侯寧+費(fèi)樹岷
摘 要:本文針對陶瓷燒成窯爐具有大滯后、非線性、不確定性等特點,提出一種基于小波基函數(shù)的陶瓷燒成溫度的預(yù)測函數(shù)控制方法。給出陶瓷燒成溫度預(yù)測函數(shù)控制的基本原理;利用小波的多尺度分析和緊支局部特性,選取小波函數(shù)作為基函數(shù),根據(jù)逼近要求靈活設(shè)置小波基函數(shù)的個數(shù)及位置分布,在保證系統(tǒng)整體優(yōu)化性能的同時又兼顧了局部重點要求;理論分析和仿真表明,該控制方法與普通PFC方法相比,在動態(tài)特性、控制精度、抗干擾等方面具有明顯的改善作用。
關(guān)鍵詞:陶瓷燒成窯爐;一階時滯系統(tǒng);預(yù)測函數(shù)控制;小波基函數(shù)
1 引言
窯爐是陶瓷生產(chǎn)過程中最主要的設(shè)備,是生產(chǎn)過程的“心臟”,對提高陶瓷生產(chǎn)工藝的品質(zhì)起著決定性的作用。但是由于陶瓷燒成窯爐模型為大純滯后的特征,并且控制關(guān)系具有非線性,系統(tǒng)被控制指標(biāo)(如:溫度、氣氛、壓力)之間為較強(qiáng)耦合,又表現(xiàn)為不確定性,普通的控制策略很難對其實現(xiàn)有效控制的目的。為此一些針對陶瓷燒成窯爐控制策略被提出,文獻(xiàn)[1]提出變結(jié)構(gòu)溫度控制方法,即通過模糊控制和時間比例分割相結(jié)合應(yīng)用于陶瓷燒成窯爐中,并證明其控制方法是有效的;文獻(xiàn)[2-4]將智能控制與PID控制技術(shù)相融合,通過整合兩種控制思想形成了模糊PID控制器的設(shè)計方法,對窯爐各工作區(qū)的溫度的調(diào)節(jié)是可行的;文獻(xiàn)[5]通過模糊控制和預(yù)測控制兩種策略的結(jié)合,控制陶瓷燒成溫度,在精度和快速性方面得到較好的效果。文獻(xiàn)[6]通過RBF神經(jīng)網(wǎng)絡(luò)建立對陶瓷窯爐溫度特性進(jìn)行建模,解決了用普通控制算法建立非線性對象精確模型的問題,并結(jié)合動態(tài)矩陣預(yù)測控制實現(xiàn)對溫度變化的跟蹤控制;文獻(xiàn)[7]將窯爐內(nèi)的溫度偏差及偏差變化率通過智能邏輯控制器得到控制信號,實現(xiàn)陶瓷燒成溫度的智能控制。
預(yù)測函數(shù)控制(Predictive Functional Control, 簡稱PFC)是第三代模型預(yù)測控制算法,由Richalet與Kuntze等人于1986年提出[8],廣泛應(yīng)用于機(jī)器人跟蹤、雷達(dá)跟蹤、熱焓控制等領(lǐng)域[9-14]。該方法的特點是在控制量的結(jié)構(gòu)中加入了基函數(shù)的內(nèi)容,基函數(shù)的形式以及數(shù)量可以根據(jù)控制過程預(yù)先選定,控制量的解析解為與基函數(shù)相關(guān)的線性組合,各基函數(shù)作用系統(tǒng)形成的輸出為加權(quán)組合結(jié)構(gòu),通過目標(biāo)函數(shù)的優(yōu)化得到加權(quán)系數(shù)。在普通PFC控制方法中,基函數(shù)一般可取階躍函數(shù)、斜坡函數(shù)、指數(shù)函數(shù)以及正弦多項式函數(shù)等。這類基函數(shù)結(jié)構(gòu)簡單,離線計算方便,不足的是以上函數(shù)都是全局函數(shù),對信號的逼近不能根據(jù)信號的局部特征即不同逼近精度而靈活設(shè)置,難以達(dá)到預(yù)期的控制效果[15]。本文提出一種基于小波基函數(shù)的陶瓷燒成窯溫度預(yù)測函數(shù)控制方法,仿真結(jié)果表明該方法的有效性。
2 陶瓷燒成窯溫度預(yù)測函數(shù)控制
根據(jù)控制系統(tǒng)的要求,對陶瓷燒成溫度進(jìn)行控制,要求控制過程輸出即燒成溫度能夠快、準(zhǔn)、穩(wěn)地達(dá)到設(shè)定值溫度。
2.1 陶瓷燒成窯數(shù)學(xué)模型[16]
為了獲得陶瓷燒成窯爐數(shù)學(xué)模型,可以從數(shù)學(xué)途徑,即分析其工藝過程,寫出有關(guān)的數(shù)學(xué)關(guān)系表達(dá)式,然后推導(dǎo)出被控對象的模型。作為具有代表性的生產(chǎn)過程,陶瓷燒成窯爐模型可表示為以下常見工業(yè)過程:
4.2 選取均勻分布基函數(shù)
選取5個均勻小波基函數(shù),其不同預(yù)測時刻的均勻分布如圖2.2所示。
仿真參數(shù)不變。同時,對圖1、圖2所示的兩種不同分布的小波基函數(shù)情況進(jìn)行仿真,并進(jìn)行比較,結(jié)果如圖4所示。
從圖4中可以看到,不均勻分布的即具有申縮特性的小波基函數(shù)的動態(tài)特性要比均勻分布的小波基函數(shù)更好些,可見在保證一定精度的前提下,選定不均勻分布的小波基函數(shù),減少了基函數(shù)個數(shù),優(yōu)化了待求變量的個數(shù),提高了系統(tǒng)的整體控制效果。
4.3 受干擾情況
為說明基于小波基函數(shù)PFC的抗干擾能力,在系統(tǒng)進(jìn)入穩(wěn)定時間 200s 處,加入20% 干擾信號后的響應(yīng)曲線如圖5所示。仿真結(jié)果表明,加入干擾后,小波基函數(shù)PFC的溫度回到設(shè)定值的時間比普通PFC要快5至8s??梢娨种聘蓴_的能力優(yōu)于普通PFC。
5 結(jié)語
本文利用小波基函數(shù)的緊支局部性、多尺度分析特性等特征,針對普通PFC方法中基函數(shù)的選取存在的不足,提出基于小波基函數(shù)的陶瓷燒成窯溫度預(yù)測函數(shù)控制方法。通過不同情況的仿真比較,表明小波PFC算法在顧及優(yōu)化目標(biāo)整體性的同時,又滿足了在不同預(yù)測時刻對參考軌跡逼近的精度要求,實現(xiàn)了基函數(shù)的個數(shù)和分布根據(jù)不同要求的靈活設(shè)置。該方法算法簡單,易于工程實現(xiàn),在響應(yīng)速度、控制精度、抑制外部干擾等方面比普通PFC方法都有明顯的改善,具有良好的應(yīng)用前景。
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[19] 胡家升, 潘紅華. 預(yù)測函數(shù)控制系統(tǒng)的閉環(huán)性能分析[J]. 控制
理論與應(yīng)用,2001.18(5):774-778.
Abstract: For ceramic firing kiln with large delay, nonlinear and uncertain characteristics, proposed a predictive functional control method based wavelet function to control firing temperature of the ceramic. Firstly, the basic principle of ceramic firing temperature predictive function control has been given. Then using wavelet multi-scale analysis and compact support local characteristics as a basis function of the selected wavelet function, according to the requirements of the approach requires flexibly set the number and location of distribution of wavelet basis function, in ensuring the overall optimal performance of the system while taking into account local key requirements. Theoretical analysis and simulation show that compared with the general method of PFC, the dynamic characteristics and control accuracy, anti-interference, etc of this control method has obviously improved.
Key words: ceramic firing kiln; first-order time-delay system; predictive functional control; wavelet functionendprint
[6] 劉偉,王思明,張國武.基于RBF神經(jīng)網(wǎng)絡(luò)陶瓷窯爐溫度動態(tài)
矩陣控制[J].中國陶瓷,2010,46(9):27-30.
[7] 陳靜,程明家,徐國成,等.陶瓷輥道窯的溫度特性與智能邏輯控
制研究[J].武漢理工大學(xué)學(xué)報,2009.31(2).100-103.
[8] Richalet J.Predictive functional control: Application to fast and
accurate robots[C] . Proc. of 10th IFAC World Congress, Munich,
1987.251-258.
[9] Abdelghani-Idrissi MA, Arbaouia MA, Estel L, et al. Predictive
functional control of a counter current heat exchanger using
convexity property[J].Chemical Engineering and Processing,
2001,40:449–457.
[10] Marko Lepetic, Igor Skrjanc, et al. Predictive functional control
based on fuzzy model: magnetic suspension system case study
[J]. Engineering Applications of Arti?cial Intelligence. 2003,16 :
425–430.
[11] 張泉靈,王樹青.化學(xué)反應(yīng)器溫度跟蹤預(yù)測函數(shù)控制的研究及
應(yīng)用[J]. 控制理與應(yīng)用,2001,18(4):559-563.
[12] 張日東,王樹青.基于神經(jīng)網(wǎng)絡(luò)的非線性系統(tǒng)預(yù)測函數(shù)控制[J].
控制理與應(yīng)用,2007,24(6):949-958.
[13] 王民權(quán),應(yīng)力恒. 制腈反應(yīng)釜分段升溫的多模式控制策略[J] .
計算機(jī)工程與應(yīng)用,2012, 48(17):220-223. [14] Richalet J.
Elementary Predictive functional control: A tutorial[C].
Proceedings of the 2011 4th International Symposium on
Advanced Control of Industrial Processes, China, May,
2011.306-313.
[15] 劉春波,王鮮芳,章瑤,等. 基于小波基函數(shù)和Hammerstein模
型的預(yù)測函數(shù)控制[J].系統(tǒng)工程與電子技術(shù), 2009, 31 (08):
1935 - 1939.
[16] 李穎沖,陶瓷窯爐溫度測控系統(tǒng)的設(shè)計與研究[D].蘭州交通大
學(xué),2010.
[17] Richalet J. Elementary Predictive functional control: A tutorial
[C]. Proceedings of the 2011 4th International Symposium on
Advanced Control of Industrial Processes, China, May, 2011.306-
313.
[18] 潘紅華,胡家升,朱森,等.一種改進(jìn)的預(yù)測函數(shù)控制法[J].系統(tǒng)
工程與電子技術(shù), 2003, 25 (11): 1389 - 1391.
[19] 胡家升, 潘紅華. 預(yù)測函數(shù)控制系統(tǒng)的閉環(huán)性能分析[J]. 控制
理論與應(yīng)用,2001.18(5):774-778.
Abstract: For ceramic firing kiln with large delay, nonlinear and uncertain characteristics, proposed a predictive functional control method based wavelet function to control firing temperature of the ceramic. Firstly, the basic principle of ceramic firing temperature predictive function control has been given. Then using wavelet multi-scale analysis and compact support local characteristics as a basis function of the selected wavelet function, according to the requirements of the approach requires flexibly set the number and location of distribution of wavelet basis function, in ensuring the overall optimal performance of the system while taking into account local key requirements. Theoretical analysis and simulation show that compared with the general method of PFC, the dynamic characteristics and control accuracy, anti-interference, etc of this control method has obviously improved.
Key words: ceramic firing kiln; first-order time-delay system; predictive functional control; wavelet functionendprint
[6] 劉偉,王思明,張國武.基于RBF神經(jīng)網(wǎng)絡(luò)陶瓷窯爐溫度動態(tài)
矩陣控制[J].中國陶瓷,2010,46(9):27-30.
[7] 陳靜,程明家,徐國成,等.陶瓷輥道窯的溫度特性與智能邏輯控
制研究[J].武漢理工大學(xué)學(xué)報,2009.31(2).100-103.
[8] Richalet J.Predictive functional control: Application to fast and
accurate robots[C] . Proc. of 10th IFAC World Congress, Munich,
1987.251-258.
[9] Abdelghani-Idrissi MA, Arbaouia MA, Estel L, et al. Predictive
functional control of a counter current heat exchanger using
convexity property[J].Chemical Engineering and Processing,
2001,40:449–457.
[10] Marko Lepetic, Igor Skrjanc, et al. Predictive functional control
based on fuzzy model: magnetic suspension system case study
[J]. Engineering Applications of Arti?cial Intelligence. 2003,16 :
425–430.
[11] 張泉靈,王樹青.化學(xué)反應(yīng)器溫度跟蹤預(yù)測函數(shù)控制的研究及
應(yīng)用[J]. 控制理與應(yīng)用,2001,18(4):559-563.
[12] 張日東,王樹青.基于神經(jīng)網(wǎng)絡(luò)的非線性系統(tǒng)預(yù)測函數(shù)控制[J].
控制理與應(yīng)用,2007,24(6):949-958.
[13] 王民權(quán),應(yīng)力恒. 制腈反應(yīng)釜分段升溫的多模式控制策略[J] .
計算機(jī)工程與應(yīng)用,2012, 48(17):220-223. [14] Richalet J.
Elementary Predictive functional control: A tutorial[C].
Proceedings of the 2011 4th International Symposium on
Advanced Control of Industrial Processes, China, May,
2011.306-313.
[15] 劉春波,王鮮芳,章瑤,等. 基于小波基函數(shù)和Hammerstein模
型的預(yù)測函數(shù)控制[J].系統(tǒng)工程與電子技術(shù), 2009, 31 (08):
1935 - 1939.
[16] 李穎沖,陶瓷窯爐溫度測控系統(tǒng)的設(shè)計與研究[D].蘭州交通大
學(xué),2010.
[17] Richalet J. Elementary Predictive functional control: A tutorial
[C]. Proceedings of the 2011 4th International Symposium on
Advanced Control of Industrial Processes, China, May, 2011.306-
313.
[18] 潘紅華,胡家升,朱森,等.一種改進(jìn)的預(yù)測函數(shù)控制法[J].系統(tǒng)
工程與電子技術(shù), 2003, 25 (11): 1389 - 1391.
[19] 胡家升, 潘紅華. 預(yù)測函數(shù)控制系統(tǒng)的閉環(huán)性能分析[J]. 控制
理論與應(yīng)用,2001.18(5):774-778.
Abstract: For ceramic firing kiln with large delay, nonlinear and uncertain characteristics, proposed a predictive functional control method based wavelet function to control firing temperature of the ceramic. Firstly, the basic principle of ceramic firing temperature predictive function control has been given. Then using wavelet multi-scale analysis and compact support local characteristics as a basis function of the selected wavelet function, according to the requirements of the approach requires flexibly set the number and location of distribution of wavelet basis function, in ensuring the overall optimal performance of the system while taking into account local key requirements. Theoretical analysis and simulation show that compared with the general method of PFC, the dynamic characteristics and control accuracy, anti-interference, etc of this control method has obviously improved.
Key words: ceramic firing kiln; first-order time-delay system; predictive functional control; wavelet functionendprint