CN110538881B - Hot continuous rolling thickness control method based on improved internal mold controller - Google Patents

Hot continuous rolling thickness control method based on improved internal mold controller Download PDF

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CN110538881B
CN110538881B CN201910875168.XA CN201910875168A CN110538881B CN 110538881 B CN110538881 B CN 110538881B CN 201910875168 A CN201910875168 A CN 201910875168A CN 110538881 B CN110538881 B CN 110538881B
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尹方辰
余刘齐
宋宁宁
王柴志
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Huaqiao 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
    • B21B37/16—Control of thickness, width, diameter or other transverse dimensions
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Abstract

The invention relates to a hot continuous rolling thickness control method based on an improved internal mold controller, which comprises the following steps: establishing a mathematical model of the frame hydraulic roll gap control system (HGC), and identifying the HGC system model by utilizing a Particle Swarm Optimization (PSO); based on the model, designing a traditional internal model monitoring AGC controller, and improving the traditional internal model monitoring AGC controller to make the traditional internal model monitoring AGC controller become a two-degree-of-freedom controller; an iterative learning algorithm is introduced into a monitoring AGC system based on an improved internal model controller. The iterative learning algorithm can fully utilize the historical period information of the monitoring AGC system, and the control quantity of the internal model monitoring AGC system is corrected through a certain learning law, so that the monitoring AGC system can be adaptive to the model parameter mismatch condition generated in the hot continuous rolling process. According to the technical scheme provided by the embodiment of the invention, the control quality and robustness of the hot continuous rolling monitoring AGC system can be improved.

Description

Hot continuous rolling thickness control method based on improved internal mold controller
Technical Field
The invention relates to the new technical field of hot continuous rolling processing of steel plate strips, in particular to a hot continuous rolling thickness control method based on an improved internal mold controller.
Background
The thickness precision is an important index for checking the quality of the plate and strip, and an automatic thickness control technology (AGC) is an important means for improving the thickness precision of a strip steel product and becomes an indispensable important component in the production of modern hot continuous rolling strip steel. The monitoring AGC carries out closed-loop control on the thickness of the outlet of the rack based on a thickness gauge at the outlet side of the last rack, so that the monitoring AGC ensures that the thickness of a finished product is consistent with the target thickness in the trend. Therefore, compared with other types of AGC, the monitoring AGC has irreplaceability, but certain lag time exists in outlet thickness detection due to the installation position of the thickness gauge at the outlet side of the last frame, so that a pure lag link exists in a control closed loop of the monitoring AGC, and the performance of the monitoring AGC is reduced. Especially as the pure lag time becomes larger, the robustness of the system will be worse and may cause a destabilization of the system. Therefore, in order to realize the strip rolling with high thickness precision, the technical problem that the monitoring AGC system still has good control effect under the condition of model parameter mismatch needs to be solved urgently.
Disclosure of Invention
The invention mainly aims to overcome the defects in the prior art and provides a hot continuous rolling thickness control method based on an improved internal model controller.
The invention adopts the following technical scheme:
a hot continuous rolling thickness control method based on an improved internal mold controller is characterized by comprising the following steps
1) Establishing a transfer function model for monitoring each substructure of an HGC system in an AGC system, and identifying parameters of the transfer function model by adopting a PSO algorithm;
2) establishing a transfer function model for monitoring an AGC system and introducing a control parameter lambdaaAnd λbSo that the system becomes a two-degree-of-freedom control system;
3) and (3) introducing an iterative learning algorithm into the two-degree-of-freedom control system in the step 2), and correcting an undesired control signal by the deviation of the output track and the given track according to the repeatability and the periodic signal in the action process of the monitoring AGC system to generate a new control signal to realize thickness control.
Preferably, step 1) comprises:
1.1) respectively establishing transfer functions of a servo valve amplifier, a servo valve, a displacement sensor, a pressing hydraulic cylinder and a load by adopting a Laplace transform method, and establishing a total transfer function model of the HGC system by connecting all sub-links;
1.2) a group of initial values of the transfer function model parameters are identified by a system to obtain the output of the initial values and the actual HGC system under the same external disturbance input;
1.3) calculating the error between the system identification output and the actual HGC system output, and forming an error objective function;
1.4) keeping an initial value with a small error objective function value, and continuously adjusting and identifying transfer function model parameters of the HGC system through multiple times of PSO algorithm iteration so as to enable the error objective function value to be minimum.
Preferably, step 2) comprises:
2.1) connecting the transfer function model of the HGC system obtained by identification with an actual object in parallel, taking the internal model controller as the inverse of the minimum phase part of the model, and connecting a first-order feedforward low-pass filter with the internal model controller in series to deduce the transfer function model of the internal model controller;
2.2) designing two internal model controllers in the control system, and respectively setting a control parameter lambdaaAnd λbParameter λaFor controlling the tracking speed of the system to a given value, parameter lambdabThe system is used for controlling the anti-interference performance of the system, thereby becoming a two-degree-of-freedom system and further becoming a two-degree-of-freedom control system;
and 2.3) setting the two improved internal model controllers as proportional integral PI controllers, introducing the proportional integral PI controllers into a Smith estimation monitoring AGC system, and respectively setting the response performance and the anti-interference performance of the Smith estimation monitoring AGC system.
Preferably, step 3) comprises
3.1) establishing an improved internal model monitoring AGC system block diagram based on an iterative learning algorithm, and defining all information in a control system as a function of a time variable t and an iteration number k to represent the periodicity of the system;
3.2) deducing the process control input and tracking deviation of the current period through Laplace transformation according to the established block diagram of the improved internal model monitoring AGC system;
3.3) processing the disturbance of the monitoring AGC system into a periodic fluctuation, and deducing an expression of the internal model monitoring AGC system control quantity after being corrected by a certain learning law, namely the new control signal.
As can be seen from the above description of the present invention, compared with the prior art, the present invention has the following advantages:
the method of the invention realizes the improvement of the anti-interference performance and the response performance of the hot continuous rolling monitoring AGC thickness control system under the condition of model parameter mismatch. By adopting the iterative learning algorithm, the historical period information of the monitoring AGC system can be fully utilized, and the control quantity of the internal model monitoring AGC system is corrected through a certain learning rule, so that the self-adaption of the monitoring AGC system to the model parameter mismatch condition generated in the hot continuous rolling process is realized. According to the technical scheme provided by the embodiment of the invention, the control quality and robustness of the hot continuous rolling monitoring AGC system can be improved.
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FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic flow chart of HGC system parameter identification based on PSO algorithm;
FIG. 3 is a block diagram of an improved internal model monitoring AGC system;
FIG. 4 is a block diagram of an improved internal model monitoring AGC system based on an iterative learning algorithm;
fig. 5 is a numerical simulation analysis of the control effect of the improved internal model monitoring AGC system under the condition of model mismatch and the improved internal model monitoring AGC system based on the iterative learning algorithm.
The invention is described in further detail below with reference to the figures and specific examples.
Detailed Description
The invention is further described below by means of specific embodiments.
Referring to fig. 1, the obtained thickness control quantity of the improved internal mold monitoring AGC based on the iterative learning algorithm can improve the robustness of a monitoring AGC system and provide guarantee for high-thickness-precision strip hot continuous rolling processing. The invention specifically comprises the following steps:
1) and establishing a transfer function model for monitoring each substructure of the HGC system in the AGC system, and identifying parameters of the transfer function model by adopting a PSO algorithm.
1.1) adopting a Laplace transform method to respectively establish a transfer function of a servo valve amplifier, a servo valve, a displacement sensor, a hydraulic pressing cylinder and a load, and establishing a total transfer function model of the HGC system by connecting all sub-links. The method comprises the following steps:
the method comprises the following steps of establishing a transfer function of a servo valve of the HGC system, wherein the servo valve selected by the HGC system has higher natural frequency, and the transfer function is established as follows:
Figure GDA0002585960320000041
in the formula, Gsv(s) is the transfer function of the servo valve; q. q.ssvFor servo valve flow, m3/s；KsvFor servo valve flow gain, (m)3/s)/mA；ωsvIs the servo valve natural frequency, rad/s, ξsvIs the damping ratio of the servo valve; s is a laplace operator; i isposThe servo valve, which is the output of the servo amplifier, controls the current, a.
The displacement of the depressing cylinder is a result of the flow effect of the servo valve and the transfer function of the depressing cylinder and the load is established as follows:
Figure GDA0002585960320000042
in the formula, Glc(s) is the transfer function of the depression cylinder and the load; slcM is the displacement of the hydraulic cylinder pressed down; a. thepIs the working area of the rodless cavity of the oil cylinder, m2；KtIs the mill rigidity, N/m; kceIs the flow pressure coefficient, m, of the servo valve3/(Pa·s)；ζhIs the damping ratio of the servo valve; omegahIs the natural frequency of the hydraulic cylinder, rad/sec; omegarThe first order loop turn frequency, rad/sec.
The response frequency of the position sensor is high, the position sensor is processed into a proportional link, and the transfer function is established as follows:
Gpt(s)＝Kpt
in the formula, Gpt(s) is the transfer function of the position sensor; kptIs the gain of the position sensor.
The servo amplifier converts the control signal output by the controller into the control current of the servo valve, and processes the control current into a proportional link, and the transfer function of the proportional link is established as follows:
Figure GDA0002585960320000051
in the formula, Ga(s) is the transfer function of the servo amplifier; i isposControlling current for a servo valve output by a servo amplifier, A; kaIs the servo amplifier gain, A/V.
The HGC system is controlled by adopting a PI controller, and the transfer function of the PI controller is established as follows:
Figure GDA0002585960320000052
in the formula, Gpc(s) is the transfer function of the PI controller; eposA control signal, V, output by the controller; Δ S is the position deviation, m; kposProportional gain of PI controller; t isposThe gain is integrated for the PI controller.
On the basis of establishing the mathematical model of the links, the closed-loop transfer function model of the HGC system can be obtained by combining the mathematical model and the closed-loop transfer function model as follows:
GH(s)＝[(Ap·Ka·Ksv·Kpt)·(Kpos·Tpos+1)]/[(Ap·Ka·Ksv·Kpt)·(Kpos·Tpos+1)+s·(Tpos·Kt·Kce)·(s/ωr+1)·(s2/ωsv 2+2ξsv·s/ωsv+1)·(s2/ωh 2+2ξh·s/ωh+1)]
discretizing an HGC system and identifying parameters of the HGC system, wherein the method comprises the following steps:
according to the established transfer function model of the HGC system, a discrete transfer function model is established as follows:
Figure GDA0002585960320000053
in the formula, a1,a2,a3,a4,a5,a6,b1,b2,b3,b4,b5,b6Is the parameter to be identified.
1.2) a group of initial values of the transfer function model parameters are identified by the system, and the output of the initial values and the output of the actual HGC system under the same external disturbance input are calculated.
1.3) calculating the error between the system identification output and the actual HGC system output, and forming an error objective function as follows:
Figure GDA0002585960320000061
where y (t) is the actual HGC system output response, y*And (t) is HGC system identification output response, and n is the number of sampling points.
1.4) evaluating the quality of the system identification parameters through an error objective function, keeping an initial value with a small error objective function value, and continuously adjusting and identifying the transfer function model parameters of the HGC system through multiple times of PSO algorithm iteration to enable the error objective function value to be minimum. The PSO iterative algorithm is as follows:
Figure GDA0002585960320000062
Figure GDA0002585960320000063
in the formula, the searched space is D dimension; the total number of particles is m; the spatial position of the ith particle is denoted Xi＝(xi1,xi2,xi3,…,xiD) (ii) a The velocity is denoted Vi＝(vi1,vi2,vi3,…,viD). The local optimum position found by the ith particle in the searching process is Pi＝(pi1,pi2,pi3,…,piD)T(ii) a The global optimal position of the particle swarm in the searching process is Pg＝(pg1,pg2,pg3,…,pgD)T；r1，r2Is between [0,1]Independent random numbers in between; c. C1，c2Is a weight parameter; ω is the inertia factor.
And carrying out square wave input and step input numerical simulation on the system model obtained by identification by using a Simulink tool box provided by Matlab so as to verify the accuracy of the identification model.
2) Establishing a transfer function model for monitoring an AGC system and introducing a control parameter lambdaaAnd λbThus, the system becomes a two-degree-of-freedom control system.
2.1) connecting the transfer function model of the HGC system obtained by identification with an actual object in parallel, taking the internal model controller as the inverse of the minimum phase part of the model, and connecting a first-order feedforward low-pass filter with the internal model controller in series to deduce the transfer function model of the internal model controller.
The design of the improved internal mold controller comprises the following steps:
decomposing the HGC system mathematical model obtained after identification into two parts: containing pure lag and right-half-plane pole-zero and minimum phase parts, namely:
G'H(s)＝G'+(s)G'-(s)
in formula (II), G'+(s) -all pure hysteresis links and right half-plane zero part transfer functions are contained in the model;
the G' -(s) -model does not contain the right half plane zero portion transfer function.
Establishing a block diagram of an improved internal model monitoring AGC system, and deducing the input-output relationship as follows:
H(s)＝G'(s)Qa(s)H*(s)+[1-G'(s)Qb(s)]R(s)
G'(s)＝G'H(s)T'(s)e-τs
wherein R(s) is an interference signal; h*(s) is a set thickness; h(s) is the actual thickness; t'(s) is a mathematical model of the conversion relation between the change of the roll gap of the rolling mill and the change of the thickness of a finish rolling outlet; e.g. of the type-τsThe hysteresis link between the measured thickness of the strip steel from leaving the controlled machine frame to the thickness gauge is provided; qa(s) is a given value controller, QbAnd(s) is an external interference elimination controller.
2.2) designing two internal model controllers in the control system, and respectively setting a control parameter lambdaaAnd λbParameter λaFor controlling the tracking speed of the system to a given value, parameter lambdabThe system is used for controlling the anti-interference performance of the system, thereby becoming a two-degree-of-freedom system.
The filter for the given value controller is designed to have the form:
Figure GDA0002585960320000071
in the formula (I), the compound is shown in the specification,
Figure GDA0002585960320000072
tau is the lag time of the monitoring AGC system, a6For HGC system identification parameters, λaIs a parameter adjustable by the controller.
Design given value controller QaHas the following form:
Figure GDA0002585960320000073
under the stable condition, the closed loop characteristic equation of the improved internal model monitoring AGC system is as follows:
Figure GDA0002585960320000074
designing an external interference elimination controller Q according to the formulabHas the following form:
Figure GDA0002585960320000075
and 2.3) setting the two improved internal model controllers as proportional integral PI controllers, introducing the proportional integral PI controllers into a Smith estimation monitoring AGC system, and respectively setting the response performance and the anti-interference performance of the Smith estimation monitoring AGC system.
3) And (3) introducing an iterative learning algorithm into the two-degree-of-freedom control system in the step 2), and correcting an undesired control signal by the deviation of the output track and the given track according to the repeatability and the periodic signal in the action process of the monitoring AGC system to generate a new control signal to realize thickness control.
The design of an improved internal model monitoring AGC system based on an iterative learning algorithm comprises the following steps:
3.1) establishing an improved internal model monitoring AGC system block diagram based on an iterative learning algorithm, and defining all information in a control system as a function of a time variable t and iteration times k to represent the periodicity of the system.
The control targets of the improved internal model monitoring AGC system based on the iterative learning algorithm are set as follows:
Figure GDA0002585960320000076
establishing an improved internal model monitoring AGC system block diagram based on an iterative learning algorithm, and deducing the process control input of the current period through Laplace transformation as follows:
Figure GDA0002585960320000077
in the formula uk(s)、hk(s)、
Figure GDA0002585960320000081
vk(s) is process input, process output, process model output and iterative learning update rate, respectively, and L is iterative learning gain.
And 3.2) deducing the process control input and tracking deviation of the current period through Laplace transformation according to the established block diagram of the improved internal model monitoring AGC system.
Establishing a tracking offset E for the current cyclek(t) is of the form:
Figure GDA0002585960320000082
in the formula, τmIs the system lag time.
3.3) regarding the disturbance of the monitoring AGC system as a periodic fluctuation, as follows:
Figure GDA0002585960320000083
the method comprises the following steps of establishing an input-output relationship of an improved internal model control monitoring AGC system based on an iterative learning algorithm as follows:
Figure GDA0002585960320000084
according to the above formula, the expression of the internal model monitoring AGC system control quantity corrected by a certain learning law is deduced to be the new control signal, and the control law of the system is deduced as follows:
Figure GDA0002585960320000085
the output of the improved internal model monitoring AGC system based on the iterative learning algorithm is as follows:
Figure GDA0002585960320000086
examples of the applications
According to the method shown in fig. 1 and 2, m is set to 18, ω is set to 0.8, c1＝2，c21.84, the maximum evolution passage number is 100. And (3) compiling an HGC system parameter identification algorithm program by using m files in Malab software, wherein the HGC discrete system model obtained by identification is as follows:
Figure GDA0002585960320000087
converting the discrete system model obtained by identification into a closed-loop continuous model:
Figure GDA0002585960320000091
according to fig. 3, the filter setting the given value controller in the improved internal model controller has the following form:
Figure GDA0002585960320000092
according to FIG. 3, a setting value controller QaHas the following form:
Figure GDA0002585960320000093
according to fig. 3, the external interference cancellation filter Q is setb(s) has the form:
Figure GDA0002585960320000094
from FIG. 3, by Laplace transform, the process control inputs for the current cycle are derived as:
Figure GDA0002585960320000095
the disturbance of the monitoring AGC system is regarded as a periodic fluctuation, which is:
Figure GDA0002585960320000096
deducing an improved internal model monitoring AGC system control law based on an iterative learning algorithm as follows:
Figure GDA0002585960320000097
and carrying out numerical simulation analysis on the improved internal model monitoring AGC system and the improved internal model Smith estimation monitoring AGC system based on an iterative learning algorithm based on a Simulink graphic simulation environment software package in MTALAB software.
Setting simulation parameters as follows: the hysteresis time in the model was 0.28s and the plasticity number was 12000kN/mm2Setting the thickness to be 0.2mm, the rolling speed of a 7# rack to be 5.0m/s, the rigidity of the rack to be 2400kN/mm, the plasticity coefficient of the strip steel to be 15000kN/mm, and estimating and monitoring the control parameter lambda of the AGC system by the improved internal model Smitha＝0.08，λb0.01. Improved internal model Smith estimation monitoring AGC system control parameter lambda based on iterative learning algorithma＝0.08，λbThe iteration number k is 6, the iterative learning gain L is 0.2, a thickness step signal of 0.1mm and a thickness disturbance step signal of 0.02mm are respectively added to the two control systems, and the numerical simulation results are shown in fig. 5 and the following table.
Figure GDA0002585960320000101
The above description is only an embodiment of the present invention, but the design concept of the present invention is not limited thereto, and any insubstantial modifications made by using the design concept should fall within the scope of infringing the present invention.

Claims (4)

1. A hot continuous rolling thickness control method based on an improved internal mold controller is characterized by comprising the following steps
1) Establishing a transfer function model for monitoring each substructure of an HGC system in an AGC system, and identifying parameters of the transfer function model by adopting a PSO algorithm;
2) establishing a transfer function model for monitoring an AGC system and introducing a control parameter lambdaaAnd λbSo that the system becomes a two-degree-of-freedom control system;
3) and (3) introducing an iterative learning algorithm into the two-degree-of-freedom control system in the step 2), and correcting an undesired control signal by the deviation of the output track and the given track according to the repeatability and the periodic signal in the action process of the monitoring AGC system to generate a new control signal to realize thickness control.
2. The hot continuous rolling thickness control method based on the improved inner die controller as claimed in claim 1, wherein the step 1) comprises:
1.1) respectively establishing transfer functions of a servo valve amplifier, a servo valve, a displacement sensor, a pressing hydraulic cylinder and a load by adopting a Laplace transform method, and establishing a total transfer function model of the HGC system by connecting all sub-links;
1.2) a group of initial values of the transfer function model parameters are identified by a system to obtain the output of the initial values and the actual HGC system under the same external disturbance input;
1.3) calculating the error between the system identification output and the actual HGC system output, and forming an error objective function;
1.4) keeping an initial value with a small error objective function value, and continuously adjusting and identifying transfer function model parameters of the HGC system through multiple times of PSO algorithm iteration so as to enable the error objective function value to be minimum.
3. The hot continuous rolling thickness control method based on the improved inner die controller as claimed in claim 1, wherein the step 2) comprises:
2.1) connecting the transfer function model of the HGC system obtained by identification with an actual object in parallel, taking the internal model controller as the inverse of the minimum phase part of the model, and connecting a first-order feedforward low-pass filter with the internal model controller in series to deduce the transfer function model of the internal model controller;
2.2) designing two internal model controllers in the control system, and respectively setting a control parameter lambdaaAnd λbParameter λaFor controlling the tracking speed of the system to a given value, parameter lambdabThe system is used for controlling the anti-interference performance of the system, thereby becoming a two-degree-of-freedom system and further becoming a two-degree-of-freedom control system;
and 2.3) setting the two improved internal model controllers as proportional integral PI controllers, introducing the proportional integral PI controllers into a Smith estimation monitoring AGC system, and respectively setting the response performance and the anti-interference performance of the Smith estimation monitoring AGC system.
4. The hot continuous rolling thickness control method based on the improved internal mold controller as claimed in claim 1, wherein the step 3) comprises
3.1) establishing an improved internal model monitoring AGC system block diagram based on an iterative learning algorithm, and defining all information in a control system as a function of a time variable t and an iteration number k to represent the periodicity of the system;
3.2) deducing the process control input and tracking deviation of the current period through Laplace transformation according to the established block diagram of the improved internal model monitoring AGC system;
3.3) processing the disturbance of the monitoring AGC system into a periodic fluctuation, and deducing an expression of the internal model monitoring AGC system control quantity after being corrected by a certain learning law, namely the new control signal.
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