through θ _UsDetermine two adjacent basic voltage vectors of synthetic stator voltage: $0\&le;{\mathrm{\&theta;}}_{\mathrm{us}}<\frac{\mathrm{\&pi;}}{3},$ The stator voltage vector is at V1, and between the V2, N=1 adopts V1, V2 $\frac{\mathrm{\&pi;}}{3}\&le;{\mathrm{\&theta;}}_{\mathrm{us}}<\frac{2\mathrm{\&pi;}}{3},$ The stator voltage vector is at V2, and between the V3, N=2 adopts V2, V3 $\frac{2\mathrm{\&pi;}}{3}\&le;{\mathrm{\&theta;}}_{\mathrm{us}}<\mathrm{\&pi;},$ The stator voltage vector is at V3, and between the V4, N=3 adopts V3, V4 $\mathrm{\&pi;}\&le;{\mathrm{\&theta;}}_{\mathrm{us}}<\frac{4\mathrm{\&pi;}}{3},$ The stator voltage vector is at V4, and between the V5, N=4 adopts V4, V5 $\frac{4\mathrm{\&pi;}}{3}\&le;{\mathrm{\&theta;}}_{\mathrm{us}}<\frac{5\mathrm{\&pi;}}{3},$ The stator voltage vector is at V5, and between the V6, N=5 adopts V5, V6 $\frac{5\mathrm{\&pi;}}{3}{\&le;\mathrm{\&theta;}}_{\mathrm{us}}<2\mathrm{\&pi;},$ The stator voltage vector is at V6, and between the V1, N=6 adopts V6, V1;

(5.4). current time, stator voltage vector adopt by following formula and calculate the adjacent inverter basic voltage vectors V of stator voltage vector in interval N _N, V _N+1If (N=6 gets V _N+1=V1) and action time of zero vector V0, V7: the SVM period T of setting _pIn, $\mathrm{\&gamma;}={\mathrm{\&theta;}}_{\mathrm{us}}-\frac{(N-1)\mathrm{\&pi;}}{3}$ $0\&le;\mathrm{\&gamma;}<\frac{\mathrm{\&pi;}}{3}$ V _NT action time _N: $T_N=T_P\frac{{2U}_s}{\sqrt{3}{V}_{\mathrm{dc}}}\sin (\frac{\mathrm{\&pi;}}{3}-\mathrm{\&gamma;}),$ V _N+1T action time _N+1: $T_{N+1}=T_P\frac{{2U}_s}{\sqrt{3}{V}_{\mathrm{dc}}}\sin \left(\mathrm{\&gamma;}\right),$ T action time of V0 and V7 ₀, T ₇: ${\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="A0214865000231.png,A0214865000242.png"\; state="\{\{state\}\}">T</figure-callout>}}_0=T_7=\frac{T_P-T_1{-\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A0214865000231.png,A0214865000232.png"\; state="\{\{state\}\}">T</figure-callout>}}_2}{2};$

(5.5). according to basic voltage vectors and zero vector and determine inverter threephase switch control signal SA action time separately, SB, SC:

Basic voltage vectors and the pairing threephase switch signal of zero vector that inverter produces are respectively V ₁(SA SB SC): V0 (000), V1 (100), V2 (110), V3 (010), V4 (011), V5 (001), V6 (101) V7 (111); A SVM period T _pThe basic voltage vectors V that the internal stator voltage vector is adjacent _N, V _N+1As follows with the sequence of operation of zero vector V0, V7:

V0 effect T ₀/ 2 → V _NEffect T _N/ 2 → V _N+1Effect T _N+1/ 2 → V7 effect T ₇→ V _N+1Effect T _N+1/ 2 → V _NEffect T _N/ 2 → V0 effect T ₀/ 2;

And according to basic voltage vectors and inverter threephase switch signal SA, SB, the corresponding relation between the SC draws the switch controlling signal SA of inverter, SB, SC, thereby driven induction motor are with the torque of control of induction.Adjustment of described control system performance and controller parameter setting procedure contain successively and have the following steps:

(1). require to determine K according to following formula and systematic function _ψ, ε _ψ, K _Te, ε _Te: ${\mathrm{\&epsiv;}}_{\mathrm{\&Delta;\&psi;}}=\frac{R_s{\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="A0214865000231.png,A0214865000232.png"\; state="\{\{state\}\}">M</figure-callout>}}^2}{\mathrm{\&sigma;}{L}_s^2{L}_r}{\mathrm{\&psi;}}_{\mathrm{sREF}},$

ε _ψ≈ 2 ε _{Δ ψ}, K _ψInitial value design be K _ψ=1,

ε _Te≈ 10 ψ _SREFT _EREF, K _TeInitial value design be K _Te=1;

(2). require to set ψ according to induction motor self character and systematic function _SREF, T _EREF

(3). become structure magnetic linkage control device according to control main program increase K _ψMethod make the magnetic linkage convergence rate satisfy performance requirement;

(4). become the structure torque controller and behind the magnetic linkage amplitude stability, increase K according to control main program usefulness _TeMethod make the torque convergence rate satisfy performance requirement;

(5). determine to satisfy the K that systematic function requires _ψ, K _Te

(6). finish.

Experimental results show that it has reached its intended purposes.

Description of drawings

Fig. 1. direct torque control stator magnetic linkage tenet of dynamic state figure.

Fig. 2. the induction motor of space vector modulation becomes structure Torque Direct Control System theory diagram.

Fig. 3. stator voltage component u _SdAnd u _SqBlended space voltage vector u _sVectogram.

Fig. 4. three-phase voltage-type inverter.

Fig. 5. generate stator space voltage vector u _sVectogram.

Fig. 6. the system hardware circuit structure block diagram.

Fig. 7. the control main program flow chart.

Fig. 8. stator magnetic linkage amplitude and torque observer program flow diagram.

Fig. 9. become structure magnetic linkage and torque controller program flow diagram.

Figure 10. the synthetic and SVM generator program flow diagram of stator voltage vector.

Figure 11. the control system performance is adjusted and controller parameter setting procedure flow chart.

Figure 12. torque and stator magnetic linkage amplitude response curve:

A. torque response curve; B. stator magnetic linkage amplitude response curve.

Figure 13. induction motor stator current response curve:

A.i _{S α}Response curve; B.i _{S β}Response curve.

Figure 14. induction motor rotating speed response curve.

Figure 15. inverter switching frequency is 5KHz, induction motor torque and stator magnetic linkage amplitude response curve during 0.5s impact 4Nm load torque:

A. torque response curve; B. stator magnetic linkage amplitude response curve.

Figure 16. inverter switching frequency is 5KHz, induction motor stator current response curve during 0.5s impact 4Nm load torque:

A.i _{S α}Response curve; B.i _{S β}Response curve.

Figure 17. inverter switching frequency is 5KHz, induction motor rotating speed response curve during 0.5s impact 4Nm load torque.

Embodiment:

Magnetic linkage and torque control principle

At first, the present invention is directed to the nonlinear coupled equation of induction motor, derive the dynamical equation between stator magnetic linkage amplitude and torque and the stator voltage, and on this basis, designed change structure magnetic linkage and torque controller.Under two rest frames, the stator magnetic linkage of induction motor and rotor flux dynamical equation are Definition ψ _s=‖ _s‖, ψ _r=‖ _r‖ represents the amplitude of stator, rotor flux respectively,

Angle between expression stator magnetic linkage vector and the rotor flux vector, U _s, θ _UsAmplitude and the corner of representing the stator voltage vector respectively. is then arranged _{S α}=ψ _sCos θ _s, _{S β}=ψ _sSin θ _{s R α}=ψ _rCos θ _r, _{R β}=ψ _rSin θ _ru _{S α}=U _sCos θ _Us, u _{S β}=U _sSin θ _UsBy conversion as above, the dynamical equation that can obtain stator magnetic linkage amplitude and corner is

U in the formula _Sd=U _sCos (θ _Us-θ _s), u _Sq=U _sSin (θ _Us-θ _s).The dynamical equation of torque is

And then the dynamical equation that draws between stator magnetic linkage amplitude and torque and the stator voltage is

By equation (13), by stator voltage u _SdAnd u _SqComponent can be controlled stator magnetic linkage amplitude and torque.The change structure magnetic linkage in the system and the control principle of torque controller are as follows.

Become structure magnetic linkage and torque controller

The inventive method is based on the dynamic and torque dynamical equation (13) of stator magnetic linkage, and design becomes structure magnetic linkage and torque controller, respectively by adjusting the u of stator voltage _SdAnd u _SqComponent comes the stator magnetic linkage amplitude of control of induction and torque to converge to reference value ψ _SREFAnd T _EREF

Become structure magnetic linkage control device by changing the u of stator voltage _SdComponent is controlled the amplitude of stator magnetic linkage, and control law is $u_{\mathrm{sd}}=\frac{R_s}{\mathrm{\&sigma;}{L}_s}{\mathrm{\&psi;}}_s+K_{\mathrm{\&psi;}}{e}_{\mathrm{\&psi;}}+{\mathrm{\&epsiv;}}_{\mathrm{\&psi;}}\mathrm{sgn}{e}_{\mathrm{\&psi;}}---\left(14\right)$ E in the formula _ψ=ψ _SREF-ψ _s, parameter K in the control law _ψAnd ε _ψSatisfy following constraints respectively

K _ψ＞0 ${\mathrm{\&epsiv;}}_{\mathrm{\&Delta;\&psi;}}=\frac{R_s{\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="A0214865000231.png,A0214865000232.png"\; state="\{\{state\}\}">M</figure-callout>}}^2}{\mathrm{\&sigma;}{L}_s^2{L}_r}{\mathrm{\&psi;}}_{\mathrm{sREF}}---\left(15\right)$

ε _ψ＞ε _Δψ

The stator magnetic linkage amplitude of induction motor can converge to reference value ψ in finite time under change structure magnetic linkage control device effect as above _SREF, promptly the stator magnetic linkage amplitude satisfies

ψ _s(t)＝ψ _sREF， $\&ForAll;t\&GreaterEqual;t_{\mathrm{\&psi;}}+{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="A0214865000231.png,A0214865000242.png"\; state="\{\{state\}\}">t</figure-callout>}}_0^{\mathrm{\&psi;}}$ $t_{\mathrm{\&psi;}}\&le;\frac{|{\mathrm{\&psi;}}_{\mathrm{sREF}}\left({\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="A0214865000231.png,A0214865000242.png"\; state="\{\{state\}\}">t</figure-callout>}}_0^{\mathrm{\&psi;}}\right)-{\mathrm{\&psi;}}_s\left({\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="A0214865000231.png,A0214865000242.png"\; state="\{\{state\}\}">t</figure-callout>}}_0^{\mathrm{\&psi;}}\right)|}{{\mathrm{\&epsiv;}}_{\mathrm{\&psi;}}-{\mathrm{\&epsiv;}}_{\mathrm{\&Delta;\&psi;}}}---\left(16\right)$

T wherein ₀ ^ψInitial time for magnetic linkage control.The stability proof of change structure magnetic linkage control device and the system of selection of parameter have been provided in the appendix A.

The initial time of induction motor torque control $t_0^T>t_{\mathrm{\&psi;}}+{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="A0214865000231.png,A0214865000242.png"\; state="\{\{state\}\}">t</figure-callout>}}_0^{\mathrm{\&psi;}},$ Promptly this moment, the stator magnetic linkage amplitude entered stable state.As t≤t ₀ ^TThe time torque control reference value T _EREF=0.Torque become structure controller into: $u_{\mathrm{sq}}=\frac{R_s}{{\mathrm{\&psi;}}_{\mathrm{sREF}}}{T}_{\mathrm{eREF}}+{\&Integral;}_{t_T^0}^t(K_{\mathrm{Te}}{e}_{\mathrm{Te}}+{\mathrm{\&epsiv;}}_{\mathrm{Te}}\mathrm{sgn}{e}_{\mathrm{Te}})\mathrm{d\&tau;}---\left(17\right)$ E in the formula _Te=T _EREF-T _e, parameter K in the control law _TeAnd ε _TeSatisfy following constraints K respectively _Te＞0 ${\mathrm{\&epsiv;}}_{\mathrm{Te}}>\left|{\mathrm{\&psi;}}_{\mathrm{sREF}}{\stackrel{..}{\mathrm{\&theta;}}}_s\right|---\left(18\right)$

The torque of induction motor converges to reference value T under the effect of as above change structure torque controller _EREFAppendix B has provided the stability proof of change structure torque controller and the system of selection of parameter.

Synthetic and the SVM generator of voltage vector conversion

Become structure magnetic linkage and the torque controller u of output stator voltage respectively _SdAnd u _SqComponent through conversion blended space voltage vector, thereby can adopt the SVM generator to generate the switching signal of inverter.

The stator voltage vector is: $u_s=\left[\begin{array}{c}{u}_{\mathrm{s\&alpha;}}\\ u_{\mathrm{s\&beta;}}\end{array}\right]=\left[\begin{array}{cc}\cos {\mathrm{\&theta;}}_s& -\sin {\mathrm{\&theta;}}_s\\ \sin {\mathrm{\&theta;}}_s& \cos {\mathrm{\&theta;}}_s\end{array}\right]\left[\begin{array}{c}{u}_{\mathrm{sd}}\\ u_{\mathrm{sq}}\end{array}\right]---\left(19\right)$ $U_s=\sqrt{u_{\mathrm{s\&alpha;}}^2+u_{\mathrm{s\&beta;}}^2},{\mathrm{\&theta;}}_{\mathrm{us}}={\cos }^{-1}(u_{\mathrm{s\&alpha;}}/U_s)---\left(20\right)$

By stator voltage component u _SdAnd u _SqBlended space voltage vector principle as shown in Figure 3.

Fig. 4 is three-phase voltage-type inverter schematic diagram, wherein V _DcBe DC bus-bar voltage, power electronic power device is regarded as perfect switch.With the conducting of " 1 " expression upper arm, underarm turn-offs; With the conducting of " 0 " expression underarm, upper arm turn-offs.The switch controlling signal of three-phase is respectively SA, SB, and SC, corresponding value is respectively 1 or 0 correspondence.Use V _iThe space voltage vector that (SA SB SC) expression inverter generates, so by SA, SB, the combination of SC value can obtain 8 basic voltage vectors V0～V7:V0 (000) of inverter output, V1 (100), V2 (110), V3 (010), V4 (011), V5 (001), V6 (101), V7 (111).V0 wherein, the amplitude of V7 is zero, is called zero vector.The principle that adopts SVM mode span voltage vector as shown in Figure 5, at given time arbitrarily, the stator voltage vector all can drop on one of six intervals being divided by basic voltage vectors V1～V6.Table 2 has shown according to θ _UsSelect adjacent basic vector.The SVM period T of setting like this _PIn, by synthetic this stator voltage vector of just can expressing of two adjacent basic voltage vectors and zero vector.The stator voltage vector adopts by following formula and calculates two adjacent inverter basic voltage vectors V of stator voltage vector in interval N _N, V _N+1If (N=6 gets V _N+1=V1) and action time of zero vector V0, V7: $\mathrm{\&gamma;}={\mathrm{\&theta;}}_{\mathrm{us}}-\frac{(N-1)\mathrm{\&pi;}}{3}$ $0\&le;\mathrm{\&gamma;}<\frac{\mathrm{\&pi;}}{3}$ $T_N=T_P\frac{2U_s}{\sqrt{3}{V}_{\mathrm{dc}}}\sin (\frac{\mathrm{\&pi;}}{3}-\mathrm{\&gamma;})---\left(21\right)$ $T_{N+1}=T_P\frac{{2U}_s}{\sqrt{3}{V}_{\mathrm{dc}}}\sin \left(\mathrm{\&gamma;}\right)$ $T_0=T_7=\frac{T_P-T_1-T_2}{2}$

Table 2 is determined basic voltage vectors according to the stator voltage vector angle

Basic voltage vectors and the pairing threephase switch signal of zero vector that inverter produces are respectively V _i(SA SB SC): V0 (000), V1 (100), V2 (110), V3 (010), V4 (011), V5 (001), V6 (101) V7 (111): a SVM period T _PThe basic voltage vectors V that the internal stator voltage vector is adjacent _N, V _N+1As follows with the sequence of operation of zero vector V0, V7: V0 → V _N→ V _N+1→ V7 → V _N+1→ V _N→ V0 is respectively V0 effect T action time ₀/ 2, V _NEffect T _N/ 2, V _N+1Effect T _N+1/ 2, V7 effect T ₇, V _N+1Effect T _N+1/ 2, V _NEffect T _N/ 2, V0 effect T ₀/ 2.According to basic voltage vectors and inverter threephase switch signal SA, SB, the corresponding relation between the SC draws the switch controlling signal SA of inverter, SB, SC, thereby driven induction motor are with the torque of control of induction.

Magnetic linkage and torque observer

The stator magnetic linkage of induction motor and torque are not easy direct measurement, and stator voltage and stator current by the motor that can directly measure utilize magnetic linkage and torque observer to obtain the measured value of magnetic linkage and torque.The observer method for designing that multiple stator magnetic linkage and torque have been arranged at present for example can be passed through the method for stator magnetic linkage dynamical equation in integration (1) formula, and the measured value of stator magnetic linkage is:

By measuring phase current i _A, i _B, i _C, the switching signal SA of busbar voltage and inverter, SB, SC can obtain i _{S α}, i _{S β}'

Computing formula is as follows $i_{\mathrm{s\&alpha;}}=i_A-\frac{1}{2}(i_B+i_C)$ $i_{\mathrm{s\&beta;}}=\frac{\sqrt{3}}{2}(i_B-i_C)$ ${\tilde{u}}_{\mathrm{s\&alpha;}}=\frac{V_{\mathrm{dc}}}{3}(2\mathrm{SA}-\mathrm{SB}-\mathrm{SC})---\left(23\right)$ ${\tilde{u}}_{\mathrm{s\&beta;}}=\frac{V_{\mathrm{dc}}}{\sqrt{3}}(\mathrm{SB}-\mathrm{SC})$ Then the amplitude measured value of stator magnetic linkage is:

The measured value of stator magnetic linkage corner is:

The measured value of torque is:

System hardware structure is shown in Figure 6, and system comprises: rectification circuit, filter circuit, inverter circuit, buffer circuit, voltage, current detection circuit, microprocessor (CPU) and corresponding interface circuits.Also can increase rotation-speed measuring device and corresponding rotating speeds control algolithm for native system, thereby constitute the induction motor revolution speed control system.

The control main flow chart of control system is shown in Figure 7, by observer unit, becomes synthetic and three major parts of SVM generator unit of structure controller unit and space voltage vector and constitutes, and program flow diagram is respectively Fig. 8-shown in Figure 10.Figure 11 is systematic function adjustment and controller parameter setting procedure flow chart.At first require to determine the reference value ψ of stator magnetic linkage amplitude and torque according to the controller parameter system of selection according to systematic function _SREFAnd T _EREF, become the structure controller parameter K _ψ, ε _ψ, K _Te, ε _TeAnd t _ψ, the parameter of determining is sent into the control main program.Adjust K according to systematic function _ψ, K _Te, determine to satisfy the controller parameter of system requirements at last.

Be checking the inventive method, adopt MATLAB5.3-SIMULINK3 to carry out simulating, verifying.The selection of parameter of induction motor is as follows in the emulation, stator and rotor self-induction L _s=L _r=0.47H; Mutual inductance M=0.44H; Stator resistance R _s=8.0 Ω; Rotor resistance R _r=3.6 Ω; Induction motor moment of inertia J _M=0.06Kgm ²Number of pole-pairs n _p=1.Behind the via controller parameter tuning, the parameter of torque and magnetic linkage change structure controller value respectively is K _ψ=10 Ω/H; K _Te=10 Ω/H; e _ψ=160V; e _Te=40V.Emulation in two sub-sections, the theoretical validation of inventive method performance and the simplation verification of real system.In theoretical verification portion, ignore of the influence of SVM generator, ψ to systematic function _SREF=0.9Wb sets t _ψ=0.1s, T _L=0Nm, torque reference value is:

Figure 12 is torque and stator magnetic linkage amplitude response curve, and Figure 13 is the stator current response curve, and Figure 14 is the rotating speed response curve.In the analog simulation of real system, inverter switching frequency is 5KHz, DC bus-bar voltage V _Dc=380V, ψ _SREF=0.9Wb, t _ψ=0.05s, T _EREF=4Nm and in 0.5s impact 4Nm load torque.Figure 15-Figure 17 is respectively the response curve of torque, stator magnetic linkage amplitude, stator current and rotating speed.

It is little that the inventive method is compared operand with vector control, realizes simply, and the parameter variation of induction machine is had robustness; Compare with direct torque control, the inventive method calculates the stator voltage vector of these error convergences of control according to the size of magnetic linkage and torque error, and the mode that adopts SVM is sent the switching signal of inverter, both realize the constant of inverter switching device cycle, overcome the jitter problem of the magnetic linkage that exists in the direct torque control and torque control again.

Claims (2)

1. the induction motor of space voltage vector modulation becomes the direct control method of structure torque, contain stator magnetic linkage that control more easily observes and the step by direct FEEDBACK CONTROL torque, it is characterized in that, it be a kind of according to stator magnetic linkage amplitude and torque separately the size of error adopt and become the stator voltage vector that structure magnetic linkage and torque controller calculate these error convergences of control, send the switching signal of voltage inverter again in the mode of space vector modulation (SVM) generator, method with the control of induction torque, particularly, it contains following steps successively:

(1). set stator magnetic linkage amplitude reference value ψ _SREFWith torque reference value T _EREF, the input computer;

(2). the following parameter that is drawn by control system adjustment and controller parameter setting procedure is sent into computer: become structure magnetic linkage control device parameter: ε _ψ＞ε Δ _ψ, ${\mathrm{\&epsiv;}}_{\mathrm{\&Delta;\&psi;}}=R_s{M}^2{\mathrm{\&psi;}}_{\mathrm{sREF}}/\mathrm{\&sigma;}{L}_s^2{L}_r,$ K _ψ＞0: wherein, σ=1-(M ²/ L _sL _r), L _s: the stator self-induction; L _r: rotor self-induction, M: mutual inductance; R _s: stator resistance; The convergence time of stator magnetic linkage error: $t_{\mathrm{\&psi;}}\&le;\left|e_{\mathrm{\&psi;}}\left(t_0^{\mathrm{\&psi;}}\right)\right|/({\mathrm{\&epsiv;}}_{\mathrm{\&psi;}}-{\mathrm{\&epsiv;}}_{\mathrm{\&Delta;\&psi;}})$ Wherein, e _ψ=V _SREF-ψ _s, ψ _s: stator magnetic linkage amplitude, t ₀ ^ψBe stator magnetic linkage ψ _sThe initial time of control; Become structure torque controller parameter: ${\mathrm{\&epsiv;}}_{\mathrm{Te}}>\left|{\mathrm{\&psi;}}_{\mathrm{sREF}}{\stackrel{..}{\mathrm{\&theta;}}}_s\right|,$ K _Te＞0：

(3). magnetic linkage and torque observer calculate the stator magnetic linkage amplitude Measured value with torque

(3.1). computer records phase current i by the voltage and current measurement circuit from the inverter circuit of Alternating Current Power Supply _A, i _B, i _CAnd busbar voltage V _Dc, the on off state SA (t) of inverter in observation cycle, SB (t), SC (t);

(3.2). calculate the component that stator current, stator voltage are fastened in static coordinate by following formula: $i_{\mathrm{s\&alpha;}}=i_A-\frac{1}{2}(i_B+i_C),i_{\mathrm{s\&beta;}}=\frac{\sqrt{3}}{2}(i_B-i_C),$ ${\tilde{u}}_{\mathrm{s\&alpha;}}=\frac{V_{\mathrm{dc}}}{3}(2\mathrm{SA}-\mathrm{SB}-\mathrm{SC}),$ ${\tilde{u}}_{\mathrm{s\&beta;}}=\frac{V_{\mathrm{dc}}}{\sqrt{3}}(\mathrm{SB}-\mathrm{SC});$

(3.3). calculate by following formula

(3.4). calculate by following formula

(3.5). calculate by following formula

(4). become structure magnetic linkage and torque controller respectively according to e _ψ, e _TeCalculate stator voltage u _sComponent u on the stator magnetic linkage dynamic coordinate system _Sd, u _Sq:

Whether at first differentiate t＞t _ψIf: the stator magnetic linkage amplitude has entered stable state, t 〉=t constantly at t _ψ, then: $e_{\mathrm{\&psi;}}={\mathrm{\&psi;}}_{\mathrm{sREF}}-{\widehat{\mathrm{\&psi;}}}_s,e_{\mathrm{Te}}=T_{\mathrm{eREF}}-{\hat{T}}_e,$ So: $u_{\mathrm{sd}}=\frac{R_s}{\mathrm{\&sigma;}{L}_s}{\mathrm{\&psi;}}_s+K_{\mathrm{\&psi;}}{e}_{\mathrm{\&psi;}}+{\mathrm{\&epsiv;}}_{\mathrm{\&psi;}}\mathrm{sgn}{e}_{\mathrm{\&psi;}},$ $u_{\mathrm{sq}}=\frac{R_s}{{\mathrm{\&psi;}}_{\mathrm{sREF}}}{T}_{\mathrm{eREF}}+{\&Integral;}_{t_T^0}^t(K_{\mathrm{Te}}{e}_{\mathrm{Te}}+{\mathrm{\&epsiv;}}_{\mathrm{Te}}\mathrm{sgn}{e}_{\mathrm{Te}})\mathrm{d\&tau;};$ T wherein ₀ ^TInitial time for induction motor torque control; If: the stator magnetic linkage amplitude does not enter stable state, t＜t constantly at t _ψ, then: $e_{\mathrm{\&psi;}}={\mathrm{\&psi;}}_{\mathrm{sREF}}-{\widehat{\mathrm{\&psi;}}}_s,e_{\mathrm{Te}}=0-{\hat{T}}_e,$ So: $u_{\mathrm{sd}}=\frac{R_s}{\mathrm{\&sigma;}{L}_s}{\mathrm{\&psi;}}_s+K_{\mathrm{\&psi;}}{e}_{\mathrm{\&psi;}}+{\mathrm{\&epsiv;}}_{\mathrm{\&psi;}}\mathrm{sgn}{e}_{\mathrm{\&psi;}},$ $u_{\mathrm{sq}}=\frac{R_s}{{\mathrm{\&psi;}}_{\mathrm{sREF}}}{T}_{\mathrm{eREF}}+{\&Integral;}_{t_T^0}^t(K_{\mathrm{Te}}{e}_{\mathrm{Te}}+{\mathrm{\&epsiv;}}_{\mathrm{Te}}\mathrm{sgn}{e}_{\mathrm{Te}})\mathrm{d\&tau;};$

(5). synthetic space vector modulation (SVM) generator that reaches of voltage vector is according to u _Sd, u _Sq,

Calculate the needed threephase switch control signal of inverter SA, SB, SC:

(5.1). calculate u by following formula _{S α}, u _{S β}: $u_s=\left[\begin{array}{c}{u}_{\mathrm{s\&alpha;}}\\ u_{\mathrm{s\&beta;}}\end{array}\right]=\left[\begin{array}{cc}\cos {\mathrm{\&theta;}}_s& -\sin {\mathrm{\&theta;}}_s\\ \sin {\mathrm{\&theta;}}_s& \cos {\mathrm{\&theta;}}_s\end{array}\right]\left[\begin{array}{c}{u}_{\mathrm{sd}}\\ u_{\mathrm{sq}}\end{array}\right]$

(5.2). calculate the amplitude U of stator voltage vector by following formula _sAnd rotational angle theta _Us $U_s=\sqrt{u_{\mathrm{s\&alpha;}}^2+u_{\mathrm{s\&beta;}}^2},$

θ _us＝cos ^-1(u _sα/U _s)；

(5.3). pass through θ _UsDetermine two adjacent basic voltage vectors of synthetic stator voltage: $0\&le;{\mathrm{\&theta;}}_{\mathrm{us}}<\frac{\mathrm{\&pi;}}{3},$ The stator voltage vector is at V1, and between the V2, N=1 adopts V1, V2 $\frac{\mathrm{\&pi;}}{3}\&le;{\mathrm{\&theta;}}_{\mathrm{us}}<\frac{2\mathrm{\&pi;}}{3},$ The stator voltage vector is at V2, and between the V3, N=2 adopts V2, V3 $\frac{2\mathrm{\&pi;}}{3}\&le;{\mathrm{\&theta;}}_{\mathrm{us}}<\mathrm{\&pi;},$ The stator voltage vector is at V3, and between the V4, N=3 adopts V3, V4 $\mathrm{\&pi;}\&le;{\mathrm{\&theta;}}_{\mathrm{us}}<\frac{4\mathrm{\&pi;}}{3},$ The stator voltage vector is at V4, and between the V5, N=4 adopts V4, V5 $\frac{4\mathrm{\&pi;}}{3}\&le;{\mathrm{\&theta;}}_{\mathrm{us}}<\frac{5\mathrm{\&pi;}}{3},$ The stator voltage vector is at V5, and between the V6, N=5 adopts V5, V6 $\frac{5\mathrm{\&pi;}}{3}\&le;{\mathrm{\&theta;}}_{\mathrm{us}}<2\mathrm{\&pi;},$ The stator voltage vector is at V6, and between the V1, N=6 adopts V6, V1;

(5.4). current time, stator voltage vector adopt by following formula and calculate two adjacent inverter basic voltage vectors V of stator voltage vector in interval N _N, V _N+1If (N=6 gets V _N+1=V1) and action time of zero vector V0, V7: the SVM period T of setting _PIn, $\mathrm{\&gamma;}={\mathrm{\&theta;}}_{\mathrm{us}}-\frac{(N-1)\mathrm{\&pi;}}{3}$ $0\&le;\mathrm{\&gamma;}<\frac{\mathrm{\&pi;}}{3}$ V _NT action time _N: $T_N=T_P\frac{2U_s}{\sqrt{3}{V}_{\mathrm{dc}}}\sin (\frac{\mathrm{\&pi;}}{3}-\mathrm{\&gamma;}),$ V _N+1T action time _N+1: $T_{N+1}=T_P\frac{2U_s}{\sqrt{3}{V}_{\mathrm{dc}}}\sin \left(\mathrm{\&gamma;}\right),$ T action time of V0 and V7 ₀, T ₇: $T_0=T_7=\frac{T_P-T_1-T_2}{2};$

(5.5). according to basic voltage vectors and zero vector and determine inverter threephase switch control signal SA action time separately, SB, SC:

Basic voltage vectors and the pairing threephase switch signal of zero vector that inverter produces are respectively V ₁(SA SB SC): V0 (000), V1 (100), V2 (110), V3 (010), V4 (011), V5 (001), V6 (101) V7 (111); A SVM period T _pThe basic voltage vectors V that the internal stator voltage vector is adjacent _N, V _N+1As follows with the sequence of operation of zero vector V0, V7:

V0 effect T ₀/ 2 → V _NEffect T _N/ 2 → V _N+1Effect T _N+1/ 2 → V7 effect T ₇→ V _N+1Effect T _N+1/ 2 → V _NEffect T _N/ 2 → V0 effect T ₀/ 2;

And according to basic voltage vectors and inverter threephase switch signal SA, SB, the corresponding relation between the SC draws the switch controlling signal SA of inverter, SB, SC, thereby driven induction motor are with the torque of control of induction.

2. the induction motor of space voltage vector according to claim 1 modulation becomes the direct control method of structure torque, and its characteristics are, adjustment of described control system performance and controller parameter setting procedure contain successively and have the following steps:

(1). require to determine K according to following formula and systematic function _ψ, ε _ψ, K _Te, ε _Te: ${\mathrm{\&epsiv;}}_{\mathrm{\&Delta;\&psi;}}=\frac{R_s{M}^2}{\mathrm{\&sigma;}{L}_s^2{L}_r}{\mathrm{\&psi;}}_{\mathrm{sREF}},$

ε _ψ≈ 2 ε _{Δ ψ}, K _ψInitial value design be K _ψ=1,

ε _Te≈ 10 ψ _SREFT _EREF, K _TeInitial value design be K _Te=1;

(2). require to set ψ according to induction motor self character and systematic function _SREF, T _EREF

(3). become structure magnetic linkage control device according to control main program increase K _ψMethod make the magnetic linkage convergence rate satisfy performance requirement;

(4). become the structure torque controller and behind the magnetic linkage amplitude stability, increase K according to control main program usefulness _TeMethod make the torque convergence rate satisfy performance requirement;

(5). determine to satisfy the K that systematic function requires _ψ, K _Te

(6). finish.

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