CN101078912A - Self-adaptive fuzzy control system design method - Google Patents

Abstract

The invention discloses a designing method of self-adaptive ambiguity controlling system, which comprises the following steps: choosing controlled member reserve dynamics mode; importing into vector; proceeding fuzzy partition for initial sample book collection of the importing vector; using fuzzy regulation; realizing reserve dynamics course mapping of the controlled member; identifying reserve dynamics fuzzy regulation of the controlled member; using as initial controlled regulation; refreshing the sample book collection of the importing vector with on-line data; proceeding fuzzy divide repeatedly; identifying on-line; getting reverse dynamics fuzzy regulation of the controlled object; refreshing the controlled regulation; constructing the self-adaptive controlling system based on revere dynamics fuzzy regulation. This invention can improve self-adaptive ability of the controlled system.

Description

A kind of method for designing of self-adaptive fuzzy control system

Technical field

The invention belongs to the field that industrial process is controlled, relate in particular to fuzzy control technology industrial process.

Background technology

In industrial process control technology field, a kind of mathematical models that does not need controlling object is arranged, and directly adopt the fuzzy control method and the control corresponding system thereof of the control of language type control law implementation procedure.

Fuzzy control rule is the core of Fuzzy control system.At present, in existing design of Fuzzy Control process, the design of fuzzy control rule mainly based on people to the conclusion of the fuzzy message of controlled process understanding and the summary of operating experience.For the time Complex Nonlinear System that becomes when adopting fuzzy control because the fuzzy control rule that produces according to the operation experience is too coarse unavoidably or perfect inadequately, be difficult to obtain good control effect.When the operation experience of controlling object more after a little while, it is very difficult to design the satisfied Fuzzy control system of an effect, even can't apply fuzzy control to this type of controlling object.

Owing between each quantizing factor of Fuzzy control system very strong coupling is arranged, adopt method of trial and error usually or adopt priori to determine quantizing factor again, therefore, its control effect also may not be desirable in working control.

When nonlinear and time-varying system is adopted fuzzy control,, require Fuzzy control system to have than perfect control rule and adaptive ability in order to obtain good control effect.How the structure or the parameter of online effectively adjusting fuzzy control rule make it to adapt with controlling object, also are present design of Fuzzy Control field fine solution major issues not as yet.

The control law of classical Fuzzy control system derives from operator's operating experience.Usually the operator can only provide the two-dimentional fuzzy control rule of one group of following form mostly:

If (controlled variable deviation is e _i, controlled variable deviation variation rate is ec _i) the (controlled quentity controlled variable is u _i)

Controlling object for some more complicated, in order effectively to improve control performance, often need the input information of more object trip information (as the historical information of controlled quentity controlled variable, the historical information of controlled variable, the following information of desired controlled variable etc.) as control system.When the input dimension of controller greater than 3 the time, by operating personnel fuzzy control rule is set up in the summary of the conclusion of the fuzzy message of controll plant understanding and operating experience and will be become very difficult, or even out of the question.Because people are no more than three-dimensional usually to the logical thinking of a certain concrete things.Therefore, the effective information that obtains in the how integrated use control procedure, structure is suitable for the control law of complex object, is another major issue that exists in the present rule-based Control System Design.

Summary of the invention

The objective of the invention is, overcome the existing deficiency of Fuzzy control system aspect method for designing, a kind of method for designing of self-adaptive fuzzy control system is provided.This method for designing can be broken away to the dependence of operation experience and to fuzzy controller and import the restriction of dimension, and can guarantee that control system has the good adaptive ability.

Realize that described goal of the invention technical scheme is a kind of like this method for designing of self-adaptive fuzzy control system, this method for designing comprises the design procedure that utilizes fuzzy rule that industrial process is controlled.Improvement of the present invention is, obtaining of control law is summed up as the inverse dynamics process fuzzy recognition problem of controlling object, by identification directly produces fuzzy control rule based on the inverse dynamics fuzzy rule.Its method for designing comprises the steps:

(1) selects the structure of controlling object inverse dynamics model input vector, and utilize off-line data, form the sample set X that comprises N input vector;

(2) adopt the entropy method of birdsing of the same feather flock together that input vector sample set X blur divisions, with the regional center of each local data in definite input vector space and zone radius;

(3) utilize fuzzy rule to realize the mapping process of controlling object inverse dynamics, obtain controlling object inverse dynamics fuzzy rule by the recursive least-squares discrimination method, and with this inverse dynamics fuzzy rule as initial fuzzy control rule;

(4) utilize the input vector x (k) of the online current time k that obtains, existing input vector sample set X is refreshed, and utilize the method for birdsing of the same feather flock together of the entropy described in the step (two) that input vector sample set X is blured division again, redefine each local data center, zone and the zone radius in input vector space;

(5) utilize the online acquisition controlling object of step (three) inverse dynamics fuzzy rule, and with this fuzzy rule as control law, structure is based on the adaptive control system of inverse dynamics fuzzy rule.

The superiority of method for designing provided by the present invention is:

1. owing to obtaining of control law is summed up as the inverse dynamics process fuzzy recognition problem of controlling object, by the identification of controlling object inverse dynamics process fuzzy rule, directly produce the control law that adapts with the controlling object characteristics of motion, thereby broken away from traditional design of Fuzzy Control method the dependence of operation experience and the restriction of fuzzy controller being imported dimension;

2. owing to, control law is carried out online adjustment, the characteristic of control law and controlling object is adapted, thereby guaranteed the adaptive ability of control system according to controlling object inverse dynamics process fuzzy rule model on-line identification result;

3. again because fuzzy control rule is directly to produce according to the identification of controlling object inverse dynamics fuzzy rule, and then broken away from the puzzlement that quantizing factor is selected in traditional design of Fuzzy Controller method.

The present invention is further illustrated below in conjunction with accompanying drawing.

Description of drawings

Fig. 1 is the basic flow sheet based on the Adaptive Control System Design method of inverse dynamics fuzzy rule.

Fig. 2 is based on the adaptive controller of inverse dynamics fuzzy rule and control system structural drawing.

Fig. 3 is a steam temperature PID cascade control system structural drawing as a comparison.

Fig. 4 is the basic Fuzzy control system structural drawing of steam temperature as a comparison.

Fig. 5 when adopting different controller, the step response family curve of superheater outlet temperature under 100% load.

Fig. 6 when adopting different controller, the step response family curve of superheater outlet temperature under 75% load.

Embodiment

A kind of method for designing of self-adaptive fuzzy control system, this method for designing comprises the design procedure that utilizes fuzzy control rule that industrial process is controlled.Fuzzy control rule among the present invention is based on the direct control law that produces of the identification of controlling object inverse dynamics fuzzy rule, and its method for designing comprises the steps (with reference to figure 1):

(1) selects the structure of controlling object inverse dynamics model input vector, and utilize off-line data, form the sample set X that comprises N input vector;

(2) adopt the entropy method of birdsing of the same feather flock together that input vector sample set X blur divisions, with the regional center of each local data in definite input vector space and zone radius;

(3) utilize fuzzy rule to realize the mapping process of controlling object inverse dynamics, obtain controlling object inverse dynamics fuzzy rule by the recursive least-squares discrimination method, and with this inverse dynamics fuzzy rule as initial fuzzy control rule;

(4) utilize the input vector x (k) of the online current time k that obtains, existing input vector sample set X is refreshed, and utilize the method for birdsing of the same feather flock together of the entropy described in the step (two) that input vector sample set X is blured division again, redefine each local data center, zone and the zone radius in input vector space;

(5) utilize the online acquisition controlling object of step (three) inverse dynamics fuzzy rule, and with this fuzzy rule as control law, structure is based on the adaptive control system of inverse dynamics fuzzy rule.

Further, the present invention is said controlling object inverse dynamics model in step (), is the historical and following expectation information according to controlling object, and inverting current time k should impose on a kind of mapping relationship f of the controlled quentity controlled variable u (k) of controlling object, that is:

u(k)＝f[x(k)]

X in the formula (k) is the input vector at current time k controlling object inverse dynamics model; This input vector x (k) is by the historical data time series vector u of controlled quentity controlled variable u _-, controlled variable y historical data time series vector y _-Following time series vector y with desired controlled variable y ₊Constitute, that is:

$x\left(k\right)={[u_{-}^T,y_{-}^T,y_{+}^T]}^T$ Formula (1)

Vector u _-, y _-And y ₊Determine in the following manner:

u _-＝[u(k-1)，u(k-2)，…，u(k-k ₁)]

y _-＝[y(k)，y(k-1)，y(k-2)，…，y(k-k ₂)]

y ₊＝[y(k+1)，y(k+2)，…，y(k+k ₃)]

K wherein ₁, k ₂+ 1 and k ₃Be respectively the time series number of corresponding vector.

The following time series vector y of controlled variable ₊Setting value y according to controlled variable y _SpPress following formula recursion structure with the current output y (k) of controlling object:

Y (i+1)=ω y (i)+(1-ω) y _Sp(i=k, k+1 ..., k+k ₃-1) formula (2)

ω ∈ (0,1) wherein.ω is big more, and the robustness of control system is strong more, but the rapidity variation of control.In the design of Controller process, should weigh according to requirement, to determine the size of ω to the rapidity of the robustness of control system and control procedure.

According to formula (1), as each time series vector u _-, y _-And y ₊Concrete formation determine after, the structure of controlling object inverse dynamics model input vector x (k) is also determined thereupon.

Further say, the present invention's said employing entropy in step (two) method of birdsing of the same feather flock together is blured division to input vector sample set X, in the process with regional center of each local data that determines the input vector space and zone radius, be to utilize off-line data, form the sample set X that comprises N input vector x:

x＝{x(k-N+1)，x(k-N+2)，…，x(k-1)，x(k)}

At first determine i and j input vector data x _iAnd x _jBetween phase recency S _Ij:

$s_{\mathrm{ij}}=s(x_i,x_j)=e^{-\mathrm{\α}\left|\right|x_i-x_j\left|\right|}$ (i=1,2 ..., N; J=1,2 ..., N, the formula (3) of i ≠ j)

Further by phase recency S _IjDetermine the entropy E of each sample of input vector _j:

$E_j=\underset{i=1,i\≠j}{\overset{N}{\mathrm{\Σ}}}{s}_{\mathrm{ij}}{\log }_2{s}_{\mathrm{ij}}+(1-s_{\mathrm{ij}}){\log }_2(1-s_{\mathrm{ij}})$ Formula (4)

In the formula, α=-ln (0.5/ σ), σ represents the mean distance of data;

Given decision-making constant β ∈ [0,1] is with corresponding min (E _j) input vector x _jCenter c as the local data zone ₁From sample set X, remove and satisfy S (x _i, c ₁The sample of)＞β repeats this process, and sample set X is an empty set, determines the initial center c in n local data zone _i, (i=1,2 ..., n);

Obtaining input center c _iAfter, determine the radius r of each input area as follows _i:

1. initial input radius r is set _i=0 (i=1,2 ..., n);

2. select one the input sample data x (k) (k=1,2 ..., N), determine nearest with it input center c _s, refresh with this center c _sRadius r for the input area at center _s:

‖x(k)-c _s‖＝min‖x(k)-c _i‖

r _s＝max(‖x(k)-c _s‖，r _s)(s＝1，2，…，n)

According to the regional interface that said method obtained is the hypersphere with different radii, and its radius is by the sample decision farthest that belongs to this zone.In each zone, not only comprise one's own sample, and contain the sample of adjacent domain, the zone boundary is overlapped, has ambiguity.

Again further, in the said step of the present invention (three), in the process that realizes the mapping of controlling object inverse dynamics, the i bar fuzzy rule R of its controlling object inverse dynamics model _iFor:

$R_i:\mathrm{if\; x}\left(k\right)\∈(c_i,r_i)\mathrm{then}{u}_i={\mathrm{\θ}}_i^T[1,{x\left(k\right)}^T]$ (i=1,2 ..., n) formula (5)

X wherein (k) is the input vector of inverse dynamics model, c _iAnd r _iBe i local data input center and radius; θ _iBe parameter vector to be identified; u _iIt is the output center of gravity of i bar fuzzy rule correspondence;

For given input vector x (k), determine each zone output center of gravity u by this fuzzy rule _i, adopt following fuzzy reasoning inverting should put on the controlled quentity controlled variable u (k) of system constantly at k:

$u\left(k\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\left(w_i{u}_i\right)/\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{w}_i,(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{w}_i\≠0)$ Formula (6)

Perhaps

$u\left(k\right)=w_a{u}_a+w_b{u}_b,(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{w}_i=0)$ Formula (7)

Wherein, the weight coefficient w in each input vector zone _iDepend on input vector x (k) and each regional area center c _iBetween distance:

$w_i=\left\{\begin{array}{cc}1-\left|\right|x\left(k\right)-c_i\left|\right|/r_i,& \mathrm{if}\left|\right|x\left(k\right)-c_i\left|\right|\&le;{\mathrm{<figure-callout\; id="0"\; label="r\; i"\; filenames="A20071007868900172.png"\; state="\{\{state\}\}">r</figure-callout>}}_i\\ 0,& \mathrm{if}\left|\right|x\left(k\right)-c_i\left|\right|>r_i\end{array}\right.$ Formula (8)

In the formula, u _aAnd u _bThe output center of gravity of expression and nearest two input areas of input vector x (k) respectively; w _aAnd w _bBe respectively corresponding weight coefficient, they are defined by following formula:

$w_a=\frac{d_a}{d_a+d_b},w_b=\frac{d_b}{d_a+d_b}$

d _aAnd d _bExpression input vector x (k) and two nearest input area center c _aAnd c _bDistance:

d _a＝‖x(k)-c _a‖＝min‖x(k)-c _i‖(i＝1，2，…，n)

d _b＝‖x(k)-c _b‖＝min‖x(k)-c _i‖(i＝1，2，…，n?and?i≠a)

Controlling object inverse dynamics fuzzy rule Model parameter vector θ _i, according to currency y (k) and its desired value y of controlled variable _SpBetween deviation, refresh by recursive least-squares on-line identification method.

Again further, the said self-adaptive fuzzy control system based on the inverse dynamics fuzzy rule of the present invention (with reference to figure 2) is made of FRID controller, reference locus model, tapped delay line TDL and Be Controlled object.

Wherein, the FRID controller is the adaptive controller based on the inverse dynamics fuzzy rule, and it is output as controlled quentity controlled variable u (k), and it is input as current time controlling object inverse dynamics process model input vector x (k), and this vector is by u _-, y _-And y ₊Constitute, promptly

$x\left(k\right)={[u_{-}^T,y_{-}^T,y_{+}^T]}^T$

The effect of reference locus model be according to:

y(i+1)＝ωy(i)+(1-ω)y _sp (i＝k，k+1，…，k+k ₃-1)

Setting value y according to controlled variable y _SpThe following time series vector y of current output y (k) recursion structure controlled variable with controlling object ₊The effect of tapped delay line TDL (totally two) is by data being stored and operation such as delay, is the required vector form of FRID controller with data conversion, forms the historical data time series vector u of controlled quentity controlled variable u respectively _-Historical data time series vector y with controlled variable y _-

When online obtain a new input vector x (k) after, need the input vector sample set X of previous moment be refreshed, when adding up-to-date sample x (k) therein, eliminate wherein a sample the earliest, keep total number of samples N constant, obtain new samples collection X:

X＝{x(k-N+1)，x(k-N+2)，…，x(k-1)，x(k)}

New samples collection X for obtaining blurs division by preceding method, and on-line identification controlling object inverse dynamics fuzzy rule Model parameter vector θ _i, form new control law.

In self-adaptive fuzzy control system method for designing involved in the present invention, acquisition for initial control rules can be selected one of two kinds of following methods: 1. utilize the test findings of controlling object to produce the initial sample set X of input vector, obtain initial control rules; 2. utilize the correlation model of controlling object to estimate the initial sample set X of input vector, obtain initial control rules.

Need explanation, because in self-adaptive fuzzy control system method for designing provided by the present invention, in each sampling instant all according to the controlled quentity controlled variable of online acquisition and the current information of controlled variable, input vector sample set X and control law are refreshed, so levels of precision of the initial sample of input vector, control performance for controller there is no materially affect, whether the test findings (or controlling object model) that promptly is used to produce the initial sample of input vector is accurate, there is no materially affect for the performance of control system.

Below in conjunction with above-mentioned embodiment, further specify concrete application process of the present invention and superiority with the method that contrasts.

In contrast verification, the Be Controlled object is the high temperature superheater of a 600MW supercritical pressure boiler, and controlled variable y is a superheater outlet superheat steam temperature, and controlled quentity controlled variable u is the spray flow that places the direct-contact desuperheater of superheater import.At present, in actual engineering, generally adopt cascade PID control system (with reference to figure 3) that this type of steam temperature object is controlled.

Mathematical model such as the table 1 of controlling object under different load.

Steam temperature object model under table 1 different load

Wherein the input u of object leading section model is the variable quantity (kg/s) of desuperheater spray flow, be output as leading district vapor (steam) temperature variable quantity (℃); The variable quantity that is input as leading district outlet steam temperature of inertia section model (℃), output y be the superheater outlet steam temperature variable quantity (℃).

Select the input vector of inverse dynamics fuzzy rule model to be:

X (k)=[u (k-2), u (k-1), y (k-1), y (k), y (k+1), y (k+2)] formula (9)

Press the following time series vector y of following formula recursion structure controlled variable according to formula (2) ₊:

Y (i+1)=0.9y (i)+0.1y _Sp(i=k, k+1) formula (10)

The controlling object inverse dynamics model is output as spray flow u (k).Utilize the mathematical model of controlling object under 100% load, produce 30 primary data samples, constitute the initial sample set X of input vector, depend on plan constant β=0.03, initial sample set X blurs division to input vector, obtains the zone number n of local data in original input vector space, the input center c in each zone respectively _iWith zone radius r _i:

n＝3

c ₁＝[-0.9540?-0.8585?-1.5125?-1.5284?-1.5384?-1.5366] ^T

c ₂＝[-0.9240?-0.6904?-1.3930?-1.4277?-1.4592?-1.4964] ^T

c ₃＝[0.6869?0.6946?-0.0763?-0.0828?-0.0922?-0.1045] ^T

r ₁＝1.5998 r ₂＝2.1632 r ₃＝2.8940

Utilize the least square method of recursion identification to determine controlling object inverse dynamics fuzzy rule Model parameter vector θ _iObtain the initial inverse dynamics fuzzy rule of controlling object:

R ₁：if?x∈(c ₁，1.5998)then

u ₁＝-0.2181+1.4627u)(k-2)-0.4706u(k-1)+0.5530y(k-1)-

-0.2320y(k)+0.1660y(k+1)+0.4885y(k+2)

R ₂：if?x∈(c ₂，2.1632)then

u ₂＝0.0047+2.0401u(k-2)-1.0574u(k-1)+0.0725y(k-1)+

+0.0261y(k)-0.0303y(k+1)-0.0684y(k+2)

R ₃：ifx∈(c ₃，2.8940)then

u ₃＝-0.0032+2.0114u(k-2)-1.0285u(k-1)+0.0883y(k-1)-

-0.0388y(k)-0.0374y(k+1)-0.0149y(k+2)

With above-mentioned inverse dynamics fuzzy rule as initial fuzzy control rule.

By the y (k) of the current time k of online acquisition and the historical information of u and y, produce a new input vector x (k) by formula (9) and formula (10), press following formula and construct new input vector sample set X:

x＝{x(k)，x(k-1)，…，x(k-29)}

X is blured division, and according to least square method of recursion on-line identification fuzzy rule Model parameter vector θ _i, produce new inverse dynamics fuzzy rule; Inverse dynamics fuzzy rule with new generation replaces original control law, utilizes formula (6)～(8) to carry out fuzzy reasoning, obtains to form the adaptive control system based on the inverse dynamics fuzzy rule at the controlled quentity controlled variable u of current time (k).

Set-point y when overheated steam temperature _SpWhen unit step increases, the response characteristic of the steam temperature object under the different load is seen curve 3 among Fig. 5～Fig. 6 according to the controller (being the FRID controller) of the inventive method design.

In order to investigate and compare the control performance of the designed control system of the present invention, in Fig. 5～Fig. 6, also provided the cascade PID control system (with reference to figure 3) of overheating steam temperature routine and basic Fuzzy control system (with reference to figure 4) control procedure response curve (curve 1 among Fig. 5～Fig. 6 and curve 2) simultaneously to the steam temperature object under the different load.

The master controller of the conventional PID cascade control system of overheating steam temperature is the PID controller, and submaster controller is the P controller; These two controllers are all adjusted by 100% load model, and best setting parameter is: master controller proportional band δ ₂=0.83, master controller T integral time _i=94.8s, master controller T derivative time _d=23.7s; Submaster controller proportional band δ ₁=0.04.

The fuzzy control rule table 2 of basic fuzzy controller.Basic fuzzy controller quantizing factor is taken as: ke=0.05, kec=8, ku=0.05; This group quantizing factor can guarantee that object obtains gratifying control performance under 100% load.

Table 2 fuzzy control rule table

The above embodiments show, the adaptive controller based on the inverse dynamics fuzzy rule provided by the present invention even adopt less relatively control law, also can obtain to control preferably effect; When plant characteristic generation significant change, for conventional PID cascade controller and basic fuzzy controller, the overshoot and the stabilization time of response process obviously increase, and the control effect obviously worsens; And adaptive controller based on the inverse dynamics fuzzy rule provided by the present invention still has good control effect, for the time become object and have more satisfactory control effect and adaptive ability.

Claims (4)

1, a kind of method for designing of self-adaptive fuzzy control system, this method for designing comprises the design procedure that utilizes fuzzy control rule that industrial process is controlled, it is characterized in that, described fuzzy control rule is based on the direct control law that produces of the identification of controlling object inverse dynamics fuzzy rule, and its method for designing comprises the steps:

(1) selects the structure of controlling object inverse dynamics model input vector, and utilize off-line data, form the sample set X that comprises N input vector;

(2) adopt the entropy method of birdsing of the same feather flock together that input vector sample set X blur divisions, with the regional center of each local data in definite input vector space and zone radius;

(3) utilize fuzzy rule to realize the mapping process of controlling object inverse dynamics, obtain controlling object inverse dynamics fuzzy rule by the recursive least-squares discrimination method, and with this inverse dynamics fuzzy rule as initial fuzzy control rule;

(4) utilize the input vector x (k) of the online current time k that obtains, existing input vector sample set X is refreshed, and utilize the method for birdsing of the same feather flock together of the entropy described in the step (two) that input vector sample set X is blured division again, redefine each local data center, zone and the zone radius in input vector space;

(5) utilize the online acquisition controlling object of step (three) inverse dynamics fuzzy rule, and with this fuzzy rule as control law, structure is based on the adaptive control system of inverse dynamics fuzzy rule.

2, according to the method for designing of the described self-adaptive fuzzy control system of claim 1, it is characterized in that, in step (), described controlling object inverse dynamics model, be historical and following expectation information according to controlling object, inverting current time k should impose on a kind of mapping relationship f of the controlled quentity controlled variable u (k) of controlling object, that is:

u(k)＝f[x(k)]

X in the formula (k) is the input vector at current time k controlling object inverse dynamics model; This input vector x (k) is by the historical data time series vector u of controlled quentity controlled variable u _-, controlled variable y historical data time series vector y _-Following time series vector y with desired controlled variable y ₊Constitute, that is:

$x\left(k\right)={[u_{-}^T,y_{-}^T,y_{+}^T]}^T$

Vector u _-, y _-And y ₊Determine in the following manner:

u _-＝[u(k-1)，u(k-2)，…，u(k-k ₁)]

y _-＝[y(k)，y(k-1)，y(k-2)，…，y(k-k ₂)]

y ₊＝[y(k+1)，y(k+2)，…，y(k+k ₃)]

K wherein ₁, k ₂+ 1 and k ₃Be respectively the time series number of corresponding vector.

The following time series vector y of controlled variable ₊Setting value y according to controlled variable y _SpPress following formula recursion structure with the current output y (k) of controlling object:

y(i+1)＝ωy(i)+(1-ω)y _sp (i＝k，k+1，…，k+k ₃-1)

ω ∈ (0,1) wherein.

3, according to the method for designing of the described self-adaptive fuzzy control system of claim 1, it is characterized in that, in the step (two), in the described employing entropy method of birdsing of the same feather flock together input vector sample set X is blured division, in the process with regional center of each local data that determines the input vector space and zone radius, be to utilize off-line data, form the sample set X that comprises N input vector x:

X＝{x(k-N+1)，x(k-N+2)，…，x(k-1)，x(k)}

At first determine i and j input vector data x _iAnd x _jBetween phase recency S _Ij:

$s_{\mathrm{ij}}=s(x_i,x_j)=e^{-\mathrm{\&alpha;}\left|\right|x_i-x_j\left|\right|},(i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,N;j=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,N;i\&NotEqual;j)$

Further by phase recency S _IjDetermine the entropy E of each sample of input vector _j:

$E_j=\underset{i=1,i\&NotEqual;j}{\overset{N}{\mathrm{\&Sigma;}}}{s}_{\mathrm{ij}}{\log }_2{s}_{\mathrm{ij}}+(1-s_{\mathrm{ij}}){\log }_2(1-s_{\mathrm{ij}})$

In the formula, α=-ln (0.5/ σ), σ represents the mean distance of data;

Given decision-making constant β ∈ [0,1] is with corresponding min (E _j) input vector x _jCenter c as the local data zone ₁From sample set X, remove and satisfy S (x _i, c ₁The sample of)＞β repeats this process, and sample set X is an empty set, determines the initial center c in n local data zone _i, (i=1,2 ..., n);

Obtaining input center c _iAfter, determine the radius r of each input area as follows _i:

1. initial input radius r is set _i=0 (i=1,2 ..., n);

2. select one the input sample data x (k) (k=1,2 ..., N), determine nearest with it input center c _s, refresh with this center c _sRadius r for the input area at center _s:

‖x(k)-c _s‖＝min‖x(k)-c _i‖

r _s＝max(‖x(k)-c _s‖，r _s) (s＝1，2，…，n)

According to the regional interface that said method obtained is the hypersphere with different radii, and its radius is by the sample decision farthest that belongs to this zone.

4, according to the method for designing of the described self-adaptive fuzzy control system of claim 1, it is characterized in that, in the step (three), in the process of described realization controlling object inverse dynamics mapping, the i bar fuzzy rule R of its controlling object inverse dynamics model _iFor:

$R_i:\mathrm{if\; x}\left(k\right)\&Element;\left(c_i,r_i\right)\mathrm{then}{u}_i={\mathrm{\&theta;}}_i^T[1,x{\left(k\right)}^T],(i=\mathrm{1,2},...,n)$

X wherein (k) is the input vector of inverse dynamics model, c _iAnd r _iBe i local data input center and radius; θ _iBe parameter vector to be identified; u _iIt is the output center of gravity of i bar fuzzy rule correspondence;

For given input vector x (k), determine each zone output center of gravity u by this fuzzy rule _i, adopt following fuzzy reasoning inverting should put on the controlled quentity controlled variable u (k) of system constantly at k:

$u\left(k\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(w_i{u}_i\right)/\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i,(\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i\&NotEqual;0)$

Perhaps

$u\left(k\right)=w_a{u}_a+w_b{u}_b,(\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i=0)$

Wherein, the weight coefficient w in each input vector zone _iDepend on input vector x (k) and each regional area center c _iBetween distance:

$w_i=\left\{\begin{array}{cc}1-\left|\right|x\left(k\right)-c_i\left|\right|/r_i,& \mathrm{if}\left|\right|x\left(k\right)-c_i\left|\right|\&le;r_i\\ 0,& \mathrm{if}\left|\right|x\left(k\right)-c_i\left|\right|>r_i\end{array}\right.$

In the formula, u _aAnd u _bThe output center of gravity of expression and nearest two input areas of input vector x (k) respectively; w _aAnd w _bBe respectively corresponding weight coefficient, they are defined by following formula:

$w_a=\frac{d_a}{d_a+d_b},w_b=\frac{d_b}{d_a+d_b}$

d _aAnd d _bExpression input vector x (k) and two nearest input area center c _aAnd c _bDistance:

d _a＝‖x(k)-c _a‖＝min‖x(k)-c _i‖ (i＝1，2，…，n)

d _b＝‖x(k)-c _b‖＝min‖x(k)-c _i‖ (i＝1，2，…，n?and?i≠a)

Controlling object inverse dynamics fuzzy rule Model parameter vector θ _i, according to currency y (k) and its desired value y of controlled variable _SpBetween deviation, refresh by recursive least-squares on-line identification method.

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