CN1794116A - Lagging characteristics modeling method based on nerve network - Google Patents
Lagging characteristics modeling method based on nerve network Download PDFInfo
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- CN1794116A CN1794116A CN 200510022383 CN200510022383A CN1794116A CN 1794116 A CN1794116 A CN 1794116A CN 200510022383 CN200510022383 CN 200510022383 CN 200510022383 A CN200510022383 A CN 200510022383A CN 1794116 A CN1794116 A CN 1794116A
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Abstract
A method for establishing model of retardation property based on neural network includes leading retardation factor f (x) in, applying different property of retardation factor f (x) at different time T1 and T2 to transform multiple mapping relation in retardation system to be one by one mapping relation in retardation system. The method can be use in real time control on retardation property of mechanical gap system, magnetic material and piezoceramic component.
Description
(1) technical field
The present invention relates to the Application of Neural Network in the automation field, be specially a kind of lagging characteristics modeling method based on neural network.
(2) technical background
Intellectual materials such as memorial alloy, piezoelectric chip and piezoelectric ceramics are widely used in the Precision Position Location System as sensor and actuator.The lagging characteristics that parasitizes in these elements not only can reduce the control accuracy of system, even can cause system's instability.Lagging characteristics is a kind of unconventional non-level and smooth non-linear, the complicacy of lagging characteristics at first shows as many mapping property, because the influence of lagging characteristics causes dynamic system under identical input value different output can be arranged, and perhaps under identical output different inputs can be arranged.Next is its Memorability, and the output of lagging characteristics is not only relevant with the current instantaneous value of input signal, but also relevant with the situation of change of the history feature of input signal, signal.
In order to alleviate the harmful effect of Hysteresis Nonlinear to system, need sluggishness is carried out modeling, on the model based that is obtained, the design corresponding controller is to eliminate sluggish adverse effect.Traditional Preisach model
Wherein
V (t) and u (t) are respectively sluggish input and output; The sluggish mapping of Γ [] expression Preisach; (α β) is weighting function to μ; γ
α, β[v] is the sluggish unit of Preisach model (t), and β, α are respectively the switching value up and down of sluggish unit.
The Preisach model is the most a kind of model of current application, its wide accommodation, and principle is simple, and mathematical expression is convenient.But its shortcoming is the way of realization more complicated, is difficult to adjust in real time its parameter to change with conforming, therefore also is difficult to use in On-line Control.
Neural network is applicable to non-linear flood tide information processing, because its high-precision approximation capability, concurrent operation ability fast and powerful fault-tolerant ability are in recent years in the automation field widespread use.But the occasion that neural network can only be used for shining upon one by one, for the lagging characteristics of many mappings, neural network still is difficult to be competent at present.
(3) summary of the invention
The objective of the invention is the hysteresis phenomenon that exists in mechanical clearance system, magnetic material, the piezoelectric ceramic devices, by constructing a special retardation factor, convert the Hysteresis Nonlinear of shining upon to mapping one by one more, set up Hysteresis Nonlinear model then on this basis based on neural network.
For the system H[that lagging characteristics is arranged], at different moment t
1, t
2If import identical v (t
1)=v (t
2), the different H[v (t of its sluggish output
1)] ≠ H[v (t
2)].The present invention introduces retardation factor f (x), at different moment t
1And t
2, the input x (t of retardation factor
1)=x (t
2), and x (t
1), x (t
2) not extreme point, the output f[x (t of retardation factor so
1)] ≠ f[x (t
2)].If with the input of the input v (t) identical, under the effect of identical input, the output f[v (t) of retardation factor as retardation factor with hysteresis system] and the output H[v (t) of lagging characteristics] be one to one, i.e. f[v (t
1)] ≠ f[v (t
2)].(v (t), f[v (t)]) as an input, for different moment t
1, t
2, as v (t
1)=v (t
2), H[v (t
1)] ≠ H[v (t
2)], but f[v is (t
1)] ≠ f[v (t
2)], like this, (v (t
1), f[v (t
1)]) ≠ (v (t
2), f[v (t
2)]), make each input (v (t), f[v (t)]) unique corresponding to a sluggish output H[v (t)].Increase retardation factor as input, avoided identical input that different output is arranged, many mapping transformations of hysteresis system have been become mapping one by one, can set up the neural network model of lagging characteristics.
Being constructed as follows of the retardation factor that the present invention introduces:
Wherein: x represents current retardation factor input;
The retardation factor output that f (x) expression is current;
x
pRepresent the previous input extreme value adjacent with current input;
F (x
p) expression is input as extreme value x
pThe time the output extreme value.
If input signal x for be defined in the interval [0 ,+continuous function on ∞).If there is different moment t
1And t
2, x (t
1)=x (t
2), and x (t
1), x (t
2) not extreme point, f[x (t so
1)] ≠ f[x (t
2)].
Simultaneously to retardation factor f (x) and sluggish H[] behind the identical signal v (t) of input, f (x) has embodied the rising, turnover of curve, the profile of degradation lagging characteristics down, is the blank of retardant curve.
Sluggish many mappings gonosome is present: under identical input, different sluggishness output is arranged.At different moment t
1, t
2If, import identical, i.e. v (t
1)=v (t
2), and the different H[v (t of sluggish output
1)] ≠ H[v (t
2)].After introducing f (x), because x (t
1)=x (t
2), f[x (t
1)] ≠ f[x (t
2)], under the effect of identical input v (t), the output f[v (t) of retardation factor] and the output H[v (t) of lagging characteristics] be one to one, i.e. f[v (t
1)] ≠ f[v (t
2)].
(v (t), f[v (t)]) as an input, for different moment t
1, t
2, as v (t
1)=v (t
2), H[v (t
1)] ≠ H[v (t
2)], but f[v is (t
1)] ≠ f[v (t
2)], like this, (v (t
1), f[v (t
1)]) ≠ (v (t
2), f[v (t
2)]), thereby avoided identical input that different output is arranged, make each input (v (t), f[v (t)]) unique corresponding to a sluggish output H[v (t)].This shows that because the present invention introduces retardation factor, increase the input of a retardation factor, sluggish many mapping transformations become mapping one by one, lay a good foundation for set up sluggish model with neural network.
Advantage of the present invention is: 1, propose the Hysteresis Nonlinear that a kind of special retardation factor will shine upon more and change into mapping one by one, can adopt neural network that lagging characteristics is carried out modeling on this basis; Experimental result shows that this model can approach the Hysteresis Nonlinear of Preisach class exactly; 2, the lagging characteristics model that the present invention is based on neural network is compared with the Preisach model of routine, simple in structure, simplified the identification algorithm process, can be according to the online adjustment model parameter of the variation of object, have better flexibility and adaptability, can be advantageously used in real-time control.
(4) description of drawings
Fig. 1 is the retardation factor curve of the present invention's proposition and the corresponding relation figure of retardant curve;
Fig. 2 is the neural network structure figure that the proposition method is set up according to the present invention among the embodiment 1;
Fig. 3 is lagging characteristics model curve and the actual retardant curve contrast figure based on neural network that the present invention proposes among the embodiment 1;
Fig. 4 is lagging characteristics model curve of output and the actual sluggish curve of output contrast figure based on neural network that the present invention proposes among the embodiment 1.
Fig. 5 for embodiment 1 on the lagging characteristics model basis of the neural network that the inventive method obtains, pseudo-inverse controller the result that piezo actuator is controlled of structure.
(5) embodiment
For the system H[that lagging characteristics is arranged], at different moment t
1, t
2If import identical v (t
1)=v (t
2), the different H[v (t of its sluggish output
1)] ≠ H[v (t
2)].It is as follows that the present invention introduces retardation factor:
Wherein: x represents current retardation factor input;
The retardation factor output that f (x) expression is current;
x
pRepresent the previous input extreme value adjacent with current input;
F (x
p) expression is input as extreme value x
pThe time the output extreme value.
If input signal x for be defined in the interval [0 ,+continuous function on ∞).If there is different moment t
1And t
2, x (t
1)=x (t
2), and x (t
1), x (t
2) not extreme point, f[x (t so
1)] ≠ f[x (t
2)].
The retardation factor curve that the present invention among Fig. 1 introduced is a dotted line, and retardant curve is a solid line, as shown in Figure 1, under the effect of identical input v (t), the output f[v (t) of retardation factor] and the output H[v (t) of retardant curve] be one to one.For example when being input as v (1), correspond respectively to a point of retardation factor and the A point of retardant curve.When being input as v (2), correspond respectively to the b point of retardation factor and the B point of retardant curve.
Sluggish many mappings gonosome is present: under identical input, different sluggishness output is arranged.Such as at different moment t
1, t
2, v (t
1)=v (t
2)=v (3), and H[v (t
1)] ≠ H[v (t
2)], correspond respectively to C and the D point of Fig. 1.For the retardation factor that the present invention introduces, corresponding, as v (t
1)=v (t
2)=v (3), retardation factor is corresponding to c and d point, i.e. f[v (t
1)] ≠ f[v (t
2)].
When (v (t), f[v (t)]) as an input, different moment t
1, t
2, v (t
1)=v (t
2), H[v (t
1)] ≠ H[v (t
2)], (v (t
1), f[v (t
1)]) ≠ (v (t
2), f[v (t
2)]), each input (v (t), f[v (t)]) unique corresponding to a sluggish output H[v (t)].Because of having introduced retardation factor, make many mapping transformations of lagging characteristics become mapping one by one, available neural network is set up sluggish model.
Different moment t
1And t
2, work as t
1＞t
2, f[x (t
1)]-f[x (t
2)] → 0 x (t
1)-x (t
2) → 0.For lagging characteristics, [0, then there is Continuous Mappings Γ: R in+continuous function on ∞) to input signal v (t) in order to be defined in the interval
2→ R makes H[v (t)]=Γ (v (t), f[v (t)]).
For T=[t
0, ∞) ∈ R, definition
It is the set of neural network input.Obviously, to any t
i∈ T, v (t
iThe ∞ of)＜+, f[v (t
i)]＜+∞, (v (t
i), f[v (t
i)]) ∈ R
2So, input set Φ={ (v (t
i), f[v (t
i)]) | v (t
i) ∈ V, f[v (t
i)] ∈ F} is that bounded closed set promptly compacts.
By the relevant theory of neural network as can be known, Multi-layered Feedforward Networks can be approached with the continuous function to compact space of precision arbitrarily.Therefore shining upon Γ can be expressed as:
Γ(v(t)，f[v(t)])＝NN(v(t)，f[v(t)])+ε
Wherein: NN () is a multilayer feedforward neural network, and ε is an approximate error, to positive number ε arbitrarily
N, satisfy | ε |≤ε
NOn this basis, just available multilayer feedforward neural network carries out modeling to lagging characteristics, and controls in real time on this basis.
The lagging characteristics modeling method based on neural network of piezo actuator
Piezo actuator does not produce certain displacement to be used as positioning control simultaneously at input voltage.But it is, inequality in the mutually produced simultaneously displacement of different time input voltage because of piezo actuator has lagging characteristics.For grasping its lagging characteristics, introduce the Hysteresis Nonlinear model of retardation factor foundation based on neural network, be used for accurate On-line Control.
Piezo actuator is under input voltage 0-100v, and rated displacement is 0-25 μ m, and sample frequency is 1000Hz.The data that record adopt 1200 groups of data through after the filtering, and these data breaks are divided into two parts of equal amount, and first 600 groups are used to force into retardant curve, second 600 groups of generalization ability that are used to check this neural network model.
Adopt retardation factor f (x):
Wherein x is an input value, x
pRepresent the previous input extreme value adjacent with current input, its initial value is 0 to be x
p(0)=0, x
pInstantaneous value iterate computing by system and obtain.
Get x=v (t) and be the input voltage value of this piezo actuator
Sluggish model formation:
H[v(t)]＝Γ(v(t)，f[v(t)])＝NN(v(t)，f[v(t)])+ε
Wherein: NN () is a multilayer feedforward neural network, and ε is an approximate error, to positive number ε arbitrarily
N, satisfy | ε |≤ε
N
Neural network adopts BP network (Back-Propagation Network), and the performance of the neural network of the hidden neuron unit of different numbers is more as shown in table 1.The modeling accuracy of neural network that adopts 12 hidden layer unit as can be seen is than higher, so this example adopts 2 input neurons, 12 hidden neurons, and hidden neuron adopts the S type function, and output neuron adopts linear function.Adopt the Powell-Beale algorithm to come neural network training.Training step number Epochs=463, MSE=0.000139, maximum absolute error are 0.0262, maximum relative error is 0.0139.
The neural network performance of the different number hidden neuron of table 1 unit relatively
| Hidden layer unit number | Least mean-square error | Maximum |
| 10 12 14 | 0.000159559 0.000139786 0.000141292 | 0.0157 0.0139 0.0150 |
The neural network structure of being built as shown in Figure 2, wherein
V (t) is the voltage input of piezo actuator;
F (x) is a retardation factor;
S is a neuron;
W is the neural network weight;
H[v (t)] be sluggish model output.
Solid line among Fig. 3 is the actual sluggish curve of output that obtains according to many data in this example, and dotted line is the sluggish curve of output that calculates according to same mass data by the sluggish model based on neural network that this method obtains.The solid line of Fig. 4 is the actual sluggish displacement output that second 600 groups of data by this example obtain, and dotted line is the sluggish displacement output that obtains by the voltage input of second 600 groups of data of this example based on the sluggish model of neural network that obtains by this method.By block curve among Fig. 3,4 and dashed curve as seen, sluggish model and actual sluggish difference based on neural network that this method obtains are very little.
On this model basis, construct pseudo-inverse controller piezo actuator is controlled, as shown in Figure 5, wherein dotted line is actual output valve, solid line is the output valve based on the pseudo-inverse controller of this model construction, passing in time, the two overlaps substantially fully.As seen the pseudo-inverse controller based on this model construction has overcome sluggish adverse effect, and pseudoinverse control is respond well.
Lagging characteristics modeling method based on neural network of the present invention is used for the modeling of automobile suspension system damper, has also obtained satisfied result.This method all can be used in the system that mechanical clearance system, magnetic device etc. have lagging characteristics, makes real-time control more accurate.
Claims (3)
1 one kinds of lagging characteristics modeling methods based on neural network have the system H[of lagging characteristics], at different moment t
1, t
2If import identical v (t
1)=v (t
2), the different H[v (t of its sluggish output
1)] ≠ H[v (t
2)]; It is characterized in that:
Introduce retardation factor f (x), at different moment t
1And t
2, the input x (t of retardation factor
1)=x (t
2), and x (t
1), x (t
2) not extreme point, the output f[x (t of retardation factor so
1)] ≠ f[x (t
2)]; With the input of the input v (t) identical as retardation factor, f[v (t with hysteresis system
1)] ≠ f[v (t
2)]; (v (t), f[v (t)]) as an input, for different moment t
1, t
2, as v (t
1)=v (t
2), (v (t
1), f[v (t
1)]) ≠ (v (t
2), f[v (t
2)]), each input (v (t), f[(t)]) unique corresponding to a sluggish output H[v (t)], many mapping transformations of hysteresis system become mapping one by one, set up the neural network model of lagging characteristics based on this.
2 lagging characteristics modeling methods based on neural network according to claim 1 is characterized in that:
Being constructed as follows of the retardation factor of introducing:
Wherein: x represents current retardation factor input;
The retardation factor output that f (x) expression is current;
x
pRepresent the previous input extreme value adjacent with current input;
F (x
p) expression is input as extreme value x
pThe time the output extreme value;
[0 ,+continuous function on ∞) is if exist different moment t if input signal x is for being defined in the interval
1And t
2, x (t
1)=x (t
2), and x (t
1), x (t
2) not extreme point, f[x (t so
1)] ≠ f[x (t
2)].
3 lagging characteristics modeling methods based on neural network according to claim 1 and 2 is characterized in that:
Different moment t
1And t
2, work as t
1＞t
2, f[x (t
1)]-f[x (t
2)] → 0 x (t
1)-x (t
2) → 0; For lagging characteristics, [0, then there is Continuous Mappings Γ: R in+continuous function on ∞) to input signal v (t) in order to be defined in the interval
2→ R makes H[v (t)]=Γ (v (t), f[v (t)]);
For T=[t
0, ∞) ∈ R, definition
Be the set of neural network input, to any t
i∈ T, v (t
iThe ∞ of)＜+, f[v (t
i)]＜+∞, (v (t
i), f[v (t
i)]) ∈ R
2, input set Ф={ (v (t
i), f[v (t
i)]) | v (t
i) ∈ V, f[v (t
i)] ∈ F} is that bounded closed set promptly compacts;
Mapping Γ can be expressed as:
Γ(v(t)，f[v(t)])＝NN(v(t)，f[v(t)])+ε
Wherein: NN () is a multilayer feedforward neural network, and ε is an approximate error, to positive number ε arbitrarily
N, satisfy | ε |≤ε
NOn this basis, with multilayer feedforward neural network lagging characteristics is carried out modeling.
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| CN101833284A (en) * | 2010-05-28 | 2010-09-15 | 上海交通大学 | Method for compensating system in real time by using hysteresis inversion model |
| CN102540882A (en) * | 2012-03-01 | 2012-07-04 | 北京航空航天大学 | Aircraft track inclination angle control method based on minimum parameter studying method |
| CN103336429A (en) * | 2013-06-24 | 2013-10-02 | 中国科学院长春光学精密机械与物理研究所 | High-precision control method for piezoelectric ceramic executor |
| CN104678765A (en) * | 2015-01-28 | 2015-06-03 | 浙江理工大学 | Piezoelectric ceramic actuator hysteretic model and control method thereof |
| CN106019933A (en) * | 2016-07-29 | 2016-10-12 | 中国科学院自动化研究所 | Prediction control method of 'sticking-slipping' micro motion platform |
| CN106125574A (en) * | 2016-07-22 | 2016-11-16 | 吉林大学 | Piezoelectric ceramics mini positioning platform modeling method based on DPI model |
| CN106980264A (en) * | 2017-05-12 | 2017-07-25 | 南京理工大学 | The Dynamic Hysteresis modeling method of piezoelectric actuator based on neutral net |
| CN107422638A (en) * | 2017-05-12 | 2017-12-01 | 华中科技大学 | A kind of magnetic resistance actuator electromagnetism force modeling and motion control method |
| CN110108443A (en) * | 2019-05-05 | 2019-08-09 | 大连理工大学 | A kind of piezoelectric ceramic actuator output control method neural network based |
| CN111505543A (en) * | 2020-03-18 | 2020-08-07 | 中国电力科学研究院有限公司 | Method and system for compensating dynamic hysteresis based on recurrent neural network |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN101833284A (en) * | 2010-05-28 | 2010-09-15 | 上海交通大学 | Method for compensating system in real time by using hysteresis inversion model |
| CN102540882A (en) * | 2012-03-01 | 2012-07-04 | 北京航空航天大学 | Aircraft track inclination angle control method based on minimum parameter studying method |
| CN103336429A (en) * | 2013-06-24 | 2013-10-02 | 中国科学院长春光学精密机械与物理研究所 | High-precision control method for piezoelectric ceramic executor |
| CN103336429B (en) * | 2013-06-24 | 2016-08-17 | 中国科学院长春光学精密机械与物理研究所 | A kind of high-accuracy control method of piezoelectric ceramic actuator |
| CN104678765A (en) * | 2015-01-28 | 2015-06-03 | 浙江理工大学 | Piezoelectric ceramic actuator hysteretic model and control method thereof |
| CN106125574A (en) * | 2016-07-22 | 2016-11-16 | 吉林大学 | Piezoelectric ceramics mini positioning platform modeling method based on DPI model |
| CN106125574B (en) * | 2016-07-22 | 2018-11-16 | 吉林大学 | Piezoelectric ceramics mini positioning platform modeling method based on DPI model |
| CN106019933A (en) * | 2016-07-29 | 2016-10-12 | 中国科学院自动化研究所 | Prediction control method of 'sticking-slipping' micro motion platform |
| CN106980264A (en) * | 2017-05-12 | 2017-07-25 | 南京理工大学 | The Dynamic Hysteresis modeling method of piezoelectric actuator based on neutral net |
| CN107422638A (en) * | 2017-05-12 | 2017-12-01 | 华中科技大学 | A kind of magnetic resistance actuator electromagnetism force modeling and motion control method |
| CN107422638B (en) * | 2017-05-12 | 2019-05-31 | 华中科技大学 | A kind of magnetic resistance actuator electromagnetism force modeling and motion control method |
| CN110108443A (en) * | 2019-05-05 | 2019-08-09 | 大连理工大学 | A kind of piezoelectric ceramic actuator output control method neural network based |
| CN111505543A (en) * | 2020-03-18 | 2020-08-07 | 中国电力科学研究院有限公司 | Method and system for compensating dynamic hysteresis based on recurrent neural network |
| CN111505543B (en) * | 2020-03-18 | 2023-02-28 | 中国电力科学研究院有限公司 | Method and system for compensating dynamic hysteresis based on recurrent neural network |
| CN111796518A (en) * | 2020-06-09 | 2020-10-20 | 吉林大学 | Displacement control method for magnetic control shape memory alloy actuator |
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