【導(dǎo)讀】的是控制流體的流動(dòng)，所以礦井通風(fēng)網(wǎng)絡(luò)是高階非線性系統(tǒng)。過去在這一方面的研究是基于。多變量線性模型。本文提出的是一個(gè)非線性模型。開發(fā)兩個(gè)控制算法。一個(gè)人操縱所有的網(wǎng)。絡(luò)分支機(jī)構(gòu)就可實(shí)現(xiàn)全球性調(diào)控的結(jié)果。其他人只操縱網(wǎng)絡(luò)中不屬于樹圖的分行，實(shí)現(xiàn)監(jiān)管。工作點(diǎn)的附近區(qū)域。這種針對(duì)礦井通風(fēng)網(wǎng)絡(luò)提出的方法，也適用于其他類型的。流體網(wǎng)絡(luò)，如燃?xì)饣蛩姆咒N網(wǎng)絡(luò)，灌溉網(wǎng)絡(luò)，并有可能建立起通風(fēng)系統(tǒng)。石油儲(chǔ)備枯竭后，煤作為礦物燃料能源還會(huì)保持一段相當(dāng)長(zhǎng)的時(shí)間。采的一個(gè)主要困難是因?yàn)榈叵碌拿旱V存在有毒且易爆的氣體甲烷。教訓(xùn)從古至今未曾間斷。在這種通風(fēng)系統(tǒng)中通常不是直。的問題，礦井通風(fēng)需要接近基于模型的方式。分支采取RL典型非線性抵抗的電等值的形式，支的氣流是相互依賴的。的一套分支，稱余樹，分支指連接。流經(jīng)分支的流體確定動(dòng)力學(xué)網(wǎng)絡(luò)的最小表示

　　

【正文】 on work, we rst establish the dynamical equation of one branch. For simplicity, we make the following assumptions: (A1) the air is inpressible。 (A2) the temperatures in all branches are identical. Under assumptions (A1) and (A2), one branch of the mine ventilation workis described with the following equations: jjjjjjj HKRKtQ ??dd， (1) where Qj is airow quantity through a branch j。Rj =rjlj are aerodynamic resistances, rj are specific aerodynamic resistances of the branches, lj are lengths of the branches, Hj = plj plj0 are pressure drops of the branches, plj are absolute pressures at the end of the branches, plj0 are absolute pressures at the beginning of the branches, Kj = Sj=lj are inertia coefficients, Sj are crosssections of the branches, ? is air density, j =1,…, n and n is the number of work branches. Like an electrical work, a mine ventilation work must satisfy Kirchho’s current law, ., the air flow out of any node is equal to the flow into that node. Mathematically, Kirchho’s current law for mine ventilation works can be expressed as ?? ?nj jji QEQ1 0, i=2,…, nc 1 (2) or E=0, (3) where nc is the number of nodes in the work, Q is a vector of airow quantities, EQ is a full rank matrix of order (nc 2) n and EQ =[EQij], the values of EQij are defined as follows: EQij = 1 if branch j is connected to node i and the air ow goes away from node i。 EQij =1 if branch j is connected to node i and the air ow goes into node i。 EQij =0 if branch j is not connected to node i. Let us assume that the mine ventilation work employs one main fan that is connected with the ambient outside of the mine. Also let node 1 be connected to the fan branch. Then the airow in the fan branch can be expressed as ?? ?nj QmeQmjQj1 , (4) or eQmQ=Qm, (5) where Qm is airow quantity through fan (main) branch, eQm =[eQm1。:::。eQmn]is1n matrix, includes the values of eQmj。j =1。:::。n are defined as follows: eQmj =1 if branch j is connected to node 1 and the air flow goes away from node 1。eQmj =1 if branch j is connected to node 1 and the air ow goes into node 1。eQmj =0 if branch j is not connected to node 1. Similarly, a mine ventilation work also satisfies Kirchho’s voltage law, ., the sum of the pressure drops around any loop in the workmust be equal to zero, or mathematically, ?? ?nj EHijHj1 0 , i=1,…, lk (6) or EHH=0, (7) where Hj is the pressure drop of the branch j。 l is a number of the links in the work, l=nnc +1。 H is a vector of pressure drops, EH is (l k) n fundamental mesh matrix, in which each mesh is formed by a link and a unique chain in the tree connecting two endpoints of the link, k is a number of meshes, containing fan branch, it is equal to the number of links, connected to the fan branch at its end. EH =[EHij], the elements of EHij are defined as follows: EHij = 1 if branch j is contained in mesh i and has the same direction, EHij =1 if branch j is contained in mesh i and has the opposite direction, EHij =0 if branch j is not contained in mesh i. Considering meshes, containing the fan branch, express the pressure drop in the fan branch as HmeH m jH jnj ????1 ,i=1,…,k, (8) or eHmH=Hm, (9) where Hm is the pressure drop of the fan branch, eHm is kn matrix, includes the values of eHmij。j=1,…, n which defined as follows: eHmij =1 if branch j is contained in mesh i and has the same direction, eHmij =1 if branch j is contained in mesh i and has the opposite direction, eHmij = 0 if branch j is not contained in mesh i. The dynamics of the fan branch can be expressed as Hm =dRmQm。 (10) where d denotes the equivalent pressure drop generated by fan, and Rm is the resistance coefficient in the fan branch. . Nonminimal model of the work In order to establish the state equation, one has to find independent variables as states of the system. By virtue of the concepts of a tree and a link, they can easily be found. So the first step is to describe the tree of the mine ventilation work such that the fan branch is contained in it, and take the airflow quantities of link branches as state variables. For convenience of analysis, we label the air flow quantities of link branches from 1 to N nc +1, where N =n+1. Define Q=???????????????????????????????nncNncNac??211, H=???????????????????????????????nncNncNacHHHHHH??211, (11) so that Qc and Hc matrices describe airflow quantity and pressure drop, respectively, in the links, and Qa and Ha matrices describe them in the tree branches, excluding the fan branch. With the notation ????????? KaKcKnKKQnQnDQ 0 0),...,1(),...,11(2 (1) can be rewritten as KHRK D ??? 2? . (13) Proposition . There exist matrices A。 B。 C。 YRQ。YQ and Yd of appropriate dimensions so that the full order model of mine ventilation work can be expressed as CdBQRA D ??? 2? , (14) dYQYRQYQ dQDRQ ??? 2? , (15) where Q is the state, R and d are the inputs, and H is the output of the system.