CN105589334A - Characteristic model parameter identification method based on input smoothing - Google Patents

Abstract

The invention discloses a characteristic model parameter identification method based on input smoothing. The characteristic model parameter identification method is characterized in that a characteristic model of a controlled system object can be acquired, and an intermediate variable and an unknown coefficient variable can be built according the input and the output of the controlled system object; the unknown coefficient variable can be identified by adopting the identification algorithm to acquire an identification value, and then the identification value can be corrected by adopting the projection algorithm, and the corrected identification value can be used as the unknown coefficient variable of the next period; and at last, an intermediate control variable can be calculated according to the unknown coefficient variable, and therefore the input of the controlled system object of the next period can be acquired, and then the characteristic parameter identification of the current period can be completed. The characteristic model parameter identification method is advantageous in that the change of the control variable can be limited by adopting the smoothing design of the control input, and the rate of change of the characteristic model parameters can be further limited, and then the identification of the characteristic model parameters can be realized; and at the same time, the second-order model and the first-order model of the daily use can be covered, and therefore the good versatility and the good application prospect can be provided.

Description

A kind of based on the level and smooth characteristic model parameter identification method of input

Technical field

The present invention relates to aerospace field, particularly a kind of based on the level and smooth characteristic model parameter identification method of input.

Background technology

Feature modeling theory is the control theory that the prosperous academician of Wu Hong proposes the eighties in 20th century, through 30 years of researches,In theoretical and application, all obtain impressive progress, formed Adaptive Control Theory and side that a set of complete practicality is very strongMethod. The method reenters lift control, intersection docking at manned spaceship and controls, and lunar exploration returns to the application of succeeding in control,Parachute-opening precision reaches world-class levels. Therefore, feature modeling theory has important using value and application prospect. General nextSay, characteristic model becomes difference equation during by low order to be described, but different from model reduction, it is high-order and nonlinear transformationsBe compressed in the coefficient of characteristic model, therefore do not lose system information, but this also causes coefficient and the shape of characteristic model simultaneouslyState is relevant. From identification theory, classical identification algorithm, as least square method, gradient method etc., can not be used for relevant to stateThe identification problem of parameter. Therefore the Characteristic parameter identification of characteristic model can not directly adopt these classical discrimination methods, itsIdentification problem needs to be carried out further investigation, needs a kind of distinguishing based on the level and smooth characteristic model parameter of input of characteristic model that be applicable toKnowledge method.

Summary of the invention

The technical problem that the present invention solves is: overcome the deficiencies in the prior art, provide a kind of by control inputs is enteredRow sawtooth design limits the variation of controlled quentity controlled variable, and the rate of change of further limited features model parameter, has solved characteristic modelThe parameter problem relevant to state, realized characteristic model parameter identification based on the level and smooth characteristic model parameter identification of inputMethod.

Technical solution of the present invention is: a kind of based on the level and smooth characteristic model parameter identification method of input, comprise asLower step:

(1) the n rank characteristic model that obtains controlled system object is

y(k+1)＝f₁(k)y(k)+f₂(k)y(k-1)+...+f_n(k)y(k-n+1)+g₀(k)u(k)+g₁(k)u(k-1)

+...+g_m(k)u(k-m)

Wherein, u (k) is controlled system object in the input in k cycle, and y (k) is controlled system object in the k cycleOutput, k represents control cycle, for being not less than 0 integer, initial value is 0, y (k)=0, k≤0, u (k)=0, k≤0, the value of nBe 1 or 2, n > m, m is integer, f_i(k),g_j(k) be unknowm coefficient, i=1 ..., n, j=0 ..., m;

(2) build according to the input of controlled system object, output the intermediate variable that n+m+1 ties upFor

Wherein,Initial value be

The unknowm coefficient variable θ (k) that builds n+m+1 dimension is

θ(k)＝[f₁(k)…f_n(k)g₀(k)…g_m(k)]^T

Wherein, in the time that the n rank of controlled system object characteristic model is 1 rank, y (k+1)=f₁(k)y(k)+g₀(k)u(k)，f₁(0)∈[0.2,0.99]，g₀(0)∈[0.003,1]，Ω＝{f₁(k)，g₀(k)|f₁(k)∈[0.2,0.99]，g₀(k)∈[0.003,1]}，n＝1，m＝0；

In the time that the n rank of controlled system object characteristic model is 2 rank, n=2, m=0, g₀(0)∈[0.003,0.3]，f₁(0)+f₂(0)∈[0.9196,0.9999]，f₁(0)∈[1.4331,1.9974]，f₂(0)∈[-0.9999,-0.5134]，y(k+1)＝f₁(k)y(k)+f₂(k)y(k-1)+g₀(k)u(k)，

$\mathrm{\Ω}=\left\{f_1\left(k\right),f_2\left(k\right),g_0\left(k\right)|\begin{array}{c}{f}_1\left(k\right)\∈\[1.4331,1.9974\],f_2\left(k\right)\∈\[-0.9999,-0.5134\],\\ f_1\left(k\right)+f_2\left(k\right)\∈\[0\mathrm{.9196,0}\mathrm{.9999}\],g_0\left(k\right)\∈\[0.003,0.3\]\end{array}\right\};$

(3) use identification algorithm identification θ (k) to obtain the identifier of n+m+1 dimensionFor

$\widehat{\mathrm{\θ}}(k+1)={\left[\begin{array}{cccccc}{\hat{f}}_1(k+1)& \mathrm{...}& {\hat{f}}_n(k+1)& {\hat{g}}_0(k+1)& \mathrm{...}& {\hat{g}}_m(k+1)\end{array}\right]}^T$

Wherein,Represent each coefficient f in unknowm coefficient variable θ (k)_i(k+1),g_j(k+1), i=1 ..., n, j=0 ..., the identifier of m, then to identifierUse projection algorithm carries outRevise, obtain revisedAs the unknowm coefficient variable θ (k+1) in k+1 cycle;

(4) in the time of n=2, controlled quentity controlled variable u'(k+1 in the middle of calculating) be

p₁*u_L(k+1)+p₂*u_G(k+1)+p₃*u_L(k+1)+p₄*u_G(k+1)+p₅*u₀(k+1)+p₆*u_I(k+1)

+p₇*u_D(k+1)

Wherein, p₁、p₂、p₃、p₄In wantonly 1 be 1, all the other 3 is 0, p₅、p₆、p₇In at least 1 be 1, y_R(k), k >=1 isThe tracking target of controlled system object is at the movement locus in k cycle, in the time of k≤0, and y_R(k)＝0，e(k+1)＝y(k+1)-y_R(k+1)，0<L₁,L₂<1，λ>0，l₁+l₂＝1，c_D>0,l_D>0，

$u_L(k+1)=-\frac{L_1{\hat{f}}_1(k+1)y(k+1)+L_2{\hat{f}}_2(k+1)y\left(k\right)}{\mathrm{\&lambda;}+{\hat{g}}_0(k+1)}$

$u_G(k+1)=-\frac{l_1{\hat{f}}_1(k+1)y(k+1)+l_2{\hat{f}}_2(k+1)y\left(k\right)}{\mathrm{\&lambda;}+{\hat{g}}_0(k+1)}$

$u_0(k+1)=-\frac{{\hat{f}}_1(k+1)y_R(k+1)+{\hat{f}}_2(k+1)y_R\left(k\right)}{{\hat{g}}_0(k+1)}$

u_I(k+1)＝u_I(k)-k_Ie(k+1),u_I(0)＝0

u_D(k+1)＝-k_D(e(k+1)-e(k))

$k_I=\left\{\begin{array}{c}{k}_{I1},e(k+1)\left(e\right(k+1)-e\left(k\right))>0\\ k_{I2},e(k+1)\left(e\right(k+1)-e\left(k\right))\&le;0\end{array}\right.,k_{I1}>>k_{I2}>0$

$k_D=c_D\sqrt{\underset{j=0}{\overset{l_D}{\mathrm{\&Sigma;}}}\left|e(k+1-j)\right|}>0$ Or $k_D=c_D\sqrt{\underset{j=0}{\overset{l_D}{\mathrm{\&Sigma;}}}{\left(e\right(k+1-j\left)\right)}^2}>0;$

In the time of n=1, controlled quentity controlled variable u'(k+1 in the middle of calculating) be

${\stackrel{\&OverBar;}{u}}_L(k+1)+{p^{\&prime;}}_2*{\stackrel{\&OverBar;}{u}}_0(k+1)+{p^{\&prime;}}_3*u_I(k+1)+{p^{\&prime;}}_4*u_D(k+1)$

Wherein, p'₂、p'₃、p'₄Value be 1 or 0,

${\stackrel{\&OverBar;}{u}}_L(k+1)=-\frac{L{\hat{f}}_1(k+1)y(k+1)}{\mathrm{\&lambda;}+{\hat{g}}_0(k+1)},0<L<1$

${\stackrel{\&OverBar;}{u}}_0(k+1)=-\frac{{\hat{f}}_1(k+1)y_R(k+1)}{{\hat{g}}_0(k+1)}$

(5) the middle controlled quentity controlled variable u'(k+1 obtaining according to step (4)) carry out smoothing processing with u (k), weighted average obtains

u(k+1)＝λ₁u'(k+1)+(1-λ₁)u(k),0<λ₁<1

Wherein, u (0)=0;

(6) u (k+1) step (5) being obtained delivers to the input of controlled system object, completes the feature in k+1 cycleParameter identification, k=k+1, repeating step (2)-step (5) is until complete the Characteristic parameter identification in whole cycles.

Described identification algorithm is gradient algorithm, calculates identifierFor

Wherein, c>0,0<α<2,

Described projection algorithm is border sciagraphy, traversal identifierMiddle institute is important, when certain component does not belong toIn the time of Ω, by this component rectangular projection to the border of Ω, obtain revisedAnd as the k+1 cycle notKnow coefficient variation θ (k+1).

Described identification algorithm is least-squares algorithm, calculates identifierFor

Wherein,P (1)=I, P (k) is that n+m+1 is capable, the matrix of n+m+1 row, I is that n+m+1 is capable, n+m+1The unit matrix of row;

Described projection algorithm is basis transformation border sciagraphy, orderΩ is carried outLinear transformation P (k)^-1/2Obtain image spaceTraversalMiddle institute is important, when certain component does not belong toTime, shouldComponent rectangular projection is arrivedBorder on, obtain revisedAnd then obtainDoBe the unknowm coefficient variable θ (k+1) in k+1 cycle.

Described l₁＝0.382,l₂＝0.618。

The present invention's advantage is compared with prior art:

(1) the inventive method compared with prior art, by by input be smoothly incorporated in the identification of characteristic model parameter,Contain 2 rank characteristic models, the 1 rank characteristic model commonly used at present, solved their characteristic model parameter identification problem, broken throughThe characteristic model parameter identification problem relevant to state, there is good versatility;

(2) the inventive method compared with prior art, by using multiple identification algorithm, comprises classical least square methodAnd gradient method, and combine with level and smooth control, solve classical identification algorithm being suitable for for characteristic model Characteristic parameter identificationProperty problem;

(3) the inventive method compared with prior art, limits controlled quentity controlled variable by control inputs being carried out to sawtooth designChange, and the further rate of change of limited features model parameter, solved the parameter problem relevant to state of characteristic model, realityShow characteristic model parameter identification.

Brief description of the drawings

Fig. 1 is that the present invention is a kind of based on the level and smooth characteristic model parameter identification method flow chart of input.

Detailed description of the invention

The present invention is directed to the deficiencies in the prior art, propose a kind of based on the level and smooth characteristic model parameter identification method of input,Below in conjunction with accompanying drawing, the present invention is elaborated, the control that the inventive method is calculated controlled device at each control cycle is defeatedEnter, solve the parameter identification problem of characteristic model, as shown in Figure 1, the present invention realizes by step (1)-step (6).

Step (1)

Consider spacecraft controlled device, its dynamics is

$\begin{array}{c}\stackrel{\&CenterDot;}{x}=f(x,u,t),x\&Element;R^{n_x},u\&Element;R^{n_u}\\ =g(x,u,t),y\&Element;R^{n_y}\end{array}---\left(1\right)$

Wherein, f, g represents smooth function; X, u, y represents respectively state, input and output; n_x,n_u,n_yRepresent respectively shapeThe dimension of state, input and output; T represents the time, and R represents real number space.

In application, adopt computer control. The discretization model of formula (1) is:

$\begin{array}{c}x\left(k+1\right)=\stackrel{\&OverBar;}{f}\left(k,x\left(k\right),u\left(k\right)\right)\\ y\left(k+1\right)=\stackrel{\&OverBar;}{g}(k,x(k+1),u\left(k\right))\end{array},k\&GreaterEqual;0---\left(2\right)$

Wherein,Represent smooth function; K represents control cycle, and the value that initial value is 0, k is nonnegative integer; X (k), u(k), y (k) is the middle x of representation formula (1) respectively, u, and y is in the value in k moment, and initial value is: u (0)=0, x (0)=0.

In the present invention, controlled device can be intersection docking controlled device, and its dynamics is

$\stackrel{\&CenterDot;}{q}=T\left(q\right)w_s$

$I_s{\stackrel{\&CenterDot;}{w}}_s+{\tilde{w}}_s{I}_s{w}_s+F_{sls}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&eta;}}}_{ls}+F_{srs}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&eta;}}}_{rs}+R_{asls}{\stackrel{\&CenterDot;}{w}}_{als}+R_{asrs}{\stackrel{\&CenterDot;}{w}}_{ars}=T_s$

$I_{als}{\stackrel{\&CenterDot;}{w}}_{als}+F_{als}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&eta;}}}_{ls}+R_{asls}^T{\stackrel{\&CenterDot;}{w}}_s=T_{als}$

$I_{ars}{\stackrel{\&CenterDot;}{w}}_{ars}+F_{ars}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&eta;}}}_{rs}+R_{asrs}^T{\stackrel{\&CenterDot;}{w}}_s=T_{ars}$

${\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&eta;}}}_{ls}+2x_{ls}{W}_{als}{\stackrel{\&CenterDot;}{\mathrm{\&eta;}}}_{ls}+W_{als}^2{\mathrm{\&eta;}}_{ls}+F_{tls}^T\stackrel{\&CenterDot;\&CenterDot;}{X}+F_{sls}^T{\stackrel{\&CenterDot;}{w}}_s+F_{als}^T{\stackrel{\&CenterDot;}{w}}_{als}=0$

${\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&eta;}}}_{rs}+2x_{rs}{W}_{ars}{\stackrel{\&CenterDot;}{\mathrm{\&eta;}}}_{rs}+W_{ars}^2{\mathrm{\&eta;}}_{rs}+F_{trs}^T\stackrel{\&CenterDot;\&CenterDot;}{X}+F_{srs}^T{\stackrel{\&CenterDot;}{w}}_s+F_{ars}^T{\stackrel{\&CenterDot;}{w}}_{ars}=0$

$M\stackrel{\&CenterDot;\&CenterDot;}{X}+F_{trs}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&eta;}}}_{rs}+F_{tls}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&eta;}}}_{ls}=P_s$

y＝θ

u＝T_s

Wherein, u, y represents respectively input and output. In above formula the meaning of each variable representative can referring to document (separate Yongchun,Zhang Hao, Hu Jun, Hu Haixia, Shenzhou spacecraft intersection docking Design of Automatic Control System, Chinese science (technological sciences), 2014,44(1):12-19)。

In the present invention, controlled device can be hypersonic aircraft controlled device, and its dynamics is

$\stackrel{\&CenterDot;}{V}=-\frac{\mathrm{\&mu;}}{r^2}sin\mathrm{\&gamma;}+\frac{(Pcos\mathrm{\&alpha;}-D)}{m}+{\mathrm{\&omega;}}_E^{2}rsin\mathrm{\&gamma;}$

$V\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}=-(\frac{\mathrm{\&mu;}}{r^2}-\frac{V^2}{r})cos\mathrm{\&gamma;}+\frac{(Psin\mathrm{\&alpha;}+L)}{m}+2{\mathrm{\&omega;}}_{E}V+{\mathrm{\&omega;}}_E^{2}rcos\mathrm{\&gamma;}$

$\stackrel{\&CenterDot;}{h}=Vsin\mathrm{\&gamma;}$

$\stackrel{\&CenterDot;}{q}=\frac{M_y}{I_y}$

$\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}=q-\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}$

y＝α

u＝M_y

Wherein, u, y represents respectively input and output. In above formula the meaning of each variable representative can referring to document (Meng Bin,Wu Hongxin, Lin Zongli, Li Guo, the X-34 based on characteristic model climbs and controls research, Chinese science (information science), 2009,39(11):1202-1209)。

In the present invention, controlled device can be that airship returns and reenters controlled device, and its guidance dynamics is

$\stackrel{\&CenterDot;}{r}=Vsin\mathrm{\&gamma;}$

$\stackrel{\&CenterDot;}{V}=-D-\frac{sin\mathrm{\&gamma;}}{r^2}+W_V$

$\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}=\frac{Lcos\mathrm{\&sigma;}}{V}+(V^2-\frac{1}{r})\frac{cos\mathrm{\&gamma;}}{Vr}+W_{\mathrm{\&gamma;}}$

y＝D

u＝γ

Wherein u, y represents respectively input and output. In above formula, the meaning of each variable representative can be referring to document (Wang ZeState, Meng Bin, considers that the design of feedback linearization homing guidance rule is returned in the lunar exploration of earth rotation, space control technology and application,2014，40(5):31-36)。

Step below starts to carry out from k=0. After each circulation step (6) finishes, k increases by 1.

Step (2)

According to feature modeling theory, in establishment step (1), the n rank characteristic model of controlled system object is

y(k+1)＝f₁(k)y(k)+…+f_n(k)y(k-n+1)+g₀(k)u(k)+…+g_m(k)u(k-m),n>m,k≥0

(3)

Wherein, u (k), y (k) is respectively the input and output of formula (2); f_i(k),g_j(k),i＝1,…,n,j＝0,…,M, comprises state in formula (2) and the information of input, is the unknowm coefficient of formula (3), belongs to known convex closed set Ω, belowStep (3) in obtain by identification; K represents control cycle, and the initial value of above-mentioned variable is respectively: the initial value of k is 0;

y(k)＝0,k≤0(4)

u(k)＝0,k≤0(5)

Note

Wherein, y (k), k >=1, is the output of formula (2) at k control cycle; U (k), k >=1, is to obtain in step (5)The control inputs of k the control cycle arriving. From formula (4) and formula (5),Initial value be

Note

θ(k)＝[f₁(k)…f_n(k)g₀(k)…g_m(k)]^T

Known, θ (k) ∈ Ω. And formula (3) can be written as:

In the present invention, characteristic model can be taken as 2 the most frequently used rank characteristic models (n=2, m=0)

y(k+1)＝f₁(k)y(k)+f₂(k)y(k-1)+g₀(k)u(k)

Wherein,

$\mathrm{\&Omega;}=\left\{f_1,f_2,g_0|\begin{array}{c}{f}_1\&Element;\&lsqb;1.4331,1.9974\&rsqb;,f_2\&Element;\&lsqb;-0.9999,-0.5134\&rsqb;\\ f_1+f_2\left(k\right)\&Element;\&lsqb;0\mathrm{.9196,0}\mathrm{.9999}\&rsqb;,g_0\&Element;\&lsqb;0.003,0.3\&rsqb;\end{array}\right\}$

In the present invention, characteristic model also can be taken as 1 rank characteristic model

y(k+1)＝f₁(k)y(k)+g₀(k)u(k)(n＝1，m＝0)

Wherein,

Ω＝{f₁,g₀|f₁∈[0.2,0.99],g₀∈[0.003,1]}

Step (3)

Utilize the input and output of controlled device in step (1), adopt projection identification algorithm, feature in identification step (2)The unknowm coefficient θ (k+1) of model, obtains the identifier of θ (k+1), is designated as

$\widehat{\mathrm{\&theta;}}(k+1)={\left[\begin{array}{cccccc}{\hat{f}}_1(k+1)& \mathrm{...}& {\hat{f}}_n(k+1)& {\hat{g}}_0(k+1)& \mathrm{...}& {\hat{g}}_m(k+1)\end{array}\right]}^T$

Wherein,F in representation formula (3)_i(k+1),g_j(k+1),i＝1 ..., nj=0 ..., the identifier of m.

Projection algorithm comprises two steps, and the first step is to utilize identification algorithm to carry out identification, identification amount in the middle of obtaining; Second step willMiddle identification amount projects in Ω.

The identification algorithm of the first step in the inventive method, can adopt the classical identification such as gradient algorithm, least-squares algorithmAlgorithm.

Gradient algorithm is:

Wherein,Identification amount in the middle of representing;In formula (6), provide, its initial value provides in formula (7);In set omega, choose; Y (k), k >=1, is the output of formula (2) at k control cycle.

Least-squares algorithm is:

Wherein,Identification amount in the middle of representing;In formula (6), provide, its initial value provides in formula (7);In set omega, choose; Y (k), k >=1, is the output of formula (2) at k control cycle; P (1)=I, P (k) is n+M+1 is capable, the matrix of n+m+1 row, and I is that n+m+1 is capable, the unit matrix of n+m+1 row.

In the inventive method, second step adopts projection algorithm.

In the time that identification adopts gradient algorithm, projection adopts border sciagraphy. If i.e. middle identification amountCertainComponent does not belong to Ω, by this component rectangular projection to the border of Ω. Be designated as by the output after projection identification algorithmKnown by convergence, Lyapunov functionNon-increasing, and have and classical gradient calculationThe convergence that method is identical, wherein,Represent identification deviation.

In the time that identification adopts least-squares algorithm, projection adopts basis transformation border sciagraphy. First transformation parameter spaceSubstrate, orderAnd useRepresent Ω Linear Transformation P (k)^-1/2Under image space. Then,WillRectangular projection is arrivedBorder on, obtainFinally convert go back to raw parameter space, obtainKnown by convergence, Lyapunov functionNon-Increase, and there is the convergence identical with classical least-squares algorithm, wherein,Represent identification deviation.

Step (4)

Utilize the identification amount of step (3), based on the characteristic model design control law in step (2), controlled quentity controlled variable in the middle of obtainingu'(k+1)。

Bring identification amount into formula (3), obtain

$\begin{array}{c}y\left(k+2\right)={\hat{f}}_1\left(k+1\right)y\left(k+1\right)+{\hat{f}}_2\left(k+1\right)y\left(k\right)+\mathrm{...}+{\hat{f}}_n\left(k+1\right)y\left(k-n+2\right)+\\ \hat{g}\left(k+1\right)u\left(k+1\right)+{\hat{g}}_1\left(k+1\right)u\left(k\right)+\mathrm{...}+{\hat{g}}_m\left(k+1\right)u\left(k+1-m\right)\end{array}$

On this basis, adopt the infinite control method of H, sliding-mode control etc. to obtain u'(k+1). In the inventive method, controlSystem rule can be taken as based on 1,2 ..., n rank characteristic model sliding formwork control law.

In the inventive method, for 2 rank characteristic models, control law can be taken as Linear Control rule u_L(k+1) or gold divideCut control law u_GOr u (k+1)_L(k+1)(u_G(k+1)) follow the tracks of control law u with maintaining₀(k+1), logic integral control law u_I(k+1), logic differential control law u_D(k+1) the some or multiple control laws in and, wherein,

$u_L(k+1)=-\frac{L_1{\hat{f}}_1(k+1)y(k+1)+L_2{\hat{f}}_2(k+1)y\left(k\right)}{\mathrm{\&lambda;}+{\hat{g}}_0(k+1)}$

$u_G(k+1)=-\frac{l_1{\hat{f}}_1(k+1)y(k+1)+l_2{\hat{f}}_2(k+1)y\left(k\right)}{\mathrm{\&lambda;}+{\hat{g}}_0(k+1)}$

$u_0(k+1)=-\frac{{\hat{f}}_1(k+1)y_R(k+1)+{\hat{f}}_2(k+1)y_R\left(k\right)}{{\hat{g}}_0(k+1)}$

u_I(k+1)＝u_I(k)-k_Ie(k+1),u_I(0)＝0

u_D(k+1)＝-k_D(e(k+1)-e(k))

Wherein, y (k), k >=1, is the output of formula (2) at k control cycle, y (0)=0; y_R(k), k >=1 is forThe tracking target function of knowing, y_R(0)＝0；e(k+1)＝y(k+1)-y_R(k+1)；0<L₁,L₂<1,λ>0；l₁＝0.382,l₂＝0.618,

$k_I=\left\{\begin{array}{c}{k}_{I1},e(k+1)\left(e\right(k+1)-e\left(k\right))>0\\ k_{I2},e(k+1)\left(e\right(k+1)-e\left(k\right))\&le;0\end{array}\right.,k_{I1}>>k_{I2}>0$

$k_D=c_D\sqrt{\underset{j=0}{\overset{l_D}{\mathrm{\&Sigma;}}}\left|e(k+1-j)\right|}>0,$ Or, $k_D=c_D\sqrt{\underset{j=0}{\overset{l_D}{\mathrm{\&Sigma;}}}{\left(e\right(k+1-j\left)\right)}^2}>0$

k_I1,k_I2,c_D,l_DFor required adjustment parameter.

In the present invention, for 1 rank characteristic model, control law can be taken as Linear Control ruleOrWith maintain tracking control lawLogic integral control law u_I(k+1), logic differential control law u_D(k+1) some inOr multiple control laws and, wherein,

${\stackrel{\&OverBar;}{u}}_L(k+1)=-\frac{L{\hat{f}}_1(k+1)y(k+1)}{\mathrm{\&lambda;}+{\hat{g}}_0(k+1)},0<L<1,$

${\stackrel{\&OverBar;}{u}}_0(k+1)=-\frac{{\hat{f}}_1(k+1)y_R(k+1)}{{\hat{g}}_0(k+1)}$

Step (5)

The middle controlled quentity controlled variable u'(k+1 that step (4) is obtained) carry out smoothly, obtaining the control inputs u (k+ of controlled device1)。

In the present invention, the middle controlled quentity controlled variable u'(k+1 of smoothing algorithm for step (4) is obtained), be weighted flat with u (k)Equal:

u(k+1)＝λ₁u'(k+1)+(1-λ₁)u(k),0<λ₁<1(8)

Wherein, initial value u (0)=0.

Can be obtained by formula (8):

Δu(k)＝λ₁(u'(k)-u (k-1)), wherein, Δ u (k)=u (k)-u (k-1), by adjusting λ₁Limit Δ u(k) size.

If current controlled system object meets broad sense Li Puxizi condition, k and Δ u (k) are arbitrarily had || Δ y(k) ||≤b|| Δ u (k) ||, wherein, b is known constant, Δ y (k)=y (k)-y (k-1), when Δ u (k) hour, systemThe increment of output is also less, at this moment can remove to a certain extent the relation of coefficient and input and the state of characteristic model.Therefore, under the effect of step (5), the identification algorithm that the present invention uses as least-squares algorithm or gradient algorithm be feasible.

Step (6)

The control u (k+1) that step (5) is obtained is input to the input of controlled device, forms closed loop.

To sum up, step (1)-step (6) has realized the Self Adaptive Control based on characteristic model, has solved under certain conditionThe identification problem of the coefficient that characteristic model is relevant to state.

The content not being described in detail in description of the present invention belongs to those skilled in the art's known technology.

Claims (4)

1. based on the level and smooth characteristic model parameter identification method of input, it is characterized in that comprising the steps:

(1) the n rank characteristic model that obtains controlled system object is

y(k+1)＝f₁(k)y(k)+f₂(k)y(k-1)+...+f_n(k)y(k-n+1)+g₀(k)u(k)+g₁(k)u(k-1)

+...+g_m(k)u(k-m)

Wherein, u (k) is controlled system object in the input in k cycle, and y (k) is controlled system object in the output in k cycle,K represents control cycle, and for being not less than 0 integer, initial value is 0, y (k)=0, k≤0, u (k)=0, k≤0, the value of n be 1 or2, n > m, m is integer, f_i(k),g_j(k) be unknowm coefficient, i=1 ..., n, j=0 ..., m;

(2) build according to the input of controlled system object, output the intermediate variable that n+m+1 ties upFor

Wherein,Initial value be

The unknowm coefficient variable θ (k) that builds n+m+1 dimension is

θ(k)＝[f₁(k)…f_n(k)g₀(k)…g_m(k)]^T

Wherein, in the time that the n rank of controlled system object characteristic model is 1 rank, y (k+1)=f₁(k)y(k)+g₀(k)u(k)，f₁(0)∈[0.2,0.99]，g₀(0)∈[0.003,1]，Ω＝{f₁(k)，g₀(k)|f₁(k)∈[0.2,0.99]，g₀(k)∈[0.003,1]}，n＝1，m＝0；

In the time that the n rank of controlled system object characteristic model is 2 rank, n=2, m=0, g₀(0)∈[0.003,0.3]，f₁(0)+f₂(0)∈[0.9196,0.9999]，f₁(0)∈[1.4331,1.9974]，f₂(0)∈[-0.9999,-0.5134]，y(k+1)＝f₁(k)y(k)+f₂(k)y(k-1)+g₀(k)u(k)，

$\mathrm{\&Omega;}=\{f_1\left(k\right),f_2\left(k\right),g_0\left(k\right)\}\left|\begin{array}{c}{f}_1\left(k\right)\&Element;\&lsqb;1.4331,1.9974\&rsqb;,f_2\left(k\right)\&Element;\&lsqb;-0.9999,-0.5134\&rsqb;,\\ f_1\left(k\right)+f_2\left(k\right)\&Element;\&lsqb;0.9196,0.9999\&rsqb;,g_0\left(k\right)\&Element;\&lsqb;0.003,0.3\&rsqb;\end{array}\right.\};$

(3) use identification algorithm identification θ (k) to obtain the identifier of n+m+1 dimensionFor

$\widehat{\mathrm{\&theta;}}(k+1)={\left[\begin{array}{cccccc}{\hat{f}}_1(k+1)& \mathrm{...}& {\hat{f}}_n(k+1)& {\hat{g}}_0(k+1)& \mathrm{...}& {\hat{g}}_m(k+1)\end{array}\right]}^T$

Wherein,Represent each coefficient f in unknowm coefficient variable θ (k)_i(k+1),g_j(k+1), i=1 ..., n, j=0 ..., the identifier of m, then to identifierUse projection algorithm to repairJust, obtain revisedAs the unknowm coefficient variable θ (k+1) in k+1 cycle;

(4) in the time of n=2, controlled quentity controlled variable u'(k+1 in the middle of calculating) be

p₁*u_L(k+1)+p₂*u_G(k+1)+p₃*u_L(k+1)+p₄*u_G(k+1)+p₅*u₀(k+1)+p₆*u_I(k+1)

+p₇*u_D(k+1)

Wherein, p₁、p₂、p₃、p₄In wantonly 1 be 1, all the other 3 is 0, p₅、p₆、p₇In at least 1 be 1, y_R(k), k >=1 is controlledThe tracking target of system object is at the movement locus in k cycle, in the time of k≤0, and y_R(k)＝0，e(k+1)＝y(k+1)-y_R(k+1)，0<L₁,L₂<1，λ>0，l₁+l₂＝1，c_D>0,l_D>0，

$u_L(k+1)=-\frac{L_1{\hat{f}}_1(k+1)y(k+1)+L_2{\hat{f}}_2(k+1)y\left(k\right)}{\mathrm{\&lambda;}+{\hat{g}}_0(k+1)}$

$u_G(k+1)=-\frac{l_1{\hat{f}}_1(k+1)y(k+1)+l_2{\hat{f}}_2(k+1)y\left(k\right)}{\mathrm{\&lambda;}+{\hat{g}}_0(k+1)}$

$u_0(k+1)=-\frac{{\hat{f}}_1(k+1)y_R(k+1)+{\hat{f}}_2(k+1)y_R\left(k\right)}{{\hat{g}}_0(k+1)}$

u_I(k+1)＝u_I(k)-k_Ie(k+1),u_I(0)＝0

u_D(k+1)＝-k_D(e(k+1)-e(k))

$k_I=\left\{\begin{array}{c}{k}_{I1},e(k+1)\left(e\right(k+1)-e(k\left)\right)>0\\ k_{I2},e(k+1)\left(e\right(k+1)-e(k\left)\right)\&le;0\end{array}\right.,k_{I1}>>k_{I2}>0$

$k_D=c_D\sqrt{\underset{j=0}{\overset{l_D}{\&Sigma;}}\left|e(k+1-j)\right|}>0$ Or $k_D=c_D\sqrt{\underset{j=0}{\overset{l_D}{\&Sigma;}}{\left(e\right(k+1-j\left)\right)}^2}>0;$

In the time of n=1, controlled quentity controlled variable u'(k+1 in the middle of calculating) be

${\stackrel{\&OverBar;}{u}}_L(k+1)+{p^{\&prime;}}_2*{\stackrel{\&OverBar;}{u}}_0(k+1)+{p^{\&prime;}}_3*u_I(k+1)+{p^{\&prime;}}_4*u_D(k+1)$

Wherein, p'₂、p'₃、p'₄Value be 1 or 0,

${\stackrel{\&OverBar;}{u}}_L(k+1)=-\frac{L{\hat{f}}_1(k+1)y(k+1)}{\mathrm{\&lambda;}+{\hat{g}}_0(k+1)},0<L<1$

${\stackrel{\&OverBar;}{u}}_0(k+1)=-\frac{{\hat{f}}_1(k+1)y_R(k+1)}{{\hat{g}}_0(k+1)}$

(5) the middle controlled quentity controlled variable u'(k+1 obtaining according to step (4)) carry out smoothing processing with u (k), weighted average obtains

u(k+1)＝λ₁u'(k+1)+(1-λ₁)u(k),0<λ₁<1

Wherein, u (0)=0;

(6) u (k+1) step (5) being obtained delivers to the input of controlled system object, completes the characteristic parameter in k+1 cycleIdentification, k=k+1, repeating step (2)-step (5) is until complete the Characteristic parameter identification in whole cycles.

2. according to claim 1 a kind of based on the level and smooth characteristic model parameter identification method of input, it is characterized in that: instituteThe identification algorithm of stating is gradient algorithm, calculates identifierFor

Wherein, c>0,0<α<2,

Described projection algorithm is border sciagraphy, traversal identifierMiddle institute is important, when certain component does not belong to ΩTime, by this component rectangular projection to the border of Ω, obtain revisedAnd as the unknown in k+1 cycle beNumber variable θ (k+1).

3. according to claim 1 a kind of based on the level and smooth characteristic model parameter identification method of input, it is characterized in that: instituteThe identification algorithm of stating is least-squares algorithm, calculates identifierFor

Wherein,P (1)=I, P (k) is that n+m+1 is capable, the matrix of n+m+1 row, I is that n+m+1 is capable, n+m+1 is listed asUnit matrix;

Described projection algorithm is basis transformation border sciagraphy, orderΩ is carried out to linearityConversion P (k)^-1/2Obtain image spaceTraversalMiddle institute is important, when certain component does not belong toTime, by this componentRectangular projection is arrivedBorder on, obtain revisedAnd then obtainAs kThe unknowm coefficient variable θ (k+1) in+1 cycle.

4. according to claim 1 and 2 a kind of based on the level and smooth characteristic model parameter identification method of input, its feature existsIn: described l₁＝0.382,l₂＝0.618。