CN102063133A - Adaptive control method of multiple-variable time lag process - Google Patents

Abstract

The invention provides an adaptive control method of a multiple-variable time lag process. Time lag can be output time lag and also can be input time lag. The adaptive control method utilizes a model matching controller and adopts a gradient adaptive law for adjusting parameters of the controller so as to ensure that all of signals in a closed loop system are bounded and error is converged to zero. The method has the advantages of high convergence accuracy, strong real time and high application value.

Description

A kind of self-adaptation control method of multivariable time-lag process

Technical field

The invention belongs to the process control field, be specifically related to multivariable time-lag process design auto-adaptive control scheme.

Background technology

All life period postpones in a lot of industrial processs, flow ducted as steam or fluid, and the signal transmission in the network system, we call time lag system to the system that this class contains time delay.The existence of time lag makes industrial process become complicated more and is difficult to control, reduces the effect of control.So the research to time lag system is extremely important.On the other hand, some probabilistic factors are always arranged in the industrial process, and as the variation of some controlled variable, some the unknowns is dynamic in the modeling process, and adaptive control can be done corresponding the adjustment according to the variation of these factors in the process, reaches more satisfactory control effect.So the adaptive control to industrial process is significant.

Many for the research of the control of single argument (input an output) time-lag process at present, used method has famous Smith prediction device method, it can eliminate the time lag in the closed-loop control system secular equation, but this method only is applicable to the point-device process of model, and to require process itself be stable.Also having a kind of method is that the time lag in the system is converted into disturbance earlier, and the method with robust control solves then.Because robust control is a kind of method based on optimum, and wherein used objective function can be selected a plurality of different functions, is the method that a kind of needs are repeatedly attempted, error is inevitable.And the Model Matching control technology is a kind of deterministic control method, and earlier given one is satisfied the model of controlling the target that will reach, designs a controller and make control system and this model mate fully.For the effector, this is a kind of ideal control effect.

The Model Matching controller of single argument time-lag process designs, and can be applied in the adaptive control, and promptly the system that containing parameter is changed can use the auto-adaptive control scheme of design.But a lot of industrial processs all have a plurality of variablees (a plurality of outputs of a plurality of inputs), as the control of sludge incineration fluidized bed, so significant to the Model Matching of the time-lag process that contains a plurality of variablees.

This paper proposes a kind of auto-adaptive control scheme to the multivariable time-lag process based on the Model Matching control method.

Summary of the invention

The objective of the invention is to propose a kind of controlling schemes to the multivariable time-lag process, be based on model matching technologies design, the good degree of accuracy of this scheme real-time is higher.

The present invention is based on time lag compensation device and polynomial expression and put separating of journey group the multivariable time delay system matching controller that designs a model, uncertain system to unknown parameters designs auto-adaptive control scheme then, make all signal boundeds in the closed-loop system and the output of the control procedure output of track reference model as much as possible.For achieving the above object, as shown in Figure 1, technical scheme of the present invention specifically is achieved in that

1. system is converted into the non-vanishing form of gain on the diagonal line.；

2. design the Model Matching controller of nominal system;

3. controller parameterization;

4. error of calculation expression formula;

5. design parameter adaptive law.

The present invention has provided the method for a systematized multivariable time-lag process adaptive control, and the model of multivariable time-lag process also is general model, so this invention can be used for the adaptive control of multiple multivariable time-lag process.

Description of drawings

Fig. 1 is the adaptive control process flow diagram;

Fig. 2 is the Model Matching design of Controller block diagram of nominal system;

Embodiment

Developing simultaneously with reference to accompanying drawing, the present invention is described in more detail for embodiment.

At first the multivariable time-lag process is set up a unified model, process has n output of n input, from the transport function that is input to output is

$T\left(s\right)=\left[\begin{array}{ccc}\frac{g_{11}{r}_{11}\left(s\right)}{p_1\left(s\right)}{e}^{-L_{11}s}& ...& \frac{g_{1n}{r}_{1n}\left(s\right)}{p_1\left(s\right)}{e}^{-L_{1n}s}\\ ...& ...& ...\\ \frac{g_{n1}{r}_{n1}\left(s\right)}{p_n\left(s\right)}{e}^{-L_{n1}s}& ...& \frac{g_{\mathrm{nn}}{r}_{\mathrm{nn}}\left(s\right)}{p_n\left(s\right)}{e}^{-L_{\mathrm{nn}}s}\end{array}\right]$

Wherein being input to each output from each all has time lag, and note is L from j time lag that is input to i output _Ijr _Ij(s) and p _i(s) be monic polynomial, their exponent number is respectively m _IjAnd n _i, be designated as

Selected model that satisfies our desired control effect is called reference model.Because each output is ideal control effect by an input control only, so Model Selection is

$T_r\left(s\right)=\mathrm{diag}(\frac{g_{r1}{r}_{r1}\left(s\right)}{P_{r1}\left(s\right)}{e}^{-L_{r1}s},...,\frac{g_{\mathrm{rn}}{r}_{\mathrm{rn}}\left(s\right)}{p_{\mathrm{rn}}\left(s\right)}{e}^{-L_{\mathrm{rn}}s})$

Our controlled target is exactly that auto-adaptive control scheme of design makes the output of output tracking reference model of process.The right controlled target that reaches has three assumed conditions to this model.

Suppose 1 note

R (s) is asymptotically stable, i.e. minimum phase.

The relative rank of supposing every row in 2 reference models are all more than or equal to the relative rank of every row in the controlling models.

Suppose 3 constant matricess

Be nonsingular, d wherein _iBe a constant, make It is the limited vector of non-zero.T ⁱ(s) be that the i of T (s) is capable.

1 is converted into the non-vanishing form of gain on the diagonal line with system.Because B ^*Be nonsingular, always can find a constant matrices to make system's post-multiplication be converted into b afterwards _Ii=g _Ii≠ 0, so at first system is converted into b _Ii=g _Ii≠ 0 form.

2 nominal system Model Matching design of Controller

At first be the design of time lag compensation device, the total minimum time lag of the every row of control system is L _Il, following expression is arranged

$\frac{r_i^{*}\left(s\right)p_i\left(s\right)-g_{\mathrm{ij}}{r}_{\mathrm{ij}}\left(s\right)p_i^{*}\left(s\right)}{r_i^{*}\left(s\right)p_i\left(s\right)}=\underset{k=1}{\overset{m_i+n_i}{\mathrm{\Σ}}}\frac{{\mathrm{\β}}_{\mathrm{ij}}^k{e}^{(L_{\mathrm{ij}}-L_{\mathrm{il}})z_i^k}}{s-z_i^k}+1-b_{\mathrm{ij}},j\≠l$

Defining polynomial φ _Ij(s) satisfy following equation

$\frac{r_i^{*}\left(s\right)p_i\left(s\right)-{\mathrm{\φ}}_{\mathrm{ij}}\left(s\right)}{r_i^{*}\left(s\right)p_i\left(s\right)}=\underset{k=1}{\overset{m_i+n_i}{\mathrm{\Σ}}}\frac{{\mathrm{\β}}_{\mathrm{ij}}^k{e}^{L_{\mathrm{ij}}{z}_i^k}}{s-z_i^k}+1-b_{\mathrm{ij}},j\≠l$

The selection exponent number is m _IjPolynomial expression

(j ≠ l), can be written as

$-\frac{g_{\mathrm{ij}}{\stackrel{\‾}{r}}_{\mathrm{ij}}\left(s\right)}{r_i^{*}\left(s\right)}=\underset{k=1}{\overset{m_i}{\mathrm{\Σ}}}\frac{{\stackrel{\‾}{\mathrm{\β}}}_{\mathrm{ij}}^k}{s-z_i^k}-b_{\mathrm{ij}}$

Defining polynomial

Equation below satisfying

$-\frac{{\stackrel{\‾}{\mathrm{\φ}}}_{\mathrm{ij}}\left(s\right)}{r_i^{*}\left(s\right)}=\underset{k=1}{\overset{m_i}{\mathrm{\Σ}}}\frac{{\stackrel{\‾}{\mathrm{\β}}}_{\mathrm{ij}}^k{e}^{(L_{\mathrm{ij}}-L_{\mathrm{il}})z_i^k}}{s-z_i^k}-b_{\mathrm{ij}}$

Be that the polynomial equation group is found the solution then.Selecting an exponent number is n _i-m _i-1 polynomial expression τ _i(s), then following polynomial equation group is separated.

k _ij(s)p _i(s)+g _ijh _i(s)r _ij(s)＝b _ijτ _i(s)r ^* _i(s)p _i(s)-τ _i(s)φ _ij(s)

Polynomial expression k wherein _Ij(s), h _i(s) exponent number is respectively

The Model Matching controller of design is [u ₁, u ₂..., u _n] ^T=(B ^*) ^-1[c ₁, c ₂..., c _n] ^T

Wherein

$c_i=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\frac{k_{\mathrm{ij}}\left(s\right)}{{\mathrm{\τ}}_i\left(s\right)r_i^{*}\left(s\right)}{u}_j\left(s\right)e^{-L_{\mathrm{ij}}s}+\frac{h_i\left(s\right)}{{\mathrm{\τ}}_i\left(s\right)r_i^{*}\left(s\right)}{y}_i\left(s\right)+\underset{j\≠l}{\overset{n}{\mathrm{\Σ}}}\frac{g_{\mathrm{ij}}{\stackrel{\‾}{r}}_{\mathrm{ij}}\left(s\right)}{r_i^{*}\left(s\right)}{u}_j\left(s\right)$

$+\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_{-L_{\mathrm{ij}}}^{-(L_{\mathrm{ij}}-L_{\mathrm{il}})}\underset{k=1}{\overset{m_i+n_i}{\mathrm{\Σ}}}{\mathrm{\β}}_{\mathrm{ij}}^k{e}^{-\mathrm{\σ}{z}_i^k}{u}_j\left(s\right)e^{\mathrm{\σs}}\mathrm{d\σ}+\underset{j\≠l}{\overset{n}{\mathrm{\Σ}}}{\∫}_{-(L_{\mathrm{ij}}-L_{\mathrm{il}})}^0\underset{k=1}{\overset{m_i+n_i}{\mathrm{\Σ}}}{\mathrm{\β}}_{\mathrm{ij}}^k{e}^{-\mathrm{\σ}{z}_i^k}{u}_j\left(s\right)e^{\mathrm{\σs}}\mathrm{d\σ}$

$-\underset{j\≠l}{\overset{n}{\mathrm{\Σ}}}\frac{{\stackrel{\‾}{\mathrm{\φ}}}_{\mathrm{ij}}\left(s\right)}{r_i^{*}\left(s\right)}{u}_j\left(s\right)e^{-(L_{\mathrm{ij}}-L_{\mathrm{il}})s}+\frac{g_{\mathrm{ri}}{r}_{\mathrm{ri}}{p^{*}}_i\left(s\right)}{p_{\mathrm{ri}}{r^{*}}_i\left(s\right)}{\mathrm{\υ}}_i\left(s\right)e^{-(L_{\mathrm{ri}}-L_{\mathrm{il}})s}$

3 controller parameterizations

Above controller architecture design after, design auto-adaptive control scheme make controller can be in the process of reality parameter excellent control effect is also arranged when changing.At first will be with controller parameterization.Controller can be written as

$u_i=\frac{1}{b_{\mathrm{ii}}}\{\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\frac{k_{\mathrm{ij}}\left(p\right)}{{\mathrm{\τ}}_i\left(p\right)r_i^{*}\left(p\right)}{u}_j(t-L_{\mathrm{ij}})+\frac{h_i\left(p\right)}{{\mathrm{\τ}}_i\left(p\right)r_i^{*}\left(p\right)}{y}_i\left(t\right)+\underset{j\≠l}{\overset{n}{\mathrm{\Σ}}}\frac{g_{\mathrm{ij}}{\stackrel{\‾}{r}}_{\mathrm{ij}}\left(p\right)}{r_i^{*}\left(p\right)}{u}_j\left(t\right)$

$+\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_{-L_{\mathrm{ij}}}^{-(L_{\mathrm{ij}}-L_{\mathrm{il}})}\underset{k=1}{\overset{m_i+n_i}{\mathrm{\Σ}}}{\mathrm{\β}}_{\mathrm{ij}}^k{e}^{-\mathrm{\σ}{z}_i^k}{u}_j(t+\mathrm{\σ})d\mathrm{\σ}+\underset{j\≠l}{\overset{n}{\mathrm{\Σ}}}{\∫}_{-(L_{\mathrm{ij}}-L_{\mathrm{il}})}^0\underset{k=1}{\overset{m_i}{\mathrm{\Σ}}}{\stackrel{\‾}{\mathrm{\β}}}_{\mathrm{ij}}^k{e}^{-\mathrm{\σ}{z}_i^k}{u}_j(t+\mathrm{\σ})\mathrm{d\σ}$

$-\underset{j\≠l}{\overset{n}{\mathrm{\Σ}}}\frac{{\stackrel{\‾}{\mathrm{\φ}}}_{\mathrm{ij}}\left(p\right)}{r_i^{*}\left(p\right)}{u}_j(t-(L_{\mathrm{ij}}-L_{\mathrm{il}}))-\underset{j\≠i}{\overset{n}{\mathrm{\Σ}}}{b}_{\mathrm{ij}}{u}_j\left(t\right)+\frac{g_{\mathrm{ri}}{r}_{\mathrm{ri}}\left(p\right){p^{*}}_i\left(p\right)}{p_{\mathrm{ri}}\left(p\right){r^{*}}_i\left(p\right)}{\mathrm{\υ}}_i(t-(L_{\mathrm{ri}}-L_{\mathrm{il}}))\}$

With polynomial expression h _i(s), k _Ij(s) and

Be written as respectively

$h_i\left(s\right)=h_{n_i-1}^i{s}^{n_i-1}+h_{n_i-2}^i{s}^{n_i-2}+...+h_0^i,$ $k_{\mathrm{ij}}\left(s\right)=k_{n_i-2}^{\mathrm{ij}}{s}^{n_i-2}+k_{n_i-3}^{\mathrm{ij}}{s}^{n_i-3}+...+k_0^{\mathrm{ij}},$

${\stackrel{\‾}{\mathrm{\φ}}}_{\mathrm{ij}}\left(s\right)=q_{m_i}^{\mathrm{ij}}{s}^{m_i}+q_{m_i-1}^{\mathrm{ij}}{s}^{m_i-1}+...+q_0^{\mathrm{ij}},j\≠l,$

The defined parameters vector

${\mathrm{\&theta;}}_i=\frac{1}{g_{\mathrm{ii}}}[k_{n_i-2}^{i1},...,k_0^{i1},...,k_{n_i-2}^{\mathrm{in}},...,k_0^{\mathrm{in}},h_{n_i-1}^i,...,h_0^i,g_{i1},...,g_{i,(l-1)},g_{i,(l-1)},...,g_{\mathrm{in}},q_{{\mathrm{<figure-callout\; id="1"\; label="m\; i\; i"\; filenames="HSA00000359802700012.png"\; state="\{\{state\}\}">m</figure-callout>}}_i}^i,$

$...,q_0^{\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="HSA00000359802700012.png"\; state="\{\{state\}\}">i</figure-callout>}1},...,q_{m_i}^{i,(l-1)},...,q_0^{i,(l-1)},q_{m_i}^{i,(l+1)},...,q_0^{i,(l+1)},...,q_{m_i}^{\mathrm{in}},...,q_0^{\mathrm{in}},b_{i1},...,$

${b_{i,i-1},b_{i,i+1},...,b_{\mathrm{in}},1]}^T$

${\mathrm{\&lambda;}}_{\mathrm{ij}}=\underset{k=1}{\overset{m_i+n_i}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{ij}}^k{e}^{-\mathrm{\&sigma;}{z}_i^k},i,j=\mathrm{1,2},...,n,$

${\mathrm{\&rho;}}_{\mathrm{ij}}=\underset{k=1}{\overset{m_i}{\mathrm{\&Sigma;}}}{\stackrel{\&OverBar;}{\mathrm{\&beta;}}}_{\mathrm{ij}}^k{e}^{-\mathrm{\&sigma;}{z}_i^k},j\&NotEqual;l$

Signal vector

${\mathrm{\&omega;}}_i\left(t\right)=[\frac{p^{n_i-2}}{{\mathrm{\&tau;}}_i\left(p\right)r_i^{*}\left(p\right)}{u}_1(t-L_{i1}),...,\frac{1}{{\mathrm{\&tau;}}_i\left(p\right)r_i^{*}\left(p\right)}{u}_1(t-L_{i1}),...,\frac{p^{n_i-2}}{{\mathrm{\&tau;}}_i\left(p\right)r_i^{*}\left(p\right)}{u}_n(t-L_{\mathrm{in}}),...,$

$\frac{1}{{\mathrm{\&tau;}}_i\left(p\right)r_i^{*}\left(p\right)}{u}_n(t-L_{\mathrm{in}}),\frac{p^{n_i-1}}{{\mathrm{\&tau;}}_i\left(p\right)r_i^{*}\left(p\right)}{y}_i\left(t\right),...,\frac{1}{{\mathrm{\&tau;}}_i\left(p\right)r_i^{*}\left(p\right)}{y}_i\left(t\right),\frac{{\stackrel{\&OverBar;}{r}}_{i1}\left(p\right)}{r_i^{*}\left(p\right)}{u}_1\left(t\right),...,$

$\frac{{\stackrel{\&OverBar;}{r}}_{i,(l-1)}\left(p\right)}{r_i^{*}\left(p\right)}{u}_{l-1}\left(t\right),\frac{{\stackrel{\&OverBar;}{r}}_{i,(l+1)}\left(p\right)}{r_i^{*}\left(p\right)}{u}_{l+1}\left(t\right),...\frac{{\stackrel{\&OverBar;}{r}}_{\mathrm{in}}\left(p\right)}{r_i^{*}\left(p\right)}{u}_n\left(t\right),-\frac{p^{m_i}}{r_i^{*}\left(p\right)}{u}_1(t-(L_{i1}-L_{\mathrm{il}})),...,$

$-\frac{1}{r_i^{*}\left(p\right)}{u}_1(t-(L_{i1}-L_{\mathrm{il}})),...,-\frac{p^{m_i}}{r_i^{*}\left(p\right)}{u}_{l-1}(t-(L_{i,(l-1)}-L_{\mathrm{il}})),...,$

$-\frac{1}{r_i^{*}\left(p\right)}{u}_{l-1}(t-(L_{i,(l-1)}-L_{\mathrm{il}})),...,-\frac{p^{m_i}}{r_i^{*}\left(p\right)}{u}_{l+1}(t-(L_{i,(l+1)}-L_{\mathrm{il}})),...,$

$-\frac{1}{r_i^{*}\left(p\right)}{u}_{l+1}(t-(L_{i(l+1)}-L_{\mathrm{il}})),...,-\frac{p^{m_i}}{r_i^{*}\left(p\right)}{u}_n(t-(L_{\mathrm{in}}-L_{\mathrm{il}})),...,$

$-\frac{1}{r_i^{*}\left(p\right)}{u}_n(t-(L_{\mathrm{in}}-L_{\mathrm{il}})),-u_1\left(t\right),...,-u_{i-1}\left(t\right),-u_{i+1}\left(t\right)...,-u_n\left(t\right),{\stackrel{\&OverBar;}{\mathrm{\&upsi;}}}_i(t-L_{\mathrm{il}}){]}^T$

Then the parametric expressions of controller is

$u_i\left(t\right)={\widehat{\mathrm{\&theta;}}}_i^T\left(t\right){\mathrm{\&omega;}}_i\left(t\right)+\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\&Integral;}_{-L_{\mathrm{ij}}}^{-(L_{\mathrm{ij}}-L_{\mathrm{il}})}{\widehat{\mathrm{\&lambda;}}}_{\mathrm{ij}}(t,\mathrm{\&sigma;})u_j(t+\mathrm{\&sigma;})\mathrm{d\&sigma;}+\underset{j\&NotEqual;l}{\overset{n}{\mathrm{\&Sigma;}}}{\&Integral;}_{-(L_{\mathrm{ij}}-L_{\mathrm{il}})}^0{\widehat{\mathrm{\&rho;}}}_{\mathrm{ij}}(t,\mathrm{\&sigma;})u_j(t+\mathrm{\&sigma;})\mathrm{d\&sigma;}$

Wherein

Be respectively θ _i, λ _Ij, ρ _IjEstimation.

4 error of calculation expression formulas

The definition error is

e _i(t)＝y _i(t)-y _ri(t)(i＝1，2，…，n)

The expression formula that calculates error is

$e_i\left(t\right)=b_{\mathrm{ii}}\frac{r_i^{*}\left(p\right)}{p_i^{*}\left(p\right)}{q}^{-L_{\mathrm{il}}}\{{\widetilde{\mathrm{\&theta;}}}_i^T\left(t\right){\mathrm{\&omega;}}_i\left(t\right)+\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\&Integral;}_{-L_{\mathrm{ij}}}^{-(L_{\mathrm{ij}}-L_{\mathrm{il}})}{\widetilde{\mathrm{\&lambda;}}}_{\mathrm{ij}}(t,\mathrm{\&sigma;})u_j(t+\mathrm{\&sigma;})\mathrm{d\&sigma;}+\underset{j\&NotEqual;l}{\overset{n}{\mathrm{\&Sigma;}}}{\&Integral;}_{-(L_{\mathrm{ij}}-L_{\mathrm{il}})}^0{\widetilde{\mathrm{\&rho;}}}_{\mathrm{ij}}(t,\mathrm{\&sigma;})u_j(t+\mathrm{\&sigma;})\mathrm{d\&sigma;}\}$

Wherein be

Be the time lag operator, promptly

Estimate parameter in the controller in order to design adaptive law, need utilize the augmentation error.Definition

${\mathrm{\&eta;}}_i\left(t\right)=\{{\widetilde{\mathrm{\&theta;}}}_i^T\left(t\right){\stackrel{\&OverBar;}{\mathrm{\&omega;}}}_i\left(t\right)+\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\&Integral;}_{-L_{\mathrm{ij}}}^{-(L_{\mathrm{ij}}-L_{\mathrm{il}})}{\widetilde{\mathrm{\&lambda;}}}_{\mathrm{ij}}(t,\mathrm{\&sigma;}){\stackrel{\&OverBar;}{u}}_j(t+\mathrm{\&sigma;})\mathrm{d\&sigma;}+\underset{j\&NotEqual;l}{\overset{n}{\mathrm{\&Sigma;}}}{\&Integral;}_{-(L_{\mathrm{ij}}-L_{\mathrm{il}})}^0{\widetilde{\mathrm{\&rho;}}}_{\mathrm{ij}}(t,\mathrm{\&sigma;}){\stackrel{\&OverBar;}{u}}_j(t+\mathrm{\&sigma;})\mathrm{d\&sigma;}\}$

$-\frac{r_i^{*}\left(p\right)}{p_i^{*}\left(p\right)}{q}^{-L_{\mathrm{il}}}\{{\widetilde{\mathrm{\&theta;}}}_i^T\left(t\right){\mathrm{\&omega;}}_i\left(t\right)+\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\&Integral;}_{-L_{\mathrm{ij}}}^{-(L_{\mathrm{ij}}-L_{\mathrm{il}})}{\widetilde{\mathrm{\&lambda;}}}_{\mathrm{ij}}(t,\mathrm{\&sigma;})u_j(t+\mathrm{\&sigma;})\mathrm{d\&sigma;}$

$+\underset{j\&NotEqual;l}{\overset{n}{\mathrm{\&Sigma;}}}{\&Integral;}_{-(L_{\mathrm{ij}}-L_{\mathrm{il}})}^0{\widetilde{\mathrm{\&rho;}}}_{\mathrm{ij}}(t,\mathrm{\&sigma;})u_j(t+\mathrm{\&sigma;})\mathrm{d\&sigma;}\}$

Wherein

${\stackrel{\&OverBar;}{\mathrm{\&omega;}}}_i\left(t\right)=\frac{r_i^{*}\left(p\right)}{p_i^{*}\left(p\right)}{q}^{-L_{\mathrm{il}}}{\mathrm{\&omega;}}_i\left(t\right),$ ${\stackrel{\&OverBar;}{u}}_j\left(t\right)=\frac{r_i^{*}\left(p\right)}{p_i^{*}\left(p\right)}{q}^{-L_{\mathrm{ij}}}{u}_j\left(t\right),j=\mathrm{1,2}...,n$

Definition augmentation error is

${\mathrm{\&epsiv;}}_i\left(t\right)=e_i\left(t\right)+{\hat{g}}_{\mathrm{ii}}\left(t\right){\mathrm{\&eta;}}_i\left(t\right)$

$=g_{\mathrm{ii}}\{{\widetilde{\mathrm{\&theta;}}}_i^T\left(t\right){\stackrel{\&OverBar;}{\mathrm{\&omega;}}}_i\left(t\right)+\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\&Integral;}_{-L_{\mathrm{ij}}}^{-(L_{\mathrm{ij}}-L_{\mathrm{il}})}{\widetilde{\mathrm{\&lambda;}}}_{\mathrm{ij}}(t,\mathrm{\&sigma;}){\stackrel{\&OverBar;}{u}}_j(t+\mathrm{\&sigma;})\mathrm{d\&sigma;}+\underset{j\&NotEqual;l}{\overset{N}{\mathrm{\&Sigma;}}}{\&Integral;}_{-(L_{\mathrm{ij}}-L_{\mathrm{il}})}^0{\widetilde{\mathrm{\&rho;}}}_{\mathrm{ij}}(t,\mathrm{\&sigma;}){\stackrel{\&OverBar;}{u}}_j(t+\mathrm{\&sigma;})\mathrm{d\&sigma;}\}+{\tilde{g}}_{\mathrm{ii}}\left(t\right){\mathrm{\&eta;}}_i\left(t\right)$

Wherein

Be g _IiEstimation.

5 according to error expression selection adaptive law

Define a signal vector

${\mathrm{\&Omega;}}_i\left(t\right)=[{\stackrel{\&OverBar;}{\mathrm{\&omega;}}}_i\left(t\right),\underset{-{\mathrm{<figure-callout\; id="1"\; label="L\; i"\; filenames="HSA00000359802700012.png"\; state="\{\{state\}\}">L</figure-callout>}}_i\&le;\mathrm{\&sigma;}\&le;-(L_{i1}-L_{\mathrm{il}})}{\sup }{\stackrel{\&OverBar;}{u}}_1(t+\mathrm{\&sigma;}),...\underset{-L_{i,(l-1)}\&le;\mathrm{\&sigma;}\&le;-(L_{i,(l-1)}-L_{\mathrm{il}})}{\sup }{\stackrel{\&OverBar;}{u}}_{l-1}(t+\mathrm{\&sigma;}),\underset{-L_{\mathrm{il}}\&le;\mathrm{\&sigma;}\&le;0}{\sup }{\stackrel{\&OverBar;}{u}}_l(t+\mathrm{\&sigma;}),$

$\underset{-L_{i,(l+1)}\&le;\mathrm{\&sigma;}\&le;-(L_{i,(l+1)}-L_{\mathrm{il}})}{\sup }{\stackrel{\&OverBar;}{u}}_{l+1}(t+\mathrm{\&sigma;}),...\underset{-L_{\mathrm{in}}\&le;\mathrm{\&sigma;}\&le;-(L_{\mathrm{in}}-L_{\mathrm{il}})}{\sup }{\stackrel{\&OverBar;}{u}}_n(t+\mathrm{\&sigma;}),\underset{-(L_{i,(l-1)}-L_{\mathrm{il}})\&le;\mathrm{\&sigma;}\&le;0}{\sup }{\stackrel{\&OverBar;}{u}}_1(t+\mathrm{\&sigma;}),...$

$\underset{-L_{i,(l-1)}\&le;\mathrm{\&sigma;}\&le;0}{\sup }{\stackrel{\&OverBar;}{u}}_{l-1}(t+\mathrm{\&sigma;}),\underset{-(L_{i,(l+1)}-L_{\mathrm{il}})\&le;\mathrm{\&sigma;}\&le;0}{\sup }{\stackrel{\&OverBar;}{u}}_{l+1}(t+\mathrm{\&sigma;}),...\underset{-(L_{\mathrm{in}}-L_{\mathrm{il}})\&le;\mathrm{\&sigma;}\&le;0}{\sup }{\stackrel{\&OverBar;}{u}}_n(t+\mathrm{\&sigma;}),{\mathrm{\&eta;}}_i\left(t\right){]}^T$

Select adaptive law

${\stackrel{.}{\widehat{\mathrm{\&theta;}}}}_i\left(t\right)=-{\mathrm{\&tau;}}_{{\mathrm{\&theta;}}_i}\frac{{\stackrel{\&OverBar;}{\mathrm{\&omega;}}}_i\left(t\right){\mathrm{\&epsiv;}}_i\left(t\right)}{1+{\left|\right|{\mathrm{\&Omega;}}_i\left(t\right)\left|\right|}^2},i=\mathrm{1,2},...,n$

${\stackrel{.}{\hat{g}}}_{\mathrm{ii}}\left(t\right)=-{\mathrm{\&tau;}}_{g_{\mathrm{ii}}}\frac{{\mathrm{\&eta;}}_i\left(t\right){\mathrm{\&epsiv;}}_i\left(t\right)}{1+{\left|\right|{\mathrm{\&Omega;}}_i\left(t\right)\left|\right|}^2},i=\mathrm{1,2},...,n$

${\stackrel{.}{\widehat{\mathrm{\&lambda;}}}}_{\mathrm{ij}}(t,\mathrm{\&sigma;})=-{\mathrm{\&tau;}}_{{\mathrm{\&lambda;}}_{\mathrm{ij}}}\frac{{\stackrel{\&OverBar;}{u}}_j(t+\mathrm{\&sigma;})}{1+{\left|\right|{\mathrm{\&Omega;}}_i\left(t\right)\left|\right|}^2}{\mathrm{\&epsiv;}}_i\left(t\right),-L_{\mathrm{ij}}\&le;\mathrm{\&sigma;}\&le;-(L_{\mathrm{ij}}-L_{\mathrm{il}}),j=\mathrm{1,2},...,n$

${\stackrel{.}{\widehat{\mathrm{\&rho;}}}}_{\mathrm{ij}}(t,\mathrm{\&sigma;})=-{\mathrm{\&tau;}}_{{\mathrm{\&rho;}}_{\mathrm{ij}}}\frac{{\stackrel{\&OverBar;}{u}}_j(t+\mathrm{\&sigma;})}{1+{\left|\right|{\mathrm{\&Omega;}}_i\left(t\right)\left|\right|}^2}{\mathrm{\&epsiv;}}_i\left(t\right),-(L_{\mathrm{ij}}-L_{\mathrm{il}})\&le;\mathrm{\&sigma;}\&le;0,j\&NotEqual;l$

Wherein

It is adjustable parameter.By adjusting these parameters, come the parameter in the controlled device, thereby come control system.The auto-adaptive control scheme design is finished thus, and promptly it is made up of controller and adaptive law.

Claims (6)

1. the self-adaptation control method of a multivariable time-lag process is characterized in that:

The design of time lag compensation device;

The polynomial equation group is found the solution;

Nominal system Model Matching design of Controller;

Controller parameterization;

Select adaptive law according to error expression.

2. method according to claim 1 is characterized in that we have designed the time lag compensation device, is used for compensating a plurality of time lags of multivariable time-lag process.

3. method according to claim 1 is characterized in that, finds the solution the polynomial equation group, obtains separating of they.

4. method according to claim 1 is characterized in that, designs the Model Matching controller of nominal system, and this controller can make the closed-loop system transport function equal the reference model transport function.

5. method according to claim 1 is characterized in that, the Model Matching controller parameterization with obtaining obtains parametric expressions.

6. method according to claim 1 is characterized in that, utilizes the parametric expressions of controller, calculates the parametric expressions of error, thereby selects the adaptive law of unknown parameter.

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