CN102310090A - 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 as a whole owing to the contact of being with steel forms, and between the second flow amount that belt steel thickness that AGC (Automatic Gauge Control, automatic thickness control) device is controlled and kink are controlled, the tension force, and exists coupling phenomenon between each frame.In less demanding routine control, this coupling phenomenon is left in the basket and disregards.Along with down-pressing system of rolling mill changes the raising day by day of hydraulic way and customer requirements into by electronic mode, influencing each other between AGC device and the kink control device can not ignore and become the key of further improving the quality of products.Research AGC-kink complex control system is imperative.

Analysis by rolling therory can know that the technological parameter performance 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 in a small scope (is benchmark with the operating point) to pressure function, the sliding function in advancing slip back etc.The emulation of handling like this for the operation of rolling all has enough precision with control, and makes the simplicity of designization of control system.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 hot continuous rolling course control method for use; Adopt decentralized control method, every group of milling train designs PID or PI controller separately, regulates the exit thickness of the band steel of 7 groups of milling trains through the AGC device; Through the angle that ATR regulates 6 groups of kinks, regulate the strip tension of correspondence through the ASR of 6 groups of milling trains.This control method independent operating can't be taken all factors into consideration the coupling between system's each several part, can't suppress the influence that overall disturbance brings whole system, more can't realize the performance optimization of closed-loop control from the angle of the overall situation.

Summary of the invention

Because the above-mentioned defective 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 realizing above-mentioned purpose, 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 said system carry out linear approximation near the operating point of said system, obtain the relevant said hot strip rolling DYNAMIC PROCESS incremental model of coupling between said each parts with said system;

B) with the key variables of said system as the global system state variable; With the input of the actuator of said system input as global system; With the surveyed output of said system output as global system; And combine the coupling between each parts of said system, set up the overall incremental model of said hot strip rolling process;

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

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

Further, wherein said dynamic increment model comprises kink increment equation, tension increment equation, thickness increment equation, moment adjuster increment equation, automatic speed regulator increment equation and automatic thickness are controlled the increment equation automatically.

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 roll gap of input and said milling train of regulated quantity of the main motor speed of the input of the control moment of said kink, said milling train.

Further, wherein said system comprises 8 sub-systems altogether, is respectively the subsystem of the automatic thickness control device formation of 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 constitute; The subsystem that the automatic speed regulator of the 7th milling train constitutes, 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; Said Distributed Predictive Control System comprises a plurality of subsystems and a plurality of local prediction controllers that are used for said subsystem; Said subsystem is identical with the quantity of said local prediction controller; Intercouple between said a plurality of subsystem, carry out the mutual of system state variables information between said a plurality of local prediction controllers, 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 said subsystem is 8, and the quantity of said local prediction controller is 8.

Further, wherein 8 said subsystems are respectively the subsystem that the automatic thickness control device of first milling train constitutes; 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 constitute; The subsystem that the automatic speed regulator of the 7th milling train constitutes, wherein, 1≤i≤6.

Beneficial effect of the present invention is following:

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

Below will combine accompanying drawing that the technique effect of design of the present invention, concrete structure and generation is described further, to understand the object of the invention, characteristic and effect fully.

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 kink tenslator.

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

The specific embodiment

The represented physical quantity of 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, hot strip rolling control system comprises a plurality of milling trains and a plurality of kink.In the present embodiment, hot strip rolling control system comprises 7 groups of milling trains and 6 groups of kinks.In addition, hot strip rolling control system also comprises tension pick-up, is used to measure the tension force of kink; Hydraulic test is used to drive kink; Angular transducer is used to measure the angle of kink; ASR (Automatic Speed Regulator, automatic speed regulator), the speed that is used to regulate kink; ATR (Automatic Torque Regulator, moment adjuster automatically); Controller is used for through network (fieldbus) control being coordinated by whole hot strip rolling control system.

Fig. 2 is the floor map of the deformed area of a certain milling train.Fig. 3 is the geometry figure of kink tenslator.

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 the generation plastic deformation in the deformed area.Based on the theoretical SIMS formula of the dynamic balance of OROWAN deformed area is the theoretical formula that is best suited for the power calculating of belt steel rolling at present, and its reduced form is following:

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

In the formula;

is the length of the contact arc floor projection of simplification; A is the thickness of band steel; K is the deformation drag under the metal flat distortion; Q is the Geometric corrections coefficient,

be respectively the band steel forward pull with the band steel backward pull.

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

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

In formula (2), h _iBe the exit thickness of band 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 following:

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

Wherein,

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

For actuator acts on the kinetic moment of kink,

Loading moment for kink.

Kink loading moment is made up of three parts usually, promptly

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

Wherein,

acts on the loading moment on the kink for the tension force of band steel;

acts on the loading moment on the kink for the gravity of band steel;

then is the loading moment that the deadweight of kink produces, and the computational methods of above-mentioned variable are following:

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

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

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:

$\mathrm{\&alpha;}={\tan }^{-1}\left[\frac{R_l\sin {\mathrm{\&theta;}}_i-{\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">H</figure-callout>}}_1+{\mathrm{<figure-callout\; id="1"\; label="R\; r\; L"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">R</figure-callout>}}_r}{L_{}}\right]---\left(8\right)$

$\mathrm{\&beta;}={\tan }^{-1}\left[\frac{R_l\sin {\mathrm{\&theta;}}_i-{\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">H</figure-callout>}}_1+R_r}{L_4-R_l\cos {\mathrm{\&theta;}}_i}\right]---\left(9\right)$

The dynamic mechanism model of the tension force of band steel:

In the actual operation of rolling, the geometrical length of the band steel between the milling train of front and back greater than the physical length of band steel, also promptly is with steel to be in extended state usually.The tension force of band steel can estimate that with the Young's modulus of band steel formula is following by the level of stretch of band 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 of band steel, L _i+ ξ _i(t) be the physical length of front and back band steel, ξ _i(t) be the muzzle velocity and the accumulation of the difference of the entrance velocity of the band steel of a milling train afterwards of the band steel of last milling train, computing formula is following:

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

In formula (11); The muzzle velocity and the entrance velocity of the band steel of deformed area; Depend on the speed

of the working roll of milling train and the slide coefficient between band steel and the working roll, concrete computing formula is following:

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

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

Wherein,

for the advancing slip coefficient between band steel and the working roll,

is the back sliding coefficient between band steel and the working roll.

and

change along with the variation of the backward pull of the forward pull of band steel, band steel, and concrete computing formula is (the physical quantity implication of related symbol is referring to table 1) as follows:

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

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

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 metal deformation resistance.

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

L′ _i(θ _i)＝l ₁(θ _i)+l ₂(θ _i) (16)

$l_1\left({\mathrm{\&theta;}}_i\right)=\sqrt{{({\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">L</figure-callout>}}_1+R_l\cos {\mathrm{\&theta;}}_i)}^2+{(R_l\sin {\mathrm{\&theta;}}_i+R_r-H_1)}^2}$

$l_2\left({\mathrm{\&theta;}}_i\right)=\sqrt{{({\mathrm{<figure-callout\; id="4"\; label="L"\; filenames="HDA0000081145320000031.png"\; state="\{\{state\}\}">L</figure-callout>}}_4+R_l\cos {\mathrm{\&theta;}}_i)}^2+{(R_l\sin {\mathrm{\&theta;}}_i+R_r-H_1)}^2}$

In the actual operation of rolling, than the distance L between the milling train, the actual accumulation amount ξ of band 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 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 made up 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 response speed is fast, and common available first order inertial loop is similar to:

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

Wherein, is the first order inertial loop time constant;

is the kinetic moment of kink,

for controlling input.

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

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

Wherein, is the first order inertial loop time constant;

is the speed of rolls of milling train i, for controlling input.

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

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

Wherein,

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

Be the control input.

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 following:

Step 1: according to above-mentioned mechanism model, near each parts to hot strip rolling control system the 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 following:

Kink increment 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:

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

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

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

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

Thickness increment equation:

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

Make

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) increment 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) increment 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) increment equation:

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

Can know by equation (24):

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

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)

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

$\mathrm{\&Delta;}{I}_{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">h</figure-callout>}}_1},...,\mathrm{\&Delta;}{I}_{h_7},$

${\mathrm{\&Delta;<figure-callout\; id="1"\; label="T\; u"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">T</figure-callout>}}_u^{},...,{\mathrm{\&Delta;T}}_u^6,$

${\mathrm{\&Delta;<figure-callout\; id="1"\; label="V\; R"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">V</figure-callout>}}_R^{},...,\mathrm{\&Delta;}{V}_R^7,$

${\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">h</figure-callout>}}_1,...,\mathrm{\&Delta;}{h}_7]}^T$

With the input of the actuator of 6 kinks, 7 milling trains as system's control input (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):

$\mathrm{\&Delta;}\hat{u}=[u_{\mathrm{\&Delta;<figure-callout\; id="1"\; label="T"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">T</figure-callout>}}^1,...,u_{\mathrm{\&Delta;T}}^6,$

$u_{\mathrm{\&Delta;<figure-callout\; id="1"\; label="V"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">V</figure-callout>}}^1,...,u_{\mathrm{\&Delta;V}}^7,$

${u_{\mathrm{\&Delta;<figure-callout\; id="1"\; label="S"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">S</figure-callout>}}^1,...,u_{\mathrm{\&Delta;S}}^7]}^T---\left(30\right)$

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

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

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

${{\mathrm{\&Delta;<figure-callout\; id="1"\; label="h"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">h</figure-callout>}}_1,...,{\mathrm{\&Delta;h}}_7]}^T---\left(31\right)$

Adjustment on the said system state variable work order can get:

$x=[{\mathrm{\&Delta;I}}_{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">h</figure-callout>}}_1},{\mathrm{\&Delta;<figure-callout\; id="1"\; label="h"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">h</figure-callout>}}_1,$

${\mathrm{\&Delta;I}}_{{\mathrm{\&theta;}}_1},{\mathrm{\&Delta;\&theta;}}_1,{\mathrm{\&Delta;\&omega;}}_1,{\mathrm{\&Delta;I}}_{{\mathrm{\&sigma;}}_1},{\mathrm{\&Delta;\&sigma;}}_1,{\mathrm{\&Delta;I}}_{h_2},{\mathrm{\&Delta;<figure-callout\; id="1"\; label="T\; u"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">T</figure-callout>}}_u^{},{\mathrm{\&Delta;<figure-callout\; id="1"\; label="V\; R"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">V</figure-callout>}}_R^{},\mathrm{\&Delta;}{h}_2,$

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

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

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

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

$\mathrm{\&Delta;u}=[u_{\mathrm{\&Delta;<figure-callout\; id="1"\; label="S"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">S</figure-callout>}}^1,$

$u_{\mathrm{\&Delta;<figure-callout\; id="1"\; label="T"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">T</figure-callout>}}^1,u_{\mathrm{\&Delta;<figure-callout\; id="1"\; label="V"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">V</figure-callout>}}^1,u_{\mathrm{\&Delta;S}}^2,$

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

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

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

$={[{\mathrm{<figure-callout\; id="0"\; label="u"\; filenames="HDA0000081145320000031.png"\; state="\{\{state\}\}">u</figure-callout>}}_0,{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1,...,u_6,u_7]}^T$

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:

$A_0=\left[\begin{array}{cc}0& \frac{M_1}{{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">M</figure-callout>}}_1+M_s^1}\\ 0& -\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="T\; S"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">T</figure-callout>}}_S^{}}\end{array}\right],$ $A_7=[-\frac{1}{T_V^i}],$ $A_{10}=\left[\begin{array}{cc}0& 0\\ 0& 0\\ 0& 0\\ 0& 0\\ 0& -\frac{E_i}{L_i}(\frac{{\&PartialD;S}_f^i}{{\&PartialD;h}_i}{V}_R^i+\frac{{\&PartialD;S}_b^{i+1}}{\&PartialD;h_i}{V}_R^{i+1})\\ 0& 0\\ 0& 0\\ 0& 0\\ 0& 0\end{array}\right],$

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

${\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="HDA0000081145320000031.png"\; state="\{\{state\}\}">B</figure-callout>}}_0=\left[\begin{array}{c}0\\ \frac{M_1}{{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">M</figure-callout>}}_1+M_s^1}\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="T\; S"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">T</figure-callout>}}_S^{}}\end{array}\right],$ $B_7=\left[\frac{1}{T_V^i}\right],$

C ₀＝[0?1]

Remaining matrix (1≤i≤6) is:

$A_i=\left[\begin{array}{ccccccccc}0& 1& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0& 0& 0\\ 0& -\frac{1}{J_i}\left(\frac{{\&PartialD;T}_{\mathrm{load}}^i}{{\&PartialD;\mathrm{\&theta;}}_i}\right)& 0& 0& -\frac{1}{J_i}\left(\frac{{\&PartialD;T}_{\mathrm{\&sigma;}}^i}{{\&PartialD;\mathrm{\&sigma;}}_i}\right)& 0& \frac{1}{{\mathrm{<figure-callout\; id="0"\; label="J\; i"\; filenames="HDA0000081145320000031.png"\; state="\{\{state\}\}">J</figure-callout>}}_i}& 0& 0\\ 0& 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& \frac{E_i}{L_i}{F}_3\left({\mathrm{\&theta;}}_i\right)& 0& -\frac{E_i}{L_i}(\frac{{\&PartialD;S}_f^i}{{\&PartialD;\mathrm{\&sigma;}}_f^i}{V}_R^i-\frac{h_{i+1}}{h_i}\frac{{\&PartialD;S}_f^{i+1}}{{\&PartialD;\mathrm{\&sigma;}}_b^{i+1}}{V}_R^{i+1})& 0& 0& -\frac{E_i}{L_i}(1+S_f^i)& -\frac{E_i}{L_i}\frac{{\&PartialD;S}_b^{i+1}}{{\&PartialD;h}_{i+1}}{V}_R^{i+1}\\ 0& 0& 0& 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 0& -\frac{1}{{\mathrm{<figure-callout\; id="0"\; label="T\; u\; i"\; filenames="HDA0000081145320000031.png"\; state="\{\{state\}\}">T</figure-callout>}}_{ui}^{}}& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& -\frac{1}{{\mathrm{<figure-callout\; id="0"\; label="T\; V\; i"\; filenames="HDA0000081145320000031.png"\; state="\{\{state\}\}">T</figure-callout>}}_{Vi}^{}}& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& -\frac{1}{T_S^i}\end{array}\right],$

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

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 constitute;

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 each subsystem; 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:

${\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">J</figure-callout>}}_1=\underset{k=k_m+1}{\overset{k_m+N_p}{\mathrm{\&Sigma;}}}{x}_1^T\left(k\right)Q_1{x}_1\left(k\right)+\underset{k=k_m}{\overset{k_m+N_c-1}{\mathrm{\&Sigma;}}}{\mathrm{\&Delta;u}}_1{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">R</figure-callout>}}_1{\mathrm{\&Delta;u}}_1^T$

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

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

Wherein:

$x_1={\left[\begin{array}{cc}{\mathrm{\&Delta;I}}_{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">h</figure-callout>}}_1}& {\mathrm{\&Delta;h}}_1\end{array}\right]}^T$

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

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

$\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA0000081145320000021.png,HDA0000081145320000031.png"\; state="\{\{state\}\}">u</figure-callout>}}_1=\left[u_{\mathrm{\&Delta;S}}^1\right]$

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

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

When each subsystem calculates prediction optimum 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 take all factors into consideration of the influence of the pairing prognoses system track of prediction optimum control sequence of other subsystems 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), and the control system that must give PLC and be core processor brings 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 under 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, 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 hot strip rolling control system can comprise the 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 variation.Therefore, the technical staff in all present technique field all should be in the determined protection domain by claims under this invention's idea on the basis of existing technology through the available technical scheme of logical analysis, reasoning, or a limited experiment.

Claims (10)

1. the Distributed Predictive Control method of a hot strip rolling process is applied to it is characterized in that in the hot strip rolling control system, said method comprising the steps of:

A) each parts to said system carry out linear approximation near the operating point of said system, obtain the relevant said hot strip rolling DYNAMIC PROCESS incremental model of coupling between said each parts with said system;

B) with the key variables of said system as the global system state variable; With the input of the actuator of said system input as global system; With the surveyed output of said system output as global system; And combine the coupling between each parts of said system, set up the overall incremental model of said hot strip rolling process;

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

2. the Distributed Predictive Control method of hot strip rolling process as claimed in claim 1, wherein said system comprise 6 groups of kinks and 7 groups of milling trains.

3. the Distributed Predictive Control method of hot strip rolling process as claimed in claim 2, wherein said dynamic increment model comprise kink increment equation, tension increment equation, thickness increment equation, moment adjuster increment equation, automatic speed regulator increment equation and automatic thickness are controlled the increment equation automatically.

4. like the Distributed Predictive Control method of claim 2 or 3 described hot strip rolling processes, 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.

5. the Distributed Predictive Control method of hot strip rolling process as claimed in claim 4, the input of wherein said actuator comprise the input of regulated quantity of roll gap of input and said milling train of regulated quantity of the main motor speed of the input of the control moment of said kink, said milling train.

6. the Distributed Predictive Control method of hot strip rolling process as claimed in claim 5, wherein said system comprises 8 sub-systems altogether, is respectively the subsystem of the automatic thickness control device formation of 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 constitute; The subsystem that the automatic speed regulator of the 7th milling train constitutes, wherein, 1≤i≤6.

7. the Distributed Predictive Control System of a hot strip rolling process; Be applied in the hot strip rolling control system; It is characterized in that; Said Distributed Predictive Control System comprises a plurality of subsystems and a plurality of local prediction controllers that are used for said subsystem, and said subsystem is identical with the quantity of said local prediction controller, intercouples between said a plurality of subsystems; Carry out the mutual of system state variables information between said a plurality of local prediction controller, local prediction controller of the corresponding connection of a sub-systems.

8. the Distributed Predictive Control System of hot strip rolling process as claimed in claim 7, wherein said hot strip rolling control system comprises 6 groups of kinks and 7 groups of milling trains.

9. the Distributed Predictive Control System of hot strip rolling process as claimed in claim 8, the quantity of said subsystem are 8, and the quantity of said local prediction controller is 8.

10. the Distributed Predictive Control System of hot strip rolling process as claimed in claim 9, wherein 8 said subsystems are respectively the subsystem that the automatic thickness control device of first milling train constitutes; 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 constitute; The subsystem that the automatic speed regulator of the 7th milling train constitutes, wherein, 1≤i≤6.

Images