CN112742878B - 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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CN112742878B
CN112742878B CN202110133782.6A CN202110133782A CN112742878B CN 112742878 B CN112742878 B CN 112742878B CN 202110133782 A CN202110133782 A CN 202110133782A CN 112742878 B CN112742878 B CN 112742878B
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disturbance
rolling mill
servo valve
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equation
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CN112742878A (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 GDA0003246497270000021
Figure GDA0003246497270000022
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、k2Equivalent of working roll and supporting roll respectivelyRigidity, equivalent rigidity between the supporting roller and the upper frame and between the hydraulic cylinder and the upper frame; c. ClDamping 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 GDA0003246497270000023
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, and the elastic coefficient k1Coefficient of elasticity k2Damping coefficient 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 GDA0003246497270000031
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 GDA0003246497270000032
x3＝z2,
Figure GDA0003246497270000033
The state space expression is established as follows:
Figure GDA0003246497270000034
Figure GDA0003246497270000035
Figure GDA0003246497270000036
Figure GDA0003246497270000037
wherein the content of the first and second substances,
Figure GDA0003246497270000038
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 GDA0003246497270000041
selecting Lyapunov function
Figure GDA0003246497270000042
Design x2dThe following were used:
x2d＝-c1e1 (12)
wherein, c1Is an arbitrary normal number, obtained by differentiating the following equation (11):
Figure GDA0003246497270000043
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 GDA0003246497270000044
selecting Lyapunov function
Figure GDA0003246497270000045
Figure GDA0003246497270000046
Scaling using young's inequality:
Figure GDA0003246497270000051
then, the following solutions are obtained:
Figure GDA0003246497270000052
in order to process the unknown parameters of time-varying rigidity and variable disturbance rolling forces a and F, defining
Figure GDA0003246497270000053
Design reference trajectory x3d：
Figure GDA0003246497270000054
Figure GDA0003246497270000055
Wherein the content of the first and second substances,
Figure GDA0003246497270000056
is H1Estimated value of c2Is any normal number;
an adaptive method of parameter index approach is used to process unknown parameters:
Figure GDA0003246497270000057
Figure GDA0003246497270000058
wherein, yH1、kH1、H1,0All are arbitrary normal numbers, and the integral of the formula (22) is solved
Figure GDA0003246497270000059
Taking the Lyapunov function in consideration of the self-adaptive parameter error
Figure GDA00032464972700000510
Figure GDA00032464972700000511
To estimate the error, the differential (25) is again taken
Figure GDA0003246497270000061
Because of the fact that
Figure GDA0003246497270000062
Therefore:
Figure GDA0003246497270000063
the second step in equation (28) is derived by:
Figure GDA0003246497270000064
step3 control error is introduced in the same two steps
e4＝x4-x4d (30)
Defining a Lyapunov function
Figure GDA0003246497270000065
Differentiating the error (14)
Figure GDA0003246497270000066
Then, the equation (31) is differentiated and scaled by the Young inequality to obtain:
Figure GDA0003246497270000071
let H2＝max(a2,F2) Designing a reference track:
Figure GDA0003246497270000072
Figure GDA0003246497270000073
Figure GDA0003246497270000074
wherein the content of the first and second substances,
Figure GDA0003246497270000075
is H2Estimated value of yH2、kH2、H2,0、c3Is any normal number;
considering adaptive errors similarly to the foregoing
Figure GDA0003246497270000076
Wherein the content of the first and second substances,
Figure GDA0003246497270000077
differentiating equation (37)
Figure GDA0003246497270000078
Step4 differentiating the equation (30)
Figure GDA0003246497270000081
Defining a Lyapunov function
Figure GDA0003246497270000082
Differentiating equation (40) and substituting equation (38) into, solve:
Figure GDA0003246497270000083
let H3＝max(a2,b1 2,F2)，H4＝D2To counteract the positive term present, the control current is designed:
Figure GDA0003246497270000084
Figure GDA0003246497270000085
wherein the content of the first and second substances,
Figure GDA0003246497270000086
is that
Figure GDA0003246497270000087
Is determined by the estimated value of (c),
Figure GDA0003246497270000088
is b2Is determined by the estimated value of (c),
Figure GDA0003246497270000089
is an estimate of c, a parameter in step
The adaptive estimation rate is:
Figure GDA0003246497270000091
Figure GDA0003246497270000092
Figure GDA0003246497270000093
Figure GDA0003246497270000094
Figure GDA0003246497270000095
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 GDA0003246497270000096
Figure GDA0003246497270000097
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 GDA0003246497270000098
The equation (51) is differentiated and substituted with the equations (44) to (48) to obtain:
Figure GDA0003246497270000101
wherein the content of the first and second substances,
σ＝min(2c1,2aH1c2,2c3,2c4,2akH1,2kH2,2kH3，2kH4，2akP0)
Figure GDA0003246497270000102
directly integrating equation (52) yields:
Figure GDA0003246497270000103
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 GDA0003246497270000121
Figure GDA0003246497270000122
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. ClDamping between the equivalent mass block of the hydraulic cylinder of the supporting roller and the upper frame; z is a radical of1、z2Vibration of two masses respectivelyDisplacement; 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 GDA0003246497270000123
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 elastic coefficient k1Coefficient of elasticity k2Damping coefficient clAlso unlike 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 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 GDA0003246497270000131
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 GDA0003246497270000132
x3＝z2,
Figure GDA0003246497270000133
The state space expression is established as follows:
Figure GDA0003246497270000134
Figure GDA0003246497270000135
Figure GDA0003246497270000136
Figure GDA0003246497270000137
wherein the content of the first and second substances,
Figure GDA0003246497270000138
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 GDA0003246497270000139
selecting Lyapunov function
Figure GDA00032464972700001310
Design x2dThe following were used:
x2d＝-c1e1 (12)
wherein c is1Is an arbitrary normal number, obtained by differentiating the following equation (11):
Figure GDA0003246497270000141
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 GDA0003246497270000142
selecting Lyapunov function
Figure GDA0003246497270000143
Figure GDA0003246497270000144
Scaling using young's inequality:
Figure GDA0003246497270000145
then, the following solutions are obtained:
Figure GDA0003246497270000146
in order to process the unknown parameters of time-varying rigidity and variable disturbance rolling forces a and F, defining
Figure GDA0003246497270000147
Design reference trajectory x3d：
Figure GDA0003246497270000151
Figure GDA0003246497270000152
Wherein
Figure GDA0003246497270000153
Is H1Estimated value of c2Is any normal number;
an adaptive method of parameter index approach is used to process unknown parameters:
Figure GDA0003246497270000154
Figure GDA0003246497270000155
yH1、kH1、H1,0all are arbitrary normal numbers, and the integral of equation (22) is solved:
Figure GDA0003246497270000156
taking the Lyapunov function in consideration of the self-adaptive parameter error
Figure GDA0003246497270000157
Figure GDA0003246497270000158
To estimate the error, the differential (25) is again taken
Figure GDA0003246497270000159
Because of the fact that
Figure GDA00032464972700001510
Therefore:
Figure GDA00032464972700001511
the second step in equation (28) is derived by:
Figure GDA0003246497270000161
step3 control error is introduced in the same two steps
e4＝x4-x4d (30)
Defining a Lyapunov function
Figure GDA0003246497270000162
Differentiating the error pair equation (14)
Figure GDA0003246497270000163
Then, the equation (31) is differentiated and scaled by the Young inequality to obtain:
Figure GDA0003246497270000164
let H2＝max(a2,F2) Designing a reference track:
Figure GDA0003246497270000171
Figure GDA0003246497270000172
Figure GDA0003246497270000173
wherein
Figure GDA0003246497270000174
Is H2Estimated value of yH2、kH2、H2,0、c3Is any normal number;
considering adaptive errors similarly to the foregoing
Figure GDA0003246497270000175
Wherein
Figure GDA0003246497270000176
Differentiating equation (37)
Figure GDA0003246497270000177
Step4 differentiating the equation (30)
Figure GDA0003246497270000178
Defining a Lyapunov function
Figure GDA0003246497270000179
Differentiating equation (40) and substituting equation (38) into, solve:
Figure GDA0003246497270000181
let H3＝max(a2,b1 2,F2)，H4＝D2To counteract the positive term present, the control current is designed:
Figure GDA0003246497270000182
Figure GDA0003246497270000183
wherein the content of the first and second substances,
Figure GDA0003246497270000184
is that
Figure GDA0003246497270000185
Is determined by the estimated value of (c),
Figure GDA0003246497270000186
is b2Is determined by the estimated value of (c),
Figure GDA0003246497270000187
is the estimated value of c, the adaptive estimation rate of the parameters in step is:
Figure GDA0003246497270000188
Figure GDA0003246497270000189
Figure GDA00032464972700001810
Figure GDA0003246497270000191
Figure GDA0003246497270000192
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 GDA0003246497270000193
Figure GDA0003246497270000194
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 GDA0003246497270000195
The equation (51) is differentiated and substituted with the equations (44) to (48) to obtain:
Figure GDA0003246497270000196
wherein the content of the first and second substances,
σ＝min(2c1,2aH1c2,2c3,2c4,2akH1,2kH2,2kH3，2kH4，2akP0)
Figure GDA0003246497270000197
directly integrating equation (52) yields:
Figure GDA0003246497270000201
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+Δk1sinωt,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 GDA0003246497270000202
Figure GDA0003246497270000211
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 FDA0003246497260000011
Figure FDA0003246497260000012
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. ClDamping 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 FDA0003246497260000013
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, and the elastic coefficient k1Coefficient of elasticity k2Damping coefficient 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+Δk1sinωt；
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 FDA0003246497260000021
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 the state variable to be changed
Figure FDA0003246497260000022
The state space expression is established as follows:
Figure FDA0003246497260000023
Figure FDA0003246497260000024
Figure FDA0003246497260000025
Figure FDA0003246497260000026
wherein the content of the first and second substances,
Figure FDA0003246497260000027
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、x2Is obtained by differentiating equation (8):
Figure FDA0003246497260000031
selecting Lyapunov function
Figure FDA0003246497260000032
Design x2dThe following were used:
x2d＝-c1e1 (12)
wherein, c1Is an arbitrary normal number, obtained by differentiating the following equation (11):
Figure FDA0003246497260000033
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 FDA0003246497260000034
selecting Lyapunov function
Figure FDA0003246497260000035
Figure FDA0003246497260000041
Scaling using young's inequality:
Figure FDA0003246497260000042
then, the following solutions are obtained:
Figure FDA0003246497260000043
in order to process the unknown parameters of time-varying rigidity and variable disturbance rolling forces a and F, defining
Figure FDA0003246497260000044
Design reference trajectory x3d：
Figure FDA0003246497260000045
Figure FDA0003246497260000046
Wherein the content of the first and second substances,
Figure FDA0003246497260000047
is H1Estimated value of c2Is any normal number;
an adaptive method of parameter index approach is used to process unknown parameters:
Figure FDA0003246497260000048
Figure FDA0003246497260000049
wherein, yH1、kH1、H1,0All are arbitrary normal numbers, and the integral of equation (22) is solved:
Figure FDA00032464972600000410
taking the Lyapunov function in consideration of the self-adaptive parameter error
Figure FDA0003246497260000051
Figure FDA0003246497260000052
To estimate the error, the differential (25) is again taken
Figure FDA0003246497260000053
Because of the fact that
Figure FDA0003246497260000054
Therefore:
Figure FDA0003246497260000055
the second step in equation (28) is derived by:
Figure FDA0003246497260000056
step3 control error is introduced in the same two steps
e4＝x4-x4d (30)
Defining a Lyapunov function
Figure FDA0003246497260000057
Differentiating the error (14)
Figure FDA0003246497260000058
Then, the equation (31) is differentiated and scaled by the Young inequality to obtain:
Figure FDA0003246497260000061
let H2＝max(a2,F2) Designing a reference track:
Figure FDA0003246497260000062
Figure FDA0003246497260000063
Figure FDA0003246497260000064
wherein the content of the first and second substances,
Figure FDA0003246497260000065
is H2Estimated value of yH2、kH2、H2,0、c3Is any normal number;
considering adaptive errors similarly to the foregoing
Figure FDA0003246497260000066
Wherein the content of the first and second substances,
Figure FDA0003246497260000067
the differential is taken of the equation (37),
Figure FDA0003246497260000068
step4 differentiating the equation (30)
Figure FDA0003246497260000071
Defining a Lyapunov function
Figure FDA0003246497260000072
Differentiating the formula (40) and substituting the formula (38) to obtain
Figure FDA0003246497260000073
Order to
Figure FDA0003246497260000074
H4＝D2To counteract the positive term present, the control current is designed:
Figure FDA0003246497260000075
Figure FDA0003246497260000076
wherein the content of the first and second substances,
Figure FDA0003246497260000081
is that
Figure FDA0003246497260000082
Is determined by the estimated value of (c),
Figure FDA0003246497260000083
is b2Is determined by the estimated value of (c),
Figure FDA0003246497260000084
is the estimated value of c, the adaptive estimation rate of the parameters in step is:
Figure FDA0003246497260000085
Figure FDA0003246497260000086
Figure FDA0003246497260000087
Figure FDA0003246497260000088
Figure FDA0003246497260000089
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 FDA00032464972600000810
Figure FDA00032464972600000811
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 FDA00032464972600000812
The equation (51) is differentiated and substituted with the equations (44) to (48) to obtain:
Figure FDA0003246497260000091
wherein the content of the first and second substances,
σ＝min(2c1,2aH1c2,2c3,2c4,2akH1,2kH2,2kH3，2kH4，2akP0)
Figure FDA0003246497260000092
directly integrating equation (52) yields:
Figure FDA0003246497260000093
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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