FAULT-TOLERANT FIELD-ORIENTED CONTROL METHOD OF FIVE-PHASE INTERIOR PERMANENT-MAGNET LINEAR MOTOR UNDER TWO NONADJACENT SHORT-CIRCUIT PHASE FAULTS

Abstract

The invention proposes a fault-tolerant field-oriented control method of five-phase interior permanent-magnet fault-tolerant linear motor (IPM-FTLM) with two nonadjacent short-circuit phase faults. Firstly, the extended Clark transformation matrix can be obtained according to the principle that magnetic motive force (MMF) keeps constant before and after the two-phase open-circuit faults, the constraint that the sum of healthy phase currents is zero and the adjacent two-phase current amplitude is equal. The back electric motive force (EMF) can be estimated by the transposed matrix. The nonlinear strong coupling system becomes the first-order inertia system when using the internal mode controller, the first-order inertia feed-forward voltage compensator and back-EMF observer, as the motor is with fault. Then, according to the principle that the sum of MMF of the healthy phase short-circuit compensation currents and two phases short-circuit fault currents is zero, the short-circuit compensation voltage can be obtained, and then these voltages add vector-controller output voltages, respectively. The invention not only restrains the thrust force fluctuation caused by two nonadjacent short-circuit phase faults, but also more importantly keeps the same dynamic and steady performance as the normal conditions, and also it has the constant switching frequency of voltage source inverter.

Claims

1. (canceled)

2. The fault-tolerant field-oriented control method of five-phase IPM-FTLM with two nonadjacent short-circuit phase faults of claim 6 wherein: when the open-circuit phase faults only occur in phase-B and phase-E, it just needs to set the short-circuit compensation currents to zero in Step 4 and to set the short-circuit compensation voltages to zero in Step 9; This fault-tolerant field-oriented control method can achieve fault-tolerant operation of five-phase IPM-FTLM under the condition of two nonadjacent open-circuit phase faults; when the open-circuit fault occurs in phase-B and short-circuit fault occurs in phase-E, it only needs to set the expression of short-circuit compensation current i.sub.sc.sub._.sub.B=0 in Step 4, and to set the expression of short-circuit compensation voltage e.sub.B=0 in Step 9; This fault-tolerant field-oriented control method can achieve fault-tolerant operation of five-phase IPM-FTLM under phase-B open-circuit fault and phase-E short-circuit fault; when the short-circuit fault occurs in phase-B and the open-circuit fault occurs in phase-E, it just needs to set the expression of short-circuit compensation current i.sub.sc.sub._.sub.E=0 in Step 4, and to set the expression of short-circuit compensation voltage e.sub.E=0 in Step 9; This fault-tolerant field-oriented control method can achieve fault-tolerant operation of five-phase IPM-FTLM under phase-B short-circuit fault and phase-E open-circuit fault.

3. The fault-tolerant field-oriented control method of five-phase IPM-FTLM with two nonadjacent short-circuit phase faults of claim 6 wherein Step 4 further comprises: (4.1) supposing that phase-B and phase-E short-circuit currents are i.sub.sc.sub._.sub.B=I.sub.f cos(t.sub.fB) and i.sub.sc.sub._.sub.E=I.sub.f cos(t.sub.fE), respectively; where, I.sub.f is the amplitude of short-circuit current, and .sub.fB is angle between back-EMF of phase-B and short-circuit current of phase-B, .sub.fE is angle between back-EMF of phase-E and short-circuit current of phase-E, =/, is electric speed of the secondary and is pole pitch; (4.2) according to the principle that the sum of healthy phase compensation currents used to restrain the thrust force fluctuation caused by short-circuit fault-phase currents is zero, and the sum of MMFs generated by the healthy phase compensation currents and short-circuit fault-phase currents is zero; obtaining the short-circuit compensation currents (i.sub.Ai.sub.Ci.sub.D) of healthy phases can be obtained: $\{\begin{array}{c}{i}_A^{}=-0.1708.Math.\left(i_{\mathrm{sc\_B}}+i_{\mathrm{sc\_E}}\right)\\ i_C^{}=-0.7236.Math.i_{\mathrm{sc\_B}}+0.8944.Math.i_{\mathrm{sc\_E}}\\ i_D^{}=0.8944.Math.i_{\mathrm{sc\_B}}-0.7236.Math.i_{\mathrm{sc\_E}}\end{array}.$ (4.3) transforming the healthy phase compensation currents (i.sub.Ai.sub.Ci.sub.D) with the extended Clark transformation matrix T.sub.post into the short-circuit compensation currents (i.sub.i.sub.) in two-phase stationary frame, and it can be obtained: $\{\begin{array}{c}{i}_{}^{}=-0.1237.Math.\left(i_{\mathrm{sc\_B}}+i_{\mathrm{sc\_E}}\right)\\ i_{}^{}=-0.3806.Math.\left(i_{\mathrm{sc\_B}}-i_{\mathrm{sc\_E}}\right)\end{array}.$

4. The fault-tolerant field-oriented control method of five-phase IPM-FTLM with two nonadjacent short-circuit phase faults of claim 6 wherein Step 6 further comprises: (6.1) in this invention, the phase inductance is almost constant L.sub.s; After the motor phase voltages subtract the back-EMFs, the model with phase-B and phase-E short-circuit faults in natural frame can be expressed as follows: $\{\begin{array}{c}{u}_{\mathrm{Ae}}=u_A-e_A={\mathrm{Ri}}_A+L_s.Math.\frac{{\mathrm{di}}_A}{\mathrm{dt}}\\ -e_B={\mathrm{Ri}}_B+L_s.Math.\frac{{\mathrm{di}}_B}{\mathrm{dt}}\\ u_{\mathrm{Ce}}=u_C-e_C={\mathrm{Ri}}_C+L_s.Math.\frac{{\mathrm{di}}_C}{\mathrm{dt}}\\ u_{\mathrm{De}}=u_D-e_D={\mathrm{Ri}}_D+L_s.Math.\frac{{\mathrm{di}}_D}{\mathrm{dt}}\\ -e_E={\mathrm{Ri}}_E+L_s.Math.\frac{{\mathrm{di}}_E}{\mathrm{dt}}\end{array}$ where u.sub.A, u.sub.C, and u.sub.D are the healthy phase voltages, e.sub.A, e.sub.B, e.sub.C, e.sub.D and e.sub.E are the phase back-EMF; u.sub.Ae, u.sub.Ce and u.sub.De are the values of the healthy phase voltages subtracting phase back-EMFs, respectively, and R is phase resistance; (6.2) the healthy phase currents are handled according to the Step 5; then the model of two nonadjacent short-circuit phase faults in the natural frame is transformed into model in the synchronous rotating frame by using the extended Clark transformation matrix T.sub.post and Park transformation matrix C.sub.2s/2r; and $\{\begin{array}{c}{u}_{\mathrm{de}}=i_d.Math.R+L_s.Math.\frac{{\mathrm{di}}_d}{\mathrm{dt}}-.Math..Math.L_s.Math.i_q\\ u_{\mathrm{qe}}=i_q.Math.R+L_s.Math.\frac{{\mathrm{di}}_q}{\mathrm{dt}}+.Math..Math.L_s.Math.i_d\end{array}.$ (6.3) by using magnetic co-energy and transformation matrix T.sub.post, C.sub.2s/2r, and C.sub.2r/2s, when the motor is with two nonadjacent short-circuit phase faults, the thrust force equation can be obtained as: $F=2.5.Math.\frac{}{}.Math.i_q.Math.{}_m$ where .sub.m is permanent magnet linkage.

5. The fault-tolerant field-oriented control method of five-phase IPM-FTLM with two nonadjacent short-circuit phase faults of claim 6 wherein the mentioned field-oriented control method of two nonadjacent short-circuit phase faults is also suitable for the five-phase fault-tolerant permanent magnet rotary motor.

6. A fault-tolerant field-oriented control method of five-phase interior permanent magnet fault-tolerant linear motor (IPM-FTLM) with two nonadjacent short-circuit phase faults includes the following steps: (1) establishing the model of five-phase IPM-FTLM; (2) dividing an IPM-FTLM into five phases: phase-A, phase-B, phase-C, phase-D and phase-E; wherein when the short-circuit faults occur in phase-B and phase-E, it is assumed that the open-circuit faults only occur in phase-B and phase-E, according to the principle of constant traveling-wave magnetic motive force (MMF) before and after fault; and wherein and the constraint about the sum of healthy phase currents is zero, and also the constraint about the amplitude of two adjacent phase-C and phase-D currents is equal, the healthy phase currents of fault-tolerant operation can be obtained after the open-circuit faults occur in phase-B and phase-E: $\{\begin{array}{c}{i}_A^{*}=1.381.Math.\left(-i_q^{*}.Math.\sin \left(\right)+i_d^{*}.Math.\cos \left(\right)\right)\\ i_C^{*}=2.235.Math.\left(-i_q^{*}.Math.\sin \left(-\frac{3}{5}.Math.\right)+i_d^{*}.Math.\cos \left(-\frac{3}{5}.Math.\right)\right)\\ i_D^{*}=2.235.Math.\left(-i_q^{*}.Math.\sin \left(+\frac{3}{5}.Math.\right)+i_d^{*}.Math.\cos \left(+\frac{3}{5}.Math.\right)\right)\end{array};$ where i.sub.d*i.sub.q* are d-axis and q-axis current references in the synchronous rotating frame, respectively, $=\frac{.Math..Math.v}{}.Math.\mathrm{dt}$ is electric angle, is the electric speed of secondary, and is pole pitch; (3) transforming the variables in the remaining three-healthy-phase natural frame into the two-phase stationary frame with the extended Clark transformation matrix T.sub.post, which is three columns and two rows; wherein the inverse transformation matrix T.sub.post.sup.1 is two columns and three rows; wherein T.sub.post, T.sub.post.sup.1 and transposed matrix T.sub.post.sup.T are obtained according to the healthy phase currents: $T_{\mathrm{post}}=\left[\begin{array}{ccc}\frac{0.618.Math.\cos .Math..Math.0}{1.28}& \frac{\cos .Math..Math.\frac{3.Math..Math.}{5}}{1.28}& \frac{\cos \left(-\frac{3.Math.}{5}\right)}{1.28}\\ 0& \frac{\sin .Math.\frac{3.Math.}{5}}{4.043}& \frac{\sin \left(-\frac{3.Math.}{5}\right)}{4.043}\end{array}\right]$ $T_{\mathrm{post}}^{-1}=2.235\left[\begin{array}{cc}0.618.Math.\cos .Math..Math.0& 0\\ \cos .Math.\frac{3.Math.}{5}& \sin .Math.\frac{3.Math.}{5}\\ \cos \left(-\frac{3.Math.}{5}\right)& \sin \left(-\frac{3.Math.}{5}\right)\end{array}\right]$ $T_{\mathrm{post}}^T=\left[\begin{array}{cc}\frac{0.618.Math.\cos .Math..Math.0}{1.28}& 0\\ \frac{\cos .Math.\frac{3.Math.}{5}}{1.28}& \frac{\sin .Math.\frac{3.Math.}{5}}{4.043}\\ \frac{\cos \left(-\frac{3.Math.}{5}\right)}{1.28}& \frac{\sin \left(-\frac{3.Math.}{5}\right)}{4.043}\end{array}\right]$ (4) restraining thrust force fluctuation caused by the short-circuit currents of fault phases with the healthy phase currents; wherein after calculating the short-circuit compensation currents (i.sub.Ai.sub.Ci.sub.D) of healthy phases which used to restrain thrust force fluctuation caused by the short-circuit currents of fault phases, the short-circuit compensation currents (i.sub.Ai.sub.Ci.sub.D) are transformed into currents (i.sub.i.sub.) in two-phase stationary frame by using the extended Clark transformation matrix T.sub.post; (5) transforming the remaining healthy three-phase currents (i.sub.Ai.sub.Ci.sub.D) in natural frame into the currents (i.sub.i.sub.) in two-phase stationary frame by using the extended Clark transformation matrix T.sub.post, and then the currents (i.sub.i.sub.) subtract the currents (i.sub.i.sub.) obtained in Step 4, and obtaining the currents (i.sub.i.sub.); wherein the Park transformation matrix C.sub.2s/2r is used to transform the currents (i.sub.i.sub.) into the currents (i.sub.di.sub.q) in the synchronous rotating frame; (5) subtracting the short-circuit compensation currents (i.sub.Ai.sub.Ci.sub.D) of healthy phases from the remaining healthy three-phase currents (i.sub.Ai.sub.Ci.sub.D) in national frame, obtaining (i.sub.Ai.sub.Ci.sub.D) which are transformed into the currents (i.sub.di.sub.q) in synchronous rotating frame according to the extended Clark transformation matrix T.sub.post and Park transformation matrix C.sub.2s/2r; (6) establishing the mathematical model of the five-phase IPM-FTLM with two nonadjacent short-circuit phase faults in the synchronous rotating frame; (7) designing the first-order inertia voltage feed-forward compensator, wherein the feed-forward compensation voltages (u.sub.d.sup.compu.sub.q.sup.comp) can be obtained by the current references (i.sub.d*i.sub.q*) of synchronous rotating frame going through the first-order inertia $\frac{}{s+};$ and wherein control voltages (u.sub.d0u.sub.q0) can be obtained by the difference values, which are generated by the current references (i.sub.d*i.sub.q*) subtracting the feedback currents (i.sub.di.sub.q), going through the current internal mode controller $.Math..Math.L\left(1+\frac{R}{\mathrm{sL}}\right);$ and wherein the sums of the control voltages (u.sub.d0u.sub.q0) and the feed-forward compensation voltages (u.sub.d.sup.compu.sub.q.sup.comp) are the voltage references (u.sub.d*u.sub.q*) in the synchronous rotating frame; and wherein the voltage references (u.sub.d*u.sub.q*) can be transformed into voltages (u.sub.*u.sub.*) in two-phase stationary frame by using Park inverse transformation matrix C.sub.2r/2s; (8) observing the back electromotive forces (EMFs) (e.sub.Ae.sub.Ce.sub.D) of the healthy phases by the back-EMF observer according to T.sub.post.sup.T, C.sub.2r/3s and the permanent magnet linkage of the secondary: $\left[\begin{array}{c}{e}_A\\ e_C\\ e_D\end{array}\right]=\left(T_{\mathrm{post}}^T.Math.C_{2.Math.r/2.Math.s}\left[\begin{array}{c}0\\ 2.5.Math.{}_m\end{array}\right]+0.206.Math.{}_m.Math.\sin .Math..Math.\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]\right)$ wherein the back-EMFs (e.sub.Be.sub.E) of the faulty phases can be calculated according to the back-EMFs (e.sub.Ae.sub.Ce.sub.D) of healthy phases: $\{\begin{array}{c}{e}_B=\frac{e_A+e_C}{2.Math.\cos .Math.\frac{2.Math.}{5}}\\ e_E=\frac{e_A+e_D}{2.Math.\cos .Math.\frac{2.Math.}{5}}\end{array}$ (9) verifying that the remaining healthy phase of the motor can output the short-circuit compensation currents (i.sub.Ai.sub.Ci.sub.D), which used to restrain thrust force fluctuation caused by short-circuit currents; wherein the short-circuit compensation voltages of the remaining healthy three-phases (u.sub.Au.sub.Cu.sub.D) can be defined as $\{\begin{array}{c}{u}_A^{}=0.1708.Math.\left(e_B+e_E\right)\\ u_C^{}=0.7236.Math.e_B-0.8944.Math.e_E\\ u_D^{}=-0.8944.Math.e_B+0.7236.Math.e_E\end{array},$ according to the relationship between phase-B short-circuit current i.sub.B=i.sub.sc.sub._.sub.B; and wherein phase-B back-EMF e.sub.B, the relationship between phase-E short-circuit current i.sub.E=i.sub.sc.sub._.sub.E; and phase-E back-EMF e.sub.E, and the mathematical expression of short-circuit compensation currents; wherein short-circuit compensation currents can be transformed into the short-circuit compensation voltages $\{\begin{array}{c}{u}_{}^{}=0.1237.Math.\left(e_B+e_E\right)\\ u_{}^{}=0.3806.Math.\left(e_B-e_E\right)\end{array}$ in two-phase stationary frame by using the extended Clark transformation matrix T.sub.post; (10) adding the voltage references (u.sub.*u.sub.*) in two-phase stationary frame and short-circuit compensation voltages (u.sub.u.sub.) are added up to the voltage references $\{\begin{array}{c}{u}_{}^{**}=u_{}^{*}+0.1237.Math.\left(e_B+e_E\right)\\ u_{}^{**}=u_{}^{*}+0.3806.Math.\left(e_B-e_E\right)\end{array};$ wherein the voltage references (u.sub.**u.sub.**) can be transformed into the voltage references (u.sub.A*u.sub.C*u.sub.D*) in national frame by using the extended Clark inverse transformation matrix T.sub.post.sup.1; wherein voltage references (u.sub.A*u.sub.C*u.sub.D*) and the back-EMFs (e.sub.Ae.sub.Ce.sub.D) of the remaining healthy phases are added up to the expected phase voltage references (u.sub.A**u.sub.C**u.sub.D**), respectively; (10) transforming the voltage references (u.sub.*u.sub.*) in two-phase stationary frame into the voltage references (u.sub.A*u.sub.C*u.sub.D*) in natural frame by using the extended Clark inverse transformation matrix T.sub.post.sup.1; wherein the voltage references (u.sub.A*u.sub.C*u.sub.D*) add the short-circuit compensation voltages (u.sub.Au.sub.Cu.sub.D) of remaining three healthy phases; wherein expected voltage references (u.sub.A**u.sub.C**u.sub.D) can be obtained by adding the back-EMFs (e.sub.Ae.sub.Ce.sub.D) of the remaining healthy phases, respectively; and (11) reacting to the occurrence of two nonadjacent short-circuit phase faults the expected voltage references (u.sub.A**u.sub.C**u.sub.D**) of Step 10 are passed through the voltage source inverter, then the fault-tolerant vector non-disturbed operation of five-phase IPM-FTLM is accomplished by adopting carrier pulse width modulation (CPWM) method.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0033] FIG. 1 shows the topology of the five-phase IPM-FTLM in the invention.

[0034] FIG. 2 shows the block diagram of field-oriented control strategy of the five-phase IPM-FTLM in the invention.

[0035] FIG. 3 shows the block diagram 1 of fault-tolerant field-oriented control for the five-phase IPM-FTLM with phase-B and phase-E short-circuit faults in the invention.

[0036] FIG. 4 shows the block diagram 2 of fault-tolerant field-oriented control for the five-phase IPM-FTLM with phase-B and phase-E short-circuit faults in the invention.

[0037] FIG. 5 shows phase-current waveform of no-fault-tolerant and fault-tolerant field-oriented operation under phase-B and phase-E short-circuit fault condition in the invention.

[0038] FIG. 6 shows thrust force waveform of no-fault-tolerant and fault-tolerant field-oriented operation under phase-B and phase-E short-circuit fault condition in the invention.

[0039] FIG. 7 shows the current waveform in synchronous rotating frame when the thrust force reference steps in the healthy operation in the invention.

[0040] FIG. 8 shows motor output thrust force waveform in synchronous rotating frame when the thrust force reference steps in the healthy operation in the invention.

[0041] FIG. 9 shows current waveform in synchronous rotating frame when the thrust force reference steps in the fault-tolerant operation under the phase-B and phase-E short-circuit faults condition in the invention.

[0042] FIG. 10 shows motor output thrust force waveform in synchronous rotating frame when the thrust force reference steps in the fault-tolerant operation under the phase-B and phase-E short-circuit faults condition in the invention.

[0043] In the Figures, 1 is primary, 2 is secondary, 3 is silicon steel sheet, 4 is pole shoe, 5 is fault-tolerant teeth, 6 is armature teeth, 7 is end tooth, 8 is permeability magnetic materials, 9 is winding coils.

DETAILED DESCRIPTION OF THE PRESENT INVENTION

[0044] The following is combined with the attached drawings of the invention, it is detailed description about the technical solutions of the invention in clear and complete form.

[0045] In order to illustrate the structure characteristics and beneficial effects of the five-phase IPM-FTLM of the invention more simply and clearly, a special five-phase IPM-FTLM is used to describe in the following.

[0046] (1) The model of five-phase IPM-FTLM is built.

[0047] FIG. 1 shows the topology structure of the five-phase IPM-FTLM in the invention, including primary 1 and secondary 2. The primary 1 includes pole shoes 4, armature teeth 6, fault-tolerant teeth 5 and concentrated winding coils 9. Meanwhile, the number of armature teeth 6 and fault-tolerant teeth 5 both are 10. Rare earth permanent magnet 8 is embedded in secondary 2, and there is air gap between primary 1 and secondary 2. The part of primary 1 and secondary 2 are made of silicon steel sheet 3 axially laminated expect permanent magnets, winding coils and pole shoes. At the same time, pole shoes 4 are made of electrical iron. In addition, two end teeth 7 of primary 1 are asymmetric, and they are wider than fault-tolerant teeth and armature teeth.

[0048] On the basis of traditional CPWM which uses sinusoidal wave as modulation wave, the CPWM method can achieve the same flux-linkage control effect as five-phase SVPWM method, when five-phase sinusoidal modulation wave is injected with c0=(max(ui)+min(ui))/2 zero sequence voltage harmonic (u.sub.i is the each-phase function of five-phase sine-modulation wave) in CPWM method. So the CPWM method based on zero sequence voltage harmonic injection is adopted in the invention.

[0049] The five-phase IPM-FTLM is powered by a voltage source inverter. The motor is divided into phase-A, phase-B, phase-C, phase-D and phase-E. The field-oriented control strategy with CPWM technology based on zero sequence voltage harmonic injection is adopted, and zero sequence current is controlled to zero, the control block diagram is shown in FIG. 2. When the motor operates in the healthy condition, each phase current can be expressed as:

[00001]$\begin{array}{cc}\{\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}{i}_A^{*}=-i_q^{*}.Math.\sin \left(\right)+i_d^{*}.Math.\cos \left(\right)\\ i_B^{*}=-i_q^{*}.Math.\sin \left(-2.Math./5\right)+i_d^{*}.Math.\cos \left(-2.Math./5\right)\end{array}\\ i_C^{*}=-i_q^{*}.Math.\sin \left(-4.Math./5\right)+i_d^{*}.Math.\cos \left(-4.Math./5\right)\end{array}\\ i_D^{*}=-i_q^{*}.Math.\sin \left(-6.Math./5\right)+i_d^{*}.Math.\cos \left(-6.Math./5\right)\end{array}\\ i_E^{*}=-i_q^{*}.Math.\sin \left(-8.Math./5\right)+i_d^{*}.Math.\cos \left(-8.Math./5\right)\end{array}& \left(1\right)\end{array}$

where i.sub.d*i.sub.q* are d-axis current reference and q-axis current reference in the synchronous rotating frame, respectively,

[00002]$=\frac{.Math..Math.v}{}.Math.\mathrm{dt}$

is electric angle, and is the electric speed of secondary and is pole pitch.

[0050] The travelling-wave MMF generated by the motor can be expressed as:

[00003]$\begin{array}{cc}\mathrm{MMF}=\underset{i=A}{\overset{E}{.Math.}}.Math.{\mathrm{MMF}}_i={\mathrm{Ni}}_A+{\mathrm{aNi}}_B+a^2.Math.{\mathrm{Ni}}_C+a^3.Math.{\mathrm{Ni}}_D+a^4.Math.{\mathrm{Ni}}_E& \left(2\right)\end{array}$

where a=e.sup.j2/5, N is the effective turns of each phase winding coils.

[0051] (2) When motor is with phase-B and phase-E short-circuit faults, it is assumed that the open-circuit faults only occur in phase-B and phase-E. According to the principle of constant travelling-wave MMF before and after fault, and the constraint about the sum of remaining healthy phase currents is zero, and also the constraint about the amplitude of two adjacent phase-C and phase-D currents is equal, the healthy phase currents of fault-tolerant operation can be obtained after the open-circuit faults occur in phase-B and phase-E.

[0052] When the motor is with two nonadjacent phase faults, it can suppose that the short-circuit faults occur in phase-B and phase-E. Firstly, the remaining healthy phase currents can be used to compensate the missing normal thrust force generated by the two phases of short-circuit faults. Then, supposing that open-circuit faults occur in phase-B and phase-E and their phase currents are zero, the travelling-wave MMF is generated by the remaining three-phase healthy phase windings, it can be expressed as:

[00004]$\begin{array}{cc}\begin{array}{c}\mathrm{MMF}=.Math.\underset{i=A,C,D}{.Math.}.Math.{\mathrm{MMF}}_i\\ =.Math.{\mathrm{Ni}}_A^{*}+a^2.Math.{\mathrm{Ni}}_C^{*}+a^3.Math.{\mathrm{Ni}}_D^{*}\end{array}& \left(3\right)\end{array}$

[0053] To realize undisturbed operation when the motor is with two nonadjacent short-circuit phase faults, it needs to keep the travelling-wave MMF constant before and after fault. Therefore, it is necessary to adjust the remaining healthy phase currents to keep the amplitude and speed of travelling-wave MMF constant before and after fault. Thus, the real and imaginary parts of (2) and (3) are required to equal, respectively.

[0054] The motor phase windings are connected in star, and its center point is not connected with the center point of dc-bus voltage. Thus, the sum of phase currents is zero. The healthy phase currents are optimized according to the principle of equal amplitude of adjacent two-phase currents. Supposing that

[00005]$\begin{array}{cc}\{\begin{array}{c}{I}_C=I_D\\ i_A^{*}+i_C^{*}+i_D^{*}=0\end{array}& \left(4\right)\end{array}$

where I.sub.C and I.sub.D are phase-C and phase-D current amplitude, respectively.

[0055] The healthy phase currents are optimized according to the above constraints. Then, the phase-current references of fault-tolerant operation can be expressed as:

[00006]$\begin{array}{cc}\{\begin{array}{c}{i}_A^{*}=1.381.Math.\left(-i_q^{*}.Math.\sin \left(\right)+i_d^{*}.Math.\cos \left(\right)\right)\\ i_B^{*}=0\\ i_C^{*}=2.235.Math.\left(-i_q^{*}.Math.\sin \left(-\frac{3}{5}.Math.\right)+i_d^{*}.Math.\cos \left(-\frac{3}{5}.Math.\right)\right)\\ i_D^{*}=2.235.Math.\left(-i_q^{*}.Math.\sin \left(+\frac{3}{5}.Math.\right)+i_d^{*}.Math.\cos \left(+\frac{3}{5}.Math.\right)\right)\\ i_E^{*}=0\end{array}& \left(5\right)\end{array}$

[0056] Equation (5) can be represented in matrix form as follows:

[00007]$\begin{array}{cc}\left[\begin{array}{c}{i}_A^{*}\\ i_C^{*}\\ i_D^{*}\end{array}\right]=2.235\left[\begin{array}{cc}0.618.Math.\cos .Math..Math.0& 0\\ \cos .Math.\frac{3.Math.}{5}& \sin .Math.\frac{3.Math.}{5}\\ \cos \left(-\frac{3.Math.}{5}\right)& \sin \left(-\frac{3.Math.}{5}\right)\end{array}\right]\left[\begin{array}{cc}\cos .Math..Math.& -\sin .Math..Math.\\ \sin .Math..Math.& \cos .Math..Math.\end{array}\right]\left[\begin{array}{c}{i}_d^{*}\\ i_q^{*}\end{array}\right]& \left(6\right)\end{array}$

[0057] According to (6), it can be obtained:

[00008]$\begin{array}{cc}\left[\begin{array}{c}{i}_{}^{*}\\ i_{}^{*}\end{array}\right]=\left[\begin{array}{cc}\cos .Math..Math.& -\sin .Math..Math.\\ \sin .Math..Math.& \cos .Math..Math.\end{array}\right]\left[\begin{array}{c}{i}_d^{*}\\ i_q^{*}\end{array}\right]=C_{r/s}\left[\begin{array}{c}{i}_d^{*}\\ i_q^{*}\end{array}\right]& \left(7\right)\\ \left[\begin{array}{c}{i}_A^{*}\\ i_C^{*}\\ i_D^{*}\end{array}\right]=2.235\left[\begin{array}{cc}0.618.Math.\cos .Math..Math.0& 0\\ \cos .Math.\frac{3.Math.}{5}& \sin .Math.\frac{3.Math.}{5}\\ \cos \left(-\frac{3.Math.}{5}\right)& \sin \left(-\frac{3.Math.}{5}\right)\end{array}\right]\left[\begin{array}{c}{i}_{}^{*}\\ i_{}^{*}\end{array}\right]& \left(8\right)\end{array}$

[0058] The extended Clark transformation matrix T.sub.post is three columns and two rows, it can be used to transform the variables in the remaining three-healthy-phase natural frame into the two-phase stationary frame, the inverse transformation matrix T.sub.post.sup.1 is two columns and three rows. T.sub.post, T.sub.post.sup.1, and transposed matrix T.sub.post.sup.T are obtained according to the healthy phase currents.

[0059] According to (8), the transformation matrix which used to transform two-phase stationary frame into the remaining healthy phase natural frame can be defined as:

[00009]$\begin{array}{cc}{T}_{\mathrm{post}}^{-1}=2.235\left[\begin{array}{ccc}0.618.Math.\cos .Math..Math.0& 0& k\\ \cos .Math.\frac{3.Math.}{5}& \sin .Math.\frac{3.Math.}{5}& k\\ \cos \left(-\frac{3.Math.}{5}\right)& \sin \left(-\frac{3.Math.}{5}\right)& k\end{array}\right]& \left(9\right)\end{array}$

[0060] Since the sum of remaining healthy phase currents is zero, the inverse transformation matrix of (9) can be expressed as:

[00010]$\begin{array}{cc}{T}_{\mathrm{post}}=\left[\begin{array}{ccc}\frac{0.618.Math.\cos .Math..Math.0}{1.28}& \frac{\cos .Math.\frac{3.Math.}{5}}{1.28}& \frac{\cos \left(-\frac{3.Math.}{5}\right)}{1.28}\\ 0& \frac{\sin .Math.\frac{3.Math.}{5}}{4.043}& \frac{\sin \left(-\frac{3.Math.}{5}\right)}{4.043}\\ k& k& k\end{array}\right]& \left(10\right)\end{array}$

where k is equal to 0.386.

[0061] Due to the star connection windings, the sum of phase currents is zero. Thus, when removing the third column of (9) and the third row of (10), the extended Clark inverse transformation matrix and the extended Clark transformation matrix can be re-pressed as:

[00011]$\begin{array}{cc}{T}_{\mathrm{post}}^{-1}=2.235\left[\begin{array}{cc}0.618.Math.\cos .Math..Math.0& 0\\ \cos .Math.\frac{3.Math.}{5}& \sin .Math.\frac{3.Math.}{5}\\ \cos \left(-\frac{3.Math.}{5}\right)& \sin \left(-\frac{3.Math.}{5}\right)\end{array}\right]& \left(11\right)\\ T_{\mathrm{post}}=\left[\begin{array}{ccc}\frac{0.618.Math.\cos .Math..Math.0}{1.28}& \frac{\cos .Math.\frac{3.Math.}{5}}{1.28}& \frac{\cos \left(-\frac{3.Math.}{5}\right)}{1.28}\\ 0& \frac{\sin .Math.\frac{3.Math.}{5}}{4.043}& \frac{\sin \left(-\frac{3.Math.}{5}\right)}{4.043}\end{array}\right]& \left(12\right)\end{array}$

[0062] The transposed matrix of (12) can be expressed as:

[00012]$\begin{array}{cc}{T}_{\mathrm{post}}^T=\left[\begin{array}{cc}\frac{0.618.Math.\cos .Math..Math.0}{1.28}& 0\\ \frac{\cos .Math.\frac{3.Math.}{5}}{1.28}& \frac{\sin .Math.\frac{3.Math.}{5}}{4.043}\\ \frac{\cos \left(-\frac{3.Math.}{5}\right)}{1.28}& \frac{\sin \left(-\frac{3.Math.}{5}\right)}{4.043}\end{array}\right]& \left(13\right)\end{array}$

[0063] The healthy phase currents are used to restrain thrust force fluctuation caused by the short-circuit currents of fault phases. After calculating the short-circuit compensation currents (i.sub.Ai.sub.D) of healthy phases which used to restrain thrust force fluctuation caused by the short-circuit currents of fault phases, the short-circuit compensation currents (i.sub.Ai.sub.Ci.sub.D) can be transformed into currents (i.sub.i.sub.) in two-phase stationary frame by using the extended Clark transformation matrix T.sub.post.

[0064] Since the current of zero sequence subspace is zero, it does not need to be transformed into synchronous rotating frame. Energy conversion works in fundamental wave subspace, so it is necessary to transform the energy of fundamental wave subspace into the synchronous rotating frame. Therefore, the transformation matrix C.sub.2s/2r which used to transform two-phase stationary frame into the synchronous rotating frame and its inverse transformation matrix C.sub.2r/2s can be defined as:

[00013]$\begin{array}{cc}{C}_{2.Math.s/2.Math.r}=\left[\begin{array}{cc}\cos .Math..Math.& \sin .Math..Math.\\ -\sin .Math..Math.& \cos .Math..Math.\end{array}\right]& \left(14\right)\\ C_{2.Math.r/2.Math.s}=\left[\begin{array}{cc}\cos .Math..Math.& -\sin .Math..Math.\\ \sin .Math..Math.& \cos .Math..Math.\end{array}\right]& \left(15\right)\end{array}$

[0065] On the basis of part one, the healthy phase currents are used to restrain thrust force fluctuation caused by short-circuit phase currents when motor is with short-circuit phase faults.

[0066] Supposing that phase-B and phase-E short-circuit currents are i.sub.sc.sub._.sub.B=I.sub.f cos(t.sub.fB) and i.sub.sc.sub._.sub.E=I.sub.f cos(t.sub.fE), respectively. I.sub.f is the amplitude of short-circuit current, and .sub.fB is angle between back-EMF of phase-B and short-circuit current of phase-B. .sub.fE is angle between back-EMF of phase-E and short-circuit current of phase-E. =/, is the speed of secondary and is pole pitch.

[0067] The compensation currents of phase-A, phase-C and phase-D can be defined as:

[00014]$\begin{array}{cc}\{\begin{array}{c}{i}_A^{}=x_A.Math.\cos .Math..Math.+y_A.Math.\sin .Math..Math.\\ i_C^{}=x_C.Math.\cos .Math..Math.+y_C.Math.\sin .Math..Math.\\ i_D^{}=x_D.Math.\cos .Math..Math.+y_D.Math.\sin .Math..Math.\end{array}& \left(16\right)\end{array}$

where x.sub.Ay.sub.Ax.sub.Cy.sub.Cx.sub.Dy.sub.D are the amplitude of cosine terms and sin terms of the healthy phase compensation currents, respectively.

[0068] According to the principle that the sum of health-phase compensation currents which restrain the thrust force fluctuation caused by short-circuit fault phase currents is zero, and the sum of MMFs generated by the healthy phase compensation currents and short-circuit fault-phase currents is zero. The short-circuit compensation currents (i.sub.Ai.sub.Ci.sub.D) of healthy phases which used to restrain thrust force fluctuation caused by fault-phase short-circuit currents can be obtained:

[00015]$\begin{array}{cc}\{\begin{array}{c}{i}_A^{}=-0.1708.Math.\left(i_{\mathrm{sc\_B}}+i_{\mathrm{sc\_E}}\right)\\ i_C^{}=-0.7236.Math.i_{\mathrm{sc\_B}}+0.8944.Math.i_{\mathrm{sc\_E}}\\ i_D^{}=0.8944.Math.i_{\mathrm{sc\_B}}-0.7236.Math.i_{\mathrm{sc\_E}}\end{array}& \left(17\right)\end{array}$

[0069] The extended Clark transformation matrix T.sub.post transforms the health-phase compensation currents (i.sub.Ai.sub.Ci.sub.D) into the short-circuit compensation currents (ii.sub.) in two-phase stationary frame, and it can be obtained:

[00016]$\begin{array}{cc}\{\begin{array}{c}{i}_{}^{}=-0.1237.Math.\left(i_{\mathrm{sc\_B}}+i_{\mathrm{sc\_E}}\right)\\ i_{}^{}=-0.3806.Math.\left(i_{\mathrm{sc\_B}}-i_{\mathrm{sc\_E}}\right)\end{array}& \left(18\right)\end{array}$

[0070] The mathematical model of the motor with two nonadjacent short-circuit phase faults

[0071] Compared with the self-inductance, the mutual inductance of the IPM-FTLM is much smaller, so the mutual inductance can be ignored. Supposing that phase inductance is almost constant and the back-EMF is sinusoidal waveform. The phasor angles of back-EMFs are determined by their phase windings space location, and the proposed transformation matrices in the invention cannot be used to transform the back-EMFs as currents' transformation. To realize the field-oriented control for the fault-tolerant permanent-magnet linear motor with phase-B and phase-E short-circuit faults, the model of the motor with short-circuit faults can be expressed as follows in natural frame:

[00017]$\begin{array}{cc}\{\begin{array}{c}{u}_{\mathrm{Ae}}=u_A-e_A={\mathrm{Ri}}_A+L_s.Math.\frac{{\mathrm{di}}_A}{\mathrm{dt}}\\ -e_B={\mathrm{Ri}}_B+L_s.Math.\frac{{\mathrm{di}}_B}{\mathrm{dt}}\\ u_{\mathrm{Ce}}=u_C-e_C={\mathrm{Ri}}_C+L_s.Math.\frac{{\mathrm{di}}_C}{\mathrm{dt}}\\ u_{\mathrm{De}}=u_D-e_D={\mathrm{Ri}}_D+L_s.Math.\frac{{\mathrm{di}}_D}{\mathrm{dt}}\\ -e_E={\mathrm{Ri}}_E+L_s.Math.\frac{{d.Math.i}_E}{\mathrm{dt}}\end{array}& \left(19\right)\end{array}$

where u.sub.A, u.sub.C and u.sub.D are healthy phase voltages, e.sub.A, e.sub.C and e.sub.D are phase back-EMFs. u.sub.Ae, u.sub.Ce and u.sub.De are the values of the healthy phase voltages subtracting the phase back-EMFs, respectively, and R is phase resistance.

[0072] (5) The extended Clark transformation matrix T.sub.post can be used to transform the remaining healthy three-phase currents (i.sub.Ai.sub.Ci.sub.D) in natural frame into the currents (i.sub.i.sub.) in two-phase stationary frame. The currents (i.sub.i.sub.) subtract the short-circuit compensation currents (i.sub.i.sub.), respectively, it can be obtained the currents (i.sub.i.sub.), and the Park transformation matrix C.sub.2s/2r transforms (i.sub.i.sub.) into the currents (i.sub.di.sub.q) in synchronous rotating frame.

[0073] Or, the remaining three-phase healthy phase currents (i.sub.Ai.sub.Ci.sub.D) in the natural frame subtract the short-circuit compensation currents (i.sub.Ai.sub.Ci.sub.D) of healthy phases which restrain the thrust force fluctuation caused by short-circuit faulty phase currents, and then it can be obtained the currents (i.sub.Ai.sub.Ci.sub.D). Then, the extended Clark transformation matrix T.sub.post and Park transformation matrix C.sub.2s/2r are used to transform the (i.sub.Ai.sub.Ci.sub.D) into the feedback currents (i.sub.di.sub.q) in synchronous rotating frame.

[0074] (6) Building the mathematical model of five-phase IPM-FTLM in synchronous rotating frame under two nonadjacent short-circuit phase faults condition.

[0075] The model of the motor with nonadjacent two-phase short-circuit faults in natural frame is transformed into the model which can be expressed in synchronous rotating frame as follows:

[00018]$\begin{array}{cc}\{\begin{array}{c}{u}_{\mathrm{de}}=i_d.Math.R+L_s.Math.\frac{{\mathrm{di}}_d}{\mathrm{dt}}-.Math..Math.L_s.Math.i_q\\ u_{\mathrm{qe}}=i_q.Math.R+L_s.Math.\frac{{\mathrm{di}}_q}{\mathrm{dt}}-.Math..Math.L_s.Math.i_d\end{array}& \left(20\right)\end{array}$

[0076] By using magnetic co-energy and (5)-(18), the thrust force equation of the motor with two nonadjacent short-circuit phase fault condition can be expressed as:

[00019]$\begin{array}{cc}F=\frac{}{}.Math.\left(\frac{1}{2}.Math.I_s^T.Math.\frac{L_s}{}.Math.I_s+I_s^T.Math.\frac{{}_m}{}\right)=2.5.Math.\frac{}{}.Math.i_q.Math.{}_m& \left(21\right)\end{array}$

where .sub.m is the permanent-magnet linkage of the secondary.

[0077] Thus, the five-phase IPM-FTLM with two nonadjacent short-circuit phase faults can output the expected thrust force as long as the currents i.sub.di.sub.q are controlled well in the synchronous rotating frame.

[0078] The fault-tolerant field-oriented control strategy of the motor with two nonadjacent short-circuit phases

[0079] (7) After designing first-order inertia feed-forward voltage compensator, the compensation voltages (u.sub.d.sup.compu.sub.q.sup.comp) can be obtained by the current references (i.sub.d*i.sub.q*) in synchronous rotating frame going through the first-order inertia

[00020]$\frac{.Math..Math.}{s+}.$

The compensation voltages (u.sub.d.sup.compu.sub.q.sup.comp) can be expressed as:

[00021]$\begin{array}{cc}\{\begin{array}{c}{u}_d^{\mathrm{comp}}=\frac{}{s+}.Math.i_q^{*}\\ u_q^{\mathrm{comp}}=\frac{}{s+}.Math.i_d^{*}\end{array}& \left(22\right)\end{array}$

[0080] It can be obtained the control voltages (u.sub.d0u.sub.q0) when the difference values, which are obtained by the current references (i.sub.d*i.sub.q*) subtracting the feedback currents (i.sub.di.sub.q), going through the current internal mode controller

[00022]$.Math..Math.L\left(1+\frac{R}{\mathrm{sL}}\right).$

The sums of the control voltages (u.sub.d0u.sub.q0) and the feed-forward compensation voltages are the voltage references (u.sub.d*u.sub.q*) in synchronous rotating frame. Then, the voltage references (u.sub.d*u.sub.q*) can be expressed as:

[00023]$\begin{array}{cc}\{\begin{array}{c}{u}_d^{*}=.Math..Math.L\left(1+\frac{R}{\mathrm{sL}}\right).Math.\left(i_d^{*}-i_d\right)-u_q^{\mathrm{comp}}\\ u_q^{*}=.Math..Math.L\left(1+\frac{R}{\mathrm{sL}}\right).Math.\left(i_q^{*}-i_q\right)-u_q^{\mathrm{comp}}\end{array}& \left(23\right)\end{array}$

[0081] The Park inverse transformation matrix C.sub.2r/2s is used to transform the voltage references (u.sub.d*u.sub.q*) into the voltages (u.sub.*u.sub.*) in two-phase stationary frame.

[0082] (8) By using T.sub.post.sup.T, C.sub.2r/2s and the permanent-magnetic linkage of secondary, the back-EMF observer can be designed, which can be used to observe the back-EMFs (e.sub.Ae.sub.Ce.sub.D) of healthy phases, and it can be expressed as:

[00024]$\begin{array}{cc}\left[\begin{array}{c}{e}_A\\ e_C\\ e_D\end{array}\right]=\left(T_{\mathrm{post}}^T.Math.C_{2.Math.r/2.Math.s}\left[\begin{array}{c}0\\ 2.5.Math.{}_m\end{array}\right]+0.206.Math.{}_m.Math.\sin .Math..Math.\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]\right)& \left(24\right)\end{array}$

[0083] According to the back-EMFs (e.sub.Ae.sub.Ce.sub.D) of healthy phases, the back-EMFs of fault phases can be obtained as:

[00025]$\begin{array}{cc}\{\begin{array}{c}{e}_B=\frac{e_A+e_C}{2.Math..Math.\cos .Math.\frac{2.Math.}{5}}\\ e_E=\frac{e_A+e_D}{2.Math..Math.\cos .Math.\frac{2.Math.}{5}}\end{array}& \left(25\right)\end{array}$

[0084] (9) According to the relationship between the short-circuit current of phase-B i.sub.B=i.sub.sc.sub._.sub.B and the back-EMF of phase-B e.sub.B, the relationship between the short-circuit current i.sub.E=i.sub.sc.sub._.sub.E of phase-E and back-EMF e.sup.E of phase-E, and the mathematical expression of short-circuit compensation currents, the short-circuit compensation voltages of the remaining healthy three-phases (u.sub.Au.sub.Cu.sub.D) can be defined as:

[00026]$\begin{array}{cc}\{\begin{array}{c}{u}_A^{}=0.1708.Math.\left(e_B+e_E\right)\\ u_C^{}=0.7236.Math.e_B-0.8944.Math.e_E\\ u_D^{}=-0.8944.Math.e_B+0.7236.Math.e_E\end{array}& \left(26\right)\end{array}$

[0085] The extended Clark transformation matrix T.sub.post is used to transform (26) into the short-circuit compensation voltages in two-phase stationary frame, and it can be expressed as:

[00027]$\begin{array}{cc}\{\begin{array}{c}{u}_{}^{}=0.1237.Math.\left(e_B+e_E\right)\\ u_{}^{}=0.3806.Math.\left(e_B-e_E\right)\end{array}& \left(27\right)\end{array}$

[0086] (10) The voltage references (u.sub.*u.sub.*) in two-phase stationary frame and the short-circuit compensation voltages (u.sub.u.sub.) are added up to

[00028]$\begin{array}{cc}\{\begin{array}{c}{u}_{}^{**}=u_{}^{*}+0.1237.Math.\left(e_B+e_E\right)\\ u_{}^{**}=u_{}^{*}+0.3806.Math.\left(e_B-e_E\right)\end{array}& \left(28\right)\end{array}$

[0087] The extended Clark inverse transformation matrix T.sub.post.sup.1 is used to transform voltage references (u**u.sup.**) into the voltage references (u.sub.A*u.sub.C*u.sub.D*) in natural frame. The voltage references (u.sub.A*u.sub.C*u.sub.D*) and their phases back-EMFs are added up to the expected phase voltage references (u.sub.A**u.sub.C**u.sub.D**), respectively, which can be expressed as:

[00029]$\begin{array}{cc}\left[\begin{array}{c}{u}_A^{**}\\ u_C^{**}\\ u_D^{**}\end{array}\right]=T_{\mathrm{post}}^{-1}\left[\begin{array}{c}{u}_{}^{**}\\ u_{}^{**}\end{array}\right]+\left[\begin{array}{c}{e}_A\\ e_C\\ e_D\end{array}\right]& \left(29\right)\end{array}$

[0088] (10) The extended Clark inverse transformation matrix T.sub.post.sup.1 is used to transform voltage references (u.sub.*u.sub.*) in two-phase stationary frame into the voltage references (u.sub.A*u.sub.C*.sub.D*) in natural frame. The voltage references (u.sub.A*u.sub.C*u.sub.D*) add the short-circuit compensation voltages (u.sub.Au.sub.Cu.sub.D) of remaining healthy three-phases, respectively. Finally, by adding the back-EMFs (e.sub.Ae.sub.Ce.sub.D) of remaining healthy phases again, respectively, the expected voltage references (u.sub.A**u.sub.C**u.sub.D**) can be expressed as:

[00030]$\begin{array}{cc}\left[\begin{array}{c}{u}_A^{**}\\ u_C^{**}\\ u_D^{**}\end{array}\right]=T_{\mathrm{post}}^{-1}\left[\begin{array}{c}{u}_{}^{**}\\ u_{}^{**}\end{array}\right]+\left[\begin{array}{c}{u}_A^{}\\ u_C^{}\\ u_D^{}\end{array}\right]\left[\begin{array}{c}{e}_A\\ e_C\\ e_D\end{array}\right]& \left(30\right)\end{array}$

[0089] (11) The expected phase-voltage references (u.sub.A**u.sub.C**u.sub.D**) obtained in Step 10 go through voltage source inverter, then CPWM method is used to achieve fault-tolerant field-oriented undisturbed operation when five-phase IPM-FTLM is with two nonadjacent short-circuit phase faults.

[0090] The expected phase voltages of (29) or (30) is modulated by the CPWM method based on zero-sequence voltage harmonic injection when they are taken into voltage source inverter, and then the fault-tolerant field-oriented undisturbed operation is achieved when five-phase IPM-FTLM is with phase-B and phase-E short-circuit faults. The fault-tolerant field-oriented control strategy of the two nonadjacent short-circuit phase faults proposed in the invention are shown in FIGS. 3 and 4.

[0091] When open-circuit faults occur in phase-B and phase-E, it just needs to set the short-circuit compensation currents of Step 4 to zero, and to set the short-circuit compensation voltages of Step 9 to zero. The fault-tolerant field-oriented control method can achieve the fault-tolerant operation of five-phase IPM-FTLM under two nonadjacent open-circuit phase faults.

[0092] When open-circuit fault occurs in phase-B and short-circuit fault occurs in phase-E, it only needs to set the expression of short-circuit compensation current i.sub.sc.sub._.sub.B=0 in Step 4, and to set the expression of short-circuit compensation voltage e.sub.B=0 in Step 9. This fault-tolerant field-oriented control method can achieve fault-tolerant operation of five-phase IPM-FTLM under phase-B open-circuit fault and phase-E short-circuit fault.

[0093] When short-circuit fault occurs in phase-B and open-circuit fault occurs in phase-E, it just needs to set the expression of short-circuit compensation current i.sub.sc.sub._.sub.E=0 in Step 4, and to set the expression of short-circuit compensation voltage e.sub.E=0 in Step 9. This fault-tolerant field-oriented control method can achieve fault-tolerant operation of five-phase IPM-FTLM under phase-B short-circuit fault and phase-E open-circuit fault.

[0094] When other two nonadjacent phases are with faults, it just needs to counterclockwise rotate the natural frame by

[00031]$\frac{2.Math.}{5}.Math.k$

electric angle (k=01234; when phase-B and phase-E are with faults, K=0; when phase-C and phase-A are with faults, K=1; when phase-D and phase-B are with faults, K=2; when phase-E and phase-C are with faults, K=3; when phase-A and phase-D are with faults, K=4), and the Park transformation matrix and its inverse transformation matrix can be expressed as:

[00032]$\begin{array}{cc}{C}_{2.Math.s/2.Math.r}=\left[\begin{array}{cc}\cos \left(-\frac{2.Math.k.Math..Math.}{5}\right)& \sin \left(-\frac{2.Math.k.Math..Math.}{5}\right)\\ -\sin \left(-\frac{2.Math.k.Math..Math.}{5}\right)& \cos \left(-\frac{2.Math.k.Math..Math.}{5}\right)\end{array}\right]& \left(31\right)\\ C_{2.Math.r/2.Math.s}=\left[\begin{array}{cc}\cos \left(.Math..Math.t-\frac{2.Math.k.Math..Math.}{5}\right)& -\sin \left(.Math..Math.t-\frac{2.Math.k.Math..Math.}{5}\right)\\ \sin \left(.Math..Math.t-\frac{2.Math.k.Math..Math.}{5}\right)& \cos \left(.Math..Math.t-\frac{2.Math.k.Math..Math.}{5}\right)\end{array}\right]& \left(32\right)\end{array}$

[0095] According to FIG. 2, FIG. 3 or FIG. 4, the control system simulation model of five-phase IPM-FTLM as shown in FIG. 1 is built in MATLAB/SIMLINK. By simulation, the simulated results of the fault-tolerant field-oriented control for five-phase IPM-FTLM with two nonadjacent short-circuit phase faults can be obtained.

[0096] FIG. 5 is the phase-current waveforms under phase-B and phase-E short-circuit faults. When short-circuit faults occur at 0.1 s, the current waveforms are distorted seriously. However, the sinusoidal currents are obtained when the fault-tolerant field-oriented control strategy is activated at 0.2 s. FIG. 6 is thrust force waveform under phase-B and phase-E short-circuit faults. When short-circuit faults occur at 0.1 s, the thrust force fluctuation is high. The thrust force fluctuation of motor output is obviously restrained when the fault-tolerant field-oriented control strategy is activated at 0.2 s, and thrust force fluctuation almost has no fluctuation. FIGS. 7 and 8 are the current in synchronous rotating frame and output thrust force response, respectively, when thrust force reference steps under healthy condition, and the response time of thrust force is 0.2 s. FIGS. 9 and 10 are the current in synchronous rotating frame and output thrust force response, respectively, when thrust force reference steps under phase-B and phase-E short-circuit faults condition with the fault-tolerant field-oriented control strategy, and the response time of thrust force is 0.3 s. Thus, by using the fault-tolerant field-oriented control strategy, the five-phase IPM-FTLM under two nonadjacent phase faults condition has the same dynamic performance and steady performance as that under healthy condition. Additionally, it also has good current-tracking performance and achieves non-disturbed fault-tolerant operation.

[0097] From the above mentioned, under the maximum permissible current of the motor driven system, the inventive fault-tolerant field-oriented control strategy for five-phase IPM-FTLM with two nonadjacent short-circuit phase faults not only ensures the same output thrust force as that under healthy condition, but also clearly restrains the thrust force fluctuation, when the motor is with two nonadjacent phase faults (open-circuit phase faults, short-circuit phase faults, or one open-circuit phase fault and the other short-circuit phase fault). The mostly important is that it has almost the same dynamic performance, steady performance and current tracking accuracy as that under healthy condition, and it is also suitable for the any two nonadjacent phase faults (open-circuit phase faults, short-circuit phase faults, or one open-circuit phase fault and the other short-circuit phase fault). This control strategy has the good generality, and also it does not need complex calculation. In addition, its CPU cost is small, and the setting of current regular parameters is simple. Thus, the invention has a very good application prospect on the system, where a high requirement on operation reliability needs, such as electromagnetic active suspension.

[0098] Although the present invention has been made public as above implement example, the example is not used to limit the invention. Any equivalent change or retouching within the spirit and field of the present invention belongs to the protective range of the invention.