CN100465294C

CN100465294C - Intelligent Control Method of Argon Blowing at the Bottom of Refining Furnace

Info

Publication number: CN100465294C
Application number: CNB2006101021335A
Authority: CN
Inventors: 吴学礼; 贾辉然; 孟华; 李平; 孟凡华; 甄然
Original assignee: Hebei University of Science and Technology
Current assignee: Hebei University of Science and Technology
Priority date: 2006-11-09
Filing date: 2006-11-09
Publication date: 2009-03-04
Anticipated expiration: 2026-11-09
Also published as: CN1966733A

Abstract

The invention relates to an intelligent control method for argon blowing at the bottom of a refining furnace, which is a control method for argon blowing at the bottom of a refining furnace based on a fuzzy self-adaptive algorithm with a hierarchical structure. The hierarchical structure divides the whole control system into three levels of control structure: (1) basic fuzzy control level. In order to meet the real-time control requirements of the system, the basic fuzzy control level adopts the fuzzy logic control method. (2) Adaptive adjustment level. In order to adapt to the time-varying situation of the parameters of the controlled system, an adaptive control method is adopted to adjust the parameters of the fuzzy controller on-line at regular intervals. (3) Process status judgment level. In order to overcome the influence of process state changes (or different actual working conditions) and improve the robust performance of the control system, the process state judgment is used as an auxiliary input, and the corresponding fuzzy controller parameter set is used according to the process state of the system. The beneficial effect of the invention is that the control precision of the control system is greatly improved, thereby improving the production efficiency and steelmaking quality, and the control system is simple in structure and low in cost.

Description

Intelligent Control Method of Argon Blowing at the Bottom of Refining Furnace

技术领域 technical field

本发明涉及一种精炼炉底吹氩智能控制方法，具体地说，是一种基于具有分级结构的模糊自适应控制算法的精炼炉底吹氩控制方法。The invention relates to an intelligent control method for argon blowing at the bottom of a refining furnace, in particular to a control method for argon blowing at the bottom of a refining furnace based on a fuzzy self-adaptive control algorithm with a hierarchical structure.

背景技术 Background technique

精炼炉底吹氩炼钢技术具有成本低、操作方便、搅拌效果好的优点，并由此产生了一系列极其有益的冶金效果。它可以明显缩短冶炼时间、降低能耗、提高脱硫脱磷能力，促进合金均匀化。冶炼不锈钢时可促进去碳保铬，增加合金收得率，并且可大大降低工人的劳动强度。The argon-blowing steelmaking technology at the bottom of the refining furnace has the advantages of low cost, convenient operation and good stirring effect, and thus produces a series of extremely beneficial metallurgical effects. It can significantly shorten smelting time, reduce energy consumption, improve desulfurization and dephosphorization capabilities, and promote alloy homogenization. When smelting stainless steel, it can promote the removal of carbon and preserve chromium, increase the yield of alloy, and greatly reduce the labor intensity of workers.

1998年宝钢从日本引进底吹氩气控制技术，并建成投入运行，取得较好的效果。目前，虽然国内所采用的精炼技术中大多数采用钢包底吹氩气法，但由于进口设备价格比较昂贵、维护成本高而且对操作人员的要求高，所以国内大多数厂家基本上采用人工直接操作的控制方法。In 1998, Baosteel introduced the bottom blowing argon gas control technology from Japan, and put it into operation with good results. At present, although most of the refining technologies adopted in China adopt the argon blowing method at the bottom of the ladle, due to the relatively expensive price of imported equipment, high maintenance costs and high requirements for operators, most domestic manufacturers basically use manual direct operation control method.

发明内容 Contents of the invention

本发明所要解决的技术问题是提供一种系统构成简单、成本低、控制精度高的精炼炉底吹氩智能控制方法。The technical problem to be solved by the present invention is to provide an intelligent control method for blowing argon at the bottom of the refining furnace with simple system structure, low cost and high control precision.

本发明解决其技术问题所采用的技术方案：The technical solution adopted by the present invention to solve its technical problems:

本发明的技术核心是采用具有分级结构的模糊自适应控制方法，所述的分级结构即将整个控制系统分为三级控制结构：(1)基本模糊控制级。为了满足系统实时控制要求，基本模糊控制级采用模糊逻辑控制方式。(2)自适应调整级。为了适应被控系统参数时变情况，采用自适应控制方式，定时在线调整模糊控制器参数。(3)过程状态判级别。为了克服过程状态变化(或不同实际工况)的影响，提高控制系统的鲁棒性能，将过程状态判断作为辅助输入量，根据系统所处过程状态，采用相应的模糊控制器参数集。The technical core of the present invention is to adopt a fuzzy self-adaptive control method with a hierarchical structure, and the said hierarchical structure divides the whole control system into a three-level control structure: (1) basic fuzzy control level. In order to meet the real-time control requirements of the system, the basic fuzzy control level adopts the fuzzy logic control method. (2) Adaptive adjustment level. In order to adapt to the time-varying situation of the parameters of the controlled system, an adaptive control method is adopted to adjust the parameters of the fuzzy controller on-line at regular intervals. (3) Process status judgment level. In order to overcome the influence of process state changes (or different actual working conditions) and improve the robust performance of the control system, the process state judgment is used as an auxiliary input, and the corresponding fuzzy controller parameter set is used according to the process state of the system.

本发明的具体方法步骤如下：Concrete method steps of the present invention are as follows:

一、输入步骤：1. Input steps:

把下列参数输入工业计算机中：精炼炉的钢包号、钢种号、与其对应的各阶段吹氩流量设定值、选择所采用的模糊规则库、模糊变量论域的范围；Input the following parameters into the industrial computer: the ladle number of the refining furnace, the steel grade number, the set value of the argon blowing flow rate at each stage corresponding to it, the fuzzy rule base used for selection, and the scope of the fuzzy variable universe;

二、数据采集步骤：2. Data collection steps:

由工业计算机实时采集下列各传感器的实时值：测量氩气流量的流量传感器、测量氩气压力的压力传感器、测量供氩支路环境温度的温度传感器；The real-time values of the following sensors are collected in real time by the industrial computer: the flow sensor for measuring the flow rate of argon, the pressure sensor for measuring the pressure of argon, the temperature sensor for measuring the ambient temperature of the argon supply branch;

三、计算步骤：3. Calculation steps:

通过装有具有分级结构的模糊自适应算法的工业计算机完成以下计算步骤：The following calculation steps are completed through an industrial computer equipped with a fuzzy adaptive algorithm with a hierarchical structure:

(1)基本模糊控制级：(1) Basic fuzzy control level:

a.计算出系统的误差e及误差变化率△e；a. Calculate the system error e and error change rate △e;

b.将系统的误差e及误差变化率△e通过尺度变换到各自的论域范围；b. Transform the system error e and error change rate △e to their respective domains of discourse through scaling;

c.将已变换到论域范围的输入量进行模糊处理，使原先精确的输入量变成模糊量；c. Perform fuzzy processing on the input quantity that has been transformed into the domain of discourse, so that the original accurate input quantity becomes fuzzy quantity;

d.通过模糊推理计算控制量u的模糊值；d. Calculate the fuzzy value of the control variable u through fuzzy reasoning;

e.控制量u的确定：e. Determination of the control quantity u:

首先通过加权平均法得到控制量u在论域中的值z₀；然后通过尺度变换将z₀变为实际的控制量u输出；Firstly, the value z ₀ of the control quantity u in the domain of discourse is obtained by the weighted average method; then z ₀ is converted into the actual output of the control quantity u by scale transformation;

(2)自适应调整级：(2) Adaptive adjustment level:

当上述控制量u输出不满足控制要求时，采用调整隶属度输出值法进行自适应调整，然后进入上述(1)步中的d项，最终修正控制量u的输出值；When the output of the above-mentioned control variable u does not meet the control requirements, the method of adjusting the output value of the membership degree is used for adaptive adjustment, and then enters the item d in the above step (1), and finally corrects the output value of the control variable u;

(3)过程状态判断级：(3) Process state judgment level:

当系统工况发生较大变化时，如钢种、钢包变化，由工业计算机判断所发生的变化，并自动选择模糊控制规则库来适应这种变化；When the working condition of the system changes greatly, such as the change of steel type and ladle, the industrial computer judges the change, and automatically selects the fuzzy control rule base to adapt to this change;

四、执行步骤：4. Execution steps:

控制量u通过执行机构实施控制吹氩。The control quantity u implements the control of argon blowing through the actuator.

所述的执行机构为安装在供氩系统的正常支路上的调节阀。The actuator is a regulating valve installed on the normal branch of the argon supply system.

所述的流量传感器安装在正常支路的管道上。The flow sensor is installed on the pipeline of the normal branch.

所述的压力传感器装在正常支路的管道上。The pressure sensor is installed on the pipeline of the normal branch.

所述的温度传感器安装在正常支路的管道的管壁上或者正常支路的管道周围。The temperature sensor is installed on the pipe wall of the pipeline of the normal branch or around the pipeline of the normal branch.

本发明的有益效果是由于采用了具有分级结构的模糊自适应控制方法，大大提高了控制系统的控制精度，从而提高了生产效率与炼钢质量，另外控制系统构成简单、成本较低。The beneficial effect of the present invention is that the control precision of the control system is greatly improved by adopting the fuzzy self-adaptive control method with hierarchical structure, thereby improving the production efficiency and steelmaking quality, and the control system is simple in structure and low in cost.

附图说明 Description of drawings

图1为本发明的系统结构示意图。Fig. 1 is a schematic diagram of the system structure of the present invention.

图2为具有分级结构的模糊自适应控制原理图。Figure 2 is a schematic diagram of fuzzy adaptive control with hierarchical structure.

图3为本发明的软件流程图。Fig. 3 is a software flow chart of the present invention.

具体实施方式 Detailed ways

本实施例的系统结构图如图1所示，本系统由氩气罐16、压力缓冲罐14、正常支路、事故支路、三个传感器、流量积算仪12、工业计算机10、调节阀7、减压阀1、逆止阀8、安全阀15、电磁阀2等组成(详见图1)；压力缓冲罐14、流量传感器3、压力传感器4安装在正常支路的管道上，温度传感器5安装在正常支路的管道的管壁上或正常支路的管道周围。调节阀7(执行机构)和电磁阀2也安装在正常支路上，调节阀7的开度受控于工业计算机10的输出(控制量u)。The system structural diagram of the present embodiment is as shown in Figure 1, and this system is made up of argon gas tank 16, pressure buffer tank 14, normal branch, accident branch, three sensors, flow totalizer 12, industrial computer 10, control valve 7. Pressure reducing valve 1, check valve 8, safety valve 15, solenoid valve 2, etc. (see Figure 1 for details); pressure buffer tank 14, flow sensor 3, and pressure sensor 4 are installed on the pipeline of the normal branch, and the temperature The sensor 5 is installed on the pipe wall of the pipeline of the normal branch or around the pipeline of the normal branch. The regulating valve 7 (actuator) and the solenoid valve 2 are also installed on the normal branch, and the opening of the regulating valve 7 is controlled by the output of the industrial computer 10 (control quantity u).

流量传感器3、压力传感器4、温度传感器5的输出分别经流量积算仪12接工业计算机10的输入端。流量积算仪12和工业计算机10安装在控制室11中。The outputs of the flow sensor 3 , the pressure sensor 4 , and the temperature sensor 5 are respectively connected to the input end of the industrial computer 10 through the flow totalizer 12 . A flow totalizer 12 and an industrial computer 10 are installed in the control room 11 .

本系统能实现手动控制和计算机自动控制两种功能。一方面，底吹氩系统正常工作时，被控的氩气由正常支路吹入精炼炉，实现吹氩过程；在启动吹氩工作时，能够提供较大的压力来吹开堵塞的透气砖，以保证吹氩工作的正常开始。另一方面，为了增加系统的可靠性，以防止在吹氩过程中控制系统发生故障后，能及时切换到事故支路进行手动操作，确保生产的正常运行。The system can realize two functions of manual control and computer automatic control. On the one hand, when the bottom argon blowing system is working normally, the controlled argon gas is blown into the refining furnace from the normal branch to realize the argon blowing process; when starting the argon blowing work, it can provide a larger pressure to blow off the blocked ventilation bricks , to ensure the normal start of argon blowing work. On the other hand, in order to increase the reliability of the system, in order to prevent the failure of the control system during the argon blowing process, it can switch to the accident branch for manual operation in time to ensure the normal operation of production.

流量积算仪12采用涡接流量计；逆止阀8是为了防止事故支路高压气体进入正常支路，损坏正常支路的器件。The flow totalizer 12 adopts a vortex flowmeter; the check valve 8 is to prevent the high-pressure gas from the accident branch from entering the normal branch and damaging the normal branch.

在图1、2中6、9、13为阀门，15为安全阀，16为氩气罐，r(K)为设定值，e(K)为系统的误差，u(K)为控制量，y(K)为实际氩气流量值。In Figures 1 and 2, 6, 9, and 13 are valves, 15 is a safety valve, 16 is an argon tank, r(K) is the set value, e(K) is the error of the system, and u(K) is the control amount , y(K) is the actual argon flow value.

本实施例包括以下四个步骤：This embodiment includes the following four steps:

一、输入步骤，1. Input steps,

把下列参数输入工业计算机中：精炼炉的钢包号、钢种号、与其对应的各阶段吹氩流量设定值、选择所采用的模糊规则库，模糊变量论域的范围；Input the following parameters into the industrial computer: the ladle number of the refining furnace, the steel grade number, the set value of the argon blowing flow rate at each stage corresponding to it, the fuzzy rule base used for selection, and the scope of the fuzzy variable universe;

二、数据采集步骤：2. Data collection steps:

三、计算步骤：3. Calculation steps:

(1)基本模糊控制级：(1) Basic fuzzy control level:

a.计算出系统的误差e及误差变化率△e：a. Calculate the system error e and error change rate △e:

e＝r-ye=r-y

△e＝de/dt＝e(i)-e(i-1)/T△e=de/dt=e(i)-e(i-1)/T

其中T为系统的控制周期，r为氩气流量设定值，y为实际氩气流量值，e(i)为第i时刻的误差，e(i-1)为第i-1时刻的误差。Where T is the control period of the system, r is the set value of argon gas flow, y is the actual argon gas flow value, e(i) is the error at the i-th moment, and e(i-1) is the error at the i-1th moment .

b.将系统的误差e及误差变化率△e通过尺度变换到各自的论域范围，其通用公式为：b. Transform the system error e and error change rate △e to their respective domains of discourse through scaling. The general formula is:

${x x}_{00} = = \frac{{x x}_{min min} + + {x x}_{max max}}{22} + + {k k}_{l l} (({x x}_{00}^{* *} - - \frac{{x x}^{* *}_{min min} + + {x x}^{* *}_{max max}}{22}))$

${k k}_{l l} = = \frac{{x x}_{max max} - - {x x}_{min min}}{{x x}^{* *}_{max max} - - {x x}^{* *}_{min min}}$

其中，k_l称为比例因子Among them, k _l is called the scaling factor

为实际的输入量

for the actual input

　　　 $[x_{\min}^{*}, x_{\max}^{*}]$ 为

变化范围

[x_{\min}^{*}, x_{\max}^{*}]

for

variation range

　　　[x_min，x_max]为要求的论域范围；[x _min , x _max ] is the required domain of discourse;

c.将已变换到论域范围的输入量进行模糊处理，使原先精确的输入量变成模糊量，采用如下的铃形隶属函数：c. Perform fuzzy processing on the input quantity that has been transformed into the domain of discourse, so that the original accurate input quantity becomes a fuzzy quantity, and adopt the following bell-shaped membership function:

${μ μ}_{A A} ((x x)) = = {e e}^{- - \frac{{((x x - - {x x}_{00}))}^{22}}{22 {σ σ}^{22}}}$

其中x₀为隶属度函数的中心值，σ²为方差；Where x ₀ is the central value of the membership function, σ ² is the variance;

d.通过模糊推理计算控制量u的模糊值，模糊推理采用下述公式：d. Calculate the fuzzy value of the control variable u through fuzzy reasoning, and the fuzzy reasoning uses the following formula:

其中，

为代表误差e的语言变量值in,

is the linguistic variable value representing the error e

为代表误差变化率△e的语言变量值

is the linguistic variable value representing the error change rate △e

为根据控制规则库得到的模糊蕴含关系 is the fuzzy implication obtained from the control rule base

B＇为代表控制量u的语言变量值；B' is the language variable value representing the control variable u;

e.控制量u的确定：e. Determination of the control quantity u:

通过加权平均法获得控制量u在论域中的值z₀：The value z ₀ of the control quantity u in the domain of discourse is obtained by the weighted average method:

${z z}_{00} = = df df ((z z)) = = \frac{{&Integral; &Integral;}_{a a}^{b b} z z {μ μ}_{{B B}^{i i}} ((z z)) dz dz}{{&Integral; &Integral;}_{a a}^{b b} {μ μ}_{{B B}^{i i}} ((z z))}$

通过尺度变换将z₀变为实际的控制量u输出：Change z ₀ to the actual control quantity u output through scale transformation:

$u u = = \frac{{u u}_{min min} + + {u u}_{max max}}{22} + + {k k}_{O o} (({z z}_{00} - - \frac{{z z}_{min min} + + {z z}_{max max}}{22}))$

${k k}_{O o} = = \frac{{u u}_{max max} - - {u u}_{min min}}{{z z}_{max max} - - {z z}_{min min}}$

其中，k_O称为输出比例因子Among them, k _O is called the output scale factor

[z_min，z_max]为z₀的论域范围[z _min , z _max ] is the domain of discourse of z ₀

[u_min，u_max]为输出量的变化范围；[u _min , u _max ] is the variation range of the output quantity;

(2)自适应调整级：(2) Adaptive adjustment level:

这里采用的是调整隶属度输出值法的自适应调整，属于直接模糊自适应控制：What is used here is the adaptive adjustment of the method of adjusting the output value of the membership degree, which belongs to the direct fuzzy adaptive control:

u＝u_c(x|θ)+u_D u＝u _c (x|θ)+u _D

其中u_c(x|θ)为where u _c (x|θ) is

${u u}_{c c} ((x x | | θ θ)) = = [[{Σ Σ}_{l l = = 11}^{M m} {\overset{&OverBar; &OverBar;}{y the y}}_{l l} | | {Π Π}_{i i = = 11}^{n no} {μ μ}_{{F f}_{i i}^{l l}} (({x x}_{i i})) | |]] / / [[{Σ Σ}_{l l = = 11}^{M m} | | {Π Π}_{i i = = 11}^{n no} {μ μ}_{{F f}_{i i}^{l l}} (({x x}_{i i})) | |]]$

其中为第l条规则中状态x_i对模糊子集

的隶属度，n为状态个数，M为规则数，y_l为第l条规则中结论隶属度为1对应的输出值；将y_l当成可调参数，上式可以写为：in is the fuzzy subset of the state x _i pair in the l rule

membership degree of , n is the number of states, M is the number of rules, and y _l is the output value corresponding to the conclusion membership degree of the rule l being 1; taking y _l as an adjustable parameter, the above formula can be written as:

${u u}_{c c} ((x x | | θ θ)) = = {θ θ}^{T T} ξ ξ ((x x)),, {ξ ξ}^{l l} ((x x)) = = \frac{{Π Π}_{i i = = 11}^{n no} {μ μ}_{{F f}_{i i}^{l l}} (({x x}_{i i}))}{{Σ Σ}_{l l = = 11}^{M m} | | {Π Π}_{i i = = 11}^{n no} {μ μ}_{{F f}_{i i}^{l l}} (({x x}_{i i})) | |}$

其中θ＝(y₁，…，y_M)^T是参数向量，ξ(x)＝(ξ¹(x)，…，ξ^M(x))^T是回归向量，而ξ¹(x)称为模糊基函数；u_D＝k_dsgn(e^TPb_c)为D控制，k_d≥0，b_c＝[0，0，…，b]^T，如果e^TPb_c>0，则u_D＝k_d，如果e^TPb_c<0，则u_D＝-k_d；where θ=(y ₁ ,…,y _M ) ^T is the parameter vector, ξ(x)=(ξ ¹ (x),…,ξ ^M (x)) ^T is the regression vector, and ξ ¹ (x) is called Fuzzy basis function; u _D =k _d sgn(e ^T Pb _c ) is D control, k _d ≥0, b _c =[0,0,…,b] ^T , if e ^T Pb _c >0, then u _D =k _d , if e ^T Pb _c <0, then u _D =-k _d ;

参数向量θ的自适应律取为：The adaptive law of the parameter vector θ is taken as:

其中P_r[^*]定义为：where _Pr [ ^* ] is defined as:

${P P}_{r r} [[γ γ {e e}^{T T} {P P}_{n no} ξ ξ ((x x))]] = = γ γ {e e}^{T T} {p p}_{n no} ξ ξ ((x x)) - - γ γ {e e}^{T T} {P P}_{n no} \frac{{θθ θθ}^{T T} ξ ξ ((x x))}{{| | θ θ | |}^{22}}$

P_n为P最后一列，|θ|≤M_θ<∞，M_θ为θ向量的有限上界；P _n is the last column of P, |θ|≤M _θ <∞, M _θ is the finite upper bound of the θ vector;

P为一个正定矩阵且满足Lyapunov方程Λ^TP+PΛ＝-Q，式中Q是n×n的任意正定矩阵；P is a positive definite matrix and satisfies the Lyapunov equation Λ ^T P + P Λ = -Q, where Q is any positive definite matrix of n × n;

$Λ Λ = = [\begin{matrix} 00 & 11 & 00 & \cdot \cdot \cdot \cdot \cdot &Center Dot; & 00 \\ 00 & 00 & 11 & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & 00 \\ \cdot &Center Dot; \cdot &Center Dot; \cdot \cdot & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & \cdot \cdot \cdot &Center Dot; \cdot &Center Dot; & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & \cdot \cdot \cdot \cdot \cdot &Center Dot; \\ - - {k k}_{n no} & - - {k k}_{n no - - 11} & - - {k k}_{n no - - 22} & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & - - {k k}_{11} \end{matrix}];;$

(3)过程状态判断级：(3) Process state judgment level:

四、执行步骤：4. Execution steps:

Claims

1. The intelligent control method of argon blowing at the bottom of the refining furnace is characterized in that:

1. Input steps:

Input the following parameters into the industrial computer: the ladle number of the refining furnace, the steel grade number, the setting value of the argon blowing flow rate at each stage corresponding to the ladle number and the steel grade number, the fuzzy rule base used for selection, and the scope of the fuzzy variable universe ;

2. Data collection steps:

The real-time values of the following sensors are collected in real time by the industrial computer: the flow sensor for measuring the flow rate of argon, the pressure sensor for measuring the pressure of argon, the temperature sensor for measuring the ambient temperature of the argon supply branch;

3. Calculation steps:

The following calculation steps are completed through an industrial computer equipped with a fuzzy adaptive algorithm with a hierarchical structure:

(1) Basic fuzzy control level:

a. Calculate the system error e and error change rate Δe;

b. Transform the system error e and error change rate Δe to their respective domains of discourse through scaling;

c. Perform fuzzy processing on the input quantity that has been transformed into the domain of discourse, so that the original accurate input quantity becomes fuzzy quantity;

d. Calculate the fuzzy value of the control variable u through fuzzy reasoning;

e. Determination of the control quantity u:

Firstly, the value z ₀ of the control quantity u in the domain of discourse is obtained by the weighted average method; then z ₀ is converted into the actual output of the control quantity u by scale transformation;

(2) Adaptive adjustment level:

When the output of the above-mentioned control variable u does not meet the control requirements, the method of adjusting the output value of the membership degree is used for adaptive adjustment, and then enters the item d in the above step (1), and finally corrects the output value of the control variable u;

(3) Process state judgment level:

When the working condition of the system changes greatly, the industrial computer judges the change and automatically selects the fuzzy control rule base to adapt to this change;

4. Execution steps:

The control quantity u implements the control of argon blowing through the actuator.

2. The intelligent control method for argon blowing at the bottom of the refining furnace according to claim 1, characterized in that the actuator is a regulating valve (7) installed on the normal branch of the argon supply system.

3. The intelligent control method for argon blowing at the bottom of the refining furnace according to claim 2, characterized in that the flow sensor (3) is installed on the pipeline of the normal branch.

4. The intelligent control method for argon blowing at the bottom of the refining furnace according to claim 3, characterized in that the pressure sensor (4) is installed on the pipeline of the normal branch.

5. The intelligent control method for argon blowing at the bottom of the refining furnace according to claim 4, characterized in that the temperature sensor (5) is installed on the pipe wall of the normal branch pipe or around the normal branch pipe.