CN107911056A - A kind of fractional order iteration sliding-mode control, control system and device - Google Patents
A kind of fractional order iteration sliding-mode control, control system and device Download PDFInfo
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- CN107911056A CN107911056A CN201711123134.2A CN201711123134A CN107911056A CN 107911056 A CN107911056 A CN 107911056A CN 201711123134 A CN201711123134 A CN 201711123134A CN 107911056 A CN107911056 A CN 107911056A
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
- H02P21/0007—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using sliding mode control
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Abstract
The invention discloses a kind of fractional order iteration sliding-mode control, control system and device, this method passes through the Fractional Derivative according to tracking error e (t) and tracking errorTo establish the functional relation s (e) between fractional order sliding formwork prevalence face s and tracking error e (t), then u is exported using the functional relation s (e) between fractional order sliding formwork prevalence face s and tracking error e (t) as the control of the K+1 cycle t momentk+1(t) study more new law, the repeating motion characteristic of controlled device can be utilized, according to passing data, constantly correct current control performance, ensure that each cycle has preferable control performance, overcome existing iterative learning control method to cause the technical problem of anti-interference difference as study more new law according to single tracking error, enhance the interference free performance of control system.
Description
Technical field
The present invention relates to control technology field, more particularly to a kind of fractional order iteration sliding-mode control, control system and
Device.
Background technology
Existing in the industry much has the mechanical equipment of repeated periodic motion, such as the numerically-controlled machine tool in manufacturing industry, removes
Transport robot and electric injection molding machine etc..And these have the mechanical equipment of repeated periodic motion, its control system is few at present
Amount can improve the control performance of current system using the method for iterative learning.The iterative learning control that control system uses at present
Method may be summarized to be following mathematical model：
In the mathematical model, uk+1(t) be+1 cycle of kth t moment control output, uk(t) be k-th cycle t when
Carve control output, yd(t) it is tracking desired value, y (t) is t moment system real output value, and e (t) is system tracking error, and k is
Learn constant.
It is defeated using the system of upper a cycle for can be seen that existing iterative learning control method from above-mentioned mathematical model
Go out study more new laws of the tracking error e (t) of value and desired value as current period, the then control with upper a cycle exports
Superposition, the control as current period export.It is this to be controlled simply by iterative learning of the tracking error as study foundation
Method, once random disturbances occurs in system, then the tracking error of current period will increase, even if next cycle interference disappears
, but learn more new law and be still the control that the tracking error according to caused by the interference of upper a cycle draws current period come iteration
Output valve processed.Therefore, this iterative learning control method according to single tracking error, in situation existing for uncertain noises
Under, anti-robustness is poor, causes system control performance bad, and the stabilization of system can be destroyed if serious.
The content of the invention
It is a primary object of the present invention to solve the control system institute of the existing mechanical equipment with repeated periodic motion
The technical problem of the iterative learning control method anti-interference difference of the single tracking error of foundation of use.
To achieve the above object, the present invention provides a kind of fractional order iteration sliding-mode control, comprises the following steps：
Obtain the tracking error e (t) and the tracking error of operation output of the controlled device in current k-th cycle t moment
Fractional Derivative
According to tracking error e (t) and the Fractional Derivative of tracking errorVia the first relation reality fractional order
Functional relation s (e) between sliding formwork prevalence face s and tracking error e (t)；
Using the functional relation s (e) between fractional order sliding formwork prevalence face s and tracking error e (t) as during the K+1 cycle t
The control output u at quarterk+1(t) study more new law；
U is exported according to the control of current k-th cycle t momentk(t) control with the K+1 cycle t moment exports uk+1
(t) study more new law, the control that the K+1 cycle t moment is adjusted via the second relational expression export uk+1(t)。
In addition, the present invention also provides a kind of control system, including：
Acquisition module, for obtaining the tracking error e (t) of operation output of the controlled device in current k-th cycle t moment
With the Fractional Derivative of the tracking error
Module is established, for the Fractional Derivative according to tracking error e (t) and tracking errorClosed via first
It is that formula establishes functional relation s (e) between fractional order sliding formwork prevalence face s and tracking error e (t)；
Determining module, for using the functional relation s (e) between fractional order sliding formwork prevalence face s and tracking error e (t) as
The control output u of the K+1 cycle t momentk+1(t) study more new law；
Adjustment module, for exporting u according to the control of current k-th cycle t momentk(t) with the K+1 cycle t moment
Control output uk+1(t) study more new law, the control that the K+1 cycle t moment is adjusted via the second relational expression export uk+1
(t)。
Furthermore the present invention also provides a kind of telecontrol equipment, which includes the power part of repeated periodic motion,
And further include control system as described above for controlling power part.
The present invention passes through the Fractional Derivative according to tracking error e (t) and tracking errorSlided to establish fractional order
Functional relation s (e) between mould prevalence face s and tracking error e (t), then by fractional order sliding formwork prevalence face s and tracking error e
(t) the functional relation s (e) between exports u as the control of the K+1 cycle t momentk+1(t) study more new law, Ke Yili
With the repeating motion characteristic of controlled device, according to passing data, current control performance is constantly corrected, ensures that each cycle has
Preferable control performance, overcomes existing iterative learning control method to cause according to single tracking error as study more new law anti-interference
Property difference technical problem, enhance the interference free performance of control system.
Brief description of the drawings
Fig. 1 is the flow diagram of the preferred embodiment of fractional order iteration sliding-mode control of the present invention；
Fig. 2 is the high-level schematic functional block diagram of control system of the present invention；
Fig. 3 is the high-level schematic functional block diagram of apparatus of the present invention；
The embodiments will be further described with reference to the accompanying drawings for the realization, the function and the advantages of the object of the present invention.
Embodiment
It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not intended to limit the present invention.
In order to solve above-mentioned technical problem to be solved by this invention, in a preferred embodiment, the present invention provides
A kind of fractional order iteration sliding-mode control.As shown in Figure 1, fractional order iteration sliding-mode control provided by the invention can wrap
Include following steps：
Step S1：Obtain operation output of the controlled device in current k-th cycle t moment tracking error e (t) and should be with
With the Fractional Derivative of error
Specifically, when control system control controlled device carries out the movement in current K cycles, controlled device is current the
The tracking error e (t) of the operation output of K cycle t moment is that controlled device is exported in the actual motion of k-th cycle t moment
The deviation of value and tracking desired value.And in order to overcome the iterative learning control method anti-interference difference according to single tracking error
Technical problem, fractional order iteration sliding-mode control of the present invention not only obtain fortune of the controlled device in current k-th cycle t moment
The tracking error e (t) of row output, also further calculates the Fractional Derivative of the tracking error
Step S2：According to tracking error e (t) and the Fractional Derivative of tracking errorBuilt via the first relational expression
Vertical functional relation s (e) between fractional order sliding formwork prevalence face s and tracking error e (t)；
Specifically, obtain controlled device current k-th cycle t moment operation output tracking error e (t) and
The Fractional Derivative of the tracking errorAfterwards, fractional order iteration sliding-mode control of the present invention is built via the first relational expression
Vertical functional relation s (e) between fractional order sliding formwork prevalence face s and tracking error e (t).For example, the first relational expression isWherein, β is arithmetic number,For the r order derivatives of tracking error e (t), 0<r<1.The present invention
Fractional order iteration sliding-mode control is by establishing the functional relation s between fractional order sliding formwork prevalence face s and tracking error e (t)
(e), can ensure in limited a cycle, fractional order sliding mode face s (e)=0 of the operation output of controlled device.According toThen haveIt is so theoretical according to fractional calculus, as long as ensureingSet up, and β is arithmetic number, then can ensure within limited a cycle, the operation output of controlled device
Tracking error e (t)=0.
Step S3：Using the functional relation s (e) between fractional order sliding formwork prevalence face s and tracking error e (t) as K+1
The control output u of cycle t momentk+1(t) study more new law；
Specifically, after the functional relation s (e) between fractional order sliding formwork prevalence face s and tracking error e (t) is established,
Fractional order iteration sliding-mode control of the present invention is by the functional relation s between fractional order sliding formwork prevalence face s and tracking error e (t)
(e) control as the K+1 cycle t moment exports uk+1(t) study more new law, to overcome existing iterative learning controlling party
Method causes the technical problem of anti-interference difference according to single tracking error as study more new law.
Step S4：U is exported according to the control of current k-th cycle t momentk(t) with the control of the K+1 cycle t moment
Export uk+1(t) study more new law, the control that the K+1 cycle t moment is adjusted via the second relational expression export uk+1(t)。
Specifically, u is exported there is provided the control of the K+1 cycle t momentk+1(t) after study more new law, this hair
Bright fractional order iteration sliding-mode control exports u via the second relational expression to adjust the control of the K+1 cycle t momentk+1(t)。
Second relational expression is uk+1(t)=uk(t)+αs(e), wherein, α is arithmetic number.
Fractional order iteration sliding-mode control of the present invention according to tracking error e (t) and the fractional order of tracking error by leading
NumberTo establish the functional relation s (e) between fractional order sliding formwork prevalence face s and tracking error e (t), then by fractional order
Functional relation s (e) between sliding formwork prevalence face s and tracking error e (t) exports u as the control of the K+1 cycle t momentk+1
(t) study more new law, can utilize the repeating motion characteristic of controlled device, according to passing data, constantly correct current control
Performance processed, ensures that each cycle has preferable control performance, overcomes existing iterative learning control method according to single tracking error
Cause the technical problem of anti-interference difference as study more new law, enhance the interference free performance of control system.
Meanwhile in another preferred embodiment, the present invention also provides a kind of control system, each work(of the control system
Energy module and each step of above-mentioned fractional order iteration sliding-mode control correspond.As shown in Fig. 2, control provided by the invention
System 3 can include sequentially being in communication with each other the acquisition module 32 of connection, establish module 34, determining module 36, adjustment module 38.Tool
Body,
Acquisition module 32, for obtaining the tracking error e of operation output of the controlled device in current k-th cycle t moment
(t) and the tracking error Fractional DerivativeAnd what controlled device was exported in the operation of current k-th cycle t moment
Tracking error e (t) is controlled device in the actual motion output valve of k-th cycle t moment and the deviation of tracking desired value.
Module 34 is established, for the Fractional Derivative according to tracking error e (t) and tracking errorVia first
Functional relation s (e) between relation reality fractional order sliding formwork prevalence face s and tracking error e (t).For example, the first relational expression can
To beWherein, β is arithmetic number,For the r order derivatives of tracking error e (t), 0<r<1.
Determining module 36, for the functional relation s (e) between fractional order sliding formwork prevalence face s and tracking error e (t) to be made
U is exported for the control of the K+1 cycle t momentk+1(t) study more new law.
Adjustment module 38, for exporting u according to the control of current k-th cycle t momentk(t) with the K+1 cycle t when
The control output u at quarterk+1(t) study more new law, the control that the K+1 cycle t moment is adjusted via the second relational expression export
uk+1(t).For example, the second relational expression is uk+1(t)=uk(t)+α s (e), wherein, α is arithmetic number.
Control system 3 of the present invention in module 34 is established according to tracking error e (t) and the fractional order of tracking error by leading
NumberTo establish the functional relation s (e) between fractional order sliding formwork prevalence face s and tracking error e (t), then in definite mould
Using the functional relation s (e) between fractional order sliding formwork prevalence face s and tracking error e (t) as the K+1 cycle t moment in block 36
Control output uk+1(t) study more new law, can utilize the repeating motion characteristic of controlled device, according to passing data, no
It is disconnected to correct current control performance, ensure that each cycle has preferable control performance, overcome existing iterative learning control method foundation
Single tracking error causes the technical problem of anti-interference difference as study more new law, enhances the anti-interference of control system
Energy.
Further, then in another preferred embodiment, the present invention also provides a kind of telecontrol equipment, as shown in figure 3, should
Telecontrol equipment 1 can include the power part 2 of repeated periodic motion and the control system 3 for controlling power part 2.Its
In, which is permanent magnet synchronous motor.The control system 3 can apply above-mentioned fractional order iteration sliding formwork control side
The control system 3 of method.
Specifically, the mathematical model of permanent magnet synchronous motor in the rotated coordinate system is：
Wherein, u* d,u* qIt is d, the stator voltage under q- coordinates, i* d,i* qIt is stator current, λd,λqIt is stator magnetic linkage, Ld,
LqInductive component, ωf、ω* rIt is motor angular rate and setting speed respectively, LmdIt is stator phase inductance, IdfIt is equivalent current, np
It is magnetic pole of the stator logarithm, RsIt is stator resistance.
The electromagnetic torque equation of permanent magnet synchronous motor：Permanent magnetism is same
Walk the kinetic equation of motor：Wherein, TeIt is electromagnetic torque, TlFor loading moment, BmIt is friction system
Number, J is rotary inertia.By that can be simplified as using vector controlled, kinetic equation：
Kinetic equation after simplification is substituted into electromagnetic torque equation, the rotating speed equation of motor can be obtained：
As long as from the rotating speed equation of above-mentioned motor it is recognised that making the control of motor export iqEqual to the invention described above fraction
The control output u of the K+1 cycle t moment in rank iteration sliding-mode controlk+1(t)=uk(t)+α s (e), i.e. iq=uk+1(t)
=uk(t)+ks (e), then can ensure the rotational speed omega of motorrFollow setting value ω* r, realize speed follower error e (t)=0, and
Ensure that motor speed is not influenced be subject to external loading disturbance, enhance the interference free performance of control system.
It these are only the preferred embodiment of invention, be not intended to limit the scope of the invention, it is every to utilize the present invention
The equivalent structure transformation that specification and accompanying drawing content are made, is directly or indirectly used in other related technical areas, together
Reason is included within the scope of the present invention.
Claims (10)
1. a kind of fractional order iteration sliding-mode control, including：
Obtain the tracking error e (t) of operation output and point of the tracking error of the controlled device in current k-th cycle t moment
Number order derivative
According to tracking error e (t) and the Fractional Derivative of tracking errorVia the first relation reality fractional order sliding formwork
Functional relation s (e) between popular face s and tracking error e (t)；
Using the functional relation s (e) between fractional order sliding formwork prevalence face s and tracking error e (t) as the K+1 cycle t moment
Control output uk+1(t) study more new law；
U is exported according to the control of current k-th cycle t momentk(t) control with the K+1 cycle t moment exports uk+1(t)
Learn more new law, the control that the K+1 cycle t moment is adjusted via the second relational expression exports uk+1(t)。
2. fractional order iteration sliding-mode control as claimed in claim 1, it is characterised in that the first relational expression isWherein, β is arithmetic number,For the r order derivatives of tracking error e (t), 0<r<1.
3. fractional order iteration sliding-mode control as claimed in claim 1 or 2, it is characterised in that the second relational expression is uk+1
(t)=uk(t)+α s (e), wherein, α is arithmetic number.
4. fractional order iteration sliding-mode control as claimed in claim 1, it is characterised in that controlled device is in current k-th
The tracking error e (t) of the operation output of cycle t moment be controlled device k-th cycle t moment actual motion output valve with
Track the deviation of desired value.
A kind of 5. control system, it is characterised in that including：
Acquisition module, for obtaining the tracking error e (t) of operation output of the controlled device in current k-th cycle t moment and being somebody's turn to do
The Fractional Derivative of tracking error
Module is established, for the Fractional Derivative according to tracking error e (t) and tracking errorBuilt via the first relational expression
Vertical functional relation s (e) between fractional order sliding formwork prevalence face s and tracking error e (t)；
Determining module, for using the functional relation s (e) between fractional order sliding formwork prevalence face s and tracking error e (t) as K+1
The control output u of a cycle t momentk+1(t) study more new law；
Adjustment module, for exporting u according to the control of current k-th cycle t momentk(t) with the control of the K+1 cycle t moment
Export uk+1(t) study more new law, the control that the K+1 cycle t moment is adjusted via the second relational expression export uk+1(t)。
6. control system as claimed in claim 5, it is characterised in that establishing mould the first relational expression in the block isWherein, β is arithmetic number,For the r order derivatives of tracking error e (t), 0<r<1.
7. the control system as described in claim 5 or 6, it is characterised in that the second relational expression in adjustment module is uk+1(t)
=uk(t)+α s (e), wherein, α is arithmetic number.
8. control system as claimed in claim 5, it is characterised in that the controlled device in acquisition module is in current k-th week
The tracking error e (t) of the operation output of phase t moment be controlled device k-th cycle t moment actual motion output valve with
The deviation of track desired value.
9. a kind of telecontrol equipment, includes the power part of repeated periodic motion, it is characterised in that the device is further included for controlling
Brake force component such as claim 5 to 8 any one of them control system.
10. telecontrol equipment as claimed in claim 9, it is characterised in that the power part is permanent magnet synchronous motor.
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| CN110032066A (en) * | 2019-01-10 | 2019-07-19 | 廊坊师范学院 | The adaptive iterative learning control method of fractional order nonlinear system trajectory tracking |
| CN110083066A (en) * | 2019-05-22 | 2019-08-02 | 杭州电子科技大学 | The fractional order iteration control method of multi-agent system |
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Cited By (5)
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| CN109557816A (en) * | 2018-12-28 | 2019-04-02 | 武汉工程大学 | A kind of suppressing method, system and the medium of piezoelectric ceramic actuator lagging characteristics |
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| CN110032066A (en) * | 2019-01-10 | 2019-07-19 | 廊坊师范学院 | The adaptive iterative learning control method of fractional order nonlinear system trajectory tracking |
| CN110032066B (en) * | 2019-01-10 | 2022-10-18 | 廊坊师范学院 | Adaptive iterative learning control method for fractional order nonlinear system trajectory tracking |
| CN110083066A (en) * | 2019-05-22 | 2019-08-02 | 杭州电子科技大学 | The fractional order iteration control method of multi-agent system |
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Application publication date: 20180413 |