CN107991883A - The robust controller of Advanced Manufacturing Modes diffusion - Google Patents
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Abstract
The present invention is the robust controller of Advanced Manufacturing Modes diffusion, and weighting function W is added after error signal1, the constraint to whole foreign intervention system performance requirements is represented, by W1Adjustment can effectively suppress the influence of foreign intervention, obtain the signal results for wishing to export；Weighting function W is added after controller2, represent limitation of the system to Additive Generator, the constraint to exterior intervention signal amplitude can be regarded as；Weighting function W is added after controlled system3, expression system determined the probabilistic limitation of multiplying property by Advanced Manufacturing Modes diffusion model self character.When perturbing to model in some point, the reaction of system external portion disturbance is sensitivity, and it is robust stability that stable ability is kept under external disturbance.It is conflicting between both of which, is handled present invention introduces the design method of Mixed Sensitivity to compromise, both considered robust performance requirement, and in turn ensure that robust stability index.
Description
Technical field
The present invention relates to advanced manufacturing field, especially a kind of robust controller of Advanced Manufacturing Modes diffusion.
Background technology
11.1 research backgrounds
Industry of the manufacturing industry as a national pillar, is the important embodiment of a national overall national strength.With science
The continuous progress of technology, traditional manufacturing mode have been difficult to meet dynamic, the diversified market demand, therefore, manufacture enterprise
Industry must complete the transition to Advanced Manufacturing Modes as early as possible.Certainly, implementing Advanced Manufacturing Modes can help enterprise quick
The diversified market demand is responded, improves competitiveness, one seat is kept to obtain in the market of the survival of the fittest, or even harvest bigger
Benefit.Up to the present, Advanced Manufacturing Modes have been widely used for all kinds of manufacturing enterprises, have promoted manufacturing quick hair
Exhibition, becomes manufacturing industry and wins the market competition, the inevitable choice of realizing long term growth.
However, the implementation process of Advanced Manufacturing Modes is a long-term, complicated process, there is shortage of resources, wind
The high great number of issues in danger, the implementation result of the Advanced Manufacturing Modes of many manufacturing enterprises far can not be satisfactory.Whether enterprise
Implement Advanced Manufacturing Modes, when implement and implement which kind of Advanced Manufacturing Modes must just be faced into policymaker it is main
Problem, therefore, the correlation theory that Advanced Manufacturing Modes are badly in need of implementing in enterprise are supported.Meanwhile the implementation of Advanced Manufacturing Modes also with
The foreign intervention factor such as government, intermediary is inseparable, when intervenes, how to intervene and intervenes and what degree arrived, also all
Need the theories integration of system.
11.2 research significances
On theory significance, the research of diffusing external intervention is summarized on the basis of the more data of crowd before the study herein
Method, first by diffusion research of the robust control theory applied to Advanced Manufacturing Modes, there is diffusing external intervention aspect
Certain innovation effect and directive significance, enriches diffusion theory and application.
In practice, the decision-making in relation to Advanced Manufacturing Modes not only is carried out to corporate decision maker and provides a kind of decision theory
Foundation, and there is important decision-making reference value to the implementation process of government driving Advanced Manufacturing Modes.
2.1 Advanced Manufacturing Modes are theoretical
2.1.1 Advanced Manufacturing Modes theory summary
Advanced manufacture, i.e. Advanced Manufacturing System, it combines Advanced Manufacturing Modes and advanced manufacturing technology, is one opposite
Compare widely concept.To it is advanced manufacture theory have deeper understanding, it is necessary first to distinguished Advanced Manufacturing System,
Advanced manufacturing technology, the concept and its relation of Advanced Manufacturing Modes three.
(1) Advanced Manufacturing System
Advanced Manufacturing System is advanced manufacturing technology and the synthesis of Advanced Manufacturing Modes, is to certain Advanced Manufacturing Modes
Explanation, be to one of certain manufacturing mode realization.Specifically refer to by coordinating to use advanced manufacturing technology and pattern, in matter
The various aspects such as amount, cost meet the market demand, reach the manufacture system of total optimization, and Advanced Manufacturing System can be used for industry
The all trades and professions of industry are manufactured, are the keys for improving product quality and efficiency.
(2) advanced manufacturing technology
Manufacturing technology refers to raw material and other production factors being converted into by rational processing finished product, semi-finished product
Technology group, is the general name of all production technologies used in manufacturing industry.Advanced manufacturing technology is on the basis of traditional manufacturing technology
It is upper, gather the new and high technology that a variety of advanced technologies grow up, it has merged traditional manufacturing technology, information technology, automatic
Change technology and modern management technology, obtain the general name of the manufacturing technology of preferable economic benefit and social benefit.
(3) Advanced Manufacturing Modes
Advanced Manufacturing Modes refer to combine different environmental condition and manufacturing objective, using advanced manufacturing technology, to various
Production factors are effectively organized, and to complete specific production task, realize a kind of advanced production side of good manufacturing effect
Method and organizational form.
In summary, in manufacturing industry, advanced manufacturing technology is the technology branch of Advanced Manufacturing Modes and Advanced Manufacturing System
Support, Advanced Manufacturing System is an application process of the enterprise to Advanced Manufacturing Modes, and Advanced Manufacturing Modes are advanced manufacturing technologies
The determinant of implementation result.Three complements each other, and interacts.The implementation of Advanced Manufacturing System, is actually advanced manufacture
The process that the diffusion process of pattern, i.e. Advanced Manufacturing Modes are chosen, apply.
2.1.2 Advanced Manufacturing Modes present Research
The research both at home and abroad to Advanced Manufacturing Modes is concentrated mainly on the following aspects at present：
(1) theoretical research of Advanced Manufacturing Modes.Such as Tao Yong by the analysis to world's advanced manufacturing industry development trend,
With reference to China's manufacturing industry present situation, elaborate to promote a kind of new method and viewpoint of China's development Advanced Manufacturing Modes.
(2) technical research of Advanced Manufacturing Modes.As Chen Quanpeng describes the related notion and hair of advanced manufacturing technology
Exhibition trend, and the development characteristic of advanced manufacturing technology is analyzed.The intension and feature to advanced manufacturing technology such as Luo Xun
Detailed elaboration has been carried out, and several advanced manufacturing technologies and developing direction have been discussed.
(3) application study of Advanced Manufacturing Modes.Such as Wang builds has carried out real example investigation to 98 enterprises, it is proposed that a kind of
It is integrated with the new thought of Advanced Manufacturing Modes and adaptability in tactics manufacturing strategy.
(4) the foreign intervention research of Advanced Manufacturing Modes diffusion.The diffusion to Advanced Manufacturing Modes is special first by Xue Chaogai etc.
Point and flooding mechanism are discussed, and the diffusion process of Advanced Manufacturing Modes monotype has been carried out modeling and emulated to divide
Analysis.Cao Haiwang etc. establishes the Controlling model of Advanced Manufacturing Modes monotype diffusion from the visual angle of Controlling model, and to institute
The Controlling model of foundation has carried out correlated performance analysis, has finally carried out the design of feedback controller simultaneously according to pole-assignment
Emulated.
In conclusion existing literature be related to Advanced Manufacturing Modes content be concentrated mainly on Advanced Manufacturing Modes it is theoretical,
Technology and its it is combined with diffusion theory using angle, rare document, is directed to the diffusion of Advanced Manufacturing Modes multi-mode
Foreign intervention is analyzed even more rare.Based on this, herein on the basis of fully research bibliography, choose the most effective
Method foreign intervention research is carried out to the diffusion of the multi-modes of Advanced Manufacturing Modes, carried for a variety of Advanced Manufacturing Modes of enterprise implement
For decision support, while the development for government regulation Advanced Manufacturing Modes provides theoretical foundation.
2.2 diffusion theory
2.2.1 diffusion theory is summarized
Diffusion theory, as one of theory the most classical in communication effect research, refers to by after a certain period of time, innovating
Via specific channel, the propagation in the member of a certain public organization.The main purpose of diffusion research is exactly to find some to do
Method shortens this process.By the substantial amounts of empirical studies of scholars, diffusion theory has had very big perfect, there is that oneself is only
Vertical a whole set of research method, data collection and analysis model.
Diffusion of innovation theory is to be proposed in the 1960s by Rogers, is one on being advised by way of medium
Take people and receive new idea, new things, the theory of new product.Know, persuade, certainly it considers that Process of Technical Innovation Diffusion should include at least
Fixed, implementation and definite 5 stages.Diffusion theory has invited numerous scholars to fall over each other to study since being suggested, and research field is very
Extensively, news, education, agricultural, society, economic dispatch various aspects are had been directed to.
2.2.2 diffusion theory present Research
Diffusion theory has attracted substantial amounts of scholars it to be unfolded in-depth study since being suggested, and can mainly divide
For the following aspects：
(1) research of diffusion theory." Innovation Diffusion " theory that good beautiful woman proposes for Rogers is such as heard to be explained, it is right
Four key factors and other new concepts proposed in theory are illustrated.Poplar has been inspected since two thousand for good fortune system
Latest developments and future trend of the west in terms of innovation in policy diffusion research, and China's concrete condition is explored.
(2) research of diffusion model.Such as open young tiger and be based on Theories of Technological Innovation, multinomial competing technology diffusion system is built
Model has been found, and has carried out substantial amounts of emulation experiment, has effectively demonstrated the feasibility of the diffusion model in practice.Such as Liu Fang
By being modeled analysis to the dispersal behavior of two kinds of competitive innovative products, suffered by two kinds of product market confusions of detailed examination
The influence arrived.
(3) research of Innovation Diffusion.Research to Innovation Diffusion be concentrated mainly on to innovative product diffusion research and
Research to innovative technology diffusion.For such as Xue Jun on the basis of diffusion of innovation theory, have studied, which influences consumer, selects interconnection
Three factors in net financial product path, and propose suggestion.Zhang Lei etc. combines the formation basic theory and feature of S type diffusion profiles,
Establishing one has four dimensions, unified innovative product diffusion research frame, and is made that evaluation.
2.3 robust control theory
Robust control theory refers in H∞In space (i.e. Hardy spaces), in order to obtain the controller with robust performance,
And to the H of some performance indicators∞A kind of control theory that Infinite Norm optimizes.H∞Norm is in robust optimal control theory
One of most effective performance indicator, the problem of in many Control System Designs, can be converted into make certain-H of closed loop Transitive Matrices∞
Norm minimum or less than some predetermined positive number problem.H∞The purpose of control is exactly to be controlled using nominal model G
The design of device K so that the H of controlled device stabilization and object function P∞Norm minimum.
Consider Robustness Criteria type problem as shown in Figure 1, wherein, u is the control input signal of system, and y is observed quantity, w
Signal is an externally input, z is controlled output signal.The generalized controlled object, K (s) are known as by the transmission function P (s) of u, w to z, y
Device in order to control.
Following formula is two kinds of representations of the state space realization of transmission function P (s),
Wherein, x, w, u, z are respectively n dimensions, r dimensions, p dimensions, m dimensional vectors, and y is q dimensional signals vector.
Closed loop transfer function, from w to z is equal to：
Tzw(s)=LFT (P (s), K (s))=P11+P12K(I-P22K)-1P21 (2)
Under standard state of a control, robust control problem to be solved can be divided into following three kinds of situations：
(1)H∞Optimal design Problem
Solve feedback controller K (s) meet closed loop transfer function, internal stability and | | Tzw(s)||∞Minimum, i.e.,
(2)H∞Suboptimal Design problem
Define γ (>=γ0), solve feedback controller K (s) and meet closed loop transfer function, internal stability, and | | Tzw(s)||∞
=γ0。
(3)H∞Standard design problem
Determine whether that there are feedback controller K (s) so that closed loop transfer function, internal stability, and | | Tzw(s)||∞＜ 1.
If in the presence of asking it.
The foundation and analysis of 4 diffusing external intervention models
The basic ideas of 4.1 Advanced Manufacturing Modes foreign interventions
The basic ideas of Advanced Manufacturing Modes foreign intervention modeling are as follows：The diffusions of Advanced Manufacturing Modes, external environment condition and
Foreign intervention forms a closed-loop system.The diffusion process of Advanced Manufacturing Modes is controlled device, to the outer of Advanced Manufacturing Modes
Portion intervenes the controller being consequently exerted in controlled device, and advanced manufacture mould can be effectively facilitated by designing foreign intervention strategy
The diffusion process of formula.As shown in Fig. 2, external influence factors can pass through diffusion of the designed controller to Advanced Manufacturing Modes
Process is regulated and controled, and to reach foreign intervention effect, promotes the quick diffusion of Advanced Manufacturing Modes.
The hypothesis of 4.2 Advanced Manufacturing Modes diffusion
Different from the diffusion of innovative product, innovative technology, Advanced Manufacturing Modes are diffused with the characteristics of it is unique, first system
The hypothesis of modeling formula foreign intervention modeling is as follows：
Assuming that 1：Enterprise only has the potentiality of certain scale that can just possess using Advanced Manufacturing Modes, this type enterprise can
To be divided into two classes, that is, have the ability not yet to implement the enterprise of Advanced Manufacturing Modes and potential impotentia implements Advanced Manufacturing Modes
Enterprise.Other enterprises are extremely difficult to this scale in a short time.That is, have the ability uses advanced manufacture within a certain period of time
The Number of Firms of pattern is certain, is represented in a model with permanent number.
Assuming that 2：It is in the same period interior to vie each other there are a variety of Advanced Manufacturing Modes, between them.
Assuming that 3：Compared with conventionally manufactured pattern, Advanced Manufacturing Modes have absolute advantage, and enterprise is in conditions permit
Tend to implement Advanced Manufacturing Modes.
Assuming that 4：Having been carried out the enterprise of certain Advanced Manufacturing Modes can be changed to another pattern, but this is converted
Journey needs the regular hour, i.e., enterprise can only use a kind of Advanced Manufacturing Modes in a short time.
Assuming that 5：Government can be intervened using diffusion of the various policies of regulation and control to Advanced Manufacturing Modes.
The foundation of 4.2 foreign intervention models
4.2.1 the Variational Design of diffusing external intervention model
Enterprise in Advanced Manufacturing Modes diffusion process can be divided into by following classification according to above-mentioned hypothesis：
(1)x1, have the ability that the enterprise of Advanced Manufacturing Modes is not carried out
(2)x2, the enterprise of potential impotentia implementation Advanced Manufacturing Modes
(3)y1, implement the enterprise of the first Advanced Manufacturing Modes
(4)y2, the enterprise ... of second of Advanced Manufacturing Modes of implementation
(5)yn, the enterprise of implementation n Advanced Manufacturing Modes.
Feature is spread according to Advanced Manufacturing Modes, number of the enterprise is certain i.e. x within a certain period of time1+x2+y1+y2+…
+yn=m, wherein m are enterprise's sum.
4.2.2 the foundation of diffusing external intervention model
In the starting stage of diffusion, above-mentioned all types of enterprises are all existing, their quantity is respectively x1, x2,
y1, y2..., yn, and the wherein potential Number of Firms that has no ability to is most, i.e. x2Numerical value is maximum.With the exhibition of diffusion process
Open, the quantity of all types of enterprises also changes therewith, and transforming relationship is as shown in Figure 3：
Graph of a relation between all types of enterprises according to Fig. 3, with reference to the diffusion model of Advanced Manufacturing Modes multi-mode, is examined
Consider external influence factors, using exterior pai n nursing factor as the input in foreign intervention model, that is, control variable u；Will be real
Apply the enterprise t moment cumulative number y of each Advanced Manufacturing Modes1, y2..., ynAs the output of foreign intervention model, they can be with
Express the diffusion velocity of various Advanced Manufacturing Modes；Meanwhile it will also implement each Advanced Manufacturing Modes enterprise t moment accumulated quantity weight
Newly mark is3, x4..., xn+2, with x1, x2Together, the state variable as foreign intervention system.Advanced manufacture can be established
Pattern multi-mode competition diffusion foreign intervention model such as following formula (3).
In model, q1k、q2kRefer to have the ability that enterprise x is not carried out1And the potential enterprise x of impotentia2To implementing, kth kind is advanced
The enterprise y of manufacturing modekThe conversion ratio of conversion；λ refers to enterprise x is not carried out by having the ability1To the potential enterprise x of impotentia2Conversion
Conversion ratio；θijRefer to the enterprise y by implementing i-th kind of Advanced Manufacturing ModesiTo the enterprise y for implementing jth kind Advanced Manufacturing Modesj
The conversion ratio of conversion, k1, k2..., knForeign intervention parameter of the mechanisms such as government to specific pattern intervention is represented respectively.Above formula
(3) in, a, b represent the ratio of capable enterprise and impotentia enterprise, a+b=1 respectively.
The analysis of 4.3 foreign intervention models
Next, we carry out the correlation analysis of foreign intervention model, i.e. n=by taking the competition diffusion of Three models as an example
3, x1+x2+x3+x4+x5=m, simplified model are as follows：
Wherein, 0≤x1, x2, x3, x4, x5, y1, y2, y3≤ m, 0≤q11, q12, q13, q21, q22, q23≤ 0, -1≤λ≤1, -1
≤θ12, θ13, θ21, θ23, θ31, θ32≤ 1,0≤a, b≤1, a+b=1.
4.3.1 stability analysis
Above-mentioned model (4) is an affine nonlinear system, and the quantitative solution of its analytical form hardly results in.But pass through sight
Examine the time-derivative understood in above-mentioned nonlinear systemOnly related with x, y, unrelated with variable t, therefore, above-mentioned radiation is non-
Linear system is an autonomous system, can analyze its equalization point and stability with Lyapunov Theory of Stability.Now carry out
Stability analysis is as follows：
(1) system balancing point is judged
If define 1 nonlinear systemIt is middle that there are a point Pi(xi, yi), meet f (xi, yi)=g (xi, yi)=
0, then claim PiFor an equalization point in nonlinear system.
The stability of system under exterior intervention model zero input state is judged according to above-mentioned theorem, can be by systematization
For the system of being shown below：
Above-mentioned equation group is solved using Matlab softwares, two equalization points for obtaining system are respectively P1=(0, m, 0,0,
0)、P2=(0,0, θ1M/ θ, θ2M/ θ, θ3M/ θ), wherein θ1=θ21θ31+θ21θ32+θ23θ31, θ2=θ12θ31+θ12θ32+θ13θ32, θ3
=θ13θ21+θ12θ23+θ13θ23, θ=θ1+θ2+θ3。
(2) the reduced linear matrix at equalization point is solved
If define 2 PiFor nonlinear systemAn equalization point, then nonlinear system is in PiYojan at point
Linearizing matrix is
According to definition 2, the reduced linear matrix of solving system is：
For equalization point P1=(0, m, 0,0,0), bringing above-mentioned matrix into can obtain,
For equalization point P2=(0,0, θ1M/ θ, θ2M/ θ, θ3M/ θ), bringing above-mentioned matrix into can obtain,
(3) stability of the system at equalization point is judged
According to Lyapunov theorems, nonlinear system is in equalization point PiAdequate condition in stable state is system in Pi
The characteristic value of the reduced linear matrix J at place is all less than zero.
P can be solved using Matlab softwares1、P2Locate the characteristic value of reduced linear matrix.
For point P1=(0, m, 0,0,0), it is q that can obtain an analytic solutions in its matrix exgenvalue21+q22+q23, by
In q21, q22, q23>=0, system is in equalization point P according to Lyapunov theorems1Locate unstable, i.e. P1(0, m, 0,0,0) is to be
The unstable node of system.
For point P2=(0,0, θ1M/ θ, θ2M/ θ, θ3M/ θ), the analytic solutions for obtaining its matrix exgenvalue are respectively λ1=-λ-
q11-q12-q13, λ2=-q21-q22-q23,
Wherein, θ1=θ31+θ13+θ23+θ32+θ21+θ12,θ3=θ13θ12+
θ12θ21+θ31θ32+θ23θ32+θ23θ21+θ31θ13.Consider above-mentioned restriction on the parameters limitation, it can be deduced that four characteristic values it is big
It is small to be respectively less than zero.Therefore equalization point P2(0,0, θ1M/ θ, θ2M/ θ, θ3M/ θ) be system stable node.
To sum up analysis is understood, equalization point P2(0,0, θ1M/ θ, θ2M/ θ, θ3M/ θ) be the unique stable node of system, i.e., pair
In arbitrarily meeting x1(0), x2(0), y1(0), y2(0), y3(0) starting point (x of ＞ 01(0), x2(0), y1(0), y2(0), y3
(0)), as t → ∞, x1(t) → 0, x2(t) → 0, y1(t)→θ1M/ θ, y2(t)→θ2M/ θ, y3(t)→θ3M/ θ, and y1+y2+
y3=m.Reflect in realistic model to be, when the dispersal behavior of Advanced Manufacturing Modes reaches stable, advanced manufacture to be not carried out
The enterprise of pattern is eliminated completely, all tends to implement Advanced Manufacturing Modes, and implement enterprise's number of three kinds of Advanced Manufacturing Modes
Mesh is up to stable state, is respectively θ1M/ θ, θ2M/ θ, θ3m/θ.These enterprises coexist in competitive market, and considerably long
Keep stablizing in a period of time, break this equilibrium state until there is more advanced manufacturing mode.This also with first system
The actual dispersion situation of modeling formula is more consistent.
4.3.2 the controllability analysis of foreign intervention model
The controllability of system refers to a kind of performance that the state variable of system can be by external input effect to control.If
In a limited time interval, deviate system balancing state some original state can not have by amplitude it is conditional defeated
Enter effect and return to equilibrium state, then it is to control to claim this original state.
Now it is analyzed as follows：
(1) nonlinear system approximate linearization
According to the method for nonlinear system approximate linearization, if system is in x0Point has f (x0)=0, then can be by system in x0
Point approximately linear turns to following form：
Wherein
It is as follows this paper foreign interventions can be modeled as to above-mentioned form according to the method：
(2) whether the necessary and sufficient condition for judging to control is set up
rank[B AB … An1B]=n is sufficient and necessary condition that Linear Time-Invariant System can be controlled.It is if non-after judgement
The approximate linearization system of linear system can be controlled at equalization point, then can draw nonlinear system part energy at equalization point
Control；If after judgement, the approximate linearization system of nonlinear system is not to control at equalization point, then can not judge that this is non-
The local controllability of linear system.
, can be according to judgment matrix [B AB A to system in this article2B A3B] order whether for 4 judge that it can be controlled
Property.Hereinafter listed parameter is brought into using Matlab softwares to understand, in equalization point P2(0,0, θ1M/ θ, θ2M/ θ, θ3m/θ)
Place, which is local controllability.Reflect in reality, as t=T, the enterprise that Advanced Manufacturing Modes are not carried out is complete
Portion implements Advanced Manufacturing Modes, and the enterprise for implementing three kinds of Advanced Manufacturing Modes coexists and number reaches stable state, for this
It is controllable for a state, this disperse state can be reached using controller.
4.3.3 the controllability analysis of foreign intervention model
Not all state variable can be measured or have its physical significance, therefore propose the concept of controllability.
If system is for T0At the moment, there are TaMoment, i.e. T0＜ Ta, according to [T0, Ta] when y (t) measured values that engrave can be uniquely true
System is determined in T0The original state x at moment0, then x is claimed0State can be seen for system.
Similar with controllability analysis, the ornamental method of discrimination of linear constant system is also applied for judging nonlinear system.
That is, if rank [C CA ... CAn-1]=n, then nonlinear system is considerable at equalization point.
, can be according to judgment matrix [C CA ... CA for this paper systemsn-1] order whether for 4 judge its controllability.Make
Bringing hereinafter parameter into Matlab softwares can draw, in equalization point P2(0,0, θ1M/ θ, θ2M/ θ, θ3M/ θ) place, this is non-thread
Sexual system is that part can be seen.Reflect in reality, as t=T, enterprise's whole implementation that Advanced Manufacturing Modes are not carried out is advanced
Manufacturing mode, and the enterprise for implementing three kinds of Advanced Manufacturing Modes coexists and number reaches stable state, is considerable in this state
, controller can be used to observe and estimate the state variable in diffusion process, reach this disperse state.
The dynamic structure that Advanced Manufacturing Modes foreign intervention herein controls can be expressed as shown in figure 4, the Fig. 4 is
The dynamic model of Advanced Manufacturing Modes diffusing external intervention.
Wherein, G is the diffusion model of Advanced Manufacturing Modes, is the controlled device in system；K is designed robust H∞
Controller, external input can act on diffusion model by the processing of K, realize the foreign intervention of Advanced Manufacturing Modes and influence；r
For the reference input during foreign intervention；E is such as enterprise since internal and external factors influence in Advanced Manufacturing Modes diffusion process
Systematic error caused by inside error etc.；U is the control input in foreign intervention model；D for Advanced Manufacturing Modes diffusion in by
Interference caused by external environment condition.
Since the foreign intervention process of Advanced Manufacturing Modes is in the case where itself has uncertainty, also there is outside
The influence of disturbing factor, introduces mixed sensitivity problem and carries out robust H here∞The design of controller.
Mixed sensitivity problem is established on the basis of minimum sensitivity problem and Problem of Robust Stability, is H∞Control
One of most typically problem of system.When perturbing to model in some point, the reflection of system external portion disturbance is as sensitive
Degree, and it is robust stability that stable ability is kept under external disturbance.Be between both of which it is conflicting, at this moment this
The improvement of invention is exactly that the design method for introducing Mixed Sensitivity is handled to compromise, and has not only considered robust performance requirement, but also protect
Robust stability index is demonstrate,proved.
The content of the invention
For the above situation, to overcome the defect of the prior art, the present invention provides a kind of Shandong of Advanced Manufacturing Modes diffusion
Stick controller, since the external disturbance process of Advanced Manufacturing Modes is in the case where itself has uncertainty, also there is outer
The influence of portion's disturbing factor, introduces mixed sensitivity problem and carries out robust H here∞The design of controller.
The technical scheme is that include the dynamic model of Advanced Manufacturing Modes diffusing external intervention, wherein from r to e,
The closed loop transfer function, of u to y is：
Weighting function W is added after error signal1, represent the constraint to whole foreign intervention system performance requirements, pass through
To W1Adjustment can effectively suppress the influence of foreign intervention, obtain the signal results for wishing to export；Add and add after controller
Weight function W2, represent limitation of the system to Additive Generator, the constraint to exterior intervention signal amplitude can be regarded as；In quilt
Weighting function W is added after control system3, expression system is to the probabilistic limitation of multiplying property, by Advanced Manufacturing Modes diffusion model sheet
Body characteristic is determined；W1、W2、W3Output signal be whole foreign intervention system evaluation signal；
The standard card cage of mixed sensitivity problem for considering weighting function is：
In formula,W1, W2, W3--- weighting matrix；I --- unit matrix；U=Ke, wherein, K ---
Controller gain battle array；
The generalized object that controlled system can be obtained by above formula is
Its time domain space expression formula is
Formula (13), two kinds of expression ways of formula (14) can mutual inversion of phases.
The closed-loop system transfer function matrix formed is
In formula, W1S represents the performance requirement to exterior interfering system, W2R and W3T is represented and system robust stability is wanted
Ask.Mixed sensitivity problem is exactly to obtain a true rational function controller K so that adds W1、W2、W3Advanced manufacture mould
Closed-loop system shown in the dynamic model of formula diffusing external intervention is stablized, and meets | | P | |∞The condition of ＜ 1.
Mixed sensitivity problem is established on the basis of minimum sensitivity problem and Problem of Robust Stability, is H∞Control
One of most typically problem of system.When perturbing to model in some point, the reaction of system external portion disturbance is as sensitive
Degree, and it is robust stability that stable ability is kept under external disturbance.It is conflicting, the present invention between both of which
The design method for introducing Mixed Sensitivity is handled to compromise, and had both been considered robust performance requirement, and in turn ensure that robust stability index.
Brief description of the drawings
Fig. 1 is standard H∞Control problem structure chart.
Fig. 2 is Advanced Manufacturing Modes flooding mechanism and its graph of a relation of control.
Transforming relationship figures of the Fig. 3 between different type enterprise.
Fig. 4 is the Dynamic structure diagram of Advanced Manufacturing Modes diffusing external intervention.
Fig. 5 is H in the present invention∞The illustraton of model of standard design problem.
Fig. 6 is system sensitivity function S and weight function W in the present invention1Graph of a relation.
Fig. 7 is system mending sensitivity function T and weight function W in the present invention3Graph of a relation.
Fig. 8 is the frequency characteristic figure of controller K in the present invention.
Embodiment
The embodiment of the present invention is described in further detail below in conjunction with attached drawing 1-8.
In the present invention：
5. the design of robust controller
5.1 mixed sensitivity optimization problems
The dynamic structure of Advanced Manufacturing Modes foreign intervention control in the present invention can be expressed as shown in Figure 4：
Wherein, G is the diffusion model of Advanced Manufacturing Modes, is the controlled device in system；K is designed robust H∞Control
Device processed, external input can act on diffusion model by the processing of K, realize the foreign intervention of Advanced Manufacturing Modes and influence；R is
Reference input during foreign intervention；E is since internal and external factors influence in Advanced Manufacturing Modes diffusion process, in enterprise
Systematic error caused by portion's error etc.；U is the control input in foreign intervention model；D is by outer in Advanced Manufacturing Modes diffusion
Interference caused by portion's environment.
Since the foreign intervention process of Advanced Manufacturing Modes is in the case where itself has uncertainty, also there is outside
The influence of disturbing factor, introduces mixed sensitivity problem and carries out robust H here∞The design of controller.
Mixed sensitivity problem is established on the basis of minimum sensitivity problem and Problem of Robust Stability, is H∞Control
One of most typically problem of system.When perturbing to model in some point, the reflection of system external portion disturbance is as sensitive
Degree, and it is robust stability that stable ability is kept under external disturbance.It is conflicting between both of which, at this moment may be used
Handled with introducing the design method of Mixed Sensitivity to compromise, both considered robust performance requirement, and in turn ensure that robust stability
Index.
To structure shown in Fig. 4, weighting function W is introduced1、W2、W3Carry out the analysis of mixed sensitivity optimization design problem.This
When, the H of Advanced Manufacturing Modes diffusing external interfering system∞The model of standard design problem is as shown in Figure 5.
In upper figure, from r to e, the closed loop transfer function, of u to y is
W1The constraint to whole foreign intervention system performance requirements is represented, by W1Adjustment can effectively inhibit it is outer
The influence of portion's interference, obtains the signal results for wishing to export；W2It is limitation of the system to Additive Generator, can sees herein
Into being constraint to exterior intervention signal amplitude；W3Be system to the probabilistic limitation of multiplying property, it is by Advanced Manufacturing Modes
Diffusion model self character is determined；z1、z2、z3For the evaluation signal of whole foreign intervention system.
The standard card cage of mixed sensitivity problem for considering weighting function is
In formula,W1, W2, W3--- weighting matrix；I --- unit matrix；U=Ke, wherein, K ---
Controller gain battle array.
The generalized object that controlled system can be obtained by above formula is
Its time domain space expression formula is
Formula (13), two kinds of expression ways of formula (14) can mutual inversion of phases.
The closed-loop system transfer function matrix formed is
In formula, W1S represents the performance requirement to exterior interfering system, W2R and W3T is represented and system robust stability is wanted
Ask.Mixed sensitivity problem is exactly to obtain a true rational function controller K so that closed-loop system shown in Fig. 5 is stablized, and full
Foot | | P | |∞The condition of ＜ 1.
Diffusion by Advanced Manufacturing Modes and the external environment condition residing for it regard a complete closed-loop control system as, will be outer
Intervene the control process regarded as to Advanced Manufacturing Modes diffusion in portion.The diffusion of Advanced Manufacturing Modes is controlled device, foreign intervention
Determine controller design.Controller design is exactly to determine that control law makes as defined in system satisfaction for given controlled system
Performance indicator requirement, or it is optimal some or some indexs of system.Control action rule is feedback form, control signal
Dependent on the response of system, it reflects response and the difference of expected response of system, and makes system response as close possible to actual sound
Should.The physical characteristic of system is described using the state variable of internal system, the whole that the state of system contains system is moved
State information.Designed robust controller acts on diffusion model, realizes the foreign intervention of Advanced Manufacturing Modes and influences；It can give
Determine the reference input during foreign intervention.Due to Advanced Manufacturing Modes foreign intervention process itself have it is probabilistic
In the case of, the influence also there is external interference factor, introduces mixed sensitivity problem and carries out robust H∞The design of controller.It is mixed
Sensitivity problem is closed to establish on the basis of minimum sensitivity problem and Problem of Robust Stability.When to Advanced Manufacturing Modes
Some point is diffused in when being perturbed, the reflection of system external portion disturbance is sensitivity, and is kept under external disturbance steady
Fixed ability is robust stability.It is conflicting between both of which, the design method of Mixed Sensitivity can be introduced
Come processing of compromising, robust performance requirement was both considered, in turn ensure that robust stability index.Weighting letter is added after error signal
Number W1, the constraint to whole foreign intervention system performance requirements is represented, by W1Adjustment can effectively inhibit external disturbance
Influence, obtain wish export signal results；Weighting function W is added after controller2, represent system to Additive Generator
Limitation, the constraint to exterior intervention signal amplitude can be regarded as；Weighting function W is added after controlled system3, represent system
To the probabilistic limitation of multiplying property, determined by Advanced Manufacturing Modes diffusion model self character；W1、W2、W3Output signal
For the evaluation signal of whole foreign intervention system.
The design of 5.2 controllers
5.2.1 model major parameter
Three kinds of supply chain management, green manufacturing, total quality control manufacturing modes are chosen herein for the imitative of model system
True analysis.The no intuitively data of Number of Firms due to implementing these three Advanced Manufacturing Modes, herein by national A grades of thing
The number of manufacturing enterprise is flowed as the Number of Firms for implementing supply chain management；The Number of Firms of ISO14001 environmentals will be passed through
As the Number of Firms for implementing green manufacturing mode；Implement comprehensive matter by being used as by the Number of Firms of ISO9001 quality authentications
The Number of Firms of buret reason.By inquiring about the dependency numbers such as China Federation of Logistics ＆ Purchasing, Environmental Protection Department environmental center
According to, and data are carried out with arrangement and draws all types of Number of Firms as shown in table 1.
Table 1 uses national enterprise's number of three kinds of Advanced Manufacturing Modes
By 1 data of upper table, using 2011 as starting point, enterprise of three kinds of manufacturing modes in 2011 in table 1 is chosen
Number 1506,1751,2840, respectively as y1, y2, y3Initial value.In conjunction with the issue situation of China Statistical Yearbook 2016,
Large and medium-sized enterprise's sum 63703 is used as m values, and large enterprise's number 9633 subtracts the enterprise using three kinds of Advanced Manufacturing Modes in 2011
Industry sum is used as x1Initial value, medium-sized enterprise's number 54070 are used as x2Initial value, number institute of loss-making enterprise accounting in large enterprise
Example 0.15 is a values in model.The optimization algorithm being previously mentioned using document can be determined to use parameter such as table 2 below in model：
Used relevant parameter in 2 model of table
5.2.2 computing system nominal coefficient matrix
The nominal of controlled device in Advanced Manufacturing Modes foreign intervention system can be obtained by each parameter value calculation of upper section
State Equation Coefficients matrix is as follows：
5.2.3 the selection of weighting function
W1(s) be sensitivity function characteristic reflection, be to be determined by the performance requirement of system.Missed to reduce tracking
Difference, suppress interference effect, it is necessary to assure sensitivity function as small as possible.It can choose
W2(s) size of controlled quentity controlled variable can be effectively limited, avoids the infringement to actuator.It can choose
W2(s)=0.00001 (17)
W3(s) be sensitivity function characteristic reflection, when selection must assure that molecule higher than this condition of denominator.It can select
Take
W3(s)=0.00001 (2s+0.01) (18)
5.2.4 the calculating of controller
By can be calculated H∞The state space realization of the generalized object of standard design problem is
Using Matlab robust control tool box, controller can obtain
5.3 controller performances detect
Discussed from 5.1 joints, W1S is the reflection of system performance, should be met | | W1S||∞This necessary condition of ＜ 1, i.e., it is full
FootOrFrom fig. 6 it can be seen that system meets conditionSo the controller of design meets the requirement of system performance.
W3T is the reflection to system robustness, should be met | | W3T||∞This necessary condition of ＜ 1, that is, meetOrIt can be seen from figure 7 that system meets conditionSo designed controller meets the requirement of robustness.
Fig. 8 is the frequency characteristic of designed controller.As can see from Figure 8, controller frequency characteristic is declining
During, recessed low gain suddenly can be presented for some time, the influence of interference can be again in this low gain time
It is effectively suppressed.Meanwhile by observing the transmission function relational expression of controller, designed robust H∞The zero point of controller is equal to first
Limit after being linearized into manufacturing mode diffusion model.So the two is offseted in mechanism, system pole is realized
Reconfigure, ensured the robust stability of whole system.
To sum up analysis result understands that the weighting function selected in this model is relatively reasonable, meets to weight letter in Robust Analysis
Several selection principle.And obtained controller is analyzed by Mixed Sensitivity can produce control effect well, have very
System performance and robust stability well.
Claims (1)
1. a kind of robust controller of Advanced Manufacturing Modes diffusion, it is characterised in that done including Advanced Manufacturing Modes diffusing external
Pre- dynamic model, wherein from r to e, the closed loop transfer function, of u to y is：
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Weighting function W is added after error signal1, the constraint to whole foreign intervention system performance requirements is represented, by W1's
Adjustment can effectively suppress the influence of foreign intervention, obtain the signal results for wishing to export；Weighting function is added after controller
W2, represent limitation of the system to Additive Generator, the constraint to exterior intervention signal amplitude can be regarded as；In controlled system
Weighting function W is added afterwards3, expression system is to the probabilistic limitation of multiplying property, by Advanced Manufacturing Modes diffusion model self character
Determined；W1、W2、W3Output signal be whole foreign intervention system evaluation signal；
The standard card cage of mixed sensitivity problem for considering weighting function is：
In formula,W1, W2, W3--- weighting matrix；I --- unit matrix；U=Ke, wherein, K --- controller
Gain battle array；
The generalized object that controlled system can be obtained by above formula is
Its time domain space expression formula is
Formula (13), two kinds of expression ways of formula (14) can mutual inversion of phases.
The closed-loop system transfer function matrix formed is
<mrow>
<mi>P</mi>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
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In formula, W1S represents the performance requirement to exterior interfering system, W2R and W3T represents the requirement to system robust stability.It is mixed
It is exactly to obtain a true rational function controller K to close sensitivity problem so that adds W1、W2、W3Advanced Manufacturing Modes diffusion
Closed-loop system shown in the dynamic model of foreign intervention is stablized, and meets | | P | |∞The condition of ＜ 1.
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