CN105262393B - A kind of fault-tolerant magneto method for control speed using novel transition process - Google Patents
A kind of fault-tolerant magneto method for control speed using novel transition process Download PDFInfo
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Abstract
The invention discloses a kind of fault-tolerant magneto method for control speed using novel transition process, belong to magneto controlling technology of velocity field, one quick and stable transient process is arranged according to the permitted physics peak acceleration of motor vector control system, and real-Time Compensation is carried out to acceleration using linear active disturbance rejection controller, motor is realized non-overshoot quick response in whole dynamic process；In addition, have also been devised the linear active disturbance rejection controller for fault-tolerant magneto, in addition to Nonlinear Tracking Differentiator, the parameter that need to be adjusted only has an observer bandwidth value ω0, simplify controller design difficulty.Shown by experimental verification, for conventional PI control device, the new controller that the present invention designs has very strong Ability of Resisting Disturbance, and shortens the time of system response storm.
Description
Technical field
The present invention relates to magneto controlling technology of velocity, a kind of particularly fault-tolerant permanent magnetism using novel transition process
Motor speed loop wire Active Disturbance Rejection Control (LADRC) method, suitable for permanent magnet synchronous motor high performance servo control field.
Background technology
Permanent magnet synchronous motor is one complicated non-linear, and the system of close coupling, would generally join in the process of running
Number perturbation and external disturbance.But in permanent magnet synchronous motor Vector Speed-Control System, generally use speed outer shroud and electric current
The double closed-loop control system of inner ring, and controller uses traditional PID controller.Due to conventional PID controllers, there are overshoot
The shortcomings of amount is big, response time length, Ability of Resisting Disturbance is poor, is generally unable to reach satisfied control effect.Therefore it is many advanced
Algorithm be applied to Permanent-magnet Synchronous-motor Speed Servo System, such as neural network control method, sliding mode variable structure control method, obscures
Control method, self-adaptation control method etc., but they need to carry out complicated mathematical operation and theory deduction mostly, it is difficult to really
Applied in Permanent-magnet Synchronous-motor Speed Servo System.Therefore, new simple control algolithm is studied, and applies it to fault-tolerant permanent magnetism
To improve the performance of control system it is a urgent problem to be solved in synchronous motor control system.
Although it can achieve the purpose that to reduce overshoot using traditional linearity tracking differentiator, but rotating speed still has
Overshoot, this is because traditional linearity tracking differentiator does not have the starting characteristic for considering motor completely, makes motor in starting rank
The error of section is accumulated, and finally produces overshoot.And raising system is not played in the use of traditional linearity tracking differentiator
The effect for robustness of uniting, the direction of the clear and definite adjustment parameter of neither one, the guidance of the control to motor speed are not clear and definite enough.
The content of the invention
The object of the present invention is to provide a kind of fault-tolerant permanent magnet synchronous motor method for control speed of small (nothing) tracking error, use
During solving contradiction and raising stable state of the fault-tolerant permanent magnet synchronous motor in dynamic process between response quickly of system and overshoot
Ability of Resisting Disturbance, to improve the performance of motor operation.
The technical scheme is that on the basis of linear automatic disturbance rejection controller, tracked according to the dynamic properties design of motor
Differentiator, allows motor rotating speed in dynamic process accurately to track set-point.In the speed control that the present invention designs,
Except Nonlinear Tracking Differentiator, the adjustment parameter of controller is all determined by bandwidth value (i.e. the pole value of the proper polynomial of observer system)
Difficulty fixed, that the quantity of controller parameter is reduced compared with traditional controller and is adjusted, while ensure that the robustness of system.
The technical solution adopted by the present invention has following steps：A kind of fault-tolerant magneto speed using novel transition process
Control method, comprises the following steps：
S1, gives motor speed value n*, a kind of Nonlinear Tracking Differentiator of novel transition process is designed, it is real-time to obtain motor speed
Set-point v1；The Nonlinear Tracking Differentiator is according to motor dynamics characteristic transition process arranging, according to rotational speed setup n*It is rational to arrange
Real-time rotary speed setting value v1, it is by this transient process function representation：
Wherein, n*For rotary speed setting value, v1For rotating speed transition signal, v2For the differential signal of transition signal, k is according to electricity
Dynamics and the Turbo Factor designed；
S2, by photoelectric encoder obtain permanent magnet synchronous motor rotor position, by photoelectric encoder obtain it is fault-tolerant forever
Magneto rotor position θ, is then changed into d-q electric currents, using 2r/2s coordinates by 5s/2r coordinate transformation modules by phase current
D-q shaft voltages are changed into alpha-beta shaft voltage by conversion module, and calculate rotating speed n；
S3, according to rotary speed setting value v1Speed ring linear active disturbance rejection controller is designed with speed feedback value n, speed
Linear extended state observer in loop wire automatic disturbance rejection controller be to the output of the rotating speed of control system for permanent-magnet synchronous motor and
Always disturbance is observed system, draws speed observation value z1With disturbance estimate z2, finally obtain the phase of linear active disturbance rejection controller
Close control parameter；
S4, control signal u (the i.e. quadrature axis current set-points that will be obtained by linear active disturbance rejection controller) it is used as inner ring q axis
Current controller it is given, and then realize electric machine speed regulation control, the conversion of rotated coordinate system to rest frame obtains static
The voltage U of coordinate system alpha-beta axisα、Uβ, it is sent to the PWM ripples letter that space voltage vector SVPWM modulation modules produce each phase of motor
Number, realize the rotating speed control of motor.
Further, in the step S1, the expression formula of Turbo Factor function is：
Wherein, t represents system operation time, T1、T2、T3Three time points of system operation are represented respectively, between them
Relation is determined by motor electrical time constant and mechanical time constant, amaxExpression system peak acceleration, atExpression system is real
Brief acceleration,Represent the real-time Assumption torque disturbance of linear active disturbance rejection controller, h is torque feedback coefficient.
Further, the T1、T2、T3Relation between three parameters meets 8T1=8 (T3-T2)=T2-T1。
Further, the parameter of the Turbo Factor function k is chosen for：T1=0.005, T2=0.045, T3=0.05, amax
=330, h=0.4.
Further, the detailed process of the step S3 is：
S3.1, establishes the linear extended state observer of control system for permanent-magnet synchronous motor, linear extended state observer
It is that the rotating speed output of fault-tolerant control system for permanent-magnet synchronous motor and system always disturbance are observed and obtain speed observation value z1With
Disturb estimate z2, expression is：
Wherein, e is the difference of observation and actual value,It is the differential signal of speed observation value,It is that system always disturbs
Differential signal, u are the output signal of automatic disturbance rejection controller,Determined by system model, β1、β2Device parameter in order to control；
S3.2, builds the proper polynomial of linear extended state observer, and adjusts the parameter beta in proper polynomial1、β2；
S3.3, according to linearity error Feedback Control Laws by rotating speed transition signal v1With rotating speed output observation z1Obtained as difference
Error e2, e2Original control signal u is obtained through a proportional controller0, then obtain through disturbance compensation the control signal u of automatic disturbance rejection controller：
Wherein, kpFor proportional controller gain, k is usually takenp=ωc, claim controller bandwidth；
S3.4, finally draws observer bandwidth omega0With controller bandwidth omegacIt need to meet ω0≈5-10ωc。
Further, the controller bandwidth is ωc=100, proportional controller gain kp=100, observer bandwidth omega0=
500, controller parameter β1=1000, β2=250000.
The invention has the advantages that：
1) a quick and stable transition is arranged according to the permitted physics peak acceleration of motor vector control system
Process, specially according to a kind of new Nonlinear Tracking Differentiator of dynamic properties design of five mutually fault-tolerant permanent magnet synchronous motors, makes motor dynamic
Rotating speed can accurately track set-point during state；And acceleration is mended in real time using linear active disturbance rejection controller
Repay, motor is realized non-overshoot quick response in whole dynamic process.
2) parameter of Turbo Factor function k is chosen for：T1=0.005, T2=0.045, T3=0.05, amax=330, h=
0.4.It can be seen that it and general direct current generator start or current waveform is very during shock load from the oscillogram of Turbo Factor function
It is similar, using this Turbo Factor function, it can be achieved that small (nothing) error in magneto dynamic process is run.
3) substantial amounts of experimental verification is passed through：The controller bandwidth is ωc=100, proportional controller gain kp=100, see
Survey device bandwidth omega0=500, controller parameter β1=1000, β2=250000, since motor is small during whole service
(nothing) error is run, proportional controller gain kpIn a value in a big way, can greatly strengthen the robustness of controller and
System is not caused to be shaken；Due to using linear active disturbance rejection controller, in addition to Nonlinear Tracking Differentiator, the parameter that need to be adjusted only has one
Observer bandwidth value ω0, greatly simplify controller design difficulty.
4) for conventional PI control device, the new controller that the present invention designs has very strong Ability of Resisting Disturbance,
And shorten the time of system response storm.
From described above it is known that using after new controller of the present invention, the robustness of system anti-disturbance improves
, it is often more important that system response time shortens and non-overshoot.
Brief description of the drawings
Fig. 1 is the five mutually fault-tolerant magneto space voltage vector control structure diagrams using rotational speed governor of the present invention；
Five mutually fault-tolerant cross-sectional view of permanent magnet electric machine of Fig. 2；
Fig. 3 is five mutually fault-tolerant magneto quadrature axis equivalent circuit diagrams；
Fig. 4 is Turbo Factor function waveform figure in new Nonlinear Tracking Differentiator；
Fig. 5 is speed ring linear active disturbance rejection controller block diagram；
Fig. 6 is the load torque disturbance quantity oscillogram applied at different moments；
Fig. 7 is the rotating speed response oscillogram that PI controllers are used in the case of having load torque step；
Fig. 8 is the rotating speed response oscillogram that new controller is used in the case of having load torque step；
Fig. 9 is the rotating speed step response waveform figure that PI controllers are used under no-load condition；
Figure 10 is the rotating speed step response waveform figure that new controller is used under no-load condition.
Embodiment
Below in conjunction with the attached drawing in the embodiment of the present invention, the technical solution in the embodiment of the present invention is carried out clear, complete
Site preparation describes.
The embodiment of the present invention is described below in detail, the example of the embodiment is shown in the drawings, wherein from beginning to end
Same or similar label represents same or similar element or has the function of same or like element.Below with reference to attached
The embodiment of figure description is exemplary, and is only used for explaining the present invention, and is not considered as limiting the invention.
The present invention is on five mutually fault-tolerant permanent magnet synchronous motor space voltage vector control structure diagram bases as shown in Figure 1
Upper implementation.Fig. 2 is the sectional view of the five mutually fault-tolerant magnetoes designed herein.As shown in Figure 2, the five-phase induction motor selected herein
The V-shaped arrangement of permanent magnet, permanent magnet are embedded in rotor so that processing and installation is all more convenient.For embedded permanent magnet
Motor for, reluctance torque can be produced, rationally using reluctance torque, can increase magneto electromagnetic torque density and
Expand the speed adjustable range of motor.Stator winding can be reduced copper loss, be improved efficiency using individual layer centralization distribution.The electricity of motor
Armature tooth and fault-tolerant teeth are arranged alternately, and the width of fault-tolerant teeth is less than armature tooth, optimize back-emf with this, while are reduced teeth groove and turned
Square and output torque pulsation.Individual layer centralization winding can reduce coupling between phase and phase with fault-tolerant toothing, improve motor
Fault freedom.
The present invention on the basis of der Geschwindigkeitkreis linear active disturbance rejection controller, give by one new Nonlinear Tracking Differentiator (New TD) of design
Rotating speed transition process arranging, makes fault-tolerant permanent magnet synchronous motor to ensure non-overshoot amount in dynamic process and has quick response
Speed.Specific embodiment comprises the steps of：
1) tachometer value gives n*Rotating speed transition signal v is obtained through designed new Nonlinear Tracking Differentiator1, the transient process function
It is expressed as
Wherein, n*For rotary speed setting value, v1For rotating speed transition signal, v2For the differential signal of transition signal, k is according to electricity
Dynamics and the Turbo Factor function designed, its expression formula are
Wherein, t represents system operation time, T1、T2、T3Three time points of system operation are represented respectively, between them
Relation is determined by motor electrical time constant and mechanical time constant, amaxExpression system peak acceleration, atExpression system is real
Brief acceleration,Represent the real-time Assumption torque disturbance of linear active disturbance rejection controller, h is torque feedback coefficient.
T1、T2、T3What three parameters reflected is the relation between current-responsive and rotating speed response, is choosing these three parameters
When will be in consideration of it, therefore need to find a kind of can reflect electromechanics and the constant of electrical characteristic.
If mechanical time constant tm, electrical time constant te, the specific measuring method of two constants is：
tm：On winding plus step voltage U, measurement angular velocity reach the time used during the 63.2% of maximum angular rate；
te：Rotor is fixed, step voltage U is added on winding, measures and reaches maximum current in electric current
The time required to when 63.2%.
Fig. 3 is fault-tolerant magneto quadrature axis equivalent circuit diagram, it is known that motor electrical time constant isMechanical time
ConstantLqFor the q axle inductances of magneto, RsFor motor stator resistance, J is motor rotary inertia.KeAnd KTRespectively
It is back electromotive-force constant and electromagnetic torque constant, their calculation formula is respectivelyWith(wherein p tables
Show the number of pole-pairs of motor, ψrRepresent the rotor permanent magnet magnetic flux of motor), it is computed KT=23.8Ke、tm≈0.032、te≈0.004、
tm/te≈8.For convenience of calculation, ratio is taken as 10, therefore T1、T2、T3Relation between three parameters is 8T1=8 (T3-T2)=
T2-T1。
In the Nonlinear Tracking Differentiator function that the present invention designs, the parameter of transient process Turbo Factor function k is chosen for：T1=
0.005、T2=0.045, T3=0.05, amax=330, h=0.4.
Fig. 4 is the oscillogram of Turbo Factor function, it may be seen that when it and the startup of general direct current generator or shock load
Current waveform is much like.Using this Turbo Factor function, it can be achieved that small (nothing) error in magneto dynamic process is run.
2) as shown in Figure 1, obtaining fault-tolerant permanent magnet machine rotor position θ, 5s/2r coordinate transformation modules by photoelectric encoder
Phase current is changed into d-q electric currents, d-q shaft voltages are changed into by alpha-beta shaft voltage using 2r/2s coordinate transformation modules, and calculate
Go out rotating speed n.
3) the speed ring linear active disturbance rejection controller shown in Fig. 5 is counted according to rotary speed setting value and speed feedback value
Calculate.In Fig. 5, linear extended state observer is that the rotating speed output of fault-tolerant control system for permanent-magnet synchronous motor and system are always disturbed
Dynamic be observed obtains speed observation value z1With disturbance estimate z2, expression is
Wherein, e is the difference of observation and actual value,It is the differential signal of speed observation value,It is that system always disturbs
Differential signal, u export signal for automatic disturbance rejection controller,Determined by system model, β1、β2Device parameter in order to control.
Above observer is further written as matrix form
Wherein,
Observer proper polynomial is
Regard observer as a second-order system, system performance (such as stability, response speed etc.) is met necessarily
Condition, need to adjust proper polynomial parameter beta1、β2.Since system performance and characteristic root (i.e. the limit of ssystem transfer function) have very
Important Relations, will enable observer reliable observation system mode it is necessary to make system features root entirely on the left of complex plane.System features root
The speed of the bigger observer observation state amount of absolute value is faster, but crosses conference and cause concussion, so two gains of system are joined
Number is set to β1=2 ω0、Make two POLE PLACEMENT USINGs of ssystem transfer function in-ω0, to adjust observer bandwidth.
Linearity error Feedback Control Laws are by rotating speed transition signal v1With rotating speed output observation z1Error e2Through ratio control
Device processed obtains original control signal u0, then obtain through disturbance compensation the controlled quentity controlled variable u of automatic disturbance rejection controller
Wherein, kpFor proportional controller gain, k is usually takenp=ωc, claim controller bandwidth.
Observer bandwidth omega0With controller bandwidth omegacIt need to meet following rule
ω0≈5-10ωc (7)
In the present invention, the parameter of the fault-tolerant magneto of selection is：The number of phases is 5 phases, number of pole-pairs p=11, quadrature axis inductance
Lq=0.48mH, stator resistance Rs=0.12 Ω, rotor flux ψf=0.06Wb, rotary inertia J=0.03kgm2.Due toObtain bcalculation=57.Controller parameter is chosen for ωc=100, ω0=500, take kp=100, β1=1000,
β2=250000.It can be seen that there was only the parameter ω that a need are adjusted in controllerc, remaining parameter is all associated with it.
4) control signal u (the i.e. quadrature axis current set-points that such as Fig. 1 exports automatic disturbance rejection controller) it is used as inner ring iqControl
The input of device gives to obtain quadrature-axis voltage Uq, using id=0 control mode produces direct-axis voltage Ud.Rotated coordinate system is to static seat
The conversion of mark system obtains the voltage U of rest frame alpha-beta axisα、Uβ, it is sent to the generation of space voltage vector SVPWM modulation modules
The PWM ripple signals of each phase of motor, realize the rotating speed control of motor.
5) in order to illustrate the benefit for the linear active disturbance rejection controller for using such a novel transition process, by itself and PI controllers
Simulation comparison analysis is carried out, PI controller parameters are Kp=2, Ki=100 in emulation.
Fig. 6 is in the load torque disturbance quantity applied at different moments, it can be seen from the figure that applying 30N ﹒ m in 100ms
Load torque, load torque is removed again in 200ms, observes rotation speed change in this case.Fig. 7 is controlled using PI
Device rotating speed response waveform, it can be seen that when torque rises, the maximum pulsation of rotating speed has reached 20r/min, recovery time 13ms；
And after removing load, fluctuation of speed amount reaches 10r/min, and the time for returning to given rotating speed has reached 23ms；Fig. 8 is to adopt
With the rotating speed response waveform of the new controller of this patent, it can be seen that obvious change does not occur for rotating speed, and load torque is dashed forward
The moment fluctuation of speed added only has 6r/min, and recovery time only has 4ms；Load torque fluctuation of speed when unloading of dashing forward only has 4r/
Min, and rotating speed recovery time only have 2ms.Based on the above, for conventional PI control device, the present invention designs new
Type controller has very strong Ability of Resisting Disturbance, and shortens the time of system response storm.
As can be seen from Figures 7 and 8, the time that PI controllers start is used as 55ms, and novel control using the present invention
System start-up time is 50ms after device processed.Motor speed is adjusted to 400r/min from 800r/min respectively under no-load condition,
It reaches the time of stable state from being adjusted again from 400r/min to 800/min.From the rotating speed response comparison of wave shape of Fig. 9 and Figure 10
It can be seen that, Fig. 9 uses the rotating speed of conventional PI control device to drop to 400r/min required times from 800r/min as 35ms, overshoot
It is 40r/min；It is 40ms the time required to rising to 800r/min from 400r/min, overshoot is 30r/min；And Figure 10 is using this
The new controller rotating speed of invention is 30ms the time required to dropping to 400r/min from 800r/min；Risen to from 400r/min
It is 30ms the time required to 800r/min, without generation overshoot.Illustrate that the system rotating speed of new controller using the present invention is rung
Shortened between seasonable relative to conventional PI control device, more crucially overshoot does not occur.
From the above it is known that using linear active disturbance rejection control method, abandon in traditional automatic disturbance rejection controller
Nonlinear element, is introduced into the concept of bandwidth in classical control theory frequency-domain analysis method, makes the adjustment parameter of automatic disturbance rejection controller
Greatly reduce, after new controller of the present invention, the robustness of system anti-disturbance improves, it is often more important that system is rung
Shortened between seasonable and non-overshoot.
In the description of this specification, reference term " one embodiment ", " some embodiments ", " illustrative examples ",
The description of " example ", " specific example " or " some examples " etc. means to combine specific features, the knot that the embodiment or example describe
Structure, material or feature are contained at least one embodiment of the present invention or example.In the present specification, to above-mentioned term
Schematic representation may not refer to the same embodiment or example.Moreover, specific features, structure, material or the spy of description
Point can combine in an appropriate manner in any one or more embodiments or example.
Although an embodiment of the present invention has been shown and described, it will be understood by those skilled in the art that：Not
In the case of departing from the principle of the present invention and objective a variety of change, modification, replacement and modification can be carried out to these embodiments, this
The scope of invention is limited by claim and its equivalent.
Claims (5)
1. a kind of fault-tolerant magneto method for control speed using novel transition process, it is characterised in that comprise the following steps：
S1, gives motor speed value n*, a kind of Nonlinear Tracking Differentiator of novel transition process is designed, motor speed is obtained and gives in real time
Value v1；The Nonlinear Tracking Differentiator is according to motor dynamics characteristic transition process arranging, according to given motor speed value n*It is rational to arrange
Give rotating speed real-time set-point v1, it is by this transient process function representation：
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Wherein, n*For given motor speed value, v1For the real-time set-point of rotating speed, v2For the differential signal of transition signal, k is basis
Motor dynamics characteristic and the Turbo Factor designed；
S2, fault-tolerant permanent magnet machine rotor position θ is obtained by photoelectric encoder, then by 5s/2r coordinate transformation modules by phase
Electric current is changed into d-q electric currents, and d-q shaft voltages are changed into alpha-beta shaft voltage using 2r/2s coordinate transformation modules, and calculates and turn
Fast n；
S3, according to the real-time set-point v of rotating speed1Speed ring linear active disturbance rejection controller is designed with rotating speed n, speed ring is linear
Linear extended state observer in automatic disturbance rejection controller is that the rotating speed output of Control System of AC Permanent Magnet Synchronous and system are always disturbed
It is observed, draws speed observation value z1With disturbance estimate z2, finally provide linear active disturbance rejection controller relevant control ginseng
Number；
S4, using the control signal u obtained by linear active disturbance rejection controller as the given of inner ring q shaft current controllers, Jin Ershi
Existing electric machine speed regulation control, the conversion of rotated coordinate system to rest frame obtain the voltage U of rest frame alpha-beta axisα、Uβ, will
It is sent into the PWM ripple signals that space voltage vector SVPWM modulation modules produce each phase of motor, realizes the rotating speed control of motor；
In the step S1, the expression formula of Turbo Factor function is：
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Wherein, t represents system operation time, T1、T2、T3Three time points of system operation, the relation between them are represented respectively
It is to be determined by motor electrical time constant and mechanical time constant, amaxExpression system peak acceleration, atExpression system adds in real time
Speed,Represent the real-time Assumption torque disturbance of linear active disturbance rejection controller, h is torque feedback coefficient.
2. a kind of fault-tolerant magneto method for control speed using novel transition process according to claim 1, it is special
Sign is, the T1、T2、T3Relation between three parameters meets 8T1=8 (T3-T2)=T2-T1。
3. a kind of fault-tolerant magneto method for control speed using novel transition process according to claim 1, it is special
Sign is that the parameter of the Turbo Factor function k is chosen for：T1=0.005, T2=0.045, T3=0.05, amax=330, h=
0.4。
4. a kind of fault-tolerant magneto method for control speed using novel transition process according to claim 1, it is special
Sign is that the detailed process of the step S3 is：
S3.1, establishes the linear extended state observer of control system for permanent-magnet synchronous motor, and linear extended state observer is pair
The rotating speed output of fault-tolerant control system for permanent-magnet synchronous motor and system always disturbance are observed and obtain speed observation value z1And disturbance
Estimate z2, expression is：
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<msub>
<mover>
<mi>z</mi>
<mo>&CenterDot;</mo>
</mover>
<mn>1</mn>
</msub>
<mo>=</mo>
<msub>
<mi>z</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>&beta;</mi>
<mn>1</mn>
</msub>
<msub>
<mi>e</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<mi>b</mi>
<mi>u</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mover>
<mi>z</mi>
<mo>&CenterDot;</mo>
</mover>
<mn>2</mn>
</msub>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>&beta;</mi>
<mn>2</mn>
</msub>
<msub>
<mi>e</mi>
<mn>1</mn>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein, e1For observation and the difference of actual value,It is the differential signal of speed observation value,It is micro- to be that system always disturbs
Sub-signal, u are the control signal of automatic disturbance rejection controller,Determined by system model, β1、β2Device parameter in order to control, J are electricity
Machine rotary inertia, KTFor electromagnetic torque constant；
S3.2, builds the proper polynomial of linear extended state observer, and adjusts the parameter beta in proper polynomial1、β2；
<mrow>
<mo>|</mo>
<mi>&lambda;</mi>
<mi>E</mi>
<mo>-</mo>
<mi>A</mi>
<mo>|</mo>
<mo>=</mo>
<mfenced open = "|" close = "|">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>&lambda;</mi>
<mo>+</mo>
<msub>
<mi>&beta;</mi>
<mn>1</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&beta;</mi>
<mn>2</mn>
</msub>
</mtd>
<mtd>
<mi>&lambda;</mi>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mi>&lambda;</mi>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>+</mo>
<msub>
<mi>&beta;</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>&beta;</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<msup>
<mi>&lambda;</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<msub>
<mi>&beta;</mi>
<mn>1</mn>
</msub>
<mi>&lambda;</mi>
<mo>+</mo>
<msub>
<mi>&beta;</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>+</mo>
<msub>
<mi>&omega;</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>;</mo>
</mrow>
S3.3, according to linearity error Feedback Control Laws by the real-time set-point v of rotating speed1With speed observation value z1Error e is obtained as difference2,
e2Original control signal u is obtained through a proportional controller0, then obtain through disturbance compensation the control signal u of automatic disturbance rejection controller：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<msub>
<mi>e</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<msub>
<mi>v</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>z</mi>
<mn>1</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>u</mi>
<mn>0</mn>
</msub>
<mo>=</mo>
<msub>
<mi>k</mi>
<mi>p</mi>
</msub>
<msub>
<mi>e</mi>
<mn>2</mn>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>u</mi>
<mo>=</mo>
<msub>
<mi>u</mi>
<mn>0</mn>
</msub>
<mo>-</mo>
<mfrac>
<msub>
<mi>z</mi>
<mn>2</mn>
</msub>
<mi>b</mi>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein, kpFor proportional controller gain, k is usually takenp=ωc, claim controller bandwidth；
S3.4, finally provides observer bandwidth omega0With controller bandwidth omegacIt need to meet ω0≈5-10ωc。
5. a kind of fault-tolerant magneto method for control speed using novel transition process according to claim 4, it is special
Sign is that the controller bandwidth is ωc=100, proportional controller gain kp=100, observer bandwidth omega0=500, control
Device parameter beta1=1000, β2=250000.
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