CN109189112B - A tension roller strip tension sliding mode control method and control device - Google Patents
A tension roller strip tension sliding mode control method and control device Download PDFInfo
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Abstract
Description
技术领域Technical Field
本发明设计了一种张紧辊带钢张力滑模控制方法及控制装置,属于工业自动化领域。The invention designs a tension roller strip steel tension sliding mode control method and a control device, belonging to the field of industrial automation.
背景技术Background Art
在冶金生产过程中,实现张紧辊带钢张力的精确控制是保证带钢产品质量、提升带钢生产效率的关键性因素。现有的带钢张力控制装置多数采用PID控制算法,控制精度低,控制效果不理想。In the metallurgical production process, accurate control of the tension of the tensioning roller strip is a key factor in ensuring the quality of strip products and improving strip production efficiency. Most of the existing strip tension control devices use PID control algorithms, which have low control accuracy and unsatisfactory control effects.
发明内容Summary of the invention
本发明的目的是设计了一种张紧辊带钢张力的滑模控制方法,与传统的PID控制方法相比,本发明的滑模控制方法能够有效的克服张紧辊带钢张力的非线性、未知外界干扰等控制难点;本发明的另一个目的是设计了一种能够实现上述滑模控制方法的张紧辊带钢张力滑模控制装置,该装置以西门子S7-300系列PLC(CPU型号315-2DP)作为主站,完成了控制装置的硬件设计和软件设计。The purpose of the present invention is to design a sliding mode control method for the tension of a tensioning roller strip. Compared with the traditional PID control method, the sliding mode control method of the present invention can effectively overcome the control difficulties such as nonlinearity and unknown external interference of the tension of the tensioning roller strip. Another purpose of the present invention is to design a sliding mode control device for the tension of a tensioning roller strip that can realize the above-mentioned sliding mode control method. The device uses a Siemens S7-300 series PLC (CPU model 315-2DP) as the master station to complete the hardware design and software design of the control device.
为了实现张紧辊带钢张力的先进控制系统的开发,本发明首先建立了张紧辊带钢张力控制的状态空间模型,其次运用西门子公司的工业自动控制架构开发了基于滑模变结构控制理论的PLC滑模控制器,最后建立由PLC控制系统、上位机监控系统组成的带钢张力滑模控制装置。In order to realize the development of an advanced control system for the tension of the tensioning roller strip steel, the present invention firstly establishes a state space model of the tension control of the tensioning roller strip steel, and then uses the industrial automatic control architecture of Siemens to develop a PLC sliding mode controller based on the sliding mode variable structure control theory, and finally establishes a strip steel tension sliding mode control device consisting of a PLC control system and a host computer monitoring system.
本发明是通过以下技术方案实现的:The present invention is achieved through the following technical solutions:
一种张紧辊带钢张力滑模控制方法,包括以下步骤:A tension roller strip steel tension sliding mode control method comprises the following steps:
步骤一、张紧辊带钢张力建模Step 1: Modeling the tension of the tension roller strip
(1)张紧辊结构(1) Tension roller structure
按照带钢经过各个辊子的顺序,分别将各个传动辊定义为1号、2号、3号、4号;其中1号辊和4号辊逆时针转动,2号辊和3号辊顺时针转动,v0为张紧辊的上游带钢速度,v1、v2、v3、v4分别为各个传动辊的转动线速度;其中,v0的大小由上游生产过程决定,由测量工具检测,为已知参数;vi(i=1,…,4)的大小由各个传动辊的电机控制,为可变参数;F1为张紧辊带钢入口处的张力,F2、F3和F4分别为各传动辊间的带钢张力,F5为张紧辊带钢出口处的张力;其中,Fi(i=1,…,4)通过调节4个传动辊的转速进行调节,下游带钢张力F5由下游生产设备决定;L1为张紧辊带钢入口处的带钢长度,L2、L3和L4分别为各个传动辊之间的带钢长度,各部分带钢长度为固定的已知参数;According to the order in which the strip passes through each roller, each drive roller is defined as No. 1, No. 2, No. 3, and No. 4 respectively; among them, roller No. 1 and roller No. 4 rotate counterclockwise, and roller No. 2 and roller No. 3 rotate clockwise, v0 is the upstream strip speed of the tensioning roller, and v1 , v2 , v3 , and v4 are the rotational linear speeds of each drive roller respectively; among them, the size of v0 is determined by the upstream production process and detected by the measuring tool, and is a known parameter; the size of vi (i=1,…,4) is controlled by the motor of each drive roller and is a variable parameter; F1 is the tension at the entrance of the tensioning roller strip, F2 , F3 and F4 are the strip tensions between each drive roller, and F5 is the tension at the exit of the tensioning roller strip; among them, Fi (i=1,…,4) is adjusted by adjusting the rotation speed of the four drive rollers, and the downstream strip tension F5 is determined by the downstream production equipment; L1 is the strip length at the entrance of the tensioning roller strip, L2 , L3 and L4 are the strip tensions between the drive rollers, and F5 is the strip tension at the exit of the tensioning roller. 4 are the strip lengths between the drive rollers, and the strip lengths of each part are fixed known parameters;
(2)张紧辊带钢模型建立(2) Establishment of tension roller strip model
在张紧辊带钢张力控制过程中,通过调节各传动辊电机的电磁力矩Te,i(i=1,…,4)来调节各个辊子的转速,进而控制控制带钢张力Fi(i=1,…,4);定义Te,i为模型输入变量,定义Fi为模型的输出变量,针对第i个传动辊可以得到其电机运动方程式为:In the process of controlling the tension of the tension roller strip, the rotation speed of each roller is adjusted by adjusting the electromagnetic torque Te,i (i=1,…,4) of each drive roller motor, thereby controlling the strip tension Fi (i=1,…,4); Te ,i is defined as the model input variable, and Fi is defined as the model output variable. For the i-th drive roller, the motor motion equation can be obtained as follows:
式(1)中,Ji为第i个传动辊的转动惯量,ωi为第i个传动辊的角速度,TL,i为第i个传动辊电机的负载力矩;得到TL,i同带钢张力之间的数学关系式为:In formula (1), Ji is the moment of inertia of the i-th transmission roller, ωi is the angular velocity of the i-th transmission roller, and T L,i is the load torque of the i-th transmission roller motor; the mathematical relationship between T L,i and the strip tension is obtained as follows:
TL,i=(Fi-Fi+1)×Ri,i=1,2,3,4 (2)T L,i =(Fi -F i+1 )×R i ,i=1,2,3,4 (2)
其中Ri为第i个传动辊的半径;Where R i is the radius of the i-th transmission roller;
带钢张力的产生是由带钢形变造成的,在张紧辊运行的过程中,带钢因各传动辊之间的速度差而产生秒流量差,进而产生带钢张力;得到带钢张力同带钢秒流量差间的数学关系式为:The strip tension is caused by the deformation of the strip. During the operation of the tension roller, the strip produces a flow rate difference due to the speed difference between the drive rollers, which in turn produces the strip tension. The mathematical relationship between the strip tension and the flow rate difference is:
其中,ki为带钢的弹性系数,其计算公式为:Among them, k i is the elastic coefficient of the strip steel, and its calculation formula is:
其中,E为带钢的弹性模量,S为带钢的横截面积;Among them, E is the elastic modulus of the strip steel, and S is the cross-sectional area of the strip steel;
假定了传动辊线速度与贴合在辊身表面的带钢速度一致,由角速度线速度换算公式得带钢在张紧辊内流动速度同传动辊角速度间换算关系为:Assuming that the linear velocity of the drive roller is consistent with the speed of the strip steel attached to the roller surface, the conversion relationship between the flow speed of the strip steel in the tension roller and the angular velocity of the drive roller is obtained from the angular velocity linear velocity conversion formula:
vi=ωi×Ri,i=1,2,3,4 (5)v i =ω i ×R i ,i=1,2,3,4 (5)
联立式(1)-(5)整理得张紧辊带钢张力动态机理模型为:The dynamic mechanism model of the tension of the tension roller strip steel is obtained by combining equations (1)-(5):
根据张紧辊带钢张力控制的动态机理模型,推导出张紧辊带钢张力控制的状态空间表达式;According to the dynamic mechanism model of the tension control of the tension roller strip steel, the state space expression of the tension control of the tension roller strip steel is derived;
状态空间向量x(t)为:The state space vector x(t) is:
x(t)=[x1 x2 x3 x4 x5 x6 x7 x8]T=[F1 ω1 F2 ω2 F3 ω3 F4 ω4]T,x(t)=[x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 ] T =[F 1 ω 1 F 2 ω 2 F 3 ω 3 F 4 ω 4 ] T ,
取控制变量u(t)为:u(t)=[u1 u2 u3 u4]T=[Te,1 Te,2 Te,3 Te,4]T,Take the control variable u(t) as: u(t)=[u 1 u 2 u 3 u 4 ] T =[T e,1 T e,2 T e,3 T e,4 ] T ,
输出变量y(t)为:y(t)=[y1 y2 y3 y4]T=[F1 F2 F3 F4]T,The output variable y(t) is: y(t) = [y 1 y 2 y 3 y 4 ] T = [F 1 F 2 F 3 F 4 ] T ,
根据式(6)可求得张紧辊带钢张力控制的状态空间表达式为:According to formula (6), the state space expression of the tension control of the tension roller strip can be obtained as follows:
式(7)中,A、B、T分别为系统的状态矩阵、输入矩阵、输出矩阵,d为已知的定常干扰向量;In formula (7), A, B, and T are the state matrix, input matrix, and output matrix of the system, respectively, and d is the known constant interference vector;
其中:in:
步骤二、张紧辊带钢张力滑模控制方法设计Step 2: Design of tension roller strip tension sliding mode control method
令 make
则状态矩阵A可整理为: Then the state matrix A can be organized as:
令则输入矩阵B和定常干扰向量d可整理为:make Then the input matrix B and the constant interference vector d can be arranged as:
确定控制目标,令带钢张力跟随张力设定值定义滑模函数为:Determine the control target and make the strip tension Follow tension setting value The sliding mode function is defined as:
s=CE (8)s=CE (8)
式(8)中,各变量的值分别为:In formula (8), the values of each variable are:
s=[s1 s2 s3 s4]T s=[s 1 s 2 s 3 s 4 ] T
其中,e1=yd1-y1,e2=yd2-y2,e3=yd3-y3,e4=yd4-y4,c1>0,c2>0,c3>0,c4>0;Among them, e 1 =y d1 -y 1 , e 2 =y d2 -y 2 , e 3 =y d3 -y 3 , e 4 =y d4 -y 4 , c 1 >0, c 2 >0, c 3 >0, c 4 >0;
对切换函数s求导可得:Taking the derivative of the switching function s, we get:
对于控制量u(x)的求取采用等速趋近律法,取The constant velocity approaching law is used to obtain the control quantity u(x).
其中,ε=diag[ε1,ε2,ε3,ε4],sgn(s)=[sgn(s1)sgn(s2)sgn(s3)sgn(s4)]T;Among them, ε = diag [ε 1 , ε 2 , ε 3 , ε 4 ], sgn(s) = [sgn(s 1 )sgn(s 2 )sgn(s 3 )sgn(s 4 )] T ;
联立式(7)-(10)可得控制量u(x)为:Combining equations (7)-(10), the control variable u(x) can be obtained as:
取李亚普诺夫函数为:Take the Lyapunov function as:
其中,V=diag[1,1,1,1];Where V = diag[1,1,1,1];
为验证所得张紧辊带钢张力控制器的稳定行,结合选取的等速趋近方法,对滑模对李亚普诺夫函数进行求导可得:In order to verify the stability of the obtained tensioning roller strip tension controller, combined with the selected constant velocity approach method, the sliding mode is derived from the Lyapunov function to obtain:
从而验证了设计的滑模控制器可以保证系统渐近稳定,使张紧辊带钢张力跟随张力设定值。This verifies that the designed sliding mode controller can ensure the asymptotic stability of the system and make the strip tension of the tension roller follow the tension set value.
一种张紧辊带钢张力滑模控制装置,包括监控模块和控制模块,所述控制模块与监控模块连接,控制模块将收到的信号传递给监控模块并在监控模块上显示出来,监控模块将设定的信号传递给控制模块,通过控制模块控制张紧辊。A tension roller strip steel tension slipform control device comprises a monitoring module and a control module, wherein the control module is connected to the monitoring module, the control module transmits the received signal to the monitoring module and displays it on the monitoring module, the monitoring module transmits the set signal to the control module, and the tension roller is controlled by the control module.
进一步地,所述控制模块包括主站、从站,所述主站选取西门子S7-300系列PLC,CPU型号为315-2DP;所述从站选取自带CPU的分布式I/O ET200S,CPU型号为IM151-7,主站与从站通过Profibus-DP现场总线通讯。Furthermore, the control module includes a master station and a slave station. The master station is a Siemens S7-300 series PLC with a CPU model of 315-2DP. The slave station is a distributed I/O ET200S with its own CPU with a CPU model of IM151-7. The master station and the slave station communicate via the Profibus-DP field bus.
进一步地,所述监控模块选用WinCC软件内部集成的Activex控件,包括参数显示界面、张力设定界面、状态监测界面、警报报表界面;状态监测界面用于监测张紧辊带钢张力控制模型的各个参数,参数显示界面用于实时显示控制模块中各控制对象的参数信息,并根据带钢的生产规格变化通过张力设定界面改变带钢的张力设定值,同时完成对带钢张力的实时状态检测以及张力控制过程中警报报警的作用。Furthermore, the monitoring module uses Activex controls integrated in the WinCC software, including a parameter display interface, a tension setting interface, a status monitoring interface, and an alarm report interface; the status monitoring interface is used to monitor various parameters of the tension control model of the tension roller strip steel, and the parameter display interface is used to display the parameter information of each control object in the control module in real time, and change the tension setting value of the strip steel through the tension setting interface according to the changes in the production specifications of the strip steel, while completing the real-time status detection of the strip steel tension and the alarm function during the tension control process.
本发明的有益效果为:本发明设计了一种张紧辊带钢张力的滑模控制方法,与传统的PID控制方法相比,本发明的滑模控制方法能够有效的克服张紧辊带钢张力的非线性、未知外界干扰等控制难点;本发明的另一个目的是设计了一种能够实现上述滑模控制方法的张紧辊带钢张力滑模控制装置,该控制装置选取西门子S7-300系列PLC(CPU型号315-2DP)作为主站,选取自带CPU的分布式I/O ET200S(CPU型号IM151-7)作为从站,主从站通过Profibus-DP现场总线通讯。完成了控制装置的硬件设计和软件设计。The beneficial effects of the present invention are as follows: the present invention designs a sliding mode control method for the tension of the tension roller strip steel. Compared with the traditional PID control method, the sliding mode control method of the present invention can effectively overcome the control difficulties such as nonlinearity and unknown external interference of the tension of the tension roller strip steel; another purpose of the present invention is to design a sliding mode control device for the tension of the tension roller strip steel that can realize the above sliding mode control method. The control device selects Siemens S7-300 series PLC (CPU model 315-2DP) as the master station and selects the distributed I/O ET200S (CPU model IM151-7) with its own CPU as the slave station. The master and slave stations communicate through the Profibus-DP field bus. The hardware design and software design of the control device are completed.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1为本发明控制系统结构图。FIG. 1 is a structural diagram of a control system of the present invention.
图2为本发明张紧辊结构示意图。FIG. 2 is a schematic diagram of the tensioning roller structure of the present invention.
图3为本发明控制程序流程图。FIG. 3 is a flow chart of the control program of the present invention.
具体实施方式DETAILED DESCRIPTION
下面结合附图和具体实施例对本发明做进一步的说明。The present invention is further described below in conjunction with the accompanying drawings and specific embodiments.
实施例Example
如图1-3所示,本发明一种张紧辊带钢张力的滑模控制方法,包括以下步骤:As shown in Figures 1-3, a sliding mode control method for tensioning roller strip steel tension of the present invention comprises the following steps:
步骤一、张紧辊带钢张力建模Step 1: Modeling the tension of the tension roller strip
(1)张紧辊结构(1) Tension roller structure
本发明以由4个传动辊组成的4轴张紧辊为例建立了张紧辊带钢张力控制模型。按照带钢经过各个辊子的顺序,分别将各个传动辊定义为1号、2号、3号、4号。其中1号辊和4号辊逆时针转动,2号辊和3号辊顺时针转动,v0为张紧辊的上游带钢速度,v1、v2、v3、v4分别为各个传动辊的转动线速度。其中,v0的大小由上游生产过程决定,可由测量工具检测,为已知参数;vi(i=1,…,4)的大小可有各个传动辊的电机控制,为可变参数。F1为张紧辊带钢入口处的张力,F2、F3和F4分别为各传动辊间的带钢张力,F5为张紧辊带钢出口处的张力。其中,Fi(i=1,…,4)可通过调节4个传动辊的转速进行调节,下游带钢张力F5由下游生产设备决定。L1为张紧辊带钢入口处的带钢长度,L2、L3和L4分别为各个传动辊之间的带钢长度,各部分带钢长度在退火机组设计时已经规定,为固定的已知参数。The present invention takes a four-axis tensioning roller composed of four transmission rollers as an example to establish a tensioning roller strip tension control model. According to the order in which the strip passes through each roller, each transmission roller is defined as No. 1, No. 2, No. 3, and No. 4. Among them, roller No. 1 and roller No. 4 rotate counterclockwise, roller No. 2 and roller No. 3 rotate clockwise, v0 is the upstream strip speed of the tensioning roller, and v1 , v2 , v3 , and v4 are the rotational linear speeds of each transmission roller. Among them, the size of v0 is determined by the upstream production process, which can be detected by the measuring tool and is a known parameter; the size of vi (i = 1, ..., 4) can be controlled by the motor of each transmission roller and is a variable parameter. F1 is the tension at the entrance of the tensioning roller strip, F2 , F3 and F4 are the strip tensions between each transmission roller, and F5 is the tension at the exit of the tensioning roller strip. Among them, Fi (i = 1, ..., 4) can be adjusted by adjusting the rotation speed of the four transmission rollers, and the downstream strip tension F5 is determined by the downstream production equipment. L1 is the strip length at the strip entrance of the tensioning roller, L2 , L3 and L4 are the strip lengths between each driving roller. The strip lengths of each part have been specified in the design of the annealing unit and are fixed known parameters.
(2)张紧辊带钢模型建立(2) Establishment of tension roller strip model
在张紧辊带钢张力控制过程中,通过调节各传动辊电机的电磁力矩Te,i(i=1,…,4)来调节各个辊子的转速,进而控制控制带钢张力Fi(i=1,…,4)。定义Te,i为模型输入变量,定义Fi为模型的输出变量,容易看出4轴张紧辊带钢张力控制模型为一个典型的多输入多输出模型。分析张紧辊带钢张力控制机理,忽略张紧辊内部的粘性因素和带钢传动辊之间的滑动,针对第i个传动辊可以得到其电机运动方程式为:In the process of tensioning roller strip tension control, the rotation speed of each roller is adjusted by adjusting the electromagnetic torque Te,i (i=1,…,4) of each drive roller motor, thereby controlling the strip tension F i (i=1,…,4). Define Te,i as the model input variable and F i as the model output variable. It is easy to see that the 4-axis tensioning roller strip tension control model is a typical multi-input and multi-output model. Analyze the tension control mechanism of the tensioning roller strip, ignore the viscosity factor inside the tensioning roller and the slip between the strip drive rollers, and the motor motion equation for the i-th drive roller can be obtained as follows:
式(1)中,Ji为第i个传动辊的转动惯量,ωi为第i个传动辊的角速度,TL,i为第i个传动辊电机的负载力矩。忽略带钢自重和测张仪的纵向压力等次要因素,可以得到TL,i同带钢张力之间的数学关系式为:In formula (1), Ji is the moment of inertia of the i-th transmission roller, ωi is the angular velocity of the i-th transmission roller, and T L,i is the load torque of the i-th transmission roller motor. Ignoring minor factors such as the weight of the strip and the longitudinal pressure of the tensiometer, the mathematical relationship between T L,i and the strip tension can be obtained as follows:
TL,i=(Fi-Fi+1)×Ri,i=1,2,3,4 (2)T L,i =(Fi -F i+1 )×R i ,i=1,2,3,4 (2)
其中Ri为第i个传动辊的半径。Where Ri is the radius of the i-th transmission roller.
带钢张力的产生是由带钢形变造成的,在张紧辊运行的过程中,带钢因各传动辊之间的速度差而产生秒流量差,进而产生带钢张力。忽略带钢形变过程中的时延可以得到带钢张力同带钢秒流量差间的数学关系式为:The strip tension is caused by the deformation of the strip. During the operation of the tension roller, the strip produces a flow rate difference due to the speed difference between the drive rollers, which in turn produces the strip tension. Ignoring the time delay in the strip deformation process, the mathematical relationship between the strip tension and the flow rate difference can be obtained as follows:
其中,ki为带钢的弹性系数,其计算公式为:Among them, k i is the elastic coefficient of the strip steel, and its calculation formula is:
其中,E为带钢的弹性模量,S为带钢的横截面积。Among them, E is the elastic modulus of the strip steel, and S is the cross-sectional area of the strip steel.
假定了传动辊线速度与贴合在辊身表面的带钢速度一致,由角速度线速度换算公式得带钢在张紧辊内流动速度同传动辊角速度间换算关系为:Assuming that the linear velocity of the drive roller is consistent with the speed of the strip steel attached to the roller surface, the conversion relationship between the flow speed of the strip steel in the tension roller and the angular velocity of the drive roller is obtained from the angular velocity linear velocity conversion formula:
vi=ωi×Ri,i=1,2,3,4 (5)v i =ω i ×R i ,i=1,2,3,4 (5)
联立式(1)-(5)整理得张紧辊带钢张力动态机理模型为:The dynamic mechanism model of the tension of the tension roller strip steel is obtained by combining equations (1)-(5):
根据张紧辊带钢张力控制的动态机理模型可以推导出张紧辊带钢张力控制的状态空间表达式。According to the dynamic mechanism model of the tension control of the tension roller strip steel, the state space expression of the tension control of the tension roller strip steel can be derived.
状态空间向量x(t)为:The state space vector x(t) is:
x(t)=[x1 x2 x3 x4 x5 x6 x7 x8]T=[F1 ω1 F2 ω2 F3 ω3 F4 ω4]T x(t)=[x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 ] T =[F 1 ω 1 F 2 ω 2 F 3 ω 3 F 4 ω 4 ] T
取控制变量u(t)为:Take the control variable u(t) as:
u(t)=[u1 u2 u3 u4]T=[Te,1 Te,2 Te,3 Te,4]T u(t)=[u 1 u 2 u 3 u 4 ] T =[T e,1 T e,2 T e,3 T e,4 ] T
输出变量y(t)为:The output variable y(t) is:
y(t)=[y1 y2 y3 y4]T=[F1 F2 F3 F4]T y(t)=[y 1 y 2 y 3 y 4 ] T =[F 1 F 2 F 3 F 4 ] T
根据式(6)可求得张紧辊带钢张力控制的状态空间表达式为:According to formula (6), the state space expression of the tension control of the tension roller strip can be obtained as follows:
式(7)中,A、B、T分别为系统的状态矩阵、输入矩阵、输出矩阵,d为已知的定常干扰向量。In formula (7), A, B, and T are the state matrix, input matrix, and output matrix of the system, respectively, and d is the known steady-state interference vector.
步骤二、张紧辊带钢张力滑模控制方法设计Step 2: Design of tension roller strip tension sliding mode control method
令 则状态矩阵A可整理为:make Then the state matrix A can be organized as:
令则输入矩阵B和定常干扰向量d可整理为:make Then the input matrix B and the constant interference vector d can be arranged as:
确定控制目标,令带钢张力跟随张力设定值定义滑模函数为:Determine the control target and make the strip tension Follow tension setting value The sliding mode function is defined as:
s=CE (8)s=CE (8)
式(8)中,各变量的值分别为:In formula (8), the values of each variable are:
s=[s1 s2 s3 s4]T s=[s 1 s 2 s 3 s 4 ] T
其中,e1=yd1-y1,e2=yd2-y2,e3=yd3-y3,e4=yd4-y4,c1>0,c2>0,c3>0,c4>0;Among them, e 1 =y d1 -y 1 , e 2 =y d2 -y 2 , e 3 =y d3 -y 3 , e 4 =y d4 -y 4 , c 1 >0, c 2 >0, c 3 >0, c 4 >0;
对切换函数s求导可得:Taking the derivative of the switching function s, we get:
对于控制量u(x)的求取采用等速趋近律法,取The constant velocity approaching law is used to obtain the control quantity u(x).
其中,ε=diag[ε1,ε2,ε3,ε4],sgn(s)=[sgn(s1)sgn(s2)sgn(s3)sgn(s4)]T;Among them, ε = diag [ε 1 , ε 2 , ε 3 , ε 4 ], sgn(s) = [sgn(s 1 )sgn(s 2 )sgn(s 3 )sgn(s 4 )] T ;
联立式(7)-(10)可得控制量u(x)为:Combining equations (7)-(10), the control variable u(x) can be obtained as:
取李亚普诺夫函数为:Take the Lyapunov function as:
其中,V=diag[1,1,1,1]。Among them, V=diag[1,1,1,1].
为验证所得张紧辊带钢张力控制器的稳定行,结合选取的等速趋近方法,对滑模对李亚普诺夫函数进行求导可得:In order to verify the stability of the obtained tensioning roller strip tension controller, combined with the selected constant velocity approach method, the sliding mode is derived from the Lyapunov function to obtain:
从而验证了设计的滑模控制器可以保证系统渐近稳定,使张紧辊带钢张力跟随张力设定值。This verifies that the designed sliding mode controller can ensure the asymptotic stability of the system and make the strip tension of the tension roller follow the tension set value.
如图1-图3所示,一种张紧辊带钢张力滑模控制装置,控制系统中运用PLC完成张紧辊带钢张力的滑模控制方案,将滑模控制算法以PLC梯形图和语句表语言实现。控制器采用主从站结构,满足了复杂冶金工业集中管理分散控制集散控制需求,滑模控制程序开发中充分运用了西门子PLC的程序功能块功能,完成带钢张力的过程控制。控制信号和反馈信号在控制器和张紧辊系统实时传递,使系统保持在动态响应、稳定控制的状态。As shown in Figures 1 to 3, a tension roller strip tension sliding mode control device uses PLC in the control system to complete the sliding mode control scheme of the tension roller strip tension, and the sliding mode control algorithm is implemented in PLC ladder diagram and statement table language. The controller adopts a master-slave station structure to meet the needs of centralized management and distributed control in complex metallurgical industries. The program function block function of Siemens PLC is fully utilized in the development of the sliding mode control program to complete the process control of the strip tension. The control signal and feedback signal are transmitted in real time between the controller and the tension roller system, so that the system remains in a state of dynamic response and stable control.
运用西门子上位机监控系统开发软件WinCC开发控制系统上位机监控界面,监控系统中实时显示控制系统中各主要控制对象参数信息,并可以根据带钢的生产规格变化改变带钢的张力设定值,同时完成对带钢张力的实时状态检测以及张力控制过程中警报报警等作用。监控界面设计中充分运用WinCC软件内部集成的Activex控件,在整个监控系统功能完善性能良好的基础上使得监控界面简洁美观、便于操作,最终调用并配置底层驱动程序实现上位机、PLC和张紧辊的互相通讯。The host computer monitoring interface of the control system is developed using Siemens host computer monitoring system development software WinCC. The monitoring system displays the parameter information of each major control object in the control system in real time, and can change the tension setting value of the strip according to the production specifications of the strip. At the same time, it completes the real-time state detection of the strip tension and the alarm during the tension control process. In the design of the monitoring interface, the Activex control integrated in the WinCC software is fully utilized. On the basis of the perfect function and good performance of the entire monitoring system, the monitoring interface is made simple, beautiful and easy to operate. Finally, the underlying driver is called and configured to realize the mutual communication between the host computer, PLC and tension roller.
张紧辊带钢张力控制模型包含了8个状态变量,分别是各段带钢张力与各传动辊角速度。系统包含4个控制变量,在控制中其值由PLC滑模控制器提供。系统包含4个带钢张力输出,并且在控制系统中作为反馈信号提供给PLC控制器。整个张力控制系统的控制目标为令带钢张力过程值的稳定的跟随带钢张力设定值,并且使控制系统保持良好的动态特性。The tension roller strip tension control model contains 8 state variables, namely the strip tension of each section and the angular velocity of each drive roller. The system contains 4 control variables, whose values are provided by the PLC sliding mode controller in the control. The system contains 4 strip tension outputs, which are provided to the PLC controller as feedback signals in the control system. The control goal of the entire tension control system is to make the strip tension process value stably follow the strip tension set value and keep the control system with good dynamic characteristics.
根据控制系统的控制需求,设计控制系统软件程序开发采用分布式程序结构,分别选取不同的组织块与功能块实现各部分控制功能,并且在主组织块OB1中按顺序逐次调用以满足控制需求。在控制程序的开发中,设计实现PLC控制器滑模控制算法为整个软件设计的关键部分。程序编写之前首先需要确定好系统的I/O接口,在硬件组态的部分中根据控制系统物理接线方式及各个输入输出模块的工作方式对系统的输入输出地址进行了分配,得到的系统I/O分布地址如表1所示:According to the control requirements of the control system, the distributed program structure is used to design the control system software program development. Different organization blocks and function blocks are selected to implement the control functions of each part, and they are called in sequence in the main organization block OB1 to meet the control requirements. In the development of the control program, the design and implementation of the PLC controller sliding mode control algorithm is the key part of the entire software design. Before writing the program, the I/O interface of the system needs to be determined first. In the hardware configuration part, the input and output addresses of the system are allocated according to the physical wiring method of the control system and the working mode of each input and output module. The obtained system I/O distribution address is shown in Table 1:
表1控制系统I/O地址分配表Table 1 Control system I/O address allocation table
PLC滑模控制程序运行流程图如图3所示:PLC控制器处于工作状态时,通过访问CPU系统存储器的过程映象存储区实现与控制对象的信息交换的。过程映象区主要分为过程映象输入表和过程影响输出表两部分,前者用于存放输入模块的信号状态,后者用于暂存程序执行结果的输出值,这些输出值在扫描周期结束后才能被传送到实际的输出模块上。使用循环中断组织块完成对张力控制过程中的误差及其变化率进行求取,将误差及其变化率送到滑模函数中进行计算,并得出控制信号u。The PLC sliding mode control program operation flow chart is shown in Figure 3: When the PLC controller is in working state, the information exchange with the control object is realized by accessing the process image storage area of the CPU system memory. The process image area is mainly divided into two parts: the process image input table and the process influence output table. The former is used to store the signal status of the input module, and the latter is used to temporarily store the output value of the program execution result. These output values can only be transmitted to the actual output module after the scanning cycle ends. The error and its change rate in the tension control process are obtained using the cyclic interrupt organization block, and the error and its change rate are sent to the sliding mode function for calculation, and the control signal u is obtained.
张紧辊带钢张力控制监控计算机监控界面主要有状态监测界面、参数显示界面、张力设定界面及警报报表界面4个部分组成。The computer monitoring interface of the tension roller strip tension control monitoring mainly consists of four parts: status monitoring interface, parameter display interface, tension setting interface and alarm report interface.
在状态监测界面中可以监测到张紧辊带钢张力控制模型的各个参数,包括各传动辊的转动角度度、控制系统的输入转矩、带钢张力的设定值与过程值。同时在状态监测界面中可以显示带钢张力控制过程的状态情况,当带钢张力处于正常控制状态时,传动辊中轴显示绿色,当带钢张力控制出现异常时,传动辊中轴变为红色。In the status monitoring interface, various parameters of the tension roller strip tension control model can be monitored, including the rotation angle of each drive roller, the input torque of the control system, the set value and process value of the strip tension. At the same time, the status of the strip tension control process can be displayed in the status monitoring interface. When the strip tension is in a normal control state, the transmission roller center axis displays green, and when the strip tension control is abnormal, the transmission roller center axis turns red.
进入参数显示界面,在参数显示界面同样可以监测到各段带钢张力的设定值与过程值,此外参数显示界面同时具备了修改带钢张力设定值的功能。在参数显示界面任意带钢张力框“请输入新的带钢张力设定值”栏内输入目标张力设定值,点击确定按钮即可完成对与带钢张力设定值的修改。需要注意的是,由于张紧辊带钢张力控制模型各段带钢张力设定值的调整是必须满足一定的约束条件,所以不论在参数显示界面哪一个带钢张力的设定界面内对带钢张力进行重新设定均对整体带钢张力控制系统产生影响。Enter the parameter display interface, where you can also monitor the set value and process value of each strip tension. In addition, the parameter display interface also has the function of modifying the strip tension set value. Enter the target tension set value in the "Please enter a new strip tension set value" column of any strip tension box in the parameter display interface, and click the OK button to complete the modification of the strip tension set value. It should be noted that since the adjustment of the strip tension set value of each section of the tension roller strip tension control model must meet certain constraints, no matter which strip tension setting interface in the parameter display interface is used to reset the strip tension, it will affect the overall strip tension control system.
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