李國軍,雷 薇,陳海耿
(東北大學 材料與冶金學院,沈陽 110819)
加熱爐爐溫優(yōu)化算法研究
李國軍,雷 薇,陳海耿
(東北大學 材料與冶金學院,沈陽 110819)
爐溫制度的優(yōu)化是爐子優(yōu)化控制的基礎,它包括爐溫優(yōu)化目標函數(shù)的確定和目標函數(shù)極值的求解兩方面.本文建立了連續(xù)加熱爐板坯加熱的穩(wěn)態(tài)數(shù)學模型和爐溫優(yōu)化模型.應用所建立的穩(wěn)態(tài)數(shù)學模型定量分析了各段爐溫變化對鋼坯加熱過程的影響,形成了啟發(fā)式算法規(guī)則集.建立了考慮出爐鋼坯平均溫度及斷面溫差的目標函數(shù),采用啟發(fā)式搜索算法對鋼坯加熱過程的爐溫制度進行了優(yōu)化,對優(yōu)化前后的鋼坯平均溫度及斷面溫差的進行了對比分析.計算結果表明,本文所歸納的啟發(fā)式搜索規(guī)則可以滿足該模型啟發(fā)式算法的要求,也表明啟發(fā)式搜索算法可作為加熱爐爐溫優(yōu)化的基本算法.
加熱爐模型;啟發(fā)式算法;元體平衡法;爐溫優(yōu)化
加熱爐在鋼材生產(chǎn)中占有十分重要的地位,其能耗約占軋鋼能耗的70% ~80%,提高加熱爐熱效率、降低能耗,對整個鋼鐵工業(yè)的節(jié)能具有重要的意義.同時,隨著現(xiàn)代化軋機向著連續(xù)、大型、高速、高精度和多品種方向發(fā)展,對鋼坯的加熱質量提出了越來越高的要求.因此,鋼坯加熱爐的優(yōu)化控制在國內(nèi)外都得到了普遍重視.
爐溫制度的優(yōu)化是爐子優(yōu)化控制的基礎,即在已知坯料規(guī)格、種類,目標出爐溫度,裝爐溫度,軋制節(jié)奏等情況下,設定各段爐溫,使鋼坯在合適的時間加熱到合適的溫度,且耗能最小.此問題包括爐溫優(yōu)化指標的確定和最優(yōu)控制的求解兩方面[1~3].Z.J.Wang[4~5]建立了鋼坯溫升計算模型.J.Buckley[6]將神經(jīng)網(wǎng)絡的學習機制引入了爐溫優(yōu)化系統(tǒng)中.Pike[7]通過近似集中參數(shù)模型研究了加熱爐靜態(tài)和動態(tài)優(yōu)化.吳鐵軍[8~9]建立了爐溫優(yōu)化的二次型性能指標,并應用一種求解帶約束最優(yōu)控制問題的算法求解了最優(yōu)爐溫.楊永耀[10]以板坯加熱爐離散狀態(tài)空間模型為基礎,提出了以啟發(fā)式搜索方法求解加熱爐爐溫設定值最優(yōu)化問題的原理.
本文在前人的工作基礎之上,建立了連續(xù)加下,尋找最優(yōu)的爐溫控制策略.由于動態(tài)下的加熱爐溫難以確定,因此本文以穩(wěn)態(tài)模型為基礎,建立穩(wěn)態(tài)離線爐溫優(yōu)化數(shù)學模型.爐溫優(yōu)化的關鍵問題是如何建立目標函數(shù)和確定約束條件,以及約束條件的解法.本文在已建立的穩(wěn)態(tài)數(shù)學模型的基礎上,尋找最佳爐溫制度,使鋼坯出爐既能滿足出鋼要求,同時又能使能耗最低.
要對加熱爐進行優(yōu)化,就必須首先有一個明確的優(yōu)化目標.針對以上要求,本文提出下面的優(yōu)化目標函數(shù):
該優(yōu)化指標函數(shù)分兩項,每一項代表一個優(yōu)化條件.其中第一項(ex,min)2是代表鋼坯出爐的平均溫度的指標,是預測出爐時鋼坯平均溫度,ex,min是工藝要求的鋼坯平均溫度最小值;第二項(Δtex-Δtex,max)2是代表鋼坯出爐時斷面溫差的指標,Δtex為預測出爐時的斷面溫差,Δtex,max是工藝允許的鋼坯斷面溫差最大值.
根據(jù)數(shù)學模型的特點,考慮到最優(yōu)化算法的收斂速度及計算量,本文采用啟發(fā)式搜索來求解該最優(yōu)化問題,啟發(fā)式搜索規(guī)則集見§2,求解的程序框圖如圖1所示.
圖1 爐溫優(yōu)化程序框圖Fig.1 The program diagram of furnace temperature optimization
本文算例為某軋鋼廠的步進梁式板坯加熱爐,該爐有效長43.2 m,寬11.2 m,分為四個爐段,分別為均熱段7.32 m,加熱二段9.98 m,加熱一段12.4 m,預熱段13.5 m.該爐子加熱的典型坯為普碳鋼坯,規(guī)格為10 000 mm×1 100 mm×220 mm,冷裝坯料入爐溫度為25℃,出爐平均鋼溫1 180±20℃,斷面溫差≤40℃.各段爐溫范圍分別為 600≤Tf,1≤800;950≤Tf,2≤1 200;1 100≤Tf,3≤1 300;1 1500≤Tf,4≤1 280 .此外,考慮到相鄰路段間的相互影響,優(yōu)化過程中爐溫的取值還需滿足 Tf,i+1- Tf,i≤300 ℃ .
取例爐的一個典型工況作為參照,對爐溫進行優(yōu)化,優(yōu)化的附加條件是鋼坯的鋼種和規(guī)格相同,產(chǎn)量和出爐平均溫度相等,以便進行對比.優(yōu)化前后的對比示于圖2和圖3.由圖2可以看出,優(yōu)化后的平均鋼溫的升高,總落后于優(yōu)化前的,直到出爐時二者相等.由圖3可以看出,優(yōu)化前的斷面溫差峰值較大,且較靠近低溫段;出爐時,優(yōu)化后的斷面溫差較大,但滿足約束條件.從斷面溫差的峰值與出現(xiàn)位置看,優(yōu)化方案遵循了強化端頭供熱的原則,所以是省能的.
圖2 鋼坯平均溫度沿爐長的變化Fig.2 The average temperature vs.furnace length
圖3 鋼坯斷面溫差沿爐長的變化Fig.3 The difference of temperature in cross section vs.furnace length
本文建立了連續(xù)加熱爐板坯加熱的穩(wěn)態(tài)數(shù)學模型和爐溫優(yōu)化模型.建立了考慮鋼坯平均溫度及斷面溫差的目標函數(shù),并以鋼坯出爐平均溫度、斷面溫差和爐內(nèi)段間爐溫差作為約束條件.應用所建立的穩(wěn)態(tài)數(shù)學模型定量分析了各段爐溫變化對鋼坯加熱過程的影響,形成了啟發(fā)式算法規(guī)則集.在此基礎上,采用啟發(fā)式搜索算法對鋼坯加熱過程的爐溫制度進行了優(yōu)化,證明了本文所歸納的啟發(fā)式搜索規(guī)則可以滿足該模型啟發(fā)式算法的要求,能夠求得合理的爐溫優(yōu)化制度.
[1]Ko H S,Kim J S,Yoon T W,et al.Modeling and predictive control of a reheating furnace[C]//Chicago:American Control Conference.2000.
[2]Ditzhujzen V,Staalman D,Koom A,et al.Identification and model presictive control of a slab reheating furnace[C]//Glasgow,Scotland:2002 IEEE International Conference on Control Applications.2002.
[3]Hollander F,Zuurbier S P A.Design,development and performance of on-line computer control in a 3-zone reheating furnace [J].Iron and Steel Engineer,1982,59(1):44-52.
[4]Wang Z J,Wu Q D,Chai T Y.Optimal-setting control for complicated industrial processes and its application study[J].Control Engineering Practice,2004,12(1):65-74.
[5]Wang Z J,Chai T Y,Guan S P,et al.Hybrid optimization setpoint strategy for slab reheating furnace temperature[C]//San Diego,California:American Control Conference.1999.
[6]Buckley J,Hayashi Y.Fuzzy Neural Networks:A Survey[J].Fuzzy Sets and Systems,1994,66(1):1.
[7]Pike H E,Citron S J.Optimization study of a slab reheating furnace[J].Automatica,1970,6(1):41 -50.
[8]吳鐵軍,呂勇哉.均熱爐最佳加熱策略的開發(fā)[J].自動化學報,1986,12(2):113-119.
(Wu Tiejun, Lu Yongzai. The development of optimal heating patterns for steel mill soaking pits[J].Acta Automatica Sinica,1986,12(2):113 -119.)
[9]Wu T J,Lu Y Z.An algorithm for solving constrained optimal control problems[C]//Proceedings of International Conference on Industrial Process Modelingand Control.China:Hangzhou.1985.
[10]楊永耀,呂勇哉.板坯加熱爐的遞階計算機控制[J].自動化學報,1989,15(4):303-309.
(Yang Yongyao,Lu Yongzai.Hierachical computer control for slab reheating furnace[J].Acta Automatica Sinica,1989,15(4):303-309.)
Study of optimization algorithm on reheating furnace temperature
LI Guo-jun,LEI Wei,CHEN Hai-geng
(School of Materials and Metallurgy,Northeastern University,Shenyang 110819,China)
The optimization of the furnace temperature system is on the basis of optimized control,which includes the determination of furnace temperature optimizing object function and the solving of the extreme.In this paper,the stable model and furnace temperature optimization model were established.According to the mathematical model steady quantitatively analyze the heating process influence that change of each billet temperature,the heuristic algorithm rule sets was formed,and the furnace temperature of thin slab heating process was optimal analyzed by the minimizing fuel consumption as the object function.The comparison of the average temperature and temperature difference of crosssection before and after optimization was made.The results show that the heuristic search rules established through the dynamic mathematical model can meet the requirements of the heuristic algorithm,and show that the heuristic search algorithm can be used as the basic algorithm of the heating furnace temperature optimization.
reheatingfurnace mathematical model;heuristic algorithm;elementbalance method;furnace temperature optimization
TK 124
A
1671-6620(2011)04-0325-04
2011-09-20.
國家自然科學基金資助 (50974146).
李國軍 (1972—),男,吉林扶余人,博士,東北大學講師,E-mail:ligj@smm.neu.edu.cn;陳海耿 (1944—),男,福建龍海人,東北大學教授,博士生導師.