CN112742878A - Anti-disturbance control method for vertical pressing system of rolling mill under typical working condition - Google Patents

Anti-disturbance control method for vertical pressing system of rolling mill under typical working condition Download PDF

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CN112742878A
CN112742878A CN202110133782.6A CN202110133782A CN112742878A CN 112742878 A CN112742878 A CN 112742878A CN 202110133782 A CN202110133782 A CN 202110133782A CN 112742878 A CN112742878 A CN 112742878A
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disturbance
rolling mill
servo valve
control
dead zone
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CN112742878B (en
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刘爽
周海鹏
华长春
白振华
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Yanshan University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B37/00—Control devices or methods specially adapted for metal-rolling mills or the work produced thereby
    • B21B37/58—Roll-force control; Roll-gap control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B37/00—Control devices or methods specially adapted for metal-rolling mills or the work produced thereby
    • B21B37/007—Control for preventing or reducing vibration, chatter or chatter marks
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B37/00—Control devices or methods specially adapted for metal-rolling mills or the work produced thereby
    • B21B37/48—Tension control; Compression control

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Abstract

The invention discloses an anti-disturbance control method of a rolling mill vertical screw-down system under typical working conditions, which uses an anti-disturbance controller combining adaptive parameter estimation of an exponential approach law and a backstepping control method under the condition of considering model parameter unknown and servo valve execution dead zone, splits the dead zone into a linear function and a piecewise function, and deduces the anti-disturbance controller capable of coping with system structure parameter unknown and unknown asymmetric dead zone; simulation shows that the controller can effectively inhibit disturbance caused by sudden load change to a rolling mill pressing system in the rolling process while ensuring the stability of a system closed loop, and has important significance for high-precision rolling of plate strips.

Description

Anti-disturbance control method for vertical pressing system of rolling mill under typical working condition
Technical Field
The invention relates to the field of rolling mill control, considers nonlinearity of a rolling mill system with a servo valve, and carries out control technology research aiming at the nonlinear rolling mill system, in particular to an anti-disturbance control method for a vertical pressing system of a rolling mill under a typical working condition that model parameters are unknown and a servo valve execution dead zone are considered.
Background
The invention relates to a special steel cold continuous rolling mill system, which is characterized in that the requirements of the advanced manufacturing industry on the quality of special steel are continuously improved at present, various disturbances in the rolling working environment can cause the plate strip to vibrate to generate vibration marks, and the vibration marks seriously affect the quality of plates. The conventional control method applies the hydraulic cylinder to inhibit disturbance, mostly uses the hydraulic cylinder as a first-order or second-order linear link, and generally carries out linear processing on the modeling of a rolling mill system, so that the prior production meets the application requirement, but a series of plans proposed in recent years have increasingly improved the precision requirement on steel, and the original control method cannot meet the development of advanced manufacturing industry.
In order to inhibit the disturbance vibration, the controller evaluation index is determined as the vibration displacement and the speed of the working roll under different disturbance rolling forces.
Disclosure of Invention
Aiming at the problems, the invention provides an anti-disturbance control method for a rolling mill vertical reduction system under a typical working condition that model parameters are unknown and a servo valve execution dead zone is considered, and under the condition that structural parameters are unknown and the servo valve execution dead zone exists, the system is realized to reach a stable state through the anti-disturbance control method; the correctness of the proposed model and the effectiveness of the proposed controller are verified through simulation, so that the control performance of a rolling mill system is met, and the aim of improving the quality and the precision of a plate by the rolling mill control system is fulfilled.
As a rolling mill system has typical nonlinearity, the rigidity nonlinearity of a hydraulic cylinder and the electro-hydraulic servo valve dead zone are fully considered, and the influence of rigidity time variation before and after changing and the servo valve input dead zone on the system control performance is considered aiming at the characteristics of the rolling mill in the control process, the self-adaptive control method of the rolling mill model is provided, and comprises the following steps:
step1, establishing a vertical pressing system model of a rolling mill;
step2, considering unknown model parameters and a self-adaptive controller for servo valve execution dead zone design;
step3, the parameter adjustment of the controller researched by the invention is compared with a simulation result;
step1, establishing a vertical pressing system model of the nonlinear rolling mill, specifically: establishing 1/2 a vertical vibration model of the rolling mill by fully considering the condition that model parameters are unknown and servo valve execution dead zones are not known;
the electro-hydraulic servo valve is a typical nonlinear servo valve which has a typical dead zone nonlinear form, and a dynamic model considering a vertical reduction system of the electro-hydraulic servo rolling mill is established as follows:
Figure BDA0002926336700000021
Figure BDA0002926336700000022
wherein m is1、m2Respectively the mass of the working roll, the equivalent mass of the supporting roll and the piston of the hydraulic cylinder; fvarThe rolling force is the time-varying disturbance rolling force applied to the working roll; k is a radical of1、k2The equivalent rigidity of the working roll and the supporting roll and the equivalent rigidity between the supporting roll and the upper frame and between the hydraulic cylinder and the upper frame are respectively; c is the damping between the equivalent mass block of the hydraulic cylinder of the supporting roller and the upper frame; z is a radical of1、z2Respectively the vibration displacement of the two mass blocks; i.e. icInputting a control current for the servo valve; n (i)c) The control pressure output by the hydraulic cylinder;
n (v) represents the dead band relationship between the servo valve input current and the hydraulic cylinder output pressure, expressed as:
Figure BDA0002926336700000023
wherein, KiThe proportional coefficient of pressure and current of the hydraulic cylinder servo valve system is generally determined by the internal structure of the servo valve, so that the proportional coefficient of pressure and current is considered as a constant; wherein a isr、alMore than or equal to 0 is the left and right break point of the dead zone, and a is generally the casel≠ar(ii) a During the rapid rotation of the roller of the rolling mill, the rolling mill can dynamically operateEccentricity is generated, so that the position of the mass center of the roller in the vertical direction is changed, namely m1、m2The eccentricity also changes the stress condition of the system, the elastic coefficient and the damping coefficient k1、k2、clUnlike static parameters; all the related parameters are taken as unknown parameters, and the working roll rotates to enable the center of mass eccentricity to show a periodic variation law, so that the rigidity expression is as follows: k is a radical of1＝k10+Δk1 sinωt；
The dead zone function can be divided into two parts as follows:
N(ic)＝K(ic)ic+d(ic) (4)
K(ic)＝Kiic (5)
Figure BDA0002926336700000031
the dead zone is therefore considered to be defined by a linear function K (i)c) With a time-varying function d (i)c) The structure is as follows;
the control target of the disturbance rejection control method is to design a control current icEnsuring vertical vibration displacement z of working roll1When disturbance is received, the disturbance is kept to be minimum, and meanwhile, all signals of the whole system are ensured to meet the Lyapunov gradual stabilization;
designing an anti-interference controller by considering the dead zone of the servo valve and the unknown characteristic of the system structure parameter, selecting a state variable and enabling x to be x1＝z1,
Figure BDA0002926336700000032
x3＝z2,
Figure BDA0002926336700000033
The state space expression is established as follows:
Figure BDA0002926336700000034
Figure BDA0002926336700000035
Figure BDA0002926336700000036
Figure BDA0002926336700000037
wherein the content of the first and second substances,
Figure BDA0002926336700000038
and d (i)c) And f is a bounded time-varying function, taking D as max | D (i)c)|，F＝max|f|；
Because the control target is to make the vibration speed and the displacement of the working roll as small as possible under disturbance, the ideal reference track is considered to be 0; and designing a controller by using a backstepping method, and solving the control input current of the electro-hydraulic servo valve by using a backstepping method and recursion errors in each step.
Further, the specific design steps of the disturbance rejection controller in step two are as follows:
step1 introduction of control error
e1＝x1-x1d (8)
e2＝x2-x2d (9)
Wherein x is1d、x2dAre respectively x1、x2Is obtained by differentiating equation (8):
Figure BDA0002926336700000041
selecting Lyapunov function
Figure BDA0002926336700000042
Design x2dThe following were used:
x2d＝-c1e1 (12)
wherein, c1Is an arbitrary normal number, obtained by differentiating the following equation (11):
Figure BDA0002926336700000043
e in formula (13)2From x2-x2dIt is decided, therefore, to design x in the next step2dTo counteract e2The influence of (a);
step2 introduction of control error
e3＝x3-x3d (14)
Obtaining a differential of equation (9):
Figure BDA0002926336700000044
selecting Lyapunov function
Figure BDA0002926336700000045
Figure BDA0002926336700000046
Scaling using young's inequality:
Figure BDA0002926336700000051
then, the following solutions are obtained:
Figure BDA0002926336700000052
rolling for processing unknown parameter time-varying rigidity and variable disturbanceForces a, F, definition
Figure BDA0002926336700000053
Design reference trajectory x3d：
Figure BDA0002926336700000054
Figure BDA0002926336700000055
Wherein the content of the first and second substances,
Figure BDA0002926336700000056
is H1Estimated value of c2Is any normal number;
an adaptive method of parameter index approach is used to process unknown parameters:
Figure BDA0002926336700000057
Figure BDA0002926336700000058
wherein, yH1、kH1、H1,0All are arbitrary normal numbers, and the integral of the formula (22) is solved
Figure BDA0002926336700000059
Taking the Lyapunov function in consideration of the self-adaptive parameter error
Figure BDA00029263367000000510
Figure BDA00029263367000000511
To estimate the error, the differential (25) is again taken
Figure BDA0002926336700000061
Because of the fact that
Figure BDA0002926336700000062
Therefore:
Figure BDA0002926336700000063
the second step in equation (28) is derived by:
Figure BDA0002926336700000064
step3 control error is introduced in the same two steps
e4＝x4-x4d (30)
Defining a Lyapunov function
Figure BDA0002926336700000065
Differentiating the error (14)
Figure BDA0002926336700000066
Then, the equation (31) is differentiated and scaled by the Young inequality to obtain:
Figure BDA0002926336700000071
let H2＝max(a2,F2) Designing a reference track:
Figure BDA0002926336700000072
Figure BDA0002926336700000073
Figure BDA0002926336700000074
wherein the content of the first and second substances,
Figure BDA0002926336700000075
is H2Estimate y ofH2、kH2、H2,0Value, c3Is any normal number;
considering adaptive errors similarly to the foregoing
Figure BDA0002926336700000076
Wherein the content of the first and second substances,
Figure BDA0002926336700000077
differentiating equation (37)
Figure BDA0002926336700000078
Step4 differentiating the equation (30)
Figure BDA0002926336700000081
Defining a Lyapunov function
Figure BDA0002926336700000082
Differentiating equation (40) and substituting equation (38) into, solve:
Figure BDA0002926336700000083
let H3＝max(a2,b1 2,F2)，H4＝D2To counteract the positive term present, the control current is designed:
Figure BDA0002926336700000084
Figure BDA0002926336700000085
wherein the content of the first and second substances,
Figure BDA0002926336700000086
is that
Figure BDA0002926336700000087
Is determined by the estimated value of (c),
Figure BDA0002926336700000088
is b2Is determined by the estimated value of (c),
Figure BDA0002926336700000089
is the estimated value of c, the adaptive estimation rate of the parameters in step is:
Figure BDA0002926336700000091
Figure BDA0002926336700000092
Figure BDA0002926336700000093
Figure BDA0002926336700000094
Figure BDA0002926336700000095
wherein, yH3、kH3、H3,0、yH3、kH3、H3,0、yρ、kρ、ρ2,0、yb2、kb2、b2,0、yc、kc、c0Are arbitrary normal numbers, and f is defined otherwise3、f4The following;
Figure BDA0002926336700000096
Figure BDA0002926336700000097
by designing the controller, the closed-loop signals are ensured to be gradually stable, and the vibration displacement of the working roll of the rolling mill is required to be as small as possible, namely, the vibration displacement is ensured to be smaller than any positive number, and the following proves;
firstly, selecting a Lyapunov function
Figure BDA0002926336700000098
The equation (51) is differentiated and substituted with the equations (44) to (48) to obtain:
Figure BDA0002926336700000101
wherein the content of the first and second substances,
σ＝min(2c1,2aH1 c2,2c3,2c4,2akH1,2kH2,2kH3，2kH4，2akP0)
Figure BDA0002926336700000102
directly integrating equation (52) yields:
Figure BDA0002926336700000103
further, the effectiveness of the disturbance rejection control method is verified through comparison of the simulation graphs in the step three, and the fact that the servo valve execution dead zone is considered to be more beneficial to improving the precision performance of the rolled steel plate is obtained.
Due to the adoption of the technical scheme, the invention has the following beneficial effects:
(1) the invention uses an adaptive parameter estimation method of an exponential approximation law to combine with a backstepping control scheme, divides a dead zone into a linear function and a piecewise function, deduces a control scheme for dealing with unknown structural parameters and unknown asymmetric dead zones of a system, ensures the closed loop stability of each signal of the system, and verifies the effectiveness of the control method by using computer simulation.
(2) The invention fully considers the rigidity nonlinearity of a rolling mill, establishes nonlinear rolling mill models before and after the rolling mill is controlled, and provides an active rolling mill nonlinear self-adaptive controller considering input constraint, so that a system reaches a stable state under the conditions that structural parameters are unknown and servo valve execution dead zones exist.
(3) The invention verifies the correctness of the proposed model and the effectiveness of the proposed controller through simulation, thereby meeting the control performance of a rolling mill system and achieving the purpose of improving the quality and the precision of plates by the rolling mill control system.
Drawings
FIG. 1 is a simplified diagram of the research method of the present invention;
FIG. 2 is a block diagram of an electro-hydraulic servo valve of the present invention;
FIG. 3 is a block diagram of the vertical reduction system of the rolling mill of the present invention;
FIG. 4 is a displacement diagram of a working roll in a steel biting condition according to the present invention;
FIG. 5 is a speed chart of a work roll in a steel biting condition according to the present invention;
FIG. 6 is a displacement diagram of the working roll in the steel throwing working condition of the invention;
FIG. 7 is a speed chart of the work roll in the steel throwing condition of the present invention;
FIG. 8 is a graph showing the displacement of the work rolls when the thickness of the steel sheet fluctuates according to the present invention;
FIG. 9 is a graph of work roll speed as the thickness of the steel sheet fluctuates in accordance with the present invention;
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention. It is to be noted that, unless otherwise specified, technical or scientific terms used herein shall have the ordinary meaning as understood by those skilled in the art to which the invention pertains. For example, front, rear, left and right are used for the present invention only for exemplary purposes and are words of convenience for description.
The technical scheme of the invention is further specifically described by the following embodiments and the accompanying drawings. The control method comprises the following steps:
step1, establishing a vertical pressing system model of a rolling mill;
step2, considering unknown model parameters and a self-adaptive controller for servo valve execution dead zone design;
and 3, comparing the parameter adjustment and simulation results of the controller researched by the invention.
Step1, establishing a nonlinear rolling mill vertical reduction system model, namely establishing 1/2 rolling mill vertical vibration model by fully considering the condition of unknown model parameters and servo valve execution dead zone;
the electro-hydraulic servo valve is taken as a typical nonlinear servo valve, has a typical dead zone nonlinear form, and establishes a dynamic model considering a vertical pressing system of the electro-hydraulic servo rolling mill;
Figure BDA0002926336700000121
Figure BDA0002926336700000122
wherein m is1、m2Respectively the mass of the working roll, the equivalent mass of the supporting roll and the piston of the hydraulic cylinder; fvarThe rolling force is the time-varying disturbance rolling force applied to the working roll; k is a radical of1、k2The equivalent rigidity of the working roll and the supporting roll and the equivalent rigidity between the supporting roll and the upper frame and between the hydraulic cylinder and the upper frame are respectively; c is the damping between the equivalent mass block of the hydraulic cylinder of the supporting roller and the upper frame; z is a radical of1、z2Respectively the vibration displacement of the two mass blocks; i.e. icInputting a control current for the servo valve; n (i)c) The control pressure output by the hydraulic cylinder; n (v) represents the dead band relationship of the servo valve input current to the hydraulic cylinder output pressure, the dead band being defined as follows:
Figure BDA0002926336700000123
wherein, KiThe proportional coefficient of pressure and current of the hydraulic cylinder servo valve system is generally determined by the internal structure of the servo valve, so that the proportional coefficient of pressure and current is considered as a constant; wherein a isr、alMore than or equal to 0 is the left and right break point of the dead zone, and a is generally the casel≠ar(ii) a During the rapid rotation of the roller of the rolling mill, the rolling mill can generate eccentricity during dynamic operation, so that the position of the mass center of the roller in the vertical direction changes, namely m1、m2The system stress condition can be changed due to eccentricity, and the elasticity coefficient and the damping force coefficient k are changed1、k2、clAlso unlike static parameters; all the parameters involved are treated as unknown parameters,and the working roll rotates to ensure that the eccentricity of the mass center presents a periodic change rule, so the rigidity expression is as follows: k is a radical of1＝k10+Δk1 sinωt；
The control objective of the disturbance rejection control method is to design the control current icEnsuring vertical vibration displacement z of working roll1The disturbance is kept to a minimum when the disturbance is received, and meanwhile, all signals of the whole system are ensured to meet the Lyapunov gradual stabilization.
Further, step1, establishing a vertical reduction system model of the nonlinear rolling mill, and dividing a dead zone function into two parts according to the following method:
N(ic)＝K(ic)ic+d(ic) (4)
K(ic)＝Kiic (5)
Figure BDA0002926336700000131
the dead zone is therefore considered to be defined by a linear function K (i)c) With a time-varying function d (i)c) And (3) forming.
Further, the adaptive controller considering the dead zone establishment of the servo valve in the step2 is; selecting a state variable, let x1＝z1,
Figure BDA0002926336700000132
x3＝z2,
Figure BDA0002926336700000133
The state space expression is established as follows:
Figure BDA0002926336700000134
Figure BDA0002926336700000135
Figure BDA0002926336700000136
Figure BDA0002926336700000137
wherein the content of the first and second substances,
Figure BDA0002926336700000138
and d (i)c) And f is a bounded time-varying function, taking D as max | D (i)c)|，F＝max|f|；
Because the control target is to make the vibration speed and the displacement of the working roll as small as possible under disturbance, the ideal reference track is considered to be 0; the backstepping method is used for designing the controller, the backstepping method is used, errors of each recursion step are solved, the electro-hydraulic servo valve is used for controlling input current, and the specific design steps are as follows:
step1 introduction of control error
e1＝x1-x1d (8)
e2＝x2-x2d (9)
Wherein x is1d、x2dAre respectively x1、x2Is obtained by differentiating equation (8):
Figure BDA0002926336700000139
selecting Lyapunov function
Figure BDA00029263367000001310
Design x2dThe following were used:
x2d＝-c1e1 (12)
wherein c is1Is an arbitrary normal number, obtained by differentiating the following equation (11):
Figure BDA0002926336700000141
e in formula (13)2From x2-x2dIt is decided, therefore, to design x in the next step2dTo counteract e2The influence of (a);
step2 introduction of control error
e3＝x3-x3d (14)
Obtaining a differential of equation (9):
Figure BDA0002926336700000142
selecting Lyapunov function
Figure BDA0002926336700000143
Figure BDA0002926336700000144
Scaling using young's inequality:
Figure BDA0002926336700000145
then, the following solutions are obtained:
Figure BDA0002926336700000146
in order to process the unknown parameters of time-varying rigidity and variable disturbance rolling forces a and F, defining
Figure BDA0002926336700000147
Design reference trajectory x3d：
Figure BDA0002926336700000151
Figure BDA0002926336700000152
Wherein
Figure BDA0002926336700000153
Is H1Estimated value of c2Is any normal number;
an adaptive method of parameter index approach is used to process unknown parameters:
Figure BDA0002926336700000154
Figure BDA0002926336700000155
yH1、kH1、H1,0all are arbitrary normal numbers, and the integral of equation (22) is solved:
Figure BDA0002926336700000156
taking the Lyapunov function in consideration of the self-adaptive parameter error
Figure BDA0002926336700000157
Figure BDA0002926336700000158
To estimate the error, the differential (25) is again taken
Figure BDA0002926336700000159
Because of the fact that
Figure BDA00029263367000001510
Therefore:
Figure BDA00029263367000001511
the second step in equation (28) is derived by:
Figure BDA0002926336700000161
step3 control error is introduced in the same two steps
e4＝x4-x4d (30)
Defining a Lyapunov function
Figure BDA0002926336700000162
Differentiating the error pair equation (14)
Figure BDA0002926336700000163
Then, the equation (31) is differentiated and scaled by the Young inequality to obtain:
Figure BDA0002926336700000164
let H2＝max(a2,F2) Designing a reference track:
Figure BDA0002926336700000171
Figure BDA0002926336700000172
Figure BDA0002926336700000173
wherein
Figure BDA0002926336700000174
Is H2Estimate y ofH2、kH2、H2,0Value, c3Is any normal number;
considering adaptive errors similarly to the foregoing
Figure BDA0002926336700000175
Wherein
Figure BDA0002926336700000176
Differentiating equation (37)
Figure BDA0002926336700000177
Step4 differentiating the equation (30)
Figure BDA0002926336700000178
Defining a Lyapunov function
Figure BDA0002926336700000179
Differentiating equation (40) and substituting equation (38) into, solve:
Figure BDA0002926336700000181
let H3＝max(a2,b1 2,F2)，H4＝D2To counteract the positive term present, the control current is designed:
Figure BDA0002926336700000182
Figure BDA0002926336700000183
wherein the content of the first and second substances,
Figure BDA0002926336700000184
is that
Figure BDA0002926336700000185
Is determined by the estimated value of (c),
Figure BDA0002926336700000186
is b2Is determined by the estimated value of (c),
Figure BDA0002926336700000187
is the estimated value of c, the adaptive estimation rate of the parameters in step is:
Figure BDA0002926336700000188
Figure BDA0002926336700000189
Figure BDA00029263367000001810
Figure BDA0002926336700000191
Figure BDA0002926336700000192
wherein, yH3、kH3、H3,0、yH3、kH3、H3,0、yρ、kρ、ρ2,0、yb2、kb2、b2,0、yc、kc、c0Are arbitrary normal numbers, and f is defined otherwise3、f4The following;
Figure BDA0002926336700000193
Figure BDA0002926336700000194
by designing the controller, the closed-loop signals are ensured to be gradually stable, and the vibration displacement of the working roll of the rolling mill is required to be as small as possible, namely, the vibration displacement is ensured to be smaller than any positive number, and the following proves;
firstly, selecting a Lyapunov function
Figure BDA0002926336700000195
The equation (51) is differentiated and substituted with the equations (44) to (48) to obtain:
Figure BDA0002926336700000196
wherein the content of the first and second substances,
σ＝min(2c1,2aH1 c2,2c3,2c4,2akH1,2kH2,2kH3，2kH4，2akP0)
Figure BDA0002926336700000197
directly integrating equation (52) yields:
Figure BDA0002926336700000201
step3, the parameter adjustment of the controller researched by the invention is compared with a simulation result;
taking the following parameters of a vertical pressing system of a certain rolling mill:
m1＝1050kg,m2＝820kg,k1＝k10+Δk1 sinωt,k10＝1.04×109N/m,Δk1＝1000N/m,k2＝0.82×109N/m cl＝4×106n · s/m. The current dead zone of the servo valve is selected to be (-0.1, +0.08) mA, and due to the fact that the magnitude order difference of rigidity, damping and rolling force is too large, all parameters are normalized for facilitating the design of a controller, and the parameters of the processed parameter controller are as follows:
H1＝1.02,H2＝1,H3＝3.007H4＝0.01,ρ＝0.6,b2＝1.37,cl＝0.07。
wherein the rigidity k between the working roll and the supporting roll1Time-varying part Δ k of1The selection of ω in sin ω t takes into account the structural parameters of the rolling mill, the diameter of the working roll of the rolling mill is 650mm, the maximum linear speed of the working roll is 8m/s, and the corresponding rotating speed of the working roll is 3.920r/s, namely 12.3rad/s, so ω is selected to be 10 in the simulation.
In a vertical screw-down system of a rolling mill, the head of a rolled piece enters a roll gap to be in a steel biting working condition, and the disturbance energy of a working roll is represented by step force; when the tail of a rolled piece enters a roll gap, steel is thrown due to the fact that the head of the rolled piece can jump randomly, and the disturbance energy of a working roll under the steel throwing working condition is represented by a slope signal; the deformation of the billet head caused by non-uniform rolling and temperature is extruded at the next entrance, the steel piling deformation can occur at the previous entrance, and the disturbance energy of the working roll under the steel piling working condition is represented by a sine signal. After designing the controller by integrating various working conditions, the parameters of the controller are selected as follows:
Figure BDA0002926336700000202
Figure BDA0002926336700000211
the most commonly used control mode in general industrial control is PID control, so the following compares the control effect under different working conditions by using a PID controller and the backstepping self-adapting method provided by the invention, and more powerfully explains the superiority of the control method of the invention.
Fig. 4 and 5 respectively show the vibration displacement and the vibration speed of the working roll under the steel biting working condition, the anti-interference controller can quickly reduce the vibration speeds of the working roll and the supporting roll to 0 under the steel biting working condition, the amplitude of the working roll is greatly reduced under the steel biting interference, and the direct control target is to weaken the vibration of the working roll, so the controller obtains a remarkable control effect; compared with a PID controller, the control method cannot be adjusted according to the time-varying structural parameters, although the amplitude of the working roll (47.5% new) can be reduced to a certain extent in the process of inhibiting the vibration of the working roll, oscillation exists all the time and the convergence time is too long, the self-adaptive strategy can quickly converge, the control effect is more remarkable than that of PID, the amplitude is reduced by 97.5%, and the controller has an excellent disturbance effect on steel biting signals.
FIG. 6 and FIG. 7 show the vibration displacement and speed of the working roll under the working condition of steel throwing, and the maximum displacement of the working roll is reduced by 95.4% after a backstepping controller is added under the working condition of steel throwing; in contrast, the maximum displacement reduction under PID control is only 51.0%. The control scheme is still very effective under the working condition of steel throwing,
fig. 8 and 9 show that under the fluctuation of the thickness of the steel plate, the vibration is greatly suppressed after the controller is added, the vibration displacement of the working roll can be reduced by only 57.2% by using the PID controller, and the amplitude is reduced by 96.9% by using the self-adaptive control method used in the invention, which is similar to other working conditions, so the control method designed by the application has positive significance in improving the quality of the steel plate and prolonging the service life of a rolling mill system.
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and the present invention shall be covered thereby. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (3)

1. An anti-disturbance control method for a vertical pressing system of a rolling mill under typical working conditions is characterized by comprising the following steps:
step1, establishing a vertical pressing system model of a nonlinear rolling mill;
step2, setting parameters of the anti-interference controller by considering the dead zone of the servo valve and unknown characteristics of system structure parameters to obtain a control scheme of the anti-interference controller;
step3, verifying the validity of the control scheme through computer simulation;
step1, establishing a vertical pressing system model of the nonlinear rolling mill, specifically: establishing 1/2 a vertical vibration model of the rolling mill by fully considering the condition that model parameters are unknown and servo valve execution dead zones are not known;
the electro-hydraulic servo valve is a typical nonlinear servo valve which has a typical dead zone nonlinear form, and a dynamic model considering a vertical reduction system of the electro-hydraulic servo rolling mill is established as follows:
Figure FDA0002926336690000011
Figure FDA0002926336690000012
wherein m is1、m2Respectively the mass of the working roll, the equivalent mass of the supporting roll and the piston of the hydraulic cylinder; fvarThe rolling force is the time-varying disturbance rolling force applied to the working roll; k is a radical of1、k2The equivalent rigidity of the working roll and the supporting roll and the equivalent rigidity between the supporting roll and the upper frame and between the hydraulic cylinder and the upper frame are respectively; c is equivalent mass block of hydraulic cylinder of support rollerDamping between the upper frame and the lower frame; z is a radical of1、z2Respectively the vibration displacement of the two mass blocks; i.e. icInputting a control current for the servo valve; n (i)c) The control pressure output by the hydraulic cylinder;
n (v) represents the dead band relationship between the servo valve input current and the hydraulic cylinder output pressure, expressed as:
Figure FDA0002926336690000013
wherein, KiThe proportional coefficient of pressure and current of the hydraulic cylinder servo valve system is generally determined by the internal structure of the servo valve, so that the proportional coefficient of pressure and current is considered as a constant; wherein a isr、alMore than or equal to 0 is the left and right break point of the dead zone, and a is generally the casel≠ar(ii) a During the rapid rotation of the roller of the rolling mill, the rolling mill can generate eccentricity during dynamic operation, so that the position of the mass center of the roller in the vertical direction changes, namely m1、m2The eccentricity also changes the stress condition of the system, the elastic coefficient and the damping coefficient k1、k2、clUnlike static parameters; all the related parameters are taken as unknown parameters, and the working roll rotates to enable the center of mass eccentricity to show a periodic variation law, so that the rigidity expression is as follows: k is a radical of1＝k10+Δk1 sinωt；
The dead zone function can be divided into two parts as follows:
N(ic)＝K(ic)ic+d(ic) (4)
K(ic)＝Kiic (5)
Figure FDA0002926336690000021
the dead zone is therefore considered to be defined by a linear function K (i)c) With a time-varying function d (i)c) The structure is as follows;
the control target of the disturbance rejection control method is design controlCurrent icEnsuring vertical vibration displacement z of working roll1When disturbance is received, the disturbance is kept to be minimum, and meanwhile, all signals of the whole system are ensured to meet the Lyapunov gradual stabilization;
designing an anti-interference controller by considering the dead zone of the servo valve and the unknown characteristic of the system structure parameter, selecting a state variable and enabling the state variable to be changed
Figure FDA0002926336690000022
The state space expression is established as follows:
Figure FDA0002926336690000023
Figure FDA0002926336690000024
Figure FDA0002926336690000025
Figure FDA0002926336690000026
wherein the content of the first and second substances,
Figure FDA0002926336690000027
and d (i)c) And f is a bounded time-varying function, taking D as max | D (i)c)|，F＝max|f|；
Because the control target is to make the vibration speed and the displacement of the working roll as small as possible under disturbance, the ideal reference track is considered to be 0; and designing a controller by using a backstepping method, and solving the control input current of the electro-hydraulic servo valve by using a backstepping method and recursion errors in each step.
2. The method for controlling the anti-disturbance of the vertical pressing system of the rolling mill under the typical working condition according to claim 1, wherein the specific steps of the generation of the control scheme of the anti-disturbance controller in the second step are as follows:
step1 introduction of control error
e1＝x1-x1d (8)
e2＝x2-x2d (9)
Wherein x is1d、x2dAre respectively x1、x2Ideal reference trajectory of (8)
Figure FDA0002926336690000031
Selecting Lyapunov function
Figure FDA0002926336690000032
Design x2dThe following were used:
x2d＝-c1e1 (12)
wherein, c1Is an arbitrary normal number, obtained by differentiating the following equation (11):
Figure FDA0002926336690000033
e in formula (13)2From x2-x2dIt is decided, therefore, to design x in the next step2dTo counteract e2The influence of (a);
step2 introduction of control error
e3＝x3-x3d (14)
Obtaining a differential of equation (9):
Figure FDA0002926336690000034
selecting Lyapunov function
Figure FDA0002926336690000035
Figure FDA0002926336690000041
Scaling using young's inequality:
Figure FDA0002926336690000042
then, the following solutions are obtained:
Figure FDA0002926336690000043
in order to process the unknown parameters of time-varying rigidity and variable disturbance rolling forces a and F, defining
Figure FDA0002926336690000044
Design reference trajectory x3d：
Figure FDA0002926336690000045
Figure FDA0002926336690000046
Wherein the content of the first and second substances,
Figure FDA0002926336690000047
is H1Estimated value of c2Is any normal number;
an adaptive method of parameter index approach is used to process unknown parameters:
Figure FDA0002926336690000048
Figure FDA0002926336690000049
wherein, yH1、kH1、H1,0All are arbitrary normal numbers, and the integral of equation (22) is solved:
Figure FDA00029263366900000410
taking the Lyapunov function in consideration of the self-adaptive parameter error
Figure FDA0002926336690000051
Figure FDA0002926336690000052
To estimate the error, the differential (25) is again taken
Figure FDA0002926336690000053
Because of the fact that
Figure FDA0002926336690000054
Therefore:
Figure FDA0002926336690000055
the second step in equation (28) is derived by:
Figure FDA0002926336690000056
step3 control error is introduced in the same two steps
e4＝x4-x4d (30)
Defining a Lyapunov function
Figure FDA0002926336690000057
Differentiating the error (14)
Figure FDA0002926336690000058
Then, the equation (31) is differentiated and scaled by the Young inequality to obtain:
Figure FDA0002926336690000061
let H2＝max(a2,F2) Designing a reference track:
Figure FDA0002926336690000062
Figure FDA0002926336690000063
Figure FDA0002926336690000064
wherein the content of the first and second substances,
Figure FDA0002926336690000065
is H2Estimate y ofH2、kH2、H2,0Value, c3Is any normal number;
considering adaptive errors similarly to the foregoing
Figure FDA0002926336690000066
Wherein the content of the first and second substances,
Figure FDA0002926336690000067
the differential is taken of the equation (37),
Figure FDA0002926336690000068
step4 differentiating the equation (30)
Figure FDA0002926336690000071
Defining a Lyapunov function
Figure FDA0002926336690000072
Differentiating the formula (40) and substituting the formula (38) to obtain
Figure FDA0002926336690000073
Order to
Figure FDA0002926336690000076
H4＝D2To counteract the positive term present, the control current is designed:
Figure FDA0002926336690000074
Figure FDA0002926336690000075
wherein the content of the first and second substances,
Figure FDA0002926336690000081
is that
Figure FDA0002926336690000082
Is determined by the estimated value of (c),
Figure FDA0002926336690000083
is b2Is determined by the estimated value of (c),
Figure FDA0002926336690000084
is the estimated value of c, the adaptive estimation rate of the parameters in step is:
Figure FDA0002926336690000085
Figure FDA0002926336690000086
Figure FDA0002926336690000087
Figure FDA0002926336690000088
Figure FDA0002926336690000089
wherein, yH3、kH3、H3,0、yH3、kH3、H3,0、yρ、kρ、ρ2,0、yb2、kb2、b2,0、yc、kc、c0Are arbitrary normal numbers, and f is defined otherwise3、f4The following;
Figure FDA00029263366900000810
Figure FDA00029263366900000811
through the setting of the control scheme of the controller, all closed-loop signals are ensured to be gradually stable, and the vibration displacement of the working roll of the rolling mill is required to be as small as possible, namely, the vibration displacement is ensured to be smaller than any positive number, and the following proves that the vibration displacement is gradually stable;
firstly, selecting a Lyapunov function
Figure FDA00029263366900000812
The equation (51) is differentiated and substituted with the equations (44) to (48) to obtain:
Figure FDA0002926336690000091
wherein the content of the first and second substances,
σ＝min(2c1,2aH1c2,2c3,2c4,2akH1,2kH2,2kH3，2kH4，2akP0)
Figure FDA0002926336690000092
directly integrating equation (52) yields:
Figure FDA0002926336690000093
3. the method for controlling the disturbance resistance of the vertical screw-down system of the rolling mill under the typical working condition according to claim 1, wherein the effectiveness of the disturbance resistance control scheme is verified through comparison of simulation graphs, so that the servo valve execution dead zone is considered to be more favorable for improving the precision performance of a rolled steel plate.
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