CN103117701A - Control method of mechanical elastic energy storing permanent magnet motor group under non-harmonic disturbances - Google Patents

Control method of mechanical elastic energy storing permanent magnet motor group under non-harmonic disturbances Download PDF

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CN103117701A
CN103117701A CN2013100761968A CN201310076196A CN103117701A CN 103117701 A CN103117701 A CN 103117701A CN 2013100761968 A CN2013100761968 A CN 2013100761968A CN 201310076196 A CN201310076196 A CN 201310076196A CN 103117701 A CN103117701 A CN 103117701A
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matrix
axle
permanent
nonlinear
elastic energy
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CN103117701B (en
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余洋
米增强
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North China Electric Power University
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North China Electric Power University
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Abstract

Provided is a control method of a mechanical elastic energy storing permanent magnet motor group under non-harmonic disturbances. The permanent magnet motor group comprises a permanent magnet synchronous motor, a gear gearbox and a volute spring box used for mechanical elastic energy storing. The control method includes that a full system mathematical model including the permanent magnet synchronous motor, the gear gearbox and the volute spring box is constructed, and then non-linear internal model equations and a state feedback controller are designed aiming at nonlinear disturbances generated by a nonlinear external system. According to the control method, the different non-linear internal model equations are designed on the basis of type features of external disturbances, and the state feedback controller is designed on the basis of a nominal system control law. Test results prove that the designed state feedback controller can ensure that angular velocity output by the permanent magnet motor group under various external disturbances is basically stable and enables a closed loop system to fast track reference signals, and high-accuracy servo control of the motor group is achieved.

Description

The unit of the permanent-magnet electric with mechanical elastic energy storage control method under anharmonic humorous wave interference
Technical field
The present invention relates to a kind of method for controlling permanent magnet synchronous motor with mechanical elastic energy storage, belong to technical field of motors.
Background technology
Energy storage technology is for solving the problems such as current new forms of energy networking, peak-frequency regulation, and the assurance electrical network equilibrium of supply and demand, maintenance system are stablized, and all are of great practical significance.At further investigation mechanical whirlpool spring elastic energy storage (Mechanical Elastic Energy Storage, MEES) on the basis of principle, the technical staff has proposed permanent magnetic motor type mechanical elastic energy storage method, permagnetic synchronous motor (permanent magnet synchronous motor, PMSM) having the advantages such as power density is large, efficiency is high, electromagnetic torque is large, volume is little, fast response time, is the optimal selection of the method energy storage unit servo system.Due to the electromechanical coupling characteristics of unit and the nonlinear characteristic of permagnetic synchronous motor (PMSM), one of key technical problem that this energy storage mode need to solve is exactly the nonlinear Control problem of unit.Permanent magnetic motor type mechanical elastic energy storage unit is when storage energy operation, and the continuous variation of whirlpool spring elastic torque and moment of inertia, will cause harmful effect to the performance of servo system.PMSM itself has the characteristics such as non-linear, close coupling and time variation in addition, particularly during the set grid-connection storage energy operation, unit will be subjected to non-linear external disturbance often, and the fixing PID controller adaptability of conventional parameter, by variation, is difficult to meet the control requirement of high accuracy servo system.Therefore, when the permanent-magnet electric unit storage energy operation with mechanical elastic energy storage, design a kind of control method, can guarantee externally under anharmonic humorous wave interference, the rotating speed of permagnetic synchronous motor output keeps substantially constant to have very important significance.
Summary of the invention
The object of the invention is to the drawback for prior art, the control method of the unit of the permanent-magnet electric with mechanical elastic energy storage under a kind of anharmonic humorous wave interference is provided.
Problem of the present invention realizes with following technical proposals:
The unit of the permanent-magnet electric with mechanical elastic energy storage control method under a kind of anharmonic humorous wave interference, described permanent-magnet electric unit comprises permagnetic synchronous motor, speed-changing gear box and is used as the whirlpool spring case of mechanical elastic energy storage, the total system Mathematical Modeling of the permanent-magnet electric unit that described control method model comprises permagnetic synchronous motor, speed-changing gear box and whirlpool spring case, then for by non-linear external system:
Figure 117242DEST_PATH_IMAGE001
(wherein, matrix
Figure 231828DEST_PATH_IMAGE002
, ,
Figure 778402DEST_PATH_IMAGE004
For abundant smooth function, and
Figure 88161DEST_PATH_IMAGE005
) nonlinear disturbance that produces
Figure 690043DEST_PATH_IMAGE006
, design Nonlinear Internal Model equation:
Figure 743450DEST_PATH_IMAGE007
Wherein,
Figure 114388DEST_PATH_IMAGE008
For the signal of external system generation,
Figure 126207DEST_PATH_IMAGE009
For state variable,
Figure 418648DEST_PATH_IMAGE010
For control inputs,
Figure 557636DEST_PATH_IMAGE011
With
Figure 783081DEST_PATH_IMAGE012
Be known smooth vector field,
Figure 434642DEST_PATH_IMAGE013
Be the matrix of a suitable dimension,,
Figure 11117DEST_PATH_IMAGE014
For the Hurwitz matrix, For nonsingular matrix,
Figure 486278DEST_PATH_IMAGE016
For matrix,
Figure 354746DEST_PATH_IMAGE017
For smooth function,
State feedback controller is designed to:
Figure 152937DEST_PATH_IMAGE018
Wherein,
Figure 351838DEST_PATH_IMAGE019
For the multivariable EVAC (Evacuation Network Computer Model)
Figure 286296DEST_PATH_IMAGE020
Nominal system
Figure 76397DEST_PATH_IMAGE021
State feedback control law,
Figure 112617DEST_PATH_IMAGE022
Wherein: v 1, v 2Be respectively and act on dAxle, qThe anharmonic humorous interference wave signal of axle, a, bFor being greater than zero constant, A 11, A 21, A 12, A 22For matrix parameter,
Figure 849629DEST_PATH_IMAGE023
,
Figure 904173DEST_PATH_IMAGE024
, , ,
Figure 913083DEST_PATH_IMAGE027
,
Figure 556554DEST_PATH_IMAGE028
, ,
Figure 412787DEST_PATH_IMAGE030
Be the matrix of certain dimension, c 1, c 2, c 3For constant,
Figure 22760DEST_PATH_IMAGE031
,
Figure 51896DEST_PATH_IMAGE032
For the calm rule of the undisturbed nominal system of former multivariable EVAC (Evacuation Network Computer Model),
Figure 557963DEST_PATH_IMAGE033
,
Figure 305339DEST_PATH_IMAGE034
For smooth function, F 1, F 2For the Hurwitz matrix, q 1, q 2For matrix parameter,
Figure 469736DEST_PATH_IMAGE035
,
Figure 353378DEST_PATH_IMAGE036
For the nonsingular solution of Sylvester equation, u 1, u 2For controlling voltage, u d , u q For DC permanent magnet stator voltage D, qThe axle component, ω m Angular speed for motor output;
Control and carry out as follows:
At first, according to the actual operation parameters of permanent magnetic motor type mechanical elastic energy storage unit, determine the total system Mathematical Modeling of unit; According to acting on dThe anharmonic humorous interference wave signal of axle v 1, choose a, bDetermine matrix parameter A 11, A 21, and obtain
Figure 295926DEST_PATH_IMAGE023
,
Figure 576604DEST_PATH_IMAGE024
,
Figure 997221DEST_PATH_IMAGE025
With
Figure 949DEST_PATH_IMAGE026
According to acting on qThe anharmonic humorous interference wave signal of axle v 2, choose a, b determines matrix parameter A 12, A 22, and obtain
Figure 848819DEST_PATH_IMAGE027
, ,
Figure 529516DEST_PATH_IMAGE029
With
Figure 387751DEST_PATH_IMAGE030
Choose constant according to the Laypunov function c 1, c 2With c 3, determine the calm rule of the undisturbed nominal system of former multivariable EVAC
Figure 953992DEST_PATH_IMAGE031
With
Figure 366519DEST_PATH_IMAGE032
Selection of Function
Figure 660097DEST_PATH_IMAGE033
With
Figure 372838DEST_PATH_IMAGE034
, determine matrix parameter
Figure 359249DEST_PATH_IMAGE037
With
Figure 39498DEST_PATH_IMAGE038
Choose matrix F 1, separate the Sylvester equation and obtain matrix
Figure 605608DEST_PATH_IMAGE035
, and combination
Figure 704014DEST_PATH_IMAGE025
Obtain q 1, choose matrix F 2, separate the Sylvester equation and obtain matrix
Figure 330168DEST_PATH_IMAGE036
, and combination
Figure 248445DEST_PATH_IMAGE029
Obtain q 2Will F 1,
Figure 634558DEST_PATH_IMAGE035
,
Figure 321892DEST_PATH_IMAGE026
,
Figure 650105DEST_PATH_IMAGE033
The Nonlinear Internal Model equation of substitution design, obtain dThe nonlinear disturbance signal of axle v 1Estimated value, will F 2,
Figure 790099DEST_PATH_IMAGE036
, ,
Figure 285857DEST_PATH_IMAGE034
The Nonlinear Internal Model equation of substitution design, obtain qThe nonlinear disturbance signal of axle v 2Estimated value; Again by the nonlinear disturbance signal obtained v 1Estimated value, the calm rule of undisturbed nominal system
Figure 784972DEST_PATH_IMAGE031
, matrix parameter q 1And function
Figure 881104DEST_PATH_IMAGE033
The state feedback controller that substitution designs in the lump, controlled voltage u 1, u d Equally, by the nonlinear disturbance signal obtained v 2Estimated value, the calm rule of undisturbed nominal system
Figure 140178DEST_PATH_IMAGE032
, matrix parameter q 2And function
Figure 802103DEST_PATH_IMAGE034
The state feedback controller that substitution designs in the lump, controlled voltage u 2 , u q
Finally, will control voltage u d With u q Be input in the total system Mathematical Modeling of permanent-magnet electric unit, just can guarantee the angular speed of permanent-magnet electric unit output under anharmonic humorous wave interference ω m Keep basicly stable.
The unit of the permanent-magnet electric with mechanical elastic energy storage control method under above-mentioned anharmonic humorous wave interference, the total system Mathematical Modeling of described permanent magnetic motor type mechanical elastic energy storage unit is:
Figure 940961DEST_PATH_IMAGE039
，
Figure 586706DEST_PATH_IMAGE040
，
Figure 836421DEST_PATH_IMAGE041
，
Wherein, B m For the damping coefficient of motor, T m , T L Be respectively motor output torque and elastic shaft torsional moment, ω m , ω L Be respectively the angular speed of motor and whirlpool spring elastic shaft, L d , L q For dAxle and qThe axle inductance,
Figure 602121DEST_PATH_IMAGE042
,
Figure 974197DEST_PATH_IMAGE043
With
Figure 44921DEST_PATH_IMAGE044
,
Figure 629486DEST_PATH_IMAGE045
Be respectively stator current and stator voltage D, qThe axle component,
Figure 282315DEST_PATH_IMAGE046
For stator resistance,
Figure 762975DEST_PATH_IMAGE047
For rotor velocity,
Figure 586575DEST_PATH_IMAGE048
For rotor flux, pFor number of pole-pairs,
Figure 974831DEST_PATH_IMAGE049
For rotor moment of inertia, rFor the gear reduction box gear ratio, nFor the whirlpool spring number of effective coils; E,
Figure 669117DEST_PATH_IMAGE050
, bWith hBe respectively elastic properties of materials modulus, length, width and the thickness of energy storage whorl reed; kFor whirlpool spring quality coefficient,
Figure 101104DEST_PATH_IMAGE051
For compact subset,
Figure 677579DEST_PATH_IMAGE052
For the time.
The type feature that the present invention is based on external disturbance carries out the Nonlinear Internal Model design; On the basis of nominal system control law, according to the interior modular equation built, carried out the design of state feedback controller.Result of the test shows, when the unit storage energy operation, even be subject to anharmonic humorous wave interference, closed-loop system is tracking reference signal soon still, guarantees the output speed substantially constant of permanent-magnet electric unit, realizes that the high-precision servo of unit is controlled.
The accompanying drawing explanation
Below in conjunction with accompanying drawing, the invention will be further described.
Fig. 1 is permanent magnetic motor type mechanical elastic energy storage unit total system model;
Fig. 2, Fig. 3 are Nonlinear perturbations input simulations;
Fig. 4, Fig. 5 are the system control inputs;
Fig. 6, Fig. 7, Fig. 8 are system mode output.
In literary composition, each symbol inventory is:
Figure 603947DEST_PATH_IMAGE053
For abundant smooth function,
Figure 683898DEST_PATH_IMAGE006
For nonlinear disturbance,
Figure 53831DEST_PATH_IMAGE054
For the signal of external system generation,
Figure 320864DEST_PATH_IMAGE055
For state variable,
Figure 785344DEST_PATH_IMAGE056
For control inputs, With Be known smooth vector field,
Figure 264232DEST_PATH_IMAGE013
Be the matrix of a suitable dimension,
Figure 266824DEST_PATH_IMAGE014
For the Hurwitz matrix,
Figure 570635DEST_PATH_IMAGE057
For nonsingular matrix,
Figure 266058DEST_PATH_IMAGE016
For matrix,
Figure 507684DEST_PATH_IMAGE058
For smooth function, G i For being defined in
Figure 579545DEST_PATH_IMAGE059
In the non-zero constant vector, For state feedback control law, B m For the damping coefficient of motor, T m , T L Be respectively motor output torque and elastic shaft torsional moment, ω m , ω L Be respectively the angular speed of motor and whirlpool spring elastic shaft, L d , L q For dAxle and qThe axle inductance,
Figure 89341DEST_PATH_IMAGE042
,
Figure 834574DEST_PATH_IMAGE043
With , Be respectively stator current and stator voltage D, qThe axle component,
Figure 245330DEST_PATH_IMAGE046
For stator resistance,
Figure 992706DEST_PATH_IMAGE047
For rotor velocity, For rotor flux, pFor number of pole-pairs,
Figure 8121DEST_PATH_IMAGE049
For rotor moment of inertia, rFor the gear reduction box gear ratio, nFor the whirlpool spring number of effective coils; E,
Figure 216249DEST_PATH_IMAGE050
, bWith hBe respectively elastic properties of materials modulus, length, width and the thickness of energy storage whorl reed; kFor whirlpool spring quality coefficient,
Figure 654183DEST_PATH_IMAGE052
For the time, V ( x ) be the Lyapunov function.
Embodiment
The present invention is realized by following technical scheme:
1. permanent magnetic motor type mechanical elastic energy storage unit mathematical modeling
As shown in Figure 1, gear reduction box is reduced to multiple degrees of freedom " spring-quality-damping " model to permanent magnetic motor type mechanical elastic energy storage unit total system model, wherein, B m , B L Be respectively the damping coefficient of motor and elastic shaft, T m , T L Be respectively motor output torque and elastic shaft torsional moment, ω m , ω L Be respectively the angular speed of motor and whirlpool spring elastic shaft.
In thermal energy storage process, permagnetic synchronous motor runs on electric motor state, supposes d, qThe axle inductance L d = L q , so, permanent-magnet servo motor exists D, qNonlinear mathematical model under the axle rotational coordinates can be written as:
(1)
In formula, i d , i q With u d , u q Be respectively stator current and stator voltage D, qThe axle component, R s For stator resistance,
Figure 609687DEST_PATH_IMAGE047
For rotor velocity, For rotor flux, pFor number of pole-pairs, J m For rotor moment of inertia.
Figure 461416DEST_PATH_IMAGE061
Suppose that the gear reduction box gear ratio is r, ignore the gearbox power loss, the moment of reduction box both sides, angular speed relational expression can be expressed as:
Figure 216883DEST_PATH_IMAGE062
(2)
If whirlpool spring tail end adopts fixed form, according to GB " plane scroll spring designing and calculating (JB/T7366-1994) ", whirlpool, square-section spring moment of torsion can be written as:
Figure 543959DEST_PATH_IMAGE063
(3)
Wherein: nFor the whirlpool spring number of effective coils; E, l, bWith hBe respectively elastic properties of materials modulus, length, width and the thickness of energy storage whorl reed; kFor whirlpool spring quality coefficient.
While supposing normal operation, energy-storage box main shaft and PMSM work in permanent rotating speed state, known whirlpool spring elastic shaft angular speed ω L With the whirlpool spring number of effective coils nPass be:
(4)
Formula (4) substitution formula (3) can be obtained, and the pass of whirlpool spring moment of torsion and its angular speed is:
Figure 506416DEST_PATH_IMAGE065
(5)
From formula (5), in theory, once angular speed ω L Constant, whirlpool spring elastic torque and time will present linear relationship.
The differential equation (1) has just formed permanent magnetic motor type mechanical elastic energy storage unit total system Mathematical Modeling in conjunction with equation (2) and (5).
2. control problem is described
Consider the multivariable EVAC (Evacuation Network Computer Model)
Figure 326559DEST_PATH_IMAGE066
(6)
Wherein, state variable , control inputs
Figure 25711DEST_PATH_IMAGE068
, With
Figure 22803DEST_PATH_IMAGE070
Be known smooth vector field,
Figure 58892DEST_PATH_IMAGE071
For the nonlinear disturbance of input,
Figure 966936DEST_PATH_IMAGE072
Signal for external system produces is produced by following non-linear external system:
Figure 619634DEST_PATH_IMAGE073
(7)
If do not consider the Nonlinear perturbations input, the nominal system of system (6) can be written as:
(8)
For the stability problem of multivariable input system, key is the stability problem that is translated into a plurality of single input systems.
Suppose that 1 for system (8), existence Feedback Control Laws , make the nominal closed-loop system
Figure 4982DEST_PATH_IMAGE076
Progressive stable at initial point, thereby have the Lyapunov function V ( x ) meet:
Figure 394244DEST_PATH_IMAGE077
(9)
Wherein,
Figure 302157DEST_PATH_IMAGE078
,
Figure 843997DEST_PATH_IMAGE079
With
Figure 811953DEST_PATH_IMAGE080
Belong to K ∞Class function.
The vector field path of supposing 2 non-linear external systems (7) is bounded.
Annotating 1 non linear system that meets hypothesis 2 has the limit cycle etc. of harmonic function or nonlinear dynamic system, and the non-linear external system that the present invention considers is by Zhiyong Chen and Jie Huang(" Robust output regulation with nonlinear exosystem ".Automatica, 2005,41 (8): 1447-1454.) propose:
Figure 439244DEST_PATH_IMAGE081
(10)
Wherein, matrix
Figure 682006DEST_PATH_IMAGE002
,
Figure 94664DEST_PATH_IMAGE082
,
Figure 233521DEST_PATH_IMAGE083
For abundant smooth function, and
Figure 82529DEST_PATH_IMAGE084
, the system that meets (10) has a lot, and the present invention chooses famous Van der Pol oscillator, and it is expressed as
Figure 128982DEST_PATH_IMAGE085
(11)
Wherein, a, bBe the constant that is greater than zero, now, Van der Pol oscillator will produce stable limit cycle, (11) will be written as to the form of (10), have
Figure 645414DEST_PATH_IMAGE086
(12)
Wherein,
Figure 955173DEST_PATH_IMAGE087
,
Figure 540744DEST_PATH_IMAGE088
,
Figure 125309DEST_PATH_IMAGE089
.
Suppose that 3 exist constant r i With one group of real number a i0 , a i1 ...,
Figure 965089DEST_PATH_IMAGE090
Meet
Figure 976907DEST_PATH_IMAGE091
(13)
Wherein
Figure 66086DEST_PATH_IMAGE092
, LFor the Lie derivatives operator, obviously, if
Figure 939495DEST_PATH_IMAGE093
For
Figure 430519DEST_PATH_IMAGE094
Linear representation, suppose that 3 meet automatically.
Suppose that 4 exist smooth function
Figure 82080DEST_PATH_IMAGE095
, make
Figure 392976DEST_PATH_IMAGE096
(14)
Wherein, G i For being defined in
Figure 319344DEST_PATH_IMAGE059
In the non-zero constant vector.
Problem to be solved by this invention can be described as: for any given compact subset
Figure 914142DEST_PATH_IMAGE097
, all can find state feedback controller
Figure 267763DEST_PATH_IMAGE098
, make under arbitrary initial conditions, for all
Figure 65955DEST_PATH_IMAGE099
With all t>=0, the solution of closed-loop system (6) exists and bounded, and
Figure 264855DEST_PATH_IMAGE100
.
3. Nonlinear Internal Model design
The purpose of design Nonlinear Internal Model is that inhibition is inputted and disturbed to the outside Nonlinear perturbations of estimation.
Order
Figure 464892DEST_PATH_IMAGE101
(15)
So, there is matrix
Figure 740147DEST_PATH_IMAGE102
,
Figure 494476DEST_PATH_IMAGE103
, make
Figure 28226DEST_PATH_IMAGE104
(16)
Wherein, matrix pair
Figure 613928DEST_PATH_IMAGE105
Considerable.
For setting up the Nonlinear Internal Model equation, make the following assumptions
Suppose that 5 exist matrix
Figure 778193DEST_PATH_IMAGE106
Make
(17)
If
Figure 403264DEST_PATH_IMAGE108
, For nonsingular matrix, right along (10) Differentiate, have
Figure 658293DEST_PATH_IMAGE111
(18)
Figure 376588DEST_PATH_IMAGE112
(19)
Wherein,
Figure 608986DEST_PATH_IMAGE113
, meet
Figure 911792DEST_PATH_IMAGE114
.
Based on Systems with Linear Observation device theory, for non-zero constant vector in (14) G i , choose the Hurwitz matrix F i Make matrix to ( F i , G i ) controlled.Due to matrix pair
Figure 393589DEST_PATH_IMAGE105
Considerable, and F i With
Figure 807252DEST_PATH_IMAGE115
There is disjoint frequency spectrum, therefore the Sylvester equation There is unique nonsingular solution
Figure 384175DEST_PATH_IMAGE057
.
Order
Figure 353268DEST_PATH_IMAGE117
, non-linear external system can be immersed in lower plane system:
Figure 570623DEST_PATH_IMAGE118
(20)
For this reason, the design Nonlinear Internal Model is as follows:
Figure 777614DEST_PATH_IMAGE119
(21)
If auxiliary error e i For
(22)
Along equation (6), (20) and (21), to formula (22) differentiate, can obtain
Figure 347452DEST_PATH_IMAGE121
(23)
4. state feedback controller design
Even the effect of design point feedback controller is to guarantee to exist in the situation of external disturbance, closed-loop system still can progressive tracking reference signal.For the purpose of the present invention, to guarantee exactly under anharmonic humorous wave interference, make permanent-magnet electric unit output speed keep basicly stable.
Nonlinear Internal Model (21) based on building and suppose 1, the design point feedback controller is:
Figure 352186DEST_PATH_IMAGE122
(24)
Structure Lyapunov function
Figure 679262DEST_PATH_IMAGE123
(25)
Wherein
Figure 229192DEST_PATH_IMAGE124
For positive real constant, along system (6) and auxiliary error (23) to function WDifferentiate, obtain
Figure 172878DEST_PATH_IMAGE125
(26)
Wherein,
Figure 200876DEST_PATH_IMAGE126
,
By inequality
Figure 913618DEST_PATH_IMAGE127
(get c=1) apply to (26) second of formulas, have
Figure 650761DEST_PATH_IMAGE128
(27)
Suppose to exist and compact
Figure 285004DEST_PATH_IMAGE129
, for all
Figure 382273DEST_PATH_IMAGE130
,
Figure 683942DEST_PATH_IMAGE131
The symmetrical matrix of negative definite, so, for all
Figure 841253DEST_PATH_IMAGE130
, have arithmetic number f, make
Figure 962793DEST_PATH_IMAGE132
(28)
By (27) and (28) substitutions (26), can obtain
Figure 863753DEST_PATH_IMAGE133
(29)
The Rational choice constant With
Figure 597409DEST_PATH_IMAGE134
, make
Figure 737403DEST_PATH_IMAGE135
(30)
So, have
Figure 645316DEST_PATH_IMAGE136
(31)
Therefore all variablees are bounded.In conjunction with the invariant set theorem, just can obtain With
Figure 155112DEST_PATH_IMAGE137
.Thereby obtain following conclusion: for meeting nonlinear multivariable systems (6) and the external system (7) of hypothesis 1 to hypothesis 5, Nonlinear Internal Model (21) and control inputs (24) can make the closed-loop system global bounded, and
Figure 782402DEST_PATH_IMAGE100
.
To 0.018kWh/1.1kW permanent magnetic motor type mechanical elastic energy storage unit experiment Analysis.The unit relevant parameters is: the motor nominal torque T e =5.0Nm, p=4,
Figure 494006DEST_PATH_IMAGE138
=0.18Wb, R s =1.95 Ω, L d = L q =0.0115H, J m =0.008kgm 2, r=40:1, ω L =15r/min, B m =0.01N/rad/s.
After considering Nonlinear perturbations, permanent magnetic motor type mechanical elastic energy storage unit total system Mathematical Modeling is converted into to formula (6) form of expression, the results are shown in formula (32).Visible, this unit is two variable input systems, adopts single input algorithm to be processed.
Figure 641085DEST_PATH_IMAGE139
(32)
Wherein,
Figure 779942DEST_PATH_IMAGE140
, ,
Figure 409824DEST_PATH_IMAGE142
,
Figure 660677DEST_PATH_IMAGE143
, control inputs
Figure 501594DEST_PATH_IMAGE144
.
For simplicity, non-linear external disturbance input v 1With v 2Van der Pol oscillator by formula (11) produces, and gets
Figure 176963DEST_PATH_IMAGE145
, have
Figure 230369DEST_PATH_IMAGE146
,
Figure 601308DEST_PATH_IMAGE147
(due to
Figure 613126DEST_PATH_IMAGE148
For convenience, therefore order
Figure 702305DEST_PATH_IMAGE149
),
Figure 293823DEST_PATH_IMAGE089
, now, this oscillator will produce the limit cycle of bounded, suppose 2 establishments.
Suppose c 1, c 2With c 3Be certain normal number, get control law
Figure 270001DEST_PATH_IMAGE150
(33)
Wherein,
Figure 718300DEST_PATH_IMAGE151
For the rotor reference rotation velocity, be taken as 600r/min, can verify that undisturbed nominal system (8) can quilt
Figure 29195DEST_PATH_IMAGE152
Calm.
Order
Figure 424404DEST_PATH_IMAGE153
(34)
Calculate and arrange,
Figure 769935DEST_PATH_IMAGE154
(35)
Figure 435140DEST_PATH_IMAGE155
(36)
If
Figure 108698DEST_PATH_IMAGE156
, by formula (34), (35) and (36), and choose c 1=8000, c 2=40 Hes c 3=8000, can obtain
(37)
Figure 756903DEST_PATH_IMAGE158
(38)
Figure 281426DEST_PATH_IMAGE159
(39)
Suppose 1 establishment.
Choose
Figure 566913DEST_PATH_IMAGE160
(40)
{。##.##1},
Figure 303925DEST_PATH_IMAGE161
(41)
Meet hypothesis 4.
If v 1With v 2Act on respectively d, qOn axle, v 1= w 1, v 2= w 2, characterization system has been injected into different nonlinear disturbance signals, when v 1= w 1The time, through calculating:
Figure 358469DEST_PATH_IMAGE162
(42)
There is constant
Figure 37581DEST_PATH_IMAGE163
,
Figure 561097DEST_PATH_IMAGE164
With Meet hypothesis 3;
When v 2= w 2The time, through calculating:
Figure 10850DEST_PATH_IMAGE166
(43)
There is constant
Figure 877175DEST_PATH_IMAGE163
,
Figure 606097DEST_PATH_IMAGE167
With
Figure 216069DEST_PATH_IMAGE168
Meet hypothesis 3.
According to (42), order
Figure 714047DEST_PATH_IMAGE169
(44)
So, there is matrix , , make formula (16) set up, and
Figure 161581DEST_PATH_IMAGE172
According to (43), order
(45)
So, there is matrix
Figure 987771DEST_PATH_IMAGE174
,
Figure 425706DEST_PATH_IMAGE175
, make formula (16) set up, and .
Choose
Figure 131942DEST_PATH_IMAGE177
, can be calculated
Figure 245391DEST_PATH_IMAGE178
(46)
Choose
Figure 701780DEST_PATH_IMAGE179
, can be calculated
(47)
So, suppose 5 establishments.
If
Figure 518744DEST_PATH_IMAGE181
,
Figure 803095DEST_PATH_IMAGE182
For nonsingular matrix, right along (10)
Figure 996047DEST_PATH_IMAGE183
Differentiate, have
Figure 24046DEST_PATH_IMAGE184
(48)
Wherein,
Figure 736787DEST_PATH_IMAGE185
If
Figure 926460DEST_PATH_IMAGE186
,
Figure 357441DEST_PATH_IMAGE187
For nonsingular matrix, right along (10)
Figure 454710DEST_PATH_IMAGE188
Differentiate, have
Figure 756379DEST_PATH_IMAGE189
(49)
Wherein,
Figure 398844DEST_PATH_IMAGE190
.
Choose matrix , can verify , solve the Sylvester equation
Figure 577518DEST_PATH_IMAGE193
, obtain
Figure 905732DEST_PATH_IMAGE194
(50)
Choose matrix
Figure 514567DEST_PATH_IMAGE195
, can verify
Figure 219218DEST_PATH_IMAGE196
, solve the Sylvester equation
Figure 229900DEST_PATH_IMAGE197
, obtain
Figure 978282DEST_PATH_IMAGE198
(51)
Below empirical tests system (32) and (11) meet required all conditions, the nonlinear control method proposed based on the present invention, design Nonlinear Internal Model and state feedback controller are as follows:
(52)
Utilize Matlab software to carry out numerical simulation, simulation step length Qu ⊿ t=0.001s, the system initial condition is:
Figure 317176DEST_PATH_IMAGE200
,
Figure 713522DEST_PATH_IMAGE201
With
Figure 852380DEST_PATH_IMAGE202
, simulation result accompanying drawing 2 is to Fig. 8.Fig. 4 and Fig. 5 are the control voltage input that comprises internal mold u 1With u 2 , u d With u q , this voltage is the control variables be injected in permanent-magnet electric unit total system Mathematical Modeling; Fig. 6 shows the output of permanent-magnet electric unit dShaft current i d =0; Fig. 7 is the rotating speed of permanent magnet motor output shaft ω m , substantially constant is in 600r/min; Fig. 8 is the output of permanent-magnet electric unit qShaft current i q , i q Along with the increase of spring moment of torsion in whirlpool in thermal energy storage process constantly increases.Fig. 7 shows under the multiclass external disturbance, and the state feedback controller of the present invention's design can guarantee that the permanent-magnet electric unit exports permanent rotating speed.Simulation result shows, closed-loop system has realized the progressive tracking to reference signal soon, and therefore, the multivariable controller of the present invention's design can effectively suppress external disturbance, and guarantees permanent-magnet electric unit output speed substantially constant.

Claims (2)

1. the unit of the permanent-magnet electric with the mechanical elastic energy storage control method under an anharmonic humorous wave interference, it is characterized in that, described permanent-magnet electric unit comprises permagnetic synchronous motor, speed-changing gear box and is used as the whirlpool spring case of mechanical elastic energy storage, the total system Mathematical Modeling of the permanent-magnet electric unit that described control method model comprises permagnetic synchronous motor, speed-changing gear box and whirlpool spring case, then for by non-linear external system: , wherein, matrix
Figure 984108DEST_PATH_IMAGE002
,
Figure 2013100761968100001DEST_PATH_IMAGE003
,
Figure 45736DEST_PATH_IMAGE004
For abundant smooth function, and
Figure 2013100761968100001DEST_PATH_IMAGE005
, the nonlinear disturbance of generation
Figure 972103DEST_PATH_IMAGE006
, design Nonlinear Internal Model equation:
，
Wherein,
Figure 317634DEST_PATH_IMAGE008
For the signal of external system generation,
Figure 2013100761968100001DEST_PATH_IMAGE009
For state variable,
Figure 671255DEST_PATH_IMAGE010
For control inputs,
Figure 2013100761968100001DEST_PATH_IMAGE011
With Be known smooth vector field,
Figure 2013100761968100001DEST_PATH_IMAGE013
Be the matrix of a suitable dimension,
Figure 460492DEST_PATH_IMAGE014
For the Hurwitz matrix,
Figure 2013100761968100001DEST_PATH_IMAGE015
For nonsingular matrix, For matrix,
Figure 2013100761968100001DEST_PATH_IMAGE017
For smooth function,
State feedback controller is designed to:
Figure 185051DEST_PATH_IMAGE018
，
Wherein,
Figure 2013100761968100001DEST_PATH_IMAGE019
For the multivariable EVAC (Evacuation Network Computer Model)
Figure 221271DEST_PATH_IMAGE020
Nominal system
Figure 2013100761968100001DEST_PATH_IMAGE021
State feedback control law,
Figure 489442DEST_PATH_IMAGE022
Wherein: v 1, v 2Be respectively and act on dAxle, qThe anharmonic humorous interference wave signal of axle, a, bFor being greater than zero constant, A 11, A 21, A 12, A 22For matrix parameter,
Figure 2013100761968100001DEST_PATH_IMAGE023
,
Figure 543985DEST_PATH_IMAGE024
,
Figure 2013100761968100001DEST_PATH_IMAGE025
,
Figure 285414DEST_PATH_IMAGE026
,
Figure 2013100761968100001DEST_PATH_IMAGE027
,
Figure 58198DEST_PATH_IMAGE028
,
Figure 2013100761968100001DEST_PATH_IMAGE029
,
Figure 864480DEST_PATH_IMAGE030
Be the matrix of certain dimension, c 1, c 2, c 3For constant,
Figure 2013100761968100001DEST_PATH_IMAGE031
,
Figure 39109DEST_PATH_IMAGE032
For the calm rule of the undisturbed nominal system of former multivariable EVAC (Evacuation Network Computer Model),
Figure 2013100761968100001DEST_PATH_IMAGE033
,
Figure 656167DEST_PATH_IMAGE034
For smooth function, F 1, F 2For the Hurwitz matrix, q 1, q 2For matrix parameter,
Figure 2013100761968100001DEST_PATH_IMAGE035
,
Figure 916247DEST_PATH_IMAGE036
For the nonsingular solution of Sylvester equation, u 1, u 2For controlling voltage, u d , u q For DC permanent magnet stator voltage D, qThe axle component, ω m Angular speed for motor output;
Control and carry out as follows:
At first, according to the actual operation parameters of permanent magnetic motor type mechanical elastic energy storage unit, determine the total system Mathematical Modeling of unit; According to acting on dThe anharmonic humorous interference wave signal of axle v 1, choose a, b determines matrix parameter A 11, A 21, and obtain , ,
Figure 327002DEST_PATH_IMAGE025
With
Figure 277641DEST_PATH_IMAGE026
According to acting on qThe anharmonic humorous interference wave signal of axle v 2, choose a, b determines matrix parameter A 12, A 22, and obtain
Figure 940572DEST_PATH_IMAGE027
,
Figure 293056DEST_PATH_IMAGE028
,
Figure 766763DEST_PATH_IMAGE029
With
Figure 204697DEST_PATH_IMAGE030
Choose constant according to the Laypunov function c 1, c 2With c 3, determine the calm rule of undisturbed nominal system With
Figure 160201DEST_PATH_IMAGE032
Selection of Function
Figure 273651DEST_PATH_IMAGE033
With
Figure 480772DEST_PATH_IMAGE034
, determine matrix parameter
Figure 2013100761968100001DEST_PATH_IMAGE037
With
Figure 236238DEST_PATH_IMAGE038
Choose matrix F 1, separate the Sylvester equation and obtain matrix
Figure 297735DEST_PATH_IMAGE035
, and combination
Figure 113245DEST_PATH_IMAGE025
Obtain q 1, choose matrix F 2, separate the Sylvester equation and obtain matrix
Figure 525771DEST_PATH_IMAGE036
, and combination Obtain q 2Will F 1,
Figure 266511DEST_PATH_IMAGE035
,
Figure 236610DEST_PATH_IMAGE026
,
Figure 136433DEST_PATH_IMAGE033
The Nonlinear Internal Model equation of substitution design, obtain dThe nonlinear disturbance signal of axle v 1Estimated value, will F 2, ,
Figure 535371DEST_PATH_IMAGE030
,
Figure 427103DEST_PATH_IMAGE034
The Nonlinear Internal Model equation of substitution design, obtain qThe nonlinear disturbance signal of axle v 2Estimated value; Again by the nonlinear disturbance signal obtained v 1Estimated value, the calm rule of undisturbed nominal system
Figure 814222DEST_PATH_IMAGE031
, matrix parameter q 1And function
Figure 715182DEST_PATH_IMAGE033
The state feedback controller that substitution designs in the lump, controlled voltage u 1, u d Equally, by the nonlinear disturbance signal obtained v 2Estimated value, the calm rule of undisturbed nominal system
Figure 605778DEST_PATH_IMAGE032
, matrix parameter q 2And function The state feedback controller that substitution designs in the lump, controlled voltage u 2 , u q
Finally, will control voltage u d With u q Be input in the total system Mathematical Modeling of permanent-magnet electric unit, just can guarantee the angular speed of permanent-magnet electric unit output under anharmonic humorous wave interference ω m Keep basicly stable.
2. the unit of the permanent-magnet electric with the mechanical elastic energy storage control method under a kind of anharmonic humorous wave interference according to claim 1, is characterized in that, the total system Mathematical Modeling of described permanent magnetic motor type mechanical elastic energy storage unit is:
Figure 2013100761968100001DEST_PATH_IMAGE039
，
Figure 824718DEST_PATH_IMAGE040
，
Figure 2013100761968100001DEST_PATH_IMAGE041
，
Wherein, B m , be the damping coefficient of motor, T m , T L Be respectively motor output torque and elastic shaft torsional moment, ω m , ω L Be respectively the angular speed of motor and whirlpool spring elastic shaft, L d , L q For dAxle and qThe axle inductance,
Figure 529368DEST_PATH_IMAGE042
,
Figure 2013100761968100001DEST_PATH_IMAGE043
With
Figure 71208DEST_PATH_IMAGE044
,
Figure 2013100761968100001DEST_PATH_IMAGE045
Be respectively stator current and stator voltage D, qThe axle component,
Figure 819590DEST_PATH_IMAGE046
For stator resistance,
Figure 2013100761968100001DEST_PATH_IMAGE047
For rotor velocity,
Figure 446881DEST_PATH_IMAGE048
For rotor flux, pFor number of pole-pairs,
Figure 2013100761968100001DEST_PATH_IMAGE049
For rotor moment of inertia, rFor the gear reduction box gear ratio, nFor the whirlpool spring number of effective coils; E, , bWith hBe respectively elastic properties of materials modulus, length, width and the thickness of energy storage whorl reed; kFor whirlpool spring quality coefficient,
Figure 220802DEST_PATH_IMAGE052
For compact subset,
Figure 85989DEST_PATH_IMAGE054
For the time.
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