CN103901773A - Method for designing 2D hybrid controller according to input delay - Google Patents

Abstract

The invention discloses a method for designing a 2D hybrid controller according to input delay. The method includes the steps that A, a two-dimensional state space model with input delay is built; B, according to the size of time-varying delay, the built two-dimensional state space model is converted into a two-dimensional delay augmentation conversion model; C, the controller meeting the requirement of a control law is designed according to the two-dimensional delay augmentation conversion model; D, the gain of the controller is solved by means of a linear matrix inequality. The method is based on a segmentation method, and the two-dimensional delay augmentation conversion model simultaneously containing the large delay situation and the small delay situation is adopted to design the controller, so that even if a system bears influences of unknown delay larger than a cycle, the system can keep stable, and the stability is high. Meanwhile, the method has the advantages of being simple in calculation, quick in tracking and good in control performance, and can be widely used in the field of industrial controller design.

Description

A kind of 2D for input delay mixes controller design method

Technical field

The present invention relates to industrial control unit (ICU) design field, especially a kind of 2D for input delay mixes controller design method.

Background technology

It is a kind of open loop feedforward control in essence that ILC (iterative learning) controls, revise current control inputs according to the previous control experience of system and output error, make the actual output trajectory of controlled system in finite time interval, realize the tracking completely of zero error along whole desired output track.This control method has superiority solving aspect the TRAJECTORY CONTROL of unknown structure, Complex Nonlinear System, it can be in system operation, unknown message is carried out to on-line study, in learning process, constantly make up the priori of shortage, thereby control performance is progressively improved, there is less dependence system priori, but because it does not utilize the Real-time Feedback information of system completely, in the time there is uncertain variation in the dynamic perfromance of system, control performance is as the robust stability of system, and convergence etc. are difficult to ensure.

It is a kind of universal phenomenon that batch process self has retarding characteristic, and the time lag unsettled principal element that is system is very complicated on the impact of stability, and the existence of time lag makes the stability analysis of system and controller design become more difficult.For example, in batch process control, often there is input delay, cause having or not the appearance of beat control problem.To this, traditional way is to adopt pure ILC control algolithm to control the batch process with input delay in the industry, with stablizing of maintenance system.Be less than one-period situation (being only wrong rear one situation of clapping of input delay) for unknown time lag, this control mode is effectively, can maintain the stable of system; But, being greater than the situation while clapping even more bats (be after input delay mistake two) of one-period for unknown time lag, it is even unstable that this control mode can make the stability of system obviously decline, and causing the product of production is the product of inferior quality.

Therefore, industry is needed a kind of new controller of design badly, even if the impact that makes system be greater than the unknown time lag of one-period still can keep stable, and it has good control performance.

Summary of the invention

In order to solve the problems of the technologies described above, the object of the invention is: provide that a kind of stability is high, control performance is good, mix controller design method for the 2D of input delay.

The technical solution adopted for the present invention to solve the technical problems is: a kind of 2D for input delay mixes controller design method, comprising:

A, structure have the two-dimensional state spatial model of input delay, and described two-dimensional state spatial model is as follows:

$\begin{array}{c}{\mathrm{\Σ}}_{P-\mathrm{delay}}:\\ \left\{\begin{array}{c}x(t+1,k)=(A+{\mathrm{\Δ}}_a(t,k))x(t,k)+(B+{\mathrm{\Δ}}_b(t,k))u(t-d\left(t\right),k)\\ y(t,k)=\mathrm{Cx}(t,k)\\ x(t,k)=x_{0,k};-d_M\≤t\≤0;k=\mathrm{1,2},...\end{array}\right.\end{array},$

Wherein, t represents the time, the cycle of k representative operation, X _{0, k}k ^thbatch original state; X (t, k) ∈ R ⁿ, y (t, k) ∈ R ^l, u (t-d (t), k) ∈ R ^mrepresentative system is at t moment k respectively ^thbatch state, output and input, R ^l, R ^m, R ⁿrepresentative is the vector space of l, m, n dimension respectively, along time orientation time become time lag d (t) and meet d _m≤ d (t)≤d _m, d _m, d _mit is respectively the bound of time lag; A, A _d, C and B are all known real constant matrixes, Δ _a(t, k), Δ _d(t, k) and Δ _b(t, k) is system model parameter uncertain matrix and meets [Δ _a(t, k) Δ _b(t, k)]=E Δ (t, k) [F F _b], Δ ^t(t, k) Δ (t, k)≤I, (0≤t≤T, k=1,2 ...), E, F and F _bbe known real constant matrix, I is suitable dimension unit matrix;

B, according to time become the size of time lag d (t), the two-dimensional state spatial model of structure is converted to two-dimentional time lag augmentation switching model, described two-dimentional time lag augmentation switching model is as follows:

$\begin{array}{c}{\mathrm{\Σ}}_{2D-P-\mathrm{delay}}:\\ \left\{\begin{array}{c}{x}_e(t+1,k)=({\stackrel{\‾}{A}}_1+{\stackrel{\‾}{\mathrm{\Δ}}}_a(t,k))x_e(t,k)+{\stackrel{\‾}{A}}_2{x}_e(t+1,k-1)\\ +(\stackrel{\‾}{B}+{\stackrel{\‾}{\mathrm{\Δ}}}_b(t,k))r(t-d_{\mathrm{\σ}\left(t\right)}\left(t\right),k)+\mathrm{H\ω}(t,k)\\ z(t,k)\stackrel{\mathrm{\Δ}}{=}e(t,k)={\mathrm{Gx}}_e(t,k)\end{array}\right.,\end{array}$

Wherein, $x_e(t,k)=\left[\begin{array}{c}{x}_{\mathrm{\Δ}}(t,k)\\ e(t,k)\end{array}\right]$ For the state of system, ${\stackrel{\‾}{A}}_1=\left[\begin{array}{cc}A& 0\\ \mathrm{CA}& 0\end{array}\right],\stackrel{\‾}{B}=\left[\begin{array}{c}B\\ \mathrm{CB}\end{array}\right],$

${\stackrel{\‾}{\mathrm{\Δ}}}_a(t,k)=\stackrel{\‾}{E}\mathrm{\Δ}(t,k)\stackrel{\‾}{F},{\stackrel{\‾}{\mathrm{\Δ}}}_b(t,k)=\stackrel{\‾}{E}\mathrm{\Δ}(t,k)F_b,\stackrel{\‾}{E}=\left[\begin{array}{c}E\\ \mathrm{CE}\end{array}\right],\stackrel{\‾}{F}=\left[\begin{array}{cc}F& 0\end{array}\right],H=\left[\begin{array}{c}I\\ C\end{array}\right],$ G=[0 I], ω (t, k)=(Δ _a(t, k)-Δ _a(t, k-1)) x (t, k-1)+(Δ _b(t, k)-Δ _b(t, k-1)) u (t-d (t), k-1), can regard external interference as,

for piecewise constant function, also make switching signal: σ (t)=1 expression system move in Small Time Lag situation, σ (t)=2 expression system is moved in large dead time situation;

C, design and meet control law r (t-d according to two-dimentional time lag augmentation switching model _{σ (t)}(t), controller k), described control law r (t-d _{σ (t)}(t), k) as follows:

∑ _2D-C-delay：

r(t-d _σ(t)(t)，k)＝K _σ(t)3x _e(t-d _σ(t)(t)，k-1)+K _σ(t)2x _e(t+1，k-1)+K _σ(t)1x _e(t，k)’

Wherein, K _{σ (t) 3}, K _{σ (t) 2}and K _{σ (t) 1}for controller gain and K _{σ (t) 3}=Y _{σ (t) 3}l ^-1, K _{σ (t) 2}=Y _{σ (t) 2}l ^-1, K _{σ (t) 1}=Y _{σ (t) 1}l ^-1, Y _{σ (t) 1}, Y _{σ (t) 2}and Y _{σ (t) 3}tie up matrix to be asked for fitting;

The gain K of the form of D, employing LMI to controller _{σ (t) 3}, K _{σ (t) 2}and K _{σ (t) 1}solve.

Further, described step B, it comprises:

The iterative learning control law of B1, design time lag system, described iterative learning control law is as follows:

∑ _ilcu(t-d(t)，k)＝u(t-d(t)，k-1)+r(t-d(t)，k)，

Wherein, u (t-d (t), 0)=0, t=0,1,2, U (t-d (t), k), u (t-d (t), k-1) is respectively the control inputs of k, (k-1) batch current time, (t-d (t), k) is more new law of iterative learning to r;

B2, according to time become the size of time lag d (t), the two-dimensional state spatial model of structure is converted to time lag switching model, described time lag switching model is:

$\begin{array}{c}{\mathrm{\Σ}}_{P-\mathrm{delay}}:\\ \left\{\begin{array}{c}x(t+1,k)=(A+{\mathrm{\Δ}}_a(t,k))x(t,k)+(B+{\mathrm{\Δ}}_b(t,k))u(t-d_{\mathrm{\σ}\left(t\right)}\left(t\right),k)\\ y(t,k)=\mathrm{Cx}(t,k)\\ x(t,k)=x_{0,k};-d_M\≤t\≤0;k=\mathrm{1,2},...\end{array}\right.\end{array};$

B3, the state-space model in conjunction with structure, iterative learning control law, time lag switching model, predefined current batch of output error and the predefined batch of deflection error of design, draw two-dimentional time lag augmentation switching model.

Further, described step B2, it comprises:

B21, according to time become the size of Uncertainty Δ d (t) in time lag d (t) and judge that time lag system belongs to large dead time situation or belongs to Small Time Lag situation: if Δ d (t) < 1, represent that time lag system belongs to Small Time Lag situation, now, d (t) should meet d _m≤ d (t)≤h ₁and h ₁< d _m; If Δ d (t) > 1, represents that time lag system belongs to large dead time situation, now, d (t) should meet h ₁≤ d (t)≤d _m;

B22, according to the result of judgement and time become the scope of time lag d (t), the two-dimensional state spatial model of structure is converted to time lag switching model.

Further, described predefined current batch of output error is: e (t, k)=y (t, k)-y _d(t), wherein yd (t) is given output; Described predefined batch of deflection error is: x _Δ(t, k)=x (t, k)-x (t, k-1)

Further, described step C, it is specially:

According to given stability criterion condition, the gain K of the form of employing LMI to controller _{σ (t) 3}, k _{σ (t) 2}and K _{σ (t) 1}solve, described given stability criterion condition is:

$\left[\begin{array}{cccccccc}-\mathrm{\&alpha;L}& 0& 0& 0& 0& L{\stackrel{\&OverBar;}{A}}_1^T+Y_{i1}^T{\stackrel{\&OverBar;}{B}}^T& L{\stackrel{\&OverBar;}{F}}^T+Y_{i1}^T{F}_b^T& {\mathrm{LG}}^T\\ *& -(1-\mathrm{\&alpha;})L+{\stackrel{\&OverBar;}{W}}_i+{\tilde{h}}_i{\stackrel{\&OverBar;}{Q}}_i& 0& 0& 0& L{\stackrel{\&OverBar;}{A}}_2^T+Y_{i2}^T{\stackrel{\&OverBar;}{B}}^T& Y_{i2}^T{F}_b^T& 0\\ *& *& -{\stackrel{\&OverBar;}{Q}}_i& 0& 0& Y_{i3}^T{\stackrel{\&OverBar;}{B}}^T& Y_{i3}^T{F}_b^T& 0\\ *& *& *& -{\stackrel{\&OverBar;}{W}}_i& 0& 0& 0& 0\\ *& *& *& *& -{\mathrm{\&gamma;}}_{i}I& H^T& 0& 0\\ *& *& *& *& *& -L+{\mathrm{\&epsiv;}}_i\stackrel{}{\stackrel{\&OverBar;}{E}}{\stackrel{\&OverBar;}{E}}^T& 0& 0\\ *& *& *& *& *& *& -{\mathrm{\&epsiv;}}_{i}I& 0\\ *& *& *& *& *& *& *& -{\mathrm{\&gamma;}}_{i}I\end{array}\right]<0,$

Wherein, L,

with

be positive definite symmetric matrices, matrix Y _i1, Y _i2, Y _i3∈ R ^{m × (n+l)}and constant γ _i> 0, ε _i> 0 (i=1,2), L=P ^-1,

Y _i＝[y _i1 Y _i2 Y _i3]＝[K _i1L K _i2L K _i3L]。

The invention has the beneficial effects as follows: based on the method for segmentation, adopt the two-dimentional time lag augmentation switching model that simultaneously comprises large dead time situation and Small Time Lag situation to carry out CONTROLLER DESIGN, according to time become the unknown time lag of size of time lag uncertainty input delay is carried out to segmentation, and by the method for switching, input delay is controlled, thereby carry out segmentation control by the method for switching, even if the impact that makes system be greater than the unknown time lag of one-period still can keep stable, stability is higher, also have simultaneously and calculate simply, follow the tracks of fast and the good advantage of control performance.

Brief description of the drawings

Below in conjunction with drawings and Examples, the invention will be further described.

Fig. 1 is the flow chart of steps that a kind of 2D for input delay of the present invention mixes controller design method;

Fig. 2 is the process flow diagram of step B of the present invention;

Fig. 3 is the process flow diagram of step B2 of the present invention.

Embodiment

With reference to Fig. 1, a kind of 2D for input delay mixes controller design method, comprising:

A, structure have the two-dimensional state spatial model of input delay, and described two-dimensional state spatial model is as follows:

$\begin{array}{c}{\mathrm{\&Sigma;}}_{P-\mathrm{delay}}:\\ \left\{\begin{array}{c}x(t+1,k)=(A+{\mathrm{\&Delta;}}_a(t,k))x(t,k)+(B+{\mathrm{\&Delta;}}_b(t,k))u(t-d\left(t\right),k)\\ y(t,k)=\mathrm{Cx}(t,k)\\ x(t,k)=x_{0,k};-d_M\&le;t\&le;0;k=\mathrm{1,2},...\end{array}\right.\end{array},$

Wherein, t represents the time, the cycle of k representative operation, X _{0, k}k ^thbatch original state; X (t, k) ∈ R ⁿ, y (t, k) ∈ R ^l, u (t-d (t), k) ∈ R ^mrepresentative system is at t moment k respectively ^thbatch state, output and input, R ^l, R ^m, R ⁿrepresentative is the vector space of l, m, n dimension respectively, along time orientation time become time lag d (t) and meet d _m≤ d (t)≤d _m, d _m, d _mit is respectively the bound of time lag; A, A _d, C and B are all known real constant matrixes, Δ _a(t, k), Δ _d(t, k) and Δ _b(t, k) is system model parameter uncertain matrix and meets [Δ _a(t, K) Δ _b(t, k)]=E Δ (t, k) [F F _b], Δ ^t(t, k) Δ (t, k)≤I, (0≤t≤T, k=1,2 ...), E, F and F _bbe known real constant matrix, I is suitable dimension unit matrix;

B, according to time become the size of time lag d (t), the two-dimensional state spatial model of structure is converted to two-dimentional time lag augmentation switching model, described two-dimentional time lag augmentation switching model is as follows:

$\begin{array}{c}{\mathrm{\&Sigma;}}_{2D-P-\mathrm{delay}}:\\ \left\{\begin{array}{c}{x}_e(t+1,k)=({\stackrel{\&OverBar;}{A}}_1+{\stackrel{\&OverBar;}{\mathrm{\&Delta;}}}_a(t,k))x_e(t,k)+{\stackrel{\&OverBar;}{A}}_2{x}_e(t+1,k-1)\\ +(\stackrel{\&OverBar;}{B}+{\stackrel{\&OverBar;}{\mathrm{\&Delta;}}}_b(t,k))r(t-d_{\mathrm{\&sigma;}\left(t\right)}\left(t\right),k)+\mathrm{H\&omega;}(t,k)\\ z(t,k)\stackrel{\mathrm{\&Delta;}}{=}e(t,k)={\mathrm{Gx}}_e(t,k)\end{array}\right.,\end{array}$

Wherein, $x_e(t,k)=\left[\begin{array}{c}{x}_{\mathrm{\&Delta;}}(t,k)\\ e(t,k)\end{array}\right]$ For the state of system, ${\stackrel{\&OverBar;}{A}}_1=\left[\begin{array}{cc}A& 0\\ \mathrm{CA}& 0\end{array}\right],\stackrel{\&OverBar;}{B}=\left[\begin{array}{c}B\\ \mathrm{CB}\end{array}\right],$ ${\stackrel{\&OverBar;}{\mathrm{\&Delta;}}}_a(t,k)=\stackrel{\&OverBar;}{E}\mathrm{\&Delta;}(t,k)\stackrel{\&OverBar;}{F},{\stackrel{\&OverBar;}{\mathrm{\&Delta;}}}_b(t,k)=\stackrel{\&OverBar;}{E}\mathrm{\&Delta;}(t,k)F_b,\stackrel{\&OverBar;}{E}=\left[\begin{array}{c}E\\ \mathrm{CE}\end{array}\right],\stackrel{\&OverBar;}{F}=\left[\begin{array}{cc}F& 0\end{array}\right],H=\left[\begin{array}{c}I\\ C\end{array}\right],$ G=[0 I], ω (t, k)=(Δ _a(t, k)-Δ _a(t, k-1)) x (t, k-1)+(Δ _b(t, k)-Δ _b(t, k-1)) u (t-d (t), k-1), can regard external interference as,

for piecewise constant function, also make switching signal: σ (t)=1 expression system move in Small Time Lag situation, σ (t)=2 expression system is moved in large dead time situation;

C, design and meet control law r (t-d according to two-dimentional time lag augmentation switching model _{σ (t)}(t), controller k), described control law r (t-d _{σ (t)}(t), k) as follows:

∑ _2D-C-delay：

r(t-d _σ(t)(t)，k)＝K _σ(t)3x _e(t-d _σ(t)(t)，k-1)+K _σ(t)2x _e(t+1，k-1)+K _σ(t)1x _e(t，k)’

Wherein, K _{σ (t) 3}, K _{σ (t) 2}and K _{σ (t) 1}for controller gain and K _{σ (t) 3}=Y _{σ (t) 3}l ^-1, K _{σ (t) 2}=Y _{σ (t) 2}l ^-1, K _{σ (t) 1}=Y _{σ (t) 1}l ^-1, Y _{σ (t) 1}, Y _{σ (t) 2}and Y _{σ (t) 3}tie up matrix to be asked for fitting;

The gain K of the form of D, employing LMI to controller _{σ (t) 3}, K _{σ (t) 2}and K _{σ (t) 1}solve.

Wherein, suitable dimension matrix refers to according to actual needs, can choose flexibly the dimension of matrix.

Time become the size of time lag d (t), represent that unknown time lag is the situation (Small Time Lag situation) that the situation (large dead time situation) that is greater than one-period is still less than one-period, has reflected the uncertainty of unknown time lag.

Two dimension time lag augmentation switching model comprises large dead time situation and Small Time Lag situation simultaneously, can according to time become the size of time lag d (t), automatically switch.

The present invention has adopted a kind of state-space model of two-dimensional time system, be greater than one-period situation for unknown time lag, adopt segmentation method, by unknown delay fractioning in the different cycles, thereby design corresponding controller for the different cycles, and its all controller deposit is got up, finally call corresponding controller according to actual conditions, carry out closed-loop control by changing method.

With reference to Fig. 2, be further used as preferred embodiment, described step B, it comprises:

The iterative learning control law of B1, design time lag system, described iterative learning control law is as follows:

∑ _ilc u(t-d(t)，k)＝u(t-d(t)，k-1)+r(t-d(t)，k)，

Wherein, u (t-d (t), 0)=0, t=0,1,2, U (t-d (t), k), u (t-d (t), k-1) is respectively the control inputs of k, (k-1) batch current time, (t-d (t), k) is more new law of iterative learning to r;

B2, according to time become the size of time lag d (t), the two-dimensional state spatial model of structure is converted to time lag switching model, described time lag switching model is:

$\begin{array}{c}{\mathrm{\&Sigma;}}_{P-\mathrm{delay}}:\\ \left\{\begin{array}{c}x(t+1,k)=(A+{\mathrm{\&Delta;}}_a(t,k))x(t,k)+(B+{\mathrm{\&Delta;}}_b(t,k))u(t-d_{\mathrm{\&sigma;}\left(t\right)}\left(t\right),k)\\ y(t,k)=\mathrm{Cx}(t,k)\\ x(t,k)=x_{0,k};-d_M\&le;t\&le;0;k=\mathrm{1,2},...\end{array}\right.\end{array};$

B3, the state-space model in conjunction with structure, iterative learning control law, time lag switching model, predefined current batch of output error and the predefined batch of deflection error of design, draw two-dimentional time lag augmentation switching model.

With reference to Fig. 3, be further used as preferred embodiment, described step B2, it comprises:

B21, according to time become the size of Uncertainty Δ d (t) in time lag d (t) and judge that time lag system belongs to large dead time situation or belongs to Small Time Lag situation: if Δ d (t) < 1, represent that time lag system belongs to Small Time Lag situation, now, d (t) should meet d _m≤ d (t)≤h ₁and h ₁< d _m; If Δ d (t) > 1, represents that time lag system belongs to large dead time situation, now, d (t) should meet h ₁≤ d (t)≤d _m;

B22, according to the result of judgement and time become the scope of time lag d (t), the two-dimensional state spatial model of structure is converted to time lag switching model.

Wherein, d (t)=d+ Δ d (t), wherein d is more than or equal to 0 integer, becomes the Uncertainty of time lag d (t) while representative, and Δ d (t) becomes the Uncertainty of time lag d (t) while being.

Be further used as preferred embodiment, described predefined current batch of output error is: e (t, k)=y (t, k)-y _d(t), wherein yd (t) is given output; Described predefined batch of deflection error is: x _Δ(t, k)=x (t, k)-x (t, k-1).

Be further used as preferred embodiment, described step C, it is specially:

According to given stability criterion condition, the gain K of the form of employing LMI to controller _{σ (t) 3}, K _{σ (t) 2}and K _{σ (t) 1}solve, described given stability criterion condition is:

$\left[\begin{array}{cccccccc}-\mathrm{\&alpha;L}& 0& 0& 0& 0& L{\stackrel{\&OverBar;}{A}}_1^T+Y_{i1}^T{\stackrel{\&OverBar;}{B}}^T& L{\stackrel{\&OverBar;}{F}}^T+Y_{i1}^T{F}_b^T& {\mathrm{LG}}^T\\ *& -(1-\mathrm{\&alpha;})L+{\stackrel{\&OverBar;}{W}}_i+{\tilde{h}}_i{\stackrel{\&OverBar;}{Q}}_i& 0& 0& 0& L{\stackrel{\&OverBar;}{A}}_2^T+Y_{i2}^T{\stackrel{\&OverBar;}{B}}^T& Y_{i2}^T{F}_b^T& 0\\ *& *& -{\stackrel{\&OverBar;}{Q}}_i& 0& 0& Y_{i3}^T{\stackrel{\&OverBar;}{B}}^T& Y_{i3}^T{F}_b^T& 0\\ *& *& *& -{\stackrel{\&OverBar;}{W}}_i& 0& 0& 0& 0\\ *& *& *& *& -{\mathrm{\&gamma;}}_{i}I& H^T& 0& 0\\ *& *& *& *& *& -L+{\mathrm{\&epsiv;}}_i\stackrel{}{\stackrel{\&OverBar;}{E}}{\stackrel{\&OverBar;}{E}}^T& 0& 0\\ *& *& *& *& *& *& -{\mathrm{\&epsiv;}}_{i}I& 0\\ *& *& *& *& *& *& *& -{\mathrm{\&gamma;}}_{i}I\end{array}\right]<0,$

Wherein, L,

with be positive definite symmetric matrices, matrix Y _i1, Y _i2, Y _i3∈ R ^{m × (n+l)}and constant γ _i> 0, ε _i> 0 (i=1,2), L=P ^-1,

Y _i＝[Y _i1 Y _i2 Y _i3]＝[K _i1L K _i2L K _i3L]。

Below in conjunction with specific embodiment, the present invention is described in further detail.

Embodiment 1

The present embodiment, taking injection moulding process as example, describes the detailed process that the two-dimensional state spatial model of structure is converted to two-dimentional time lag augmentation switching model.

The detailed process that the two-dimensional state spatial model of structure is converted to two-dimentional time lag augmentation switching model by the present invention is as follows:

First according to the repeat property of injection moulding process, design iteration study control law is:

∑ _ilc u(t-d(t)，k)＝u(t-d(t)，k-1)+r(t-d(t)，k) (1)

Wherein, u (t-d (t), 0)=0, t=0,1,2, (t-d (t), k), u (t-d (t), k-1) is respectively the control inputs of k, (k-1) batch current time, (t-d (t) k) is more new law of iterative learning to r to u.

Be divided into following two kinds of situations here for time lag:

(1) Δ d (t) < 1, Uncertainty Δ d (t) is less than 1 cycle, is Small Time Lag situation, and now, the scope of d (t) is d _m≤ d (t)≤h ₁and h ₁< d _m, wherein h1 is positive number.

(2) Δ d (t) > 1, Uncertainty Δ d (t) is greater than 1 cycle, is large dead time situation, and now, d (t) scope is h ₁≤ d (t)≤d _m.In actual commercial production or Industry Control, Small Time Lag situation often occurs, and large dead time situation occurs once in a while, and the controller that conventional needle designs Small Time Lag situation can not ensure the stability of system in the time of large dead time situation.Therefore, must redesign controller to guarantee the stable of system, thereby ensure the quality of product.

For above-mentioned two situations, the system based on two-dimensional state spatial model can be converted to following Switched Systems with Time Delay:

$\begin{array}{c}{\mathrm{\&Sigma;}}_{P-\mathrm{delay}}:\\ \left\{\begin{array}{c}x(t+1,k)=(A+{\mathrm{\&Delta;}}_a(t,k))x(t,k)+(B+{\mathrm{\&Delta;}}_b(t,k))u(t-d_{\mathrm{\&sigma;}\left(t\right)}\left(t\right),k)\\ y(t,k)=\mathrm{Cx}(t,k)\\ x(t,k)=x_{0,k};-d_M\&le;t\&le;0;k=\mathrm{1,2},...\end{array}\right.\end{array}---\left(2\right)$

The output error that defines current batch is:

e(t，k)＝y(t，k)-y _d(t) (3)

Definition batch deflection error is

x _Δ(t，k)＝x(t，k)-x(t，k-1) (4)

Wherein x _Δ(t, k) is the error of state variable

According to the two-dimensional state spatial model and formula (the 1)-Shi (4) that build, can obtain two-dimentional time lag augmentation switching model of the present invention and be:

$\begin{array}{c}{\mathrm{\&Sigma;}}_{2D-P-\mathrm{delay}}:\\ \left\{\begin{array}{c}{x}_e(t+1,k)=({\stackrel{\&OverBar;}{A}}_1+{\stackrel{\&OverBar;}{\mathrm{\&Delta;}}}_a(t,k))x_e(t,k)+{\stackrel{\&OverBar;}{A}}_2{x}_e(t+1,k-1)\\ +(\stackrel{\&OverBar;}{B}+{\stackrel{\&OverBar;}{\mathrm{\&Delta;}}}_b(t,k))r(t-d_{\mathrm{\&sigma;}\left(t\right)}\left(t\right),k)+\mathrm{H\&omega;}(t,k)\\ z(t,k)\stackrel{\mathrm{\&Delta;}}{=}e(t,k)={\mathrm{Gx}}_e(t,k)\end{array}\right..\end{array}$

Embodiment 2

The present embodiment solves and (uses the form of LMI to the gain K of controller given stability criterion _{σ (t) 3}, K _{σ (t) 2}and K _{σ (t) 1}the detailed process solving describes.

The controller of the present invention's design will keep stable, should meet:

$\left[\begin{array}{cccccccc}-\mathrm{\&alpha;L}& 0& 0& 0& 0& L{\stackrel{\&OverBar;}{A}}_1^T+Y_{i1}^T{\stackrel{\&OverBar;}{B}}^T& L{\stackrel{\&OverBar;}{F}}^T+Y_{i1}^T{F}_b^T& {\mathrm{LG}}^T\\ *& -(1-\mathrm{\&alpha;})L+{\stackrel{\&OverBar;}{W}}_i+{\tilde{h}}_i{\stackrel{\&OverBar;}{Q}}_i& 0& 0& 0& L{\stackrel{\&OverBar;}{A}}_2^T+Y_{i2}^T{\stackrel{\&OverBar;}{B}}^T& Y_{i2}^T{F}_b^T& 0\\ *& *& -{\stackrel{\&OverBar;}{Q}}_i& 0& 0& Y_{i3}^T{\stackrel{\&OverBar;}{B}}^T& Y_{i3}^T{F}_b^T& 0\\ *& *& *& -{\stackrel{\&OverBar;}{W}}_i& 0& 0& 0& 0\\ *& *& *& *& -{\mathrm{\&gamma;}}_{i}I& H^T& 0& 0\\ *& *& *& *& *& -L+{\mathrm{\&epsiv;}}_i\stackrel{}{\stackrel{\&OverBar;}{E}}{\stackrel{\&OverBar;}{E}}^T& 0& 0\\ *& *& *& *& *& *& -{\mathrm{\&epsiv;}}_{i}I& 0\\ *& *& *& *& *& *& *& -{\mathrm{\&gamma;}}_{i}I\end{array}\right]<0.$

In the time that closed-loop system meets above-mentioned inequality, it is asymptotically stable within the scope of different time lags, the gain K of substitution controller _{σ (t) 3}, K _{σ (t) 2}and K _{σ (t) 1}, control law can be changed into: r (t-d _{σ (t)}(t), k)=K _{σ (t) 3}x _e(t-d _{σ (t)}(t), k-1)+K _{σ (t) 2}x _e(t+1, k-1)+K _{σ (t) 1}x _e(t, k) (5)=Y _i3l ^-1x _e(t-d _{σ (t)}(t), k-1)+Y _i2l ^-1x _e(t+1, k-1)+Y _i1l ^-1x _e(t, k) (5)

Correspondingly, switching law can be designed to:

If t < is T ₁, σ (t)=1; Otherwise, σ (t)=2.

As for when switching, i.e. T ₁concrete numerical value can obtain by the observation of filter filtering or observer.

In order to solve controller gain, need to solve following protruding optimization problem:

minγ _i

s.t.：L＞0， ${\stackrel{\&OverBar;}{Q}}_i>0,{\stackrel{\&OverBar;}{W}}_i>0,\left[\begin{array}{cc}{W}_i& \tilde{L}\\ \tilde{L}& {\tilde{W}}_i\end{array}\right]\&GreaterEqual;0,\left[\begin{array}{cc}{Q}_i& \tilde{L}\\ \tilde{L}& {\tilde{Q}}_i\end{array}\right]\&GreaterEqual;0,$

$\left[\begin{array}{cc}{\stackrel{\&OverBar;}{W}}_i& I\\ I& {\tilde{W}}_i\end{array}\right]\&GreaterEqual;0,\left[\begin{array}{cc}{L}_i& I\\ I& {\tilde{L}}_i\end{array}\right]\&GreaterEqual;0,\left[\begin{array}{cc}{\stackrel{\&OverBar;}{Q}}_i& I\\ I& {\tilde{Q}}_i\end{array}\right]\&GreaterEqual;0,{\mathrm{\&epsiv;}}_i>0,(i=\mathrm{1,2}),---\left(6\right).$

According to the protruding optimization problem of above-mentioned LMI constraint and linear objective function, application Matlab software LMI tool box, just can solve the gain of controller, obtains having the controller of lag information.

Embodiment 3

The present embodiment is the embodiment that the present invention is applied to injection speed control aspect.

Injection molding process is a complicated industrial manufacture process, and the quality of injecting products depends on the reciprocation of material parameter, machine parameter, procedure parameter and these parameters.The quality of injecting products has comprised a lot of aspects, for example presentation quality, accuracy to size and machinery (optics, electricity) performance etc.These quality index are jointly to be determined by the control accuracy of the material using in process, mould and procedure parameter.Meanwhile, in injection moulding process, different links all exist various disturbing factors.

Injection moulding process is in batch production mode as main, there is the operational mode of multistage repetitive, generally need critical process variable (as the injection speed of injection stage in each production phase, dwell pressure in packing stage, melt temperature in plastic phase etc.) change according to the setting value of manufacturing technique requirent, instead of stable state control in continuous process.In order to ensure product quality, in each process segment of producing every batch products, all need critical process variable to realize high precision control, generally do not allow overshoot, vibration and excessive setting value to depart from, otherwise affect possibly the production of next stage, when serious, even can cause the product rejection of batch.

Taking injection speed control as example, injection portion is the first stage of injection molding process.In injection portion, melt is at screw drive retrofilling die cavity.In this course, the filling speed of melt is its nowed forming, solidifies one of deciding factor of rear interior molecules orientation and unrelieved stress, thereby can comprise that physical strength, deformation and dimensional accuracy etc. produce impact greatly to the quality of end article.But because mold shape is ever-changing, be difficult to directly melt filling speed be measured.Injection portion spiro rod rate, as a substitute variable, can reflect melt filling situation preferably, is convenient to again direct measurement simultaneously, therefore conventionally at the industrial controlled variable that is chosen as injection portion.The injection speed of the present embodiment all refers to screw of injection speed.

The control of injection speed causes plastics industry circle and related researcher's attention already.Although a large amount of research work has shown the importance of injection speed, closed loop injection speed to be controlled at modern molding industrial still universal, reason is mainly that its dynamic perfromance is very complicated, and can occur marked change with the change of process conditions.

In addition, in injection moulding process, operation valve is opened, the controller of setting drive screw at once, and information there will be certain hysteresis, and the overlong time of lag information can make the stability of system obviously decline even unstable.This situation is embodied in actual production, and product is exactly the product of inferior quality.Therefore say, solve the system stability problem causing because of time lag, most important for actual production.

This patent has utilized the characteristic that reruns of injection moulding process, has adopted a kind of pioneeringly based on two-dimensional time system, study is controlled and FEEDBACK CONTROL organically combines the control method being designed for uniformity.Meanwhile, to lag information, according to its uncertainty, carry out segmentation, make it to be converted into the 2D Switched Systems with Time Delay based on two-dimentional time lag augmentation switching model, utilize first the theory of 2D Switched Systems with Time Delay to carry out closed-loop control to injection speed.

For injection speed, adopt method for designing of the present invention, can obtain switching law gain is that controller gain is as follows:

K ₁₁＝[0.0119 -0.1108 0.0021]，K ₁₂＝[0.001 -0.0201 0.2552]，

K ₁₃＝[0.0005 -0.0002 0.0144]，K ₂₁＝[0.1884 -0.2104 0.0041]，

K ₂₂＝[0.0000 0-0.0078 0.4112]，K ₂₃＝[0.0005 -0.0002 0.0144]。

Now, time lag situation is that (1 < Δ d (t) < 2) clapped in a wrong rear bat (0 < Δ d (t) < 1) and wrong rear 2, and two sections of time lag upper bounds are h ₁=1 and d _m=2.Meanwhile, this part has also been considered d _m=3 situation.

In order to evaluate tracking performance, introduce performance index below:

$H\left(k\right)=\sqrt{\underset{t=1}{\overset{200}{\mathrm{\&Sigma;}}}{e}^2(t,k)}$

H (k) value is less, represents that the tracking effect of batch k is better.

Actual rig-site utilization test shows, in the time that input wrong rear is clapped, adopts controller and the controller of the present invention of classic method design, and tracking velocity is very fast and tracking performance is good.When after input is wrong, two bats or two bats are above, controller of the present invention still can make system even running, has good tracing property performance simultaneously; And the controller that adopts classic method design can not maintain the stable of system, control performance can reduce.

The present invention is based on LMI framework, the method that for time lag uncertain condition segmentation carrys out CONTROLLER DESIGN has been proposed, its design problem is converted into the control problem of 2D time lag switching model, by setting up corresponding MATRIX INEQUALITIES, utilize relevant concept and solve corresponding LMI constraint, show that the designed controller of the present invention makes the even running of system energy, the conclusion that control performance is good really.

Compared with prior art, the system that the invention enables can fast and stable, follows the tracks of fast, even if be subject to time-delay, also has good control performance.

More than that better enforcement of the present invention is illustrated, but the invention is not limited to described embodiment, those of ordinary skill in the art also can make all equivalent variations or replacement under the prerequisite without prejudice to spirit of the present invention, and the distortion that these are equal to or replacement are all included in the application's claim limited range.

Claims (5)

1. mix a controller design method for the 2D of input delay, it is characterized in that: comprising:

A, structure have the two-dimensional state spatial model of input delay, and described two-dimensional state spatial model is as follows:

$\begin{array}{c}{\mathrm{\&Sigma;}}_{P-\mathrm{delay}}:\\ \left\{\begin{array}{c}x(t+1,k)=(A+{\mathrm{\&Delta;}}_a(t,k))x(t,k)+(B+{\mathrm{\&Delta;}}_b(t,k))u(t-d\left(t\right),k)\\ y(t,k)=\mathrm{Cx}(t,k)\\ x(t,k)=x_{0,k};-d_M\&le;t\&le;0;k=\mathrm{1,2},...\end{array}\right.\end{array},$

Wherein, t represents the time, the cycle of k representative operation, X _{0, k}k ^thbatch original state; X (t, k) ∈ R ⁿ, y (t, k) ∈ R ^l, u (t-d (t), k) ∈ R ^mrepresentative system is at t moment k respectively ^thbatch state, output and input, R ^l, R ^m, R ⁿrespectively representative be 1, the vector space of m, n dimension, along time orientation time become time lag d (t) and meet d _m≤ d (t)≤d _m, d _m, d _mit is respectively the bound of time lag; A, A _d, C and B are all known real constant matrixes, Δ _a(t, k), Δ _d(t, k) and Δ _b(t, k) is system model parameter uncertain matrix and meets [Δ _a(t, K) Δ _b(t, K)]=E Δ (t, k) [F F _b], Δ ^t(t, k) Δ (t, k)≤I, (0≤t≤T, k=1,2 ...), E, F and F _bbe known real constant matrix, I is suitable dimension unit matrix;

B, according to time become the size of time lag d (t), the two-dimensional state spatial model of structure is converted to two-dimentional time lag augmentation switching model, described two-dimentional time lag augmentation switching model is as follows:

$\begin{array}{c}{\mathrm{\&Sigma;}}_{2D-P-\mathrm{delay}}:\\ \left\{\begin{array}{c}{x}_e(t+1,k)=({\stackrel{\&OverBar;}{A}}_1+{\stackrel{\&OverBar;}{\mathrm{\&Delta;}}}_a(t,k))x_e(t,k)+{\stackrel{\&OverBar;}{A}}_2{x}_e(t+1,k-1)\\ +(\stackrel{\&OverBar;}{B}+{\stackrel{\&OverBar;}{\mathrm{\&Delta;}}}_b(t,k))r(t-d_{\mathrm{\&sigma;}\left(t\right)}\left(t\right),k)+\mathrm{H\&omega;}(t,k)\\ z(t,k)\stackrel{\mathrm{\&Delta;}}{=}e(t,k)={\mathrm{Gx}}_e(t,k)\end{array}\right.,\end{array}$

Wherein, $x_e(t,k)=\left[\begin{array}{c}{x}_{\mathrm{\&Delta;}}(t,k)\\ e(t,k)\end{array}\right]$ For the state of system, ${\stackrel{\&OverBar;}{A}}_1=\left[\begin{array}{cc}A& 0\\ \mathrm{CA}& 0\end{array}\right],\stackrel{\&OverBar;}{B}=\left[\begin{array}{c}B\\ \mathrm{CB}\end{array}\right],$ ${\stackrel{\&OverBar;}{\mathrm{\&Delta;}}}_a(t,k)=\stackrel{\&OverBar;}{E}\mathrm{\&Delta;}(t,k)\stackrel{\&OverBar;}{F},{\stackrel{\&OverBar;}{\mathrm{\&Delta;}}}_b(t,k)=\stackrel{\&OverBar;}{E}\mathrm{\&Delta;}(t,k)F_b,\stackrel{\&OverBar;}{E}=\left[\begin{array}{c}E\\ \mathrm{CE}\end{array}\right],\stackrel{\&OverBar;}{F}=\left[\begin{array}{cc}F& 0\end{array}\right],H=\left[\begin{array}{c}I\\ C\end{array}\right],$ G=[0 I], ω (t, k)=(Δ _a(t, k)-Δ _a(t, k-1)) x (t, k-1)+(Δ _b(t, k)-Δ _b(t, k-1)) u (t-d (t), k-1), can regard external interference as, for piecewise constant function, also make switching signal: σ (t)=1 expression system move in Small Time Lag situation, σ (t)=2 expression system is moved in large dead time situation;

C, design and meet control law r (t-d according to two-dimentional time lag augmentation switching model _{σ (t)}(t), controller k), described control law r (t-d _{σ (t)}(t), k) as follows:

∑ _2D-C-delay：

r(t-d _σ(t)(t)，k)＝K _σ(t)3x _e(t-d _σ(t)(t)，k-1)+K _σ(t)2x _e(t+1，k-1)+K _σ(t)1x _e(t，k)’

Wherein, K _{σ (t) 3}, K _{σ (t) 2}and K _{σ (t) 1}for controller gain and K _{σ (t) 3}=Y _{σ (t) 3}l ^-1, K _{σ (t) 2}=Y _{σ (t) 2}l ^-1, K _{σ (t) 1}=Y _{σ (t) 1}l ^-1, Y _{σ (t) 1}, Y _{σ (t) 2}and Y _{σ (t) 3}tie up matrix to be asked for fitting;

The gain K of the form of D, employing LMI to controller _{σ (t) 3}, K _{σ (t) 2}and K _{σ (t) 1}solve.

2. a kind of 2D for input delay according to claim 1 mixes controller design method, it is characterized in that: described step B, and it comprises:

The iterative learning control law of B1, design time lag system, described iterative learning control law is as follows:

∑ _ilc u(t-d(t)，k)＝u(t-d(t)，k-1)+r(t-d(t)，k)，

Wherein, u (t-d (t), 0)=0, t=0,1,2, U (t-d (t), k), u (t-d (t), k-1) is respectively the control inputs of k, (k-1) batch current time, (t-d (t), k) is more new law of iterative learning to r;

B2, according to time become the size of time lag d (t), the two-dimensional state spatial model of structure is converted to time lag switching model, described time lag switching model is:

$\begin{array}{c}{\mathrm{\&Sigma;}}_{P-\mathrm{delay}}:\\ \left\{\begin{array}{c}x(t+1,k)=(A+{\mathrm{\&Delta;}}_a(t,k))x(t,k)+(B+{\mathrm{\&Delta;}}_b(t,k))u(t-d_{\mathrm{\&sigma;}\left(t\right)}\left(t\right),k)\\ y(t,k)=\mathrm{Cx}(t,k)\\ x(t,k)=x_{0,k};-d_M\&le;t\&le;0;k=\mathrm{1,2},...\end{array}\right.\end{array};$

B3, the state-space model in conjunction with structure, iterative learning control law, time lag switching model, predefined current batch of output error and the predefined batch of deflection error of design, draw two-dimentional time lag augmentation switching model.

3. a kind of 2D for input delay according to claim 2 mixes controller design method, it is characterized in that: described step B2, and it comprises:

B21, according to time become the size of Uncertainty Δ d (t) in time lag d (t) and judge that time lag system belongs to large dead time situation or belongs to Small Time Lag situation: if Δ d (t) < 1, represent that time lag system belongs to Small Time Lag situation, now, d (t) should meet d _m≤ d (t)≤h ₁and h ₁< d _m; If Δ d (t) > 1, represents that time lag system belongs to large dead time situation, now, d (t) should meet h ₁≤ d (t)≤d _m;

B22, according to the result of judgement and time become the scope of time lag d (t), the two-dimensional state spatial model of structure is converted to time lag switching model.

4. a kind of 2D for input delay according to claim 3 mixes controller design method, it is characterized in that: described predefined current batch of output error is: e (t, k)=y (t, k)-y _d(t), wherein yd (t) is given output; Described predefined batch of deflection error is: x _Δ(t, k)=x (t, k)-x (t, k-1).

5. a kind of 2D for input delay according to claim 4 mixes controller design method, it is characterized in that: described step C, and it is specially:

According to given stability criterion condition, the gain K of the form of employing LMI to controller _{σ (t) 3}, K _{σ (t) 2}and K _{σ (t) 1}solve, described given stability criterion condition is:

$\left[\begin{array}{cccccccc}-\mathrm{\&alpha;L}& 0& 0& 0& 0& L{\stackrel{\&OverBar;}{A}}_1^T+Y_{i1}^T{\stackrel{\&OverBar;}{B}}^T& L{\stackrel{\&OverBar;}{F}}^T+Y_{i1}^T{F}_b^T& {\mathrm{LG}}^T\\ *& -(1-\mathrm{\&alpha;})L+{\stackrel{\&OverBar;}{W}}_i+{\tilde{h}}_i{\stackrel{\&OverBar;}{Q}}_i& 0& 0& 0& L{\stackrel{\&OverBar;}{A}}_2^T+Y_{i2}^T{\stackrel{\&OverBar;}{B}}^T& Y_{i2}^T{F}_b^T& 0\\ *& *& -{\stackrel{\&OverBar;}{Q}}_i& 0& 0& Y_{i3}^T{\stackrel{\&OverBar;}{B}}^T& Y_{i3}^T{F}_b^T& 0\\ *& *& *& -{\stackrel{\&OverBar;}{W}}_i& 0& 0& 0& 0\\ *& *& *& *& -{\mathrm{\&gamma;}}_{i}I& H^T& 0& 0\\ *& *& *& *& *& -L+{\mathrm{\&epsiv;}}_i\stackrel{}{\stackrel{\&OverBar;}{E}}{\stackrel{\&OverBar;}{E}}^T& 0& 0\\ *& *& *& *& *& *& -{\mathrm{\&epsiv;}}_{i}I& 0\\ *& *& *& *& *& *& *& -{\mathrm{\&gamma;}}_{i}I\end{array}\right]<0,$

Wherein, L, with

be positive definite symmetric matrices, matrix Y _i1, Y _i2, Y _i3∈ R ^{m × (m+l)}and constant γ _i> 0, ε _i> 0 (i=1,2), L=P ^-1, ${\mathrm{LW}}_{i}L={\stackrel{\&OverBar;}{W}}_i,{\mathrm{LQ}}_{i}L={\stackrel{\&OverBar;}{Q}}_i,$

Y _i＝[Y _i1 Y _i2 Y _i3]＝[K _i1L K _i2L K _i3L]。

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