CN105262379B - The controller design method of twin drive system - Google Patents
The controller design method of twin drive system Download PDFInfo
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- CN105262379B CN105262379B CN201510783763.2A CN201510783763A CN105262379B CN 105262379 B CN105262379 B CN 105262379B CN 201510783763 A CN201510783763 A CN 201510783763A CN 105262379 B CN105262379 B CN 105262379B
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Abstract
The present invention provides a kind of synchronously control scheme of twin drive system, include the following steps: to build the synchronous driving experimental system of bi-motor first, wherein, the Dual-motors Driving experimental system includes two sets of permasyn morots and a synchronous belt, and two sets of permasyn morots drive the synchronous belt to operate jointly；Secondly according to principle of dynamics, the mathematical model of the Dual-motors Driving experimental system is established, which belongs to the interacted system with the first nonlinearities system and the second nonlinearities system；Finally based on the mathematical model, devises distributing robust closed-loop and obscure segment sync H∞Controller, and give the simulation test platform of system.The synchronization accuracy of bi-motor can be improved in synchronously control scheme provided by the invention, and closed-loop control system is made to have H∞Anti-interference ability.
Description
Technical field
A kind of isochronous controller design scheme of the present invention about twin drive system.
Background technique
Requirement due to people to control is higher and higher, and the control of triangular web is difficult and meets the need of social development
It wants, therefore the synchronously control of multisystem or consistency control have been suggested.However, mostly reality system be it is nonlinear,
And there are between the subsystem in parameter uncertainty and input disturbance and multisystem there may be coupling physically, these
Factor makes the synchronously control of multisystem seem extremely difficult.
Existing bi-motor synchronization system, the system drive same belt to transport jointly by two sets of permasyn morots
Turn.However, the asynchronous of them can pass through the phase of belt since this two sets of synchronous motors are impossible fully synchronized
It mutually pulls, so that the synchronization accuracy of bi-motor synchronization system is low, the disadvantages of poor anti jamming capability.
Summary of the invention
In view of the foregoing, it is necessary to a kind of isochronous controller design scheme of twin drive system is provided, it can be with
Effectively solve the above problems.
The present invention provides a kind of controller design scheme of twin drive system, includes the following steps:
The synchronous driving experimental system of bi-motor is built first, wherein the experimental system includes two sets of permanent magnet synchronous electrics
Motivation and a synchronous belt, two sets of permasyn morots drive the synchronous belt to operate jointly；
Then according to principle of dynamics, the mathematical model of the synchronous driving experimental system of the bi-motor, the mathematics are established
Model belongs to the interacted system with nonlinearities system (10) and nonlinearities system (20)；
It is finally based on the mathematical model, distributing robust closed-loop is established and obscures segment sync H∞The design side of controller
Case.
The synchronization accuracy of bi-motor can be improved in design method controller obtained provided by the invention, and makes closed loop
Control system has H∞Anti-interference ability.
Detailed description of the invention
Fig. 1 is the structural schematic diagram of the synchronous driving experimental system of bi-motor.
Fig. 2 is the structural schematic diagram of the synchronous driving experimental system of bi-motor.
Fig. 3 is that distributing closed-loop obscures dlvision synchrd control block diagram.
Fig. 4 is fuzzy membership function figure.
Fig. 5 is synchronously control experiment porch.
Specific embodiment
Fig. 1 is please referred to, the embodiment of the present invention provides a kind of isochronous controller design scheme of twin drive system, packet
Include following steps:
S1 builds the synchronous driving experimental system 100 of bi-motor, wherein the synchronous driving of the bi-motor is real referring to figure 2.
Check system 100 includes two sets of permasyn morots 11/21 and a synchronous belt 30, two sets of permasyn morots
11/21 drives the synchronous belt 30 to operate jointly；
S2 establishes the mathematical model of the Dual-motors Driving experimental system according to principle of dynamics, the mathematical model category
In an interacted system with nonlinearities system (10) and nonlinearities system (20)；
S3 is established distributing robust closed-loop and is obscured segment sync H based on the mathematical model∞The design of controller
Scheme.
In step sl, the permasyn morot 11, the first reduction gearbox 12 and the first synchronizing wheel 13 form subsystem
10；The permasyn morot 21, the second reduction gearbox 22 and the second synchronizing wheel 23 form subsystem 20.
In step s 2, the mathematical model such as formula (1) of subsystem (10):
Wherein For the angular speed of permasyn morot 11, P1For permanent-magnet synchronous
The series of motor 11,For q shaft current, R1For stator resistance, L1For stator inductance,For q shaft voltage,For permanent magnetism
The rotary inertia of synchronous motor 11,For d shaft voltage,For the electromagnetic torque of permasyn morot 11,It is
The rotary inertia of one reduction gearbox 12,For the rotary inertia of the first synchronizing wheel 13, k1(s1),k2(s1),k3For synchronous belt 30
Coefficient of elasticity, r be the first synchronizing wheel 13 radius, M is load quality,For the frictional force of the first synchronizing wheel 13, FfIt is negative
Damped coefficient under load effect,For d shaft current,For load torque,For the viscous resistance of permasyn morot 11
Buddhist nun's coefficient, λ1For magnetic flux,For the revolving speed of the first synchronizing wheel 13, BlFor linear guide viscous damping coefficient,It is first
The viscous damping coefficient of synchronizing wheel 13, G1For the reduction ratio of the first reduction gearbox 12, s is the moving distance of synchronous belt 30, and v is same
Walk the movement speed of belt 30.
The mathematical model such as formula (2) of subsystem (20):
Wherein For the angular speed of synchronous motor 21, P2For synchronous motor 21
Series,For q shaft current, R2For stator resistance, L2For stator inductance,For q shaft voltage,For synchronous motor
21 rotary inertia,For d shaft voltage,For the electromagnetic torque of synchronous motor 21,For turning for the second reduction gearbox 22
Dynamic inertia,For the rotary inertia of the second synchronizing wheel 23,For the frictional force of the second synchronizing wheel 23, FfFor under load effect
Damped coefficient,For d shaft current,For load torque,For the viscous damping coefficient of synchronous motor 21, λ2For
Magnetic flux,For the revolving speed of the second synchronizing wheel 23,For the viscous damping coefficient of the second synchronizing wheel 23, G2Slow down for second
The reduction ratio of case 22.
Further, it definesAnd state space table below is obtained after being substituted into (1) formula
Up to formula:
WhereinAnd η1Indicate the non-synchronized factor of motor rotating speed, and
In addition, to meet relational expression with the variation of temperature as follows for the resistance value of its internal copper line winding group when motor works:
Rn=R0+aR0(Tn-T0) (4)
Wherein, R0It is in temperature T0Resistance value, RnIt is in temperature TnResistance value, a be copper resistance temperature coefficient, obtain subsystem
The Parameter uncertainties of system (10) are as follows:
Similarly, the system model for obtaining subsystem (20) is as follows:
WhereinAnd η2Indicate the non-synchronized factor of motor rotating speed, and
Further, referring to figure 4., fuzzy membership function shown in, the nonlinear interconnected system can pass through
T-S fuzzy model is expressed as follows:
In step s3, referring to figure 3., the distributing robust closed-loop of establishing obscures segment sync H∞Controller is set
Meter scheme, comprising the following steps:
S31 constructs the discrete model of a virtual main shaft:
Wherein, the reference signal of virtual the main shaft output motor electric current and revolving speed and synchronous belt position；
S32, it is single linear space and fuzzy space that cutting, which obscures the former piece variable space, and it is fully closed to design following distributing
Ring moulds paste dlvision synchrd control device:
ui(t)=Kij(yi(t)-yr(t)), j ∈ { 1,2 ..., 27 }, i={ 1,2 } (8)
The parameter that the distributing closed-loop obscures dlvision synchrd control device is obtained by following method:
It is primarily based on the switching principle of the fuzzy former piece variable space, the discrete model (6) are rewritten are as follows:
Wherein,
In conjunction with formula (7)-(9), the Fuzzy control system of following closed loop is obtained:
Wherein
By way of augmentation, generalized ensemble model that the Fuzzy control system (10) of the closed loop is expressed as:
Wherein
Consider following segmentation Lyapunov functional:
Wherein,And it defines
△Vi(t)=Vi(t+1)-Vi(t), it and along the motion profile of generalized ensemble model (11), obtains:
DefinitionObtain following inequality:
DefinitionAnd matrixAnd with generalized ensemble model
(11), it obtains:
Introduce 0 < ρ of scalar parameterij≤ρi0, and by (14) and (15), it obtains:
Consider performance index function below:
And after combining (13)-(17), obtain:
Wherein
Obtain from inequality (18): in the case where zero is initial, closed-loop control system is asymptotically stability, and be can guarantee
System has H∞Performance indicator γ, when following MATRIX INEQUALITIES is set up:
Wherein, { 1,2 ..., 27 } (j, s) ∈, i ∈ { 1,2 }
By using Schur lemma, formula (19) is rewritten into form below:
Then, in order to which inequality (20) to be converted into the situation of linear matrix inequality, by matrix GijIt is defined as
Structure:
Wherein,
It is nonsingular matrix.
By Parameter uncertaintiesThe form being written as follow:
Wherein,
Formula (21) and (22) are substituted into (20), for all m ∈ Ιi(j), { 1,2 } i ∈, j={ 1,2 ..., 27 },
MATRIX INEQUALITIES below, which is set up, guarantees that formula (20) are set up:
Wherein
Design method as claimed in claim 8, which is characterized in that by the LMI solution formula (23) of MATLAB, thus
It obtains distributing robust closed-loop and obscures segment sync H∞The design parameter of controller:
After step S3, referring to figure 5., the step of can further comprising the simulation test platform for building DSPACE.
Note that the above is only a better embodiment of the present invention and the applied technical principle.It will be appreciated by those skilled in the art that
The invention is not limited to the specific embodiments described herein, be able to carry out for a person skilled in the art it is various it is apparent variation,
It readjusts and substitutes without departing from protection scope of the present invention.Therefore, although being carried out by above embodiments to the present invention
It is described in further detail, but the present invention is not limited to the above embodiments only, without departing from the inventive concept, also
It may include more other equivalent embodiments, and the scope of the invention is determined by the scope of the appended claims.
Claims (7)
1. a kind of controller design method of twin drive system, which comprises the steps of:
Build the synchronous driving experimental system of bi-motor, wherein the experimental system include two sets of permasyn morots and
One synchronous belt, two sets of permasyn morots drive the synchronous belt to operate jointly；
According to principle of dynamics, the mathematical model of the synchronous driving experimental system of the bi-motor is established, which belongs to
One interacted system with nonlinearities system 10 and nonlinearities system 20；
Based on the mathematical model, establishes distributing robust closed-loop and obscure segment sync H∞The design scheme of controller, including
Following steps:
Firstly, the discrete model of one virtual main shaft of construction:
Wherein, the reference signal of virtual the main shaft output motor electric current and revolving speed and synchronous belt position；
Then, it is single linear space and fuzzy space that cutting, which obscures the former piece variable space, and it is fully closed to design following distributing
Ring moulds paste dlvision synchrd control device:
ui(t)=Kij(yi(t)-yr(t)), { 1,2 ..., 27 } j ∈, i={ 1,2 } (8)；
The mathematical model of nonlinearities system 10 such as formula (1):
WhereinWherein,For motor angle speed, P1For motor series,
For q shaft current, R1For stator resistance, L1For stator inductance, V1 (qs)For q shaft voltage,For motor rotation inertia, V1 (ds)
For d shaft voltage,For motor electromagnetic torque,For deceleration device rotary inertia,For synchronizing wheel rotary inertia,
k1(s), k2(s), k3For synchronous belt coefficient of elasticity, r is synchronizing wheel radius, and M is load quality, T1 (w)For synchronizing wheel frictional force,
FfFor the damped coefficient under load effect,For d shaft current, T1 (L)For load torque,For motor viscous damping system
Number, λ1For magnetic flux,To drive wheel speed, BlFor linear guide viscous damping coefficient,For the viscous resistance of driving wheel
Buddhist nun's coefficient, G1For deceleration device reduction ratio, s is the moving distance of synchronous belt, and v is the movement speed of synchronous belt；
The mathematical model of nonlinearities system 20 such as formula (2):
Wherein, For motor angle speed, P2For motor series,For
Q shaft current, R2For stator resistance, L2For stator inductance,For q shaft voltage,For motor rotation inertia,For
D shaft voltage,For motor electromagnetic torque,For deceleration device rotary inertia,For synchronizing wheel rotary inertia,For synchronizing wheel frictional force, FfFor the damped coefficient under load effect,For d shaft current,For load torque,For motor viscous damping coefficient, λ2For magnetic flux,To drive wheel speed,For driving wheel viscous damping
Coefficient, G2For deceleration device reduction ratio.
2. design method as described in claim 1, which is characterized in that definitionAnd it is substituted into
(1) state-space expression of first set drive system is obtained after formula:
Wherein And η indicates the non-synchronized factor of motor rotating speed, and
Furthermore at work, it is as follows that the resistance value of internal copper line winding group can meet relational expression with the variation of temperature to motor:
Rn=R0+aR0(Tn-T0), (4)
Wherein, R0It is in temperature T0Resistance value, RnIt is in temperature TnResistance value, a be copper resistance temperature coefficient, obtain non-linear subsystem
The Parameter uncertainties of system 10 are as follows:
3. design method as claimed in claim 2 obtains the state-space expression of second set of drive system below:
Wherein
And η indicates the non-synchronized factor of motor rotating speed, and
4. design method as claimed in claim 3, which is characterized in that the nonlinear interconnected system passes through T-S fuzzy model
It is expressed as follows:
5. design method as claimed in claim 4, which is characterized in that the distributing closed-loop obscures dlvision synchrd control device
Parameter pass through following method and obtain:
Firstly, the switching principle based on the fuzzy former piece variable space, the discrete model (6) are rewritten are as follows:
Wherein,
In conjunction with formula (7)-(9), the Fuzzy control system of following closed loop is obtained:
Wherein
By way of augmentation, generalized ensemble model that the Fuzzy control system (10) of the closed loop is expressed as:
Wherein
Consider following segmentation Lyapunov functional:
Wherein, And it is fixed
Adopted △ Vi(t)=Vi(t+1)-Vi(t), it and along the motion profile of generalized ensemble model (11), obtains:
DefinitionObtain following inequality:
DefinitionAnd matrixAnd with generalized ensemble
Model (11), obtains:
Introduce 0 < ρ of scalar parameterij≤ρi0, and by (14) and (15), it obtains:
Consider performance index function below:
And after combining (13)-(17), obtain:
Wherein
Obtain from inequality (18): in the case where zero is initial, closed-loop control system is asymptotically stability, and can guarantee system
With H∞Performance indicator γ, when following MATRIX INEQUALITIES is set up:
Wherein, { 1,2 ..., 27 } j ∈, i ∈ { 1,2 }
By using Schur lemma, formula (19) is rewritten into form below:
Then, in order to which inequality (20) to be converted into the situation of linear matrix inequality, by matrix GijThe structure being defined as:
Wherein,
It is nonsingular matrix,
By Parameter uncertaintiesThe form being written as follow:
Wherein,
Formula (21) and (22) are substituted into (20), for all m ∈ Ιi(j), { 1,2 } i ∈, j={ 1,2 ..., 27 } are below
MATRIX INEQUALITIES, which is set up, guarantees that formula (20) are set up:
Wherein
6. design method as claimed in claim 5, which is characterized in that by the LMI solution formula (23) of MATLAB, thus
The design parameter of segment sync H ∞ controller is obscured to distributing robust closed-loop:
7. design method as described in claim 1, which is characterized in that further comprise build DSPACE emulation testing it is flat
Platform.
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| CN111010053A (en) * | 2019-12-26 | 2020-04-14 | 苏州精濑光电有限公司 | Dual-motor synchronous control method and system |
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| CN101299581A (en) * | 2008-03-10 | 2008-11-05 | 江苏大学 | Neural network generalized inverse coordination control frequency transformer for two induction machines and construction method thereof |
| JP2010148345A (en) * | 2008-12-19 | 2010-07-01 | Tai-Her Yang | Bidirectional non-uniform electric motor fixing direction output drive system |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN101299581A (en) * | 2008-03-10 | 2008-11-05 | 江苏大学 | Neural network generalized inverse coordination control frequency transformer for two induction machines and construction method thereof |
| JP2010148345A (en) * | 2008-12-19 | 2010-07-01 | Tai-Her Yang | Bidirectional non-uniform electric motor fixing direction output drive system |
Non-Patent Citations (1)
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| 永磁同步电机混沌系统鲁棒非脆弱模糊H∞控制;刘鑫蕊等;《电机与控制学报》;20080331;第12卷(第2期);第218-222页 * |
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