CN102310090B - Distributed predictive control method for hot continuous rolling of strip steel and system - Google Patents

Abstract

The invention discloses a distributed predictive control method for hot continuous rolling of strip steel and a distributed predictive control system. The distributed predictive control system comprises a plurality of subsystems and a plurality of local predictive controllers for the subsystems, the number of the subsystems is equal to the number of the local predictive controllers, the subsystems are coupled, interaction of system state variable information is carried out by the local predictive controllers, and one subsystem is correspondingly connected with one local predictive controller.The coupling of components of the control system for the continuous rolling of the strip steel, in particular the coupling of an AGC (automatic gain control) device and a movable sleeve device, is taken into full consideration in the distributed predictive control method and the distributed predictive control system, so as to realize full performance optimization of closed-loop control.

Description

The Distributed Predictive Control method and system of hot strip rolling process

Technical field

The present invention relates to a kind of Distributed Predictive Control method and Distributed Predictive Control System thereof, be specifically related to a kind of Distributed Predictive Control method and Distributed Predictive Control System thereof of hot strip rolling process.

Background technology

Hot continuous rolling is owing to the contact with steel forms as a whole, AGC (Automatic Gauge Control, automatic thickness control) between the second flow controlled of the belt steel thickness controlled of device and kink, the tension force, and exist coupling phenomenon between each frame.In less demanding conventional control, this coupling phenomenon is left in the basket and disregards.Along with down-pressing system of rolling mill changes the day by day raising of hydraulic way and customer requirements into by electronic mode, influencing each other between AGC device and the loop control device be can not ignore and become the key of further improving the quality of products.Research AGC-kink complex control system is imperative.

By the analysis of rolling therory as can be known, the performance of the technological parameter in the deformed area of milling train is a series of nonlinear function.In the adjustment process of hot continuous rolling, when the technological parameter of milling train changes, can carry out linearisation to pressure function, advancing slip rear sliding function etc. in a small scope (take the operating point as benchmark).Emulation and the control processed like this for the operation of rolling have enough precision, and control system design is oversimplified.The characteristics of method of addition process simulation are that the linearisation form that various Mathematical Modelings all adopt the Taylor series expansion to omit to obtain behind the high-order term is calculated.

Traditional during Hot Strip Rolling control method, adopt decentralized control method, every group of milling train designs separately PID or PI controller, regulates the exit thickness with steel of 7 groups of milling trains by the AGC device, by the angle that ATR regulates 6 groups of kinks, regulate the strip tension of correspondence by the ASR of 6 groups of milling trains.This control method independent operating can't consider the coupling between system's each several part, can't suppress the impact that overall disturbance brings whole system, more can't realize from the angle of the overall situation performance optimization of closed-loop control.

Summary of the invention

Because the defects of prior art, technical problem to be solved by this invention provides a kind of forecast Control Algorithm and Distributed Predictive Control System thereof of hot strip rolling process, taken into full account between each parts of hot strip rolling control system, especially the coupling between AGC device and the looper is to realize the overall performance optimization of closed-loop control.

For achieving the above object, the invention provides a kind of Distributed Predictive Control method of hot strip rolling process, be applied to said method comprising the steps of in the hot strip rolling control system:

A) each parts to described system carry out linear approximation near the operating point of described system, obtain the dynamic increment model of the relevant described hot strip rolling process of coupling between described each parts with described system;

B) with the key variables of described system as the global system state variable, with the input of the actuator of the described system input as global system, with the surveyed output of the described system output as global system, and in conjunction with the coupling between each parts of described system, set up the overall incremental model of described hot strip rolling process;

C) on the basis of the described overall incremental model of described hot strip rolling process, described system is carried out subsystem divide, and described system is carried out Distributed Predictive Control, with the overall performance of the closed-loop control of optimizing described system.

Further, wherein said system comprises 6 groups of kinks and 7 groups of milling trains.

Further, wherein said dynamic increment model comprises kink Incremental Equation, tension increment equation, thickness Incremental Equation, automatic moment adjuster Incremental Equation, automatic speed regulator Incremental Equation and automatic thickness controlling increment equation.

Further, wherein said global system state variable comprises kink angle step integration, kink angle step, kink angular speed increment, strip tension incremental integration, strip tension increment, belt steel thickness incremental integration, kink kinetic moment increment, rolling mill roll speed increment, band steel exports thickness.

Further, the input of wherein said actuator comprises the input of regulated quantity of the roll gap of the input of regulated quantity of main motor speed of the input of the control moment of described kink, described milling train and described milling train.

Further, wherein said system comprises 8 sub-systems altogether, is respectively the subsystem of the automatic thickness control device formation of the first milling train; The automatic moment adjuster of i kink, the subsystem that the automatic speed regulator of i-1 milling train and the automatic thickness control device of i+1 milling train consist of; The subsystem that the automatic speed regulator of the 7th milling train consists of, wherein, 1≤i≤6.

The present invention also provides a kind of Distributed Predictive Control System of hot strip rolling process, be applied in the hot strip rolling control system, described Distributed Predictive Control System comprises a plurality of subsystems and is used for a plurality of local prediction controllers of described subsystem, described subsystem is identical with the quantity of described local prediction controller, intercouple between described a plurality of subsystem, carry out the mutual of system state variables information between described a plurality of local prediction controller, local prediction controller of the corresponding connection of a sub-systems.

Further, wherein said hot strip rolling control system comprises 6 groups of kinks and 7 groups of milling trains.

Further, the quantity of described subsystem is 8, and the quantity of described local prediction controller is 8.

Further, wherein 8 described subsystems are respectively the subsystem that the automatic thickness control device of the first milling train consists of; The automatic moment adjuster of i kink, the subsystem that the automatic speed regulator of i-1 milling train and the automatic thickness control device of i+1 milling train consist of; The subsystem that the automatic speed regulator of the 7th milling train consists of, wherein, 1≤i≤6.

Beneficial effect of the present invention is as follows:

Forecast Control Algorithm of the present invention has taken into full account the coupling between individual each parts of hot strip rolling control system when obtaining dynamic increment model and overall incremental model.Further, forecast Control Algorithm of the present invention adopts the Distributed Predictive Control method, whole hot strip rolling control system is divided into a plurality of subsystems that are mutually related, can effectively reduce computation burden, can consider to realize the overall performance optimization of closed-loop control in the situation of each subsystem coupling again comprehensively.

Be described further below with reference to the technique effect of accompanying drawing to design of the present invention, concrete structure and generation, to understand fully purpose of the present invention, feature and effect.

Description of drawings

Fig. 1 is the structural representation of hot strip rolling control system.

Fig. 2 is the floor map of deformed area.

Fig. 3 is the geometry figure of loop tension control device.

Fig. 4 is the structural representation of the Distributed Predictive Control of hot strip rolling process.

The specific embodiment

The represented physical quantity of the symbol that occurs in accompanying drawing and the part formula and symbol is as shown in table 1:

Table 1

As shown in Figure 1, the hot strip rolling control system comprises a plurality of milling trains and a plurality of kink.In the present embodiment, the hot strip rolling control system comprises 7 groups of milling trains and 6 groups of kinks.In addition, the hot strip rolling control system also comprises tension pick-up, is used for measuring the tension force of kink; Hydraulic test is used for driving kink; Angular transducer is for the angle of measuring kink; ASR (Automatic Speed Regulator, automatic speed regulator), the speed that is used for regulating kink; ATR (Automatic Torque Regulator, automatically moment adjuster); Controller is used for by network (fieldbus) whole hot strip rolling control system being coordinated control.

Fig. 2 is the floor map of the deformed area of a certain milling train.Fig. 3 is the geometry figure of loop tension control device.

In addition, because ASR, ATR and automatic thickness control device are the technology of knowing in hot strip rolling field, the present invention is not described in detail in this.

The present invention is described below the mechanism model of the related hot strip rolling control system in Fig. 1～3:

The mechanism model of automatic thickness control device:

Hot strip steel is in deformed area generation plastic deformation.Be to be best suited at present the theoretical formula that the power of belt steel rolling is calculated based on the SIMS formula of the dynamic balance theory of OROWAN deformed area, its reduced form is as follows:

$P_i=\sqrt{R_W^i(h_{i-1}-h_i)}A[\mathrm{KQ}-\frac{{\mathrm{\σ}}_f^i+{\mathrm{\σ}}_b^i}{2}]---\left(1\right)$

In the formula,

Be the length of the contact arc floor projection simplified, A is the thickness with steel, and K is the deformation drag under the metal flat distortion, and Q is the Geometric corrections coefficient,

Be respectively with the forward pull of steel with the backward pull of steel.

In finishing stands, sometimes, the spring of milling train is suitable with the varied in thickness of rolling front and back band steel, and then the mill spring equation by formula (2) calculates the exit thickness with steel:

$h_i=S_i+\frac{P_i}{M_i}---\left(2\right)$

In formula (2), h _iBe the exit thickness with steel, S _iBe the roll gap of milling train, P _iBe roll-force, M _iStiffness coefficient for milling train.

The Dynamic Mechanism model of kink:

The kinetic model of kink can be obtained by the Newton's laws of motion of rotary rigid body, and concrete equation is as follows:

$J_i{\stackrel{\·\·}{\mathrm{\θ}}}_i\left(t\right)=T_u^i\left(t\right)-T_{\mathrm{load}}^i\left({\mathrm{\θ}}_i\right)---\left(3\right)$

Wherein, Be kink rotating angular acceleration, J _iFor kink with respect to total rotary inertia of axis of rotation (comprising the roller of arm, kink of kink and counter-jib etc.),

For actuator acts on the kinetic moment of kink, Loading moment for kink.

The kink loading moment

Usually formed by three parts, namely

$T_{\mathrm{load}}^i\left({\mathrm{\θ}}_i\right)=T_{\mathrm{\σ}}^i\left({\mathrm{\θ}}_i\right)+T_s^i\left({\mathrm{\θ}}_i\right)+T_L^i\left({\mathrm{\θ}}_i\right)---\left(4\right)$

Wherein,

For the tension force with steel acts on loading moment on the kink,

Be the loading moment of Action of Gravity Field on kink with steel, and

Then be the loading moment of the deadweight generation of kink, the computational methods of above-mentioned variable are as follows:

$T_{\mathrm{\σ}}^i\left({\mathrm{\θ}}_i\right)={\mathrm{\σ}}_i{h}_{i}w{R}_l[\sin ({\mathrm{\θ}}_i+\mathrm{\β})-\sin ({\mathrm{\θ}}_i-\mathrm{\α})---\left(5\right)$

$T_L^i\left({\mathrm{\θ}}_i\right)=g{M}_L{R}_G\cos {\mathrm{\θ}}_i---\left(6\right)$

T _s(θ _i)≈0.5gρLh _iwR _lcosθ _i (7)

In the formula, h _iBe belt steel thickness, w is strip width (the physical quantity implication of other symbols is referring to table 1).See also Fig. 3, the α in the formula (5), β can be calculated by geometric figure:

$\mathrm{\&alpha;}={\tan }^{-1}\left[\frac{R_l\sin {\mathrm{\&theta;}}_i-{\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">H</figure-callout>}}_1+{\mathrm{<figure-callout\; id="1"\; label="R\; r\; L"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">R</figure-callout>}}_r}{L_{}}\right]---\left(8\right)$

$\mathrm{\&beta;}={\tan }^{-1}\left[\frac{R_l\sin {\mathrm{\&theta;}}_i-{\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">H</figure-callout>}}_1+R_r}{L_4-R_l\cos {\mathrm{\&theta;}}_i}\right]---\left(9\right)$

Dynamic Mechanism model with the tension force of steel:

In the actual operation of rolling, between the milling train of front and back with the geometrical length of steel usually greater than the physical length with steel, also namely be with steel to be in extended state.Can be by with the level of stretch of steel with estimate that with the Young's modulus of steel formula is as follows with the tension force of steel:

${\mathrm{\&sigma;}}_i\left(t\right)=E_i\left[\frac{L_i^{\&prime;}\left({\mathrm{\&theta;}}_i\right)-(L_i+{\mathrm{\&xi;}}_i\left(t\right))}{L_i+{\mathrm{\&xi;}}_i\left(t\right)}\right],$ L′ _i(θ _i)＞(L _i+ξ _i(t)) (10)

Wherein, E _iBe the Young's modulus with steel, L _i+ ξ _i(t) be the physical length of front and back band steel, ξ _i(t) be the accumulation with the difference of the entrance velocity of steel with the muzzle velocity of steel and a rear milling train of last milling train, computing formula is as follows:

${\stackrel{\&CenterDot;}{\mathrm{\&xi;}}}_i\left(t\right)=v_s^i\left(t\right)-V_s^{i+1}\left(t\right)---\left(11\right)$

In formula (11), muzzle velocity and the entrance velocity with steel of deformed area depend on the speed of the working roll of milling train

And with the slide coefficient between steel and the working roll, concrete computing formula is as follows:

$v_s^i\left(t\right)=(1+S_f^i)V_R^i\left(t\right)---\left(12\right)$

$V_s^i=(1-S_b^i)V_R^i$ Or $V_s^i=\frac{h_i}{h_{i-1}}(1+S_f^i)V_R^i---\left(13\right)$

Wherein,

For with the advancing slip coefficient between steel and the working roll,

For with the rear sliding coefficient between steel and the working roll.

With

All along with the forward pull of steel, with the variation of the backward pull of steel and change specific formula for calculation following (the physical quantity implication of related symbol is referring to table 1):

$S_f^i=\frac{R_W^i}{h_i}{\left({\mathrm{\&gamma;}}_i\right)}^2---\left(14\right)$

$S_b^i=1-\frac{h_i}{h_{i-1}}(1+S_f^i)---\left(15\right)$

Wherein, γ _iBe the neutral angle of deformed area, this neutral angle can have the estimation of the geometric parameter of deformed area:

${\mathrm{\&gamma;}}_i=\sqrt{\frac{h_i}{R_W^i}}\tan [\frac{1}{2}\arctan \sqrt{\frac{{\mathrm{\&epsiv;}}_i}{1-{\mathrm{\&epsiv;}}_i}}+\frac{\mathrm{\&pi;}}{8}\ln (1-{\mathrm{\&epsiv;}}_i)\sqrt{\frac{h_i}{R_W^i}}+\frac{1}{2}\sqrt{\frac{h_i}{R_W^i}}(\frac{{\mathrm{\&sigma;}}_f^i}{K}-\frac{{\mathrm{\&sigma;}}_b^i}{K})]$

${\mathrm{\&epsiv;}}_i=\frac{h_{i-1}-h_i}{h_{i-1}}$

In above-mentioned formula, K is the deformation drag of metal.

See also Fig. 3, the geometrical length L ' (θ with steel between the milling train _i) then can be calculated by following method of geometry:

L′ _i(θ _i)＝l ₁(θ _i)+l ₂(θ _i) (16)

$l_1\left({\mathrm{\&theta;}}_i\right)=\sqrt{{({\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">L</figure-callout>}}_1+R_l\cos {\mathrm{\&theta;}}_i)}^2+{(R_l\sin {\mathrm{\&theta;}}_i+R_r-H_1)}^2}$

$l_2\left({\mathrm{\&theta;}}_i\right)=\sqrt{{(L_4+R_l\cos {\mathrm{\&theta;}}_i)}^2+{(R_l\sin {\mathrm{\&theta;}}_i+R_r-H_1)}^2}$

In the actual operation of rolling, than the distance L between the milling train, with the actual accumulation amount ξ of steel _i(t) very little.Therefore, in the denominator of formula (10), can omit ξ _i(t).But in the molecule of formula (10), L ' _i(θ _i)-L _iWith ξ _i(t) numerical value is in the same order of magnitude, at this moment ξ _i(t) then can't ignore.To formula (10) differentiate, can obtain the dynamical equation with the tension force of steel:

${\stackrel{\&CenterDot;}{\mathrm{\&sigma;}}}_i\left(t\right)=\frac{E_i}{L_i}[\frac{d}{\mathrm{dt}}{L}_i^{\&prime;}\left({\mathrm{\&theta;}}_i\right)-{\stackrel{\&CenterDot;}{\mathrm{\&xi;}}}_i\left(t\right)]---\left(17\right)$

$=\frac{E_i}{L_i}\left[R_l\right[\sin ({\mathrm{\&theta;}}_i+\mathrm{\&beta;})-\sin ({\mathrm{\&theta;}}_i-\mathrm{\&alpha;})]{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_i\left(t\right)-((1+S_f^i)V_R^i\left(t\right)-(1-S_b^{i+1})V_R^{i+1})]$

α in the formula, the same formula of the implication of β (8)～(9).

The Dynamic Mechanism model of the actuator of system:

This mechanism model is comprised of three parts:

Kink is driven by hydraulic test or high-speed electric expreess locomotive usually, and is equipped with automatic moment adjuster, and its fast response time can be similar to first order inertial loop usually:

${\stackrel{\&CenterDot;}{T}}_u^i\left(t\right)=-\frac{1}{T_u^i}{T}_u^i\left(t\right)+\frac{1}{T_u^i}{u}_T^i---\left(18\right)$

Wherein,

Be the first order inertial loop time constant,

Be the kinetic moment of kink,

Be control inputs.

The roll of milling train is driven by heavy-duty motor usually, and is equipped with automatic speed regulator (ASR), usually can be similar to first order inertial loop:

${\stackrel{\&CenterDot;}{V}}_R^i\left(t\right)=-\frac{1}{T_V^i}{V}_R^i+\frac{1}{T_V^i}{u}_V^i---\left(19\right)$

Wherein,

Be the first order inertial loop time constant,

Be the speed of rolls of milling train i,

Be control inputs.

The roll gap of milling train is often driven by hydraulic test, and is equipped with automatic thickness control device (AGC), usually can be similar to first order inertial loop:

${\stackrel{\&CenterDot;}{S}}_i=-\frac{1}{T_S^i}{S}_i+\frac{1}{T_S^i}{u}_S^i---\left(20\right)$

Wherein,

Be first order inertial loop time constant, S _iBe the speed of rolls of milling train i,

Be control inputs.

Based on above-mentioned mechanism model, the concrete steps of the Distributed Predictive Control method of hot strip rolling process of the present invention are as follows:

Step 1: according to above-mentioned mechanism model, near each parts to the hot strip rolling control system operating point of hot strip rolling control system carry out linear approximation, can obtain to take into full account the dynamic increment model of each parts of coupling, and concrete model is as follows:

The kink Incremental Equation:

$\mathrm{\&Delta;}{\stackrel{\&CenterDot;}{I}}_{{\mathrm{\&theta;}}_i}=\mathrm{\&Delta;}{\mathrm{\&theta;}}_i---\left(21\right)$

${\stackrel{\&CenterDot;}{\mathrm{\&Delta;\&theta;}}}_i=\mathrm{\&Delta;}{\mathrm{\&omega;}}_i$

${\stackrel{\&CenterDot;}{\mathrm{\&Delta;\&omega;}}}_i=-\frac{1}{J_i}\left(\frac{\&PartialD;T_{\mathrm{load}}^i}{\&PartialD;{\mathrm{\&theta;}}_i}\right)\mathrm{\&Delta;}{\mathrm{\&theta;}}_i-\frac{1}{J_i}\left(\frac{{\&PartialD;T}_{\mathrm{\&sigma;}}^i}{\&PartialD;{\mathrm{\&sigma;}}_i}\right)\mathrm{\&Delta;}{\mathrm{\&sigma;}}_i+\frac{1}{J_i}\mathrm{\&Delta;}{T}_u^i$

The tension increment equation:

$\mathrm{\&Delta;}{\stackrel{\&CenterDot;}{I}}_{{\mathrm{\&sigma;}}_i}={\mathrm{\&Delta;\&sigma;}}_i$

${\stackrel{\&CenterDot;}{\mathrm{\&Delta;\&sigma;}}}_i=-\frac{E_i}{L_i}\frac{{\&PartialD;S}_f^i}{{\&PartialD;\mathrm{\&sigma;}}_b^i}{V}_R^i{\mathrm{\&Delta;\&sigma;}}_{i-1}-\frac{E_i}{L_i}(\frac{{\&PartialD;S}_f^i}{{\&PartialD;h}_i}{V}_R^i+\frac{{\&PartialD;S}_b^{i+1}}{\&PartialD;h_i}{V}_R^{i+1})\mathrm{\&Delta;}{h}_i---\left(22\right)$

$\frac{E_i}{L_i}{F}_3\left({\mathrm{\&theta;}}_i\right)\mathrm{\&Delta;}{\mathrm{\&omega;}}_i-\frac{E_i}{L_i}(\frac{{\&PartialD;S}_f^i}{{\&PartialD;\mathrm{\&sigma;}}_f^i}{V}_R^i+\frac{{\&PartialD;S}_b^{i+1}}{\&PartialD;{\mathrm{\&sigma;}}_b^{i+1}}{V}_R^{i+1})\mathrm{\&Delta;}{\mathrm{\&sigma;}}_i-\frac{E_i}{L_i}(1+S_f^i)\mathrm{\&Delta;}{V}_R^i-\frac{E_i}{L_i}\frac{{\&PartialD;S}_b^{i+1}}{{\&PartialD;h}_{i+1}}{V}_R^{i+1}\mathrm{\&Delta;}{h}_{i+1}$

$+\frac{E_i}{L_i}\frac{h_{i+1}}{h_i}\frac{{\&PartialD;S}_f^{i+1}}{\&PartialD;{\mathrm{\&sigma;}}_f^{i+1}}{V}_R^{i+1}{\mathrm{\&Delta;\&sigma;}}_{i+1}+\frac{E_i}{L_i}(1-S_b^{i+1})\mathrm{\&Delta;}{V}_R^{i+1}$

The thickness Incremental Equation:

${\mathrm{\&Delta;h}}_i=\mathrm{\&Delta;}{S}_i+\frac{\mathrm{\&Delta;}{P}_i}{M_i}=\mathrm{\&Delta;}{S}_i+\frac{\mathrm{\&Delta;}{P}_i}{M_i}=\mathrm{\&Delta;}{S}_i+\frac{\frac{\&PartialD;P_i}{\&PartialD;h_i}\mathrm{\&Delta;}{h}_i}{M_i}---\left(23\right)$

Order

For band steel plastic coefficient, so solving equation (23) can get

$\mathrm{\&Delta;}{h}_i=\frac{M_i}{M_i+M_s^i}\mathrm{\&Delta;}{S}_i---\left(24\right)$

Automatic moment adjuster (ATR) Incremental Equation:

$\mathrm{\&Delta;}{\stackrel{\&CenterDot;}{T}}_u^i=-\frac{1}{T_u^i}\mathrm{\&Delta;}{T}_u^i\left(t\right)+\frac{1}{T_u^i}{u}_{\mathrm{\&Delta;T}}^i---\left(25\right)$

Automatic speed regulator (ASR) Incremental Equation:

$\mathrm{\&Delta;}{\stackrel{\&CenterDot;}{V}}_R^i=-\frac{1}{T_V^i}\mathrm{\&Delta;}{V}_R^i+\frac{1}{T_V^i}{u}_{\mathrm{\&Delta;V}}^i---\left(26\right)$

Automatic thickness control device (AGC) Incremental Equation:

${\stackrel{\&CenterDot;}{\mathrm{\&Delta;S}}}_i=-\frac{1}{T_S^i}\mathrm{\&Delta;}{S}_i+\frac{1}{T_S^i}{u}_{\mathrm{\&Delta;S}}^i---\left(27\right)$

By equation (24) as can be known:

${\stackrel{\&CenterDot;}{\mathrm{\&Delta;h}}}_i=\frac{M_i}{M_i+M_s^i}{\stackrel{\&CenterDot;}{\mathrm{\&Delta;S}}}_i=-\frac{M_i}{M_i+M_s^i}\frac{1}{T_S^i}{\mathrm{\&Delta;S}}_i+\frac{M_i}{M_i+M_s^i}\frac{1}{T_S^i}{u}_{\mathrm{\&Delta;S}}^i=-\frac{1}{T_S^i}\mathrm{\&Delta;}{h}_i+\frac{M_i}{M_i+M_s^i}\frac{1}{T_S^i}{u}_{\mathrm{\&Delta;S}}^i---\left(28\right)$

Step 2: with the key variables of 6 kinks, 7 milling trains as system state variables (comprise 9 kinds of system state variableses, be respectively: kink angle step integration, kink angle step, kink angular speed increment, strip tension incremental integration, strip tension increment, belt steel thickness incremental integration, kink kinetic moment increment, rolling mill roll speed increment, band steel exports thickness):

$\hat{x}=[\mathrm{\&Delta;}{I}_{{\mathrm{\&theta;}}_1},...,\mathrm{\&Delta;}{I}_{{\mathrm{\&theta;}}_6},$

$\mathrm{\&Delta;}{\mathrm{\&theta;}}_1,...,\mathrm{\&Delta;}{\mathrm{\&theta;}}_6,$

$\mathrm{\&Delta;}{\mathrm{\&omega;}}_1,...,\mathrm{\&Delta;}{\mathrm{\&omega;}}_6,$

${\mathrm{\&Delta;I}}_{{\mathrm{\&sigma;}}_1},...,{\mathrm{\&Delta;I}}_{{\mathrm{\&sigma;}}_6},$ (29)

${\mathrm{\&Delta;\&sigma;}}_1,...,{\mathrm{\&Delta;\&sigma;}}_6,$

$\mathrm{\&Delta;}{I}_{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1},...,\mathrm{\&Delta;}{I}_{h_7},$

${\mathrm{\&Delta;<figure-callout\; id="1"\; label="T\; u"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">T</figure-callout>}}_u^{},...,{\mathrm{\&Delta;T}}_u^6,$

${\mathrm{\&Delta;<figure-callout\; id="1"\; label="V\; R"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">V</figure-callout>}}_R^{},...,\mathrm{\&Delta;}{V}_R^7,$

${\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1,...,\mathrm{\&Delta;}{h}_7]}^T$

With the input of the actuator of 6 kinks, 7 milling trains as system's control inputs (comprise 3 kinds of control inputs, be respectively: the input of the regulated quantity of the input of the regulated quantity of the input of the control moment of kink, the main motor speed of milling train and the roll gap of milling train):

$\mathrm{\&Delta;}\hat{u}=[u_{\mathrm{\&Delta;<figure-callout\; id="1"\; label="T"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^1,...,u_{\mathrm{\&Delta;T}}^6,$

$u_{\mathrm{\&Delta;<figure-callout\; id="1"\; label="V"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">V</figure-callout>}}^1,...,u_{\mathrm{\&Delta;V}}^7,$

${u_{\mathrm{\&Delta;<figure-callout\; id="1"\; label="S"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">S</figure-callout>}}^1,...,u_{\mathrm{\&Delta;S}}^7]}^T---\left(30\right)$

With the kink angle step of 6 kinks, 7 milling trains, strip tension increment and with the output of steel exports thickness increment as system:

$\hat{y}=[\mathrm{\&Delta;}{\mathrm{\&theta;}}_1,...,\mathrm{\&Delta;}{\mathrm{\&theta;}}_6,$

${\mathrm{\&Delta;\&sigma;}}_1,...,{\mathrm{\&Delta;\&sigma;}}_6,$

${{\mathrm{\&Delta;<figure-callout\; id="1"\; label="h"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1,...,{\mathrm{\&Delta;h}}_7]}^T---\left(31\right)$

Can get the adjustment on the said system state variable work order:

$x=[{\mathrm{\&Delta;I}}_{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1},{\mathrm{\&Delta;<figure-callout\; id="1"\; label="h"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1,$

${\mathrm{\&Delta;I}}_{{\mathrm{\&theta;}}_1},{\mathrm{\&Delta;\&theta;}}_1,{\mathrm{\&Delta;\&omega;}}_1,{\mathrm{\&Delta;I}}_{{\mathrm{\&sigma;}}_1},{\mathrm{\&Delta;\&sigma;}}_1,{\mathrm{\&Delta;I}}_{h_2},{\mathrm{\&Delta;<figure-callout\; id="1"\; label="T\; u"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">T</figure-callout>}}_u^{},{\mathrm{\&Delta;<figure-callout\; id="1"\; label="V\; R"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">V</figure-callout>}}_R^{},\mathrm{\&Delta;}{h}_2,$

$\begin{array}{c}.\\ .\\ .\end{array}$

${\mathrm{\&Delta;I}}_{{\mathrm{\&theta;}}_6},{\mathrm{\&Delta;\&theta;}}_6,{\mathrm{\&Delta;\&omega;}}_6,{\mathrm{\&Delta;I}}_{{\mathrm{\&sigma;}}_6},{\mathrm{\&Delta;\&sigma;}}_6,{\mathrm{\&Delta;I}}_{h_7},{\mathrm{\&Delta;T}}_u^6,{\mathrm{\&Delta;V}}_R^6,\mathrm{\&Delta;}{h}_7,$

${{\mathrm{\&Delta;V}}_R^7]}^T$

$={[x_0,x_1,...,x_6,x_7]}^T$

$\mathrm{\&Delta;u}=[u_{\mathrm{\&Delta;<figure-callout\; id="1"\; label="S"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">S</figure-callout>}}^1,$

$u_{\mathrm{\&Delta;<figure-callout\; id="1"\; label="T"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^1,u_{\mathrm{\&Delta;<figure-callout\; id="1"\; label="V"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">V</figure-callout>}}^1,u_{\mathrm{\&Delta;S}}^2,$

$\begin{array}{c}.\\ .\\ .\end{array}$

$u_{\mathrm{\&Delta;T}}^6,u_{\mathrm{\&Delta;V}}^6,u_{\mathrm{\&Delta;S}}^7$

${u_{\mathrm{\&Delta;V}}^7]}^T$

$={[u_0,{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">u</figure-callout>}}_1,...,u_6,u_7]}^T$

y＝[Δh ₁，

Δθ ₁，Δσ ₁，Δh ₂，

$\begin{array}{c}.\\ .\\ .\end{array}$

Δθ ₆，Δσ ₆，Δh ₇] ^T

＝[y ₀，y ₁，…，y ₆] ^T

The overall incremental model of setting up 6 kinks, 7 milling trains is:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{x}\left(t\right)=\mathrm{Ax}\left(t\right)+\mathrm{Bu}\\ y\left(t\right)=\mathrm{Cx}\left(t\right)\end{array}\right.---\left(32\right)$

Wherein:

$A_0=\left[\begin{array}{cc}0& \frac{M_1}{{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">M</figure-callout>}}_1+M_s^1}\\ 0& -\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="T\; S"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">T</figure-callout>}}_S^{}}\end{array}\right],$ $A_7=[-\frac{1}{T_V^i}],$ $A_{10}=\left[\begin{array}{cc}0& 0\\ 0& 0\\ 0& 0\\ 0& 0\\ 0& -\frac{E_i}{L_i}(\frac{{\&PartialD;S}_f^i}{{\&PartialD;h}_i}{V}_R^i+\frac{{\&PartialD;S}_b^{i+1}}{\&PartialD;h_i}{V}_R^{i+1})\\ 0& 0\\ 0& 0\\ 0& 0\\ 0& 0\end{array}\right],$

$A_{\mathrm{6,7}}=\left[\begin{array}{ccccccccc}0& 0& 0& 0& 0& 0& 0& \frac{E_6}{L_6}(1-S_b^7)& 0\end{array}\right],$

$B_0=\left[\begin{array}{c}0\\ \frac{M_1}{{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">M</figure-callout>}}_1+M_s^1}\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="T\; S"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">T</figure-callout>}}_S^{}}\end{array}\right],$ $B_7=\left[\frac{1}{T_V^i}\right],$

C ₀＝[0 1]

Remaining matrix (1≤i≤6) is:

$A_i=\left[\begin{array}{ccccccccc}0& 1& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0& 0& 0\\ 0& -\frac{1}{J_i}\left(\frac{{\&PartialD;T}_{\mathrm{load}}^i}{{\&PartialD;\mathrm{\&theta;}}_i}\right)& 0& 0& -\frac{1}{J_i}\left(\frac{{\&PartialD;T}_{\mathrm{\&sigma;}}^i}{{\&PartialD;\mathrm{\&sigma;}}_i}\right)& 0& \frac{1}{J_i}& 0& 0\\ 0& 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& \frac{E_i}{L_i}{F}_3\left({\mathrm{\&theta;}}_i\right)& 0& -\frac{E_i}{L_i}(\frac{{\&PartialD;S}_f^i}{{\&PartialD;\mathrm{\&sigma;}}_f^i}{V}_R^i-\frac{h_{i+1}}{h_i}\frac{{\&PartialD;S}_f^{i+1}}{{\&PartialD;\mathrm{\&sigma;}}_b^{i+1}}{V}_R^{i+1})& 0& 0& -\frac{E_i}{L_i}(1+S_f^i)& -\frac{E_i}{L_i}\frac{{\&PartialD;S}_b^{i+1}}{{\&PartialD;h}_{i+1}}{V}_R^{i+1}\\ 0& 0& 0& 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 0& -\frac{1}{T_u^i}& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& -\frac{1}{T_V^i}& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& -\frac{1}{T_S^i}\end{array}\right],$

$A_{i,j+1}=\left[\begin{array}{ccccccccc}0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& \frac{E_i}{L_i}\frac{h_{i+1}}{h_i}\frac{{\&PartialD;S}_f^{i+1}}{{\&PartialD;\mathrm{\&sigma;}}_f^{i+1}}{V}_R^{i+1}& 0& \frac{E_i}{L_i}(1-S_b^{i+1})& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0\end{array}\right]$

Step 3: on the basis of the overall incremental model of the hot strip rolling process that step 2 is set up, adopt the method for Distributed Predictive Control, system is carried out subsystem divide.

See also Fig. 4, in the present embodiment, the Distributed Predictive Control System that is applied in the hot strip rolling process in the hot strip rolling control system be divided into 8 sub-systems, be respectively:

Subsystem 0: the AGC device of milling train 1;

Subsystem i, 1≤i≤6: the Comprehensive Control subsystem that the ASR of the ATR of kink i, milling train i-1 and the AGC device of milling train i+1 consist of;

Subsystem 7: the ASR of milling train 7.

Further, the Distributed Predictive Control System of hot strip rolling process also comprise 8 local prediction controllers (local prediction controller 0, local prediction controller 1 ..., local prediction controller 6, local prediction controller 7), local prediction controller of the corresponding connection of every sub-systems, for example subsystem 0 links to each other with local prediction controller 0,, local prediction controller 7 links to each other with local prediction controller 7.Intercouple between the subsystem, carry out system state variables information mutual of subsystem between the local prediction controller.

The closed-loop characteristic of above-mentioned subsystem is respectively:

${\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">J</figure-callout>}}_1=\underset{k=k_m+1}{\overset{k_m+N_p}{\mathrm{\&Sigma;}}}{x}_1^T\left(k\right)Q_1{x}_1\left(k\right)+\underset{k=k_m}{\overset{k_m+N_c-1}{\mathrm{\&Sigma;}}}{\mathrm{\&Delta;u}}_1{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">R</figure-callout>}}_1{\mathrm{\&Delta;u}}_1^T$

$J_i=\underset{k=k_m+1}{\overset{k_m+N_p}{\mathrm{\&Sigma;}}}{x}_i^T\left(k\right)Q_i{x}_i\left(k\right)+\underset{k=k_m}{\overset{k_m+N_c-1}{\mathrm{\&Sigma;}}}{\mathrm{\&Delta;u}}_i{R}_i{\mathrm{\&Delta;u}}_i^T,1\&le;i\&le;6---\left(33\right)$

$J_7=\underset{k=k_m+1}{\overset{k_m+N_p}{\mathrm{\&Sigma;}}}{x}_7^T\left(k\right)Q_7{x}_7\left(k\right)+\underset{k=k_m}{\overset{k_m+N_c-1}{\mathrm{\&Sigma;}}}{\mathrm{\&Delta;u}}_7{R}_7{\mathrm{\&Delta;u}}_7^T$

Wherein:

$x_1={\left[\begin{array}{cc}{\mathrm{\&Delta;I}}_{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1}& {\mathrm{\&Delta;h}}_1\end{array}\right]}^T$

$x_i={\left[\begin{array}{ccccccccc}{\mathrm{\&Delta;I}}_{{\mathrm{\&theta;}}_i}& {\mathrm{\&Delta;\&theta;}}_i& {\mathrm{\&Delta;\&omega;}}_i& {\mathrm{\&Delta;I}}_{{\mathrm{\&sigma;}}_i}& {\mathrm{\&Delta;\&sigma;}}_i& {\mathrm{\&Delta;I}}_{h_{i+1}}& {\mathrm{\&Delta;T}}_u^i& {\mathrm{\&Delta;V}}_R^i& {\mathrm{\&Delta;h}}_{i+1}\end{array}\right]}^T,$ 1≤i≤6

$x_7=\left[{\mathrm{\&Delta;V}}_R^7\right]$

$\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA0000081145320000021.png"\; state="\{\{state\}\}">u</figure-callout>}}_1=\left[u_{\mathrm{\&Delta;S}}^1\right]$

${\mathrm{\&Delta;u}}_i={\left[\begin{array}{ccc}{u}_{\mathrm{\&Delta;T}}^i& u_{\mathrm{\&Delta;V}}^i& u_{\mathrm{\&Delta;S}}^{i+1}\end{array}\right]}^T,$ 1≤i≤6

${\mathrm{\&Delta;u}}_7=\left[u_{\mathrm{\&Delta;V}}^7\right]$

When every sub-systems calculates prediction during optimal control sequence according to closed-loop characteristic index (33) in the prediction time domain, the prognoses system track of this subsystem is carried out information interaction to other subsystems, and consider the corresponding prognoses system track of prediction optimal control sequence of other subsystems to the impact of native system.

In step 3 of the present invention, adopted the Distributed Predictive Control method.Certainly, the present invention also can adopt concentrated forecast Control Algorithm, but because the dimension of sytem matrix too high (sytem matrix A is 57 * 57 dimension matrixes), must give PLC and is the control system of core processor and bring huge computation burden.Therefore, adopt the Distributed Predictive Control method, can effectively reduce the computation burden of system, can consider to realize the overall performance optimization of closed-loop control in the situation of the coupling between each subsystem again comprehensively.

In the present invention, Distributed Predictive Control System is divided into 8 sub-systems, and certainly, subsystem is not limited to 8, and Distributed Predictive Control System also can be divided into the subsystem of other quantity.

In the present invention, the hot strip rolling control system comprises 7 groups of milling trains and 6 groups of kinks.But the present invention is not limited to this, and the hot strip rolling control system can comprise milling train and the kink of any amount.

More than describe preferred embodiment of the present invention in detail.Should be appreciated that those of ordinary skill in the art need not creative work and just can design according to the present invention make many modifications and variations.Therefore, all those skilled in the art all should be in the determined protection domain by claims under this invention's idea on the basis of existing technology by the available technical scheme of logical analysis, reasoning, or a limited experiment.

Claims (1)

1. the Distributed Predictive Control method of a hot strip rolling process is applied in the hot strip rolling control system, and described system comprises 6 groups of kinks and 7 groups of milling trains, it is characterized in that, said method comprising the steps of:

A) each parts to described system carry out linear approximation near the operating point of described system, obtain the dynamic increment model of the relevant described hot strip rolling process of coupling between described each parts with described system, described dynamic increment model comprises kink Incremental Equation, tension increment equation, thickness Incremental Equation, automatic moment adjuster Incremental Equation, automatic speed regulator Incremental Equation and automatic thickness controlling increment equation;

B) with the key variables of described system as the global system state variable, with the input of the actuator of the described system input as global system, with the surveyed output of the described system output as global system, and in conjunction with the coupling between each parts of described system, set up the overall incremental model of described hot strip rolling process, described global system state variable comprises kink angle step integration, the kink angle step, kink angular speed increment, the strip tension incremental integration, the strip tension increment, the belt steel thickness incremental integration, kink kinetic moment increment, the rolling mill roll speed increment, band steel exports thickness; The input of described actuator comprises the input of regulated quantity of the roll gap of the input of regulated quantity of main motor speed of the input of the control moment of described kink, described milling train and described milling train;

C) on the basis of the described overall incremental model of described hot strip rolling process, described system is carried out subsystem divide, and described system is carried out Distributed Predictive Control, with the overall performance of the closed-loop control of optimizing described system.

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