CN103901773B - 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 mix controller design Method.

Background technology

ILC (iterative learning) controls are substantially a kind of open loop feedforward controls, according to the previous control experience of system and defeated Go out error to correct current control input so that the reality output track of controlled system is in finite time interval along the whole phase Hope that output trajectory realizes the perfect tracking of zero error.This control method is solving the rail of unknown structure, Complex Nonlinear System Mark control aspect has superiority, and it can carry out on-line study to unknown message, in learning process while system operation The priori of shortage is made up constantly, so that control performance is progressively improved, with less dependence system priori Advantage, but as which is not completely using the real-time feedback information of system, when the dynamic characteristic of system occurs uncertain change When, the robust stability of control performance such as system, convergence etc. are difficult to ensure that.

It is a kind of universal phenomenon that batch process itself has retarding characteristic, and time lag be system unstable it is main because Element, the impact to stability are extremely complex, and the presence of time lag causes the stability analyses of system and controller design to become more It is difficult.For example, in batch process control, input delay is commonly present, causes the appearance for having track with zero error problem.In this regard, industry Interior traditional way is being controlled to the batch process with input delay, with maintenance system using pure ILC control algolithms Stablize.For unknown time delay is less than a cycle situation (i.e. during input delay only wrong latter bat), this control mode It is effective, stablizing for system can be maintained；But, for unknown time delay be more than a cycle in the case of (input delay mistake after When two bats are even more clapped more), it is even unstable that this control mode can be such that the stability of system is decreased obviously, and causes production Product is the product of inferior quality.

Therefore, industry needs a kind of new controller of design badly, even if making system by the unknown time delay more than a cycle Impact remains to keep stable, and which has preferable control performance.

The content of the invention

In order to solve above-mentioned technical problem, the purpose of the present invention is：There is provided a kind of stability height, control performance 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 control Device method for designing, including：

A, two-dimensional state spatial model of the structure with input delay, the two-dimensional state spatial model are as follows：

Wherein, t represents the time, and k represents the cycle of operation, X_0,kIt is kth^thThe original state of batch；x(t,k)∈Rⁿ,y (t,k)∈R^l, u (t-d (t), k) ∈ R^mSystem is represented respectively in t kth^thThe state of batch, output and it is input into, R^l、R^m、Rⁿ What is represented respectively is the vector space of l, m, n dimension, and Time-varying time-delays d (t) along time orientation meet d_m≤d(t)≤d_M, d_m、d_MPoint It is not the bound of time lag；A, C and B are known real constant matrixes, Δ_a(t, k) and Δ_b(t, k) be system model parameter not Determine matrix and meet [Δ_a(t, k) Δ_b(t, k)]=E Δs (t, k) [F F_b], Δ^T(t, k)) Δ (t, k)≤I, 0≤t≤T, K=1,2 ..., E, F and F_bIt is known real constant matrix, I is suitable dimension unit matrix；

B, according to the size of Time-varying time-delays d (t), the two-dimensional state spatial model of structure is converted to into two-dimentional time lag augmentation and is cut Mold changing type, the two-dimentional time lag augmentation switching model are as follows：

Wherein,For the state of system, 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), External interference can be regarded as,For piecewise constant function, switching signal is also：σ (t)=1 represents that system exists Run in the case of Small Time Lag, σ (t)=2 represent that system is run in the case of large dead time；

C, designed according to two-dimentional time lag augmentation switching model and meet control law r (t-d_σ(t)T (), controller k) are described Control law r (t-d_σ(t)(t), it is k) as follows：

Wherein, K_σ(t)3、K_σ(t)2And K_σ(t)1For controller gain and K_σ(t)3=Y_σ(t)3L^-1, K_σ(t)2=Y_σ(t)2L^-1, K_σ(t)1= Y_σ(t)1L^-1, Y_σ(t)1、Y_σ(t)2And Y_σ(t)3Matrix to be asked is tieed up for suitable；

D, the gain K in the form of LMI to controller_σ(t)3、K_σ(t)2And K_σ(t)1Solved.

Further, step B, which includes：

The iterative learning control rule of B1, design time lag system, the iterative learning control rule are 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) be respectively kth, (k-1) control input of batch current time, (t-d (t) k) is iterative learning more new law to r；

B2, according to the size of Time-varying time-delays d (t), the two-dimensional state spatial model of structure is converted to into time lag switching model, The time lag switching model is：

B3, combine the state-space model, the iterative learning control rule of design, time lag switching model, predefined for building Present lot output error and predefined batch deflection error, draw two-dimentional time lag augmentation switching model.

Further, step B2, which includes：

B21, judge that time lag system is belonging to large dead time feelings according to the size of Uncertainty Δ d (t) in Time-varying time-delays d (t) Condition still falls within Small Time Lag situation：If Δ d (t) ＜ 1, then it represents that time lag system belongs to Small Time Lag situation, now, d (t) should meet d_m≤d(t)≤h₁And h₁＜ d_M；If Δ d (t) ＞ 1, then it represents that time lag system belongs to large dead time situation, now, d (t) should meet h₁ ≤d(t)≤d_M；

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

Further, the predefined present lot output error is：E (t, k)=y (t, k)-y_d(t), wherein yd (t) For the output for giving；The predefined batch deflection error is：x_Δ(t, k)=x (t, k)-x (t, k-1).

Further, step C, which is specially：

According to given stability criterion condition, the gain K in the form of LMI to controller_σ(t)3、 K_σ(t)2And K_σ(t)1Solved, the given stability criterion condition is：

Wherein, L,WithIt is 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, employ while including large dead time situation and Small Time Lag feelings The two-dimentional time lag augmentation switching model of condition designing controller, is the uncertain right of unknown time delay according to the size of Time-varying time-delays Input delay is segmented, and is entered so as to the method by switching being controlled to input delay by the method that switches Row Discrete control, even if making system be affected to remain to keep stable by the unknown time delay more than a cycle, stability is higher, together When also have the advantages that to calculate that simple, tracking is fast and control performance is good.

Description of the drawings

The invention will be further described with reference to the accompanying drawings and examples.

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

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

Fig. 3 is the flow chart of step B2 of the present invention.

Specific embodiment

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

A, two-dimensional state spatial model of the structure with input delay, the two-dimensional state spatial model are as follows：

Wherein, t represents the time, and k represents the cycle of operation, X_0,kIt is kth^thThe original state of batch；x(t,k)∈Rⁿ,y (t,k)∈R^l, u (t-d (t), k) ∈ R^mSystem is represented respectively in t kth^thThe state of batch, output and it is input into, R^l、R^m、Rⁿ What is represented respectively is the vector space of l, m, n dimension, and Time-varying time-delays d (t) along time orientation meet d_m≤d(t)≤d_M, d_m、d_MPoint It is not the bound of time lag；A, C and B are known real constant matrixes, Δ_a(t, k) and Δ_b(t, k) be system model parameter not Determine matrix and meet [Δ_a(t,k)Δ_b(t, k)]=E Δs (t, k) [F F_b], Δ^T(t, k) Δ (t, k)≤I, 0≤t≤T, k =1,2 ..., E, F and F_bIt is known real constant matrix, I is suitable dimension unit matrix；

B, according to the size of Time-varying time-delays d (t), the two-dimensional state spatial model of structure is converted to into two-dimentional time lag augmentation and is cut Mold changing type, the two-dimentional time lag augmentation switching model are as follows：

Wherein,For the state of system, 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), External interference can be regarded as,For piecewise constant function, switching signal is also：σ (t)=1 represents that system exists Run in the case of Small Time Lag, σ (t)=2 represent that system is run in the case of large dead time；

C, designed according to two-dimentional time lag augmentation switching model and meet control law r (t-d_σ(t)T (), controller k) are described Control law r (t-d_σ(t)(t), it is k) as follows：

Wherein, K_σ(t)3、K_σ(t)2And K_σ(t)1For controller gain and K_σ(t)3=Y_σ(t)3L^-1, K_σ(t)2=Y_σ(t)2L^-1, K_σ(t)1= Y_σ(t)1L^-1, Y_σ(t)1、Y_σ(t)2And Y_σ(t)3Matrix to be asked is tieed up for suitable；

D, the gain K in the form of LMI to controller_σ(t)3、K_σ(t)2And K_σ(t)1Solved.

Wherein, fit dimension matrix to refer to according to actual needs, can flexibly choose the dimension of matrix.

The size of Time-varying time-delays d (t), represents unknown time delay and is greater than the situation (large dead time situation) of a cycle or little In the situation (Small Time Lag situation) of a cycle, the uncertainty of unknown time delay is reflected.

Two-dimentional time lag augmentation switching model, while including large dead time situation and Small Time Lag situation, can be according to Time-varying time-delays d T the size of (), is switched over automatically.

A kind of state-space model of two-dimensional time system is present invention employs, for unknown time delay is more than a cycle Situation, using segmentation method, will unknown time delay be divided in the different cycles, so as to the cycle design for being directed to different is corresponding Controller, and its all of controller deposit is got up, corresponding controller is called finally according to practical situation, by switching side Method carries out closed loop control.

With reference to Fig. 2, it is further used as preferred embodiment, step B, which includes：

The iterative learning control rule of B1, design time lag system, the iterative learning control rule are as follows：

Σ_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) be respectively kth, (k-1) control input of batch current time, (t-d (t) k) is iterative learning more new law to r；

B2, according to the size of Time-varying time-delays d (t), the two-dimensional state spatial model of structure is converted to into time lag switching model, The time lag switching model is：

B3, combine the state-space model, the iterative learning control rule of design, time lag switching model, predefined for building Present lot output error and predefined batch deflection error, draw two-dimentional time lag augmentation switching model.

With reference to Fig. 3, it is further used as preferred embodiment, step B2, which includes：

B21, judge that time lag system is belonging to large dead time feelings according to the size of Uncertainty Δ d (t) in Time-varying time-delays d (t) Condition still falls within Small Time Lag situation：If Δ d (t) ＜ 1, then it represents that time lag system belongs to Small Time Lag situation, now, d (t) should meet d_m≤d(t)≤h₁And h₁＜ d_M；If Δ d (t) ＞ 1, then it represents that time lag system belongs to large dead time situation, now, d (t) should meet h₁ ≤d(t)≤d_M；

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

Wherein, d (t)=d+ Δs d (t), wherein d are the integer more than or equal to 0, represent the not true of Time-varying time-delays d (t) Quantitatively, and Δ d (t) is the Uncertainty of Time-varying time-delays d (t).

It is further used as preferred embodiment, the predefined present lot output error is：E (t, k)=y (t, k)-y_dT (), wherein yd (t) are given output；The predefined batch deflection error is：x_Δ(t, k)=x (t, k)-x (t,k-1)。

It is further used as preferred embodiment, step C, which is specially：

According to given stability criterion condition, the gain K in the form of LMI to controller_σ(t)3、 K_σ(t)2And K_σ(t)1Solved, the given stability criterion condition is：

Wherein, L,WithIt is 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 present invention is described in further detail with reference to specific embodiment.

Embodiment 1

The present embodiment is cut to the two-dimensional state spatial model of structure is converted to two-dimentional time lag augmentation by taking injection moulding process as an example The detailed process of mold changing type is illustrated.

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 such as Under：

Repeat property first according to injection moulding process, design iteration learn control law and are：

∑_ilcU (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 ...；U (t-d (t), k), u (t-d (t), k-1) be respectively kth, (k-1) control input of batch current time, (t-d (t) k) is iterative learning more new law to r.

For time lag is divided into the following two kinds situation here：

(1) Δ d (t) ＜ 1, i.e. Uncertainty Δ d (t) they, less than 1 cycle, are Small Time Lag situation, now, the scope of d (t) For d_m≤d(t)≤h₁And h₁＜ d_M, wherein h₁For positive number.

(2) Δ d (t) ＞ 1, i.e. Uncertainty Δ d (t), more than 1 cycle, are large dead time situation, and now, d (t) scopes are h₁≤d(t)≤d_M.In actual commercial production or Industry Control, Small Time Lag situation Jing often occurs, and large dead time situation is once in a while Occur, the controller that conventional needle is designed to Small Time Lag situation does not ensure that stability of the system in large dead time situation.Cause This, it is necessary to controller is redesigned to guarantee stablizing for system, so as to ensure the quality of product.

For above-mentioned two situations, following time lag switching system can will be converted to based on the system of two-dimensional state spatial model System：

Define present lot output error be：

E (t, k)=y (t, k)-y_d(t) (3)

Defining batch deflection error is

x_Δ(t, k)=x (t, k)-x (t, k-1) (4)

Wherein x_ΔThe error of (t, k) for state variable

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

Embodiment 2

The present embodiment is solved the (increasing i.e. with the form of LMI to controller to the stability criterion for giving Beneficial K_σ(t)3、K_σ(t)2And K_σ(t)1The detailed process for being solved is illustrated.

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

When closed loop system meets above-mentioned inequality, which is asymptotically stable in the range of different time lags, substitutes into control The gain K of device_σ(t)3、K_σ(t)2And K_σ(t)1, then control law can be changed into：

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)

=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 as：

If t is ＜ T₁, then σ (t)=1；Conversely, then σ (t)=2.

As for when switching, i.e. T₁Concrete numerical value can pass through filter filtering or observer observation obtain.

In order to solve controller gain, following convex optimization problem need to be solved：

minγ_i

According to the constraint of above-mentioned LMI and the convex optimization problem of linear objective function, using Matlab softwares LMI workboxes, just can solve the gain of controller, obtain the controller with 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 manufacturing process, and the quality of injecting products is depending on material parameter, machine The reciprocal action of device parameter, procedure parameter and these parameters.The quality of injecting products includes many aspects, such as outward appearance matter Amount, accuracy to size and machinery (optics, electricity) performance etc..These quality index are by the material used in the course of processing, mould What the control accuracy of tool and procedure parameter was together decided on.Meanwhile, in injection moulding process, different links all have various interference Factor.

Based on Batch Process mode, the operational mode with multistage repetitive produces rank at each to injection moulding process Section is typically necessary critical process variables (such as the injection speed of injection stage, the dwell pressure in packing stage, in plastic phase Melt temperature etc.) be changed according to the setting value of manufacturing technique requirent, rather than the homeostatic control in continuous process.In order to Ensure product quality, in each process segment of production per batch products, be required for realizing that high accuracy is controlled to critical process variables System, is typically not allow for overshoot, vibration and excessive setting value and deviates, and is otherwise likely to affect the production of next stage, sternly The product rejection of a batch can be even caused during weight.

By taking injection speed control as an example, injection portion is the first stage of injection molding process.In injection portion, melt exists Screw drive retrofilling die cavity.In this course, the filling rate of melt be its nowed forming, solidification after interior molecules orientation One of with the deciding factor of residual stress, thus mechanical strength, deformation and dimensional accuracy can be included to the quality of end article Deng generation strong influence.But due to mold shape it is ever-changing, it is difficult to directly measure to melt filling speed.Injection Section spiro rod rate can preferably reflect melt filling situation as a substitute variable, while and be easy to direct measurement, therefore The controlled variable of injection portion is industrially chosen as generally.The injection speed of the present embodiment is all referring to screw of injection speed.

The control of injection speed causes the attention of plastics industry circle and related researcher already.Although substantial amounts of research work The importance of injection speed is had shown that, the control of closed loop injection speed is not still popularized on modern molding industry, reason Essentially consist in its dynamic characteristic sufficiently complex, and significant changes can occur with the change of process conditions.

Additionally, in injection moulding process, control valve is opened, the controller of setting can't drive screw at once, information can go out Now certain is delayed, the overlong time of lag information, is decreased obviously can the stability of system even unstable.Such case body In actual production now, product is exactly the product of inferior quality.Therefore say, solve the problems, such as the system stability caused because of time lag, for reality Production is most important.

This patent make use of the characteristic that reruns of injection moulding process, employ a kind of pioneering based on two-dimensional time system , study control and feedback control are organically combined the control method being designed for uniformity.Meanwhile, to lag information, according to which Uncertainty, is segmented, and is allowed to be converted into the 2D Switched Systems with Time Delay based on two-dimentional time lag augmentation switching model, is utilized first The theory of 2D Switched Systems with Time Delay carries out closed loop control to injection speed.

For injection speed, using the method for designing of the present invention, switching law gain i.e. controller gain can be obtained It is as follows：

K₁₁=[0.0119-0.1108 0.0021], K₁₂=[0.001-0.0201 0.2552],

K₁₃=[0.0005-0.0002 0.0144], K₂₁=[0.1884-0.2104 0.0041],

K₂₂=[0.0000-0.0078 0.4112], K₂₃=[0.0005-0.0002 0.0144].

Now, time lag situation is 2 bats (1 ＜ Δs d (t) ＜ 2) after wrong latter bat (0 ＜ Δs d (t) ＜ 1) and mistake, i.e., when two sections The stagnant upper bound is h₁=1 and d_M=2.Meanwhile, this part have also contemplated that d_M=3 situation.

In order to evaluate tracking performance, following performance indications are introduced:

H (k) values are less, represent that the tracking effect of batch k is better.

Actual scene shows using test, when wrong latter bat is input into, using the controller and sheet of traditional method design The controller of invention, tracking velocity is quickly and tracking performance is good.Input mistake after two clap or two clap the above when, the present invention control Device processed remains to make system even running, while with good tracing property performance；And adopt the controller of traditional method design Stablizing for system, control performance can not be maintained to reduce.

The present invention is based on LMI frameworks, it is proposed that the method for being segmented to design controller for time lag uncertain condition, by which Design problem is converted into the control problem of 2D time lag switching models, by setting up corresponding MATRIX INEQUALITIES, using the general of correlation Considering corresponding LMI constraints are solved, show that designed controller of the invention enables system even running, controlling really The good conclusion of energy.

Compared with prior art, the invention enables system can fast and stable, it is quick to track, even if receiving time-delay, With preferable control performance.

It is more than that the preferable enforcement to the present invention is illustrated, but the invention is not limited to the enforcement Example, those of ordinary skill in the art on the premise of without prejudice to spirit of the invention can also be made a variety of equivalent variations or be replaced Change, the deformation or replacement of these equivalents are all contained in the application claim limited range.

Claims (5)

1. a kind of 2D for input delay mixes controller design method, it is characterised in that：Including：

A, injection moulding process two-dimensional state spatial model of the structure with input delay, the injection moulding process two-dimensional state spatial model It is as follows：

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

Wherein, t represents the time, and k represents the cycle of operation, X_0,kIt is kth^thThe original state of batch；x(t,k)∈Rⁿ,y(t,k) ∈R^l, u (t-d (t), k) ∈ R^mSystem is represented respectively in t kth^thThe state of batch, output and it is input into, R^l、R^m、RⁿRespectively What is represented is the vector space of l, m, n dimension, and Time-varying time-delays d (t) along time orientation meet d_m≤d(t)≤d_M, d_m、d_MIt is respectively The bound of time lag；A, C and B are known real constant matrixes, △_a(t, k) and △_b(t, k) is system model Parameter uncertainties Matrix and satisfaction [△_a(t,k) △_b(t, k)]=E △ (t, k) [F F_b], △^T(t, k) △ (t, k)≤I, 0≤t≤T, k=1, 2 ..., E, F and F_bIt is known real constant matrix, I is suitable dimension unit matrix；

B, according to the size of Time-varying time-delays d (t), the injection moulding process two-dimensional state spatial model of structure is converted to into injection moulding process two Dimension time lag augmentation switching model, the injection moulding process two dimension time lag augmentation switching model are as follows：

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

Wherein,For the state of system,

${\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\\ CE\end{array}\right],\stackrel{\‾}{F}=\[\begin{array}{cc}F& 0\end{array}\],H=\left[\begin{array}{c}I\\ C\end{array}\right],$

G=[0 I], ω (t, k)=(△_a(t,k)-△_a(t,k-1))x(t,k-1)+(△_b(t,k)-△_b(t,k-1))u(t-d (t), k-1), external interference can be regarded as,For piecewise constant function, switching signal is also：σ (t)=1 Expression system is run in the case of Small Time Lag, and σ (t)=2 represent that system is run in the case of large dead time；

C, design and meet control law r (t-d according to injection moulding process two dimension time lag augmentation switching model_σ(t)(t), injection moulding process k) Controller, the control law r (t-d_σ(t)(t), it is 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)2And K_σ(t)1For controller gain and K_σ(t)3=Y_σ(t)3L^-1, K_σ(t)2=Y_σ(t)2L^-1, K_σ(t)1=Y_{σ(t) 1}L^-1, Y_σ(t)1、Y_σ(t)2And Y_σ(t)3Matrix to be asked is tieed up for suitable；

D, the gain K in the form of LMI to injection moulding process controller_σ(t)3、K_σ(t)2And K_σ(t)1Solved.

2. a kind of 2D for input delay according to claim 1 mixes controller design method, it is characterised in that：Institute Step B is stated, which includes：

The iterative learning control rule of B1, design time lag system, the iterative learning control rule are 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) be kth, (k-1) respectively The control input of batch current time, (t-d (t) k) is iterative learning more new law to r；

B2, according to the size of Time-varying time-delays d (t), the injection moulding process two-dimensional state spatial model of structure is converted to into injection moulding process Time lag switching model, the injection moulding process time lag switching model is：

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

B3, combine build state-space model, design iterative learning control rule, injection moulding process time lag switching model, make a reservation for The present lot output error and predefined batch deflection error of justice, draws injection moulding process two dimension time lag augmentation switching mould Type.

3. a kind of 2D for input delay according to claim 2 mixes controller design method, it is characterised in that：Institute Step B2 is stated, which includes：

B21, judge that time lag system is belonging to large dead time situation also according to the size of Uncertainty △ d (t) in Time-varying time-delays d (t) It is belonging to Small Time Lag situation：If △ d (t)<1, then it represents that time lag system belongs to Small Time Lag situation, now, d (t) should meet d_m≤d (t)≤h₁And h₁＜ d_M；If △ d (t) ＞ 1, then it represents that time lag system belongs to large dead time situation, now, d (t) should meet h₁≤d (t)≤d_M；

B22, according to judge result and Time-varying time-delays d (t) scope, by build injection moulding process two-dimensional state spatial model turn It is changed to injection moulding process time lag switching model.

4. a kind of 2D for input delay according to claim 3 mixes controller design method, it is characterised in that：Institute Stating predefined present lot output error is：E (t, k)=y (t, k)-y_d(t), wherein y_dT () is given output；It is described pre- The batch deflection error of definition is：x_△(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 characterised in that：Institute Step C is stated, which is specially：

According to given stability criterion condition, the gain in the form of LMI to injection moulding process controller K_σ(t)3、K_σ(t)2And K_σ(t)1Solved, the given stability criterion condition is：

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

Wherein, L,WithIt is 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]。