【機(jī)械類畢業(yè)論文中英文對(duì)照文獻(xiàn)翻譯】雷達(dá)天線伺服系統(tǒng)結(jié)構(gòu)與控制

【機(jī)械類畢業(yè)論文中英文對(duì)照文獻(xiàn)翻譯】雷達(dá)天線伺服系統(tǒng)結(jié)構(gòu)與控制,機(jī)械類畢業(yè)論文中英文對(duì)照文獻(xiàn)翻譯,機(jī)械類,畢業(yè)論文,中英文,對(duì)照,對(duì)比,比照,文獻(xiàn),翻譯,雷達(dá),天線,伺服系統(tǒng),結(jié)構(gòu),控制,節(jié)制 黃河科技學(xué)院畢業(yè)設(shè)計(jì)（文獻(xiàn)翻譯） 第 11 頁 雷達(dá)天線伺服系統(tǒng)結(jié)構(gòu)與控制 摘要 雷達(dá)天線的性能主要取決于其伺服系統(tǒng)的設(shè)計(jì)水平。伺服系統(tǒng)的設(shè)計(jì)包括結(jié)構(gòu)設(shè)計(jì)和控制設(shè)計(jì)兩部分，這兩部分是相互影響緊密耦合的。一般所采用的設(shè)計(jì)方法是對(duì)結(jié)構(gòu)系統(tǒng)和控制系統(tǒng)先分別設(shè)計(jì)，然后再根據(jù)要求進(jìn)行調(diào)校，這往往會(huì)導(dǎo)致產(chǎn)品研制的周期長、成本高、性能差、結(jié)構(gòu)笨重，不能保證伺服系統(tǒng)總體的綜合性能最優(yōu)。針對(duì)雷達(dá)天線伺服系統(tǒng)設(shè)計(jì)中存在的結(jié)構(gòu)設(shè)計(jì)與控制設(shè)計(jì)相分離的問題，提出一種結(jié)構(gòu)與控制集成優(yōu)化設(shè)計(jì)的模型，給出求解策略與方法，并進(jìn)而應(yīng)用于三個(gè)典型例子，取得了滿意的結(jié)果。數(shù)值例子和實(shí)物試驗(yàn)都驗(yàn)證了上述雷達(dá)天線伺服系統(tǒng)結(jié)構(gòu)與控制的集成設(shè)計(jì)模型與方法的有效性和正確性。該模型與方法對(duì)其他伺服系統(tǒng)的設(shè)計(jì)也具有一定的參考和借鑒價(jià)值。 1 簡介 機(jī)電系統(tǒng)是由機(jī)構(gòu)(或結(jié)構(gòu))與控制兩個(gè)子系統(tǒng)組成的，兩者的集成設(shè)計(jì)是十分必要的。結(jié)構(gòu)與控制集成設(shè)計(jì)的研究自 20 世紀(jì) 80 年代開始以來，國內(nèi)外學(xué)者進(jìn)行了卓有成效的研究，主要集中在如下 3 個(gè)方面：① 太空系統(tǒng)結(jié)構(gòu)與控制的集成設(shè)計(jì)，尤其是柔性結(jié)構(gòu)系統(tǒng)，選擇結(jié)構(gòu)桿件的橫截面為設(shè)計(jì)變量，結(jié)構(gòu)的質(zhì)量和控制能量為目標(biāo)，但不適應(yīng)于可變結(jié)構(gòu)(或機(jī)構(gòu))問題；② 直流電動(dòng)機(jī)的結(jié)構(gòu)與控制的集成設(shè)計(jì)問題，以直流電動(dòng)機(jī)為例，從狀態(tài)空間模型入手，研究了結(jié)構(gòu)和控制之間的耦合，指出集成設(shè)計(jì)的必要性，但是對(duì)于復(fù)雜機(jī)構(gòu)來說，其狀態(tài)空間模型并不容易獲得； ③ 機(jī)構(gòu)系統(tǒng)中機(jī)構(gòu)與控制的集成(或協(xié)同、并行)設(shè)計(jì)問題，根據(jù)集成的理念來設(shè)計(jì)機(jī)構(gòu)。這些都未曾考慮機(jī)構(gòu)的固有頻率、動(dòng)態(tài)目標(biāo)跟蹤控制的穩(wěn)定性、準(zhǔn)確性及快速性等非線性約束，也未見給出可同時(shí)實(shí)現(xiàn)機(jī)構(gòu)輕量化與跟蹤控制穩(wěn)、準(zhǔn)、快的詳細(xì)集成設(shè)計(jì)模型。 2 提出問題 雷達(dá)天線的指向精度與快響應(yīng)等性能取決于其伺服系統(tǒng)的設(shè)計(jì)水平，而伺服系統(tǒng)的設(shè)計(jì)包括結(jié)構(gòu)設(shè)計(jì)與控制設(shè)計(jì)兩部分。結(jié)構(gòu)設(shè)計(jì)將影響到控制性能的實(shí)現(xiàn)，如伺服控制帶寬的實(shí)現(xiàn)依賴于結(jié)構(gòu)固有頻率。反過來，控制又會(huì)影響到結(jié)構(gòu)設(shè)計(jì)，如伺服系統(tǒng)中驅(qū)動(dòng)力的大小將影響天線座結(jié)構(gòu)的設(shè)計(jì)。因此，為實(shí)現(xiàn)“看得準(zhǔn)”與“看得清”的目標(biāo)要求，結(jié)構(gòu)與控制必須進(jìn)行集成設(shè)計(jì)。 遺憾的是，傳統(tǒng)的雷達(dá)天線伺服系統(tǒng)設(shè)計(jì)卻是結(jié)構(gòu)設(shè)計(jì)和控制設(shè)計(jì)相分離的，即單獨(dú)設(shè)計(jì)機(jī)械結(jié)構(gòu)和控制系統(tǒng)，再進(jìn)行調(diào)校以達(dá)到要求的指標(biāo)。而事實(shí)上，雷達(dá)天線伺服系統(tǒng)中結(jié)構(gòu)和控制卻是相互耦合的，尤其在高性能跟蹤中，二者的耦合非常緊密。如果在控制設(shè)計(jì)時(shí)未能充分考慮伺服結(jié)構(gòu)的特性，將導(dǎo)致伺服跟蹤性能降低，甚至無法達(dá)到要求的性能指標(biāo)；另一方面，在結(jié)構(gòu)設(shè)計(jì)時(shí)如未能充分考慮控制作用，就不能得到最優(yōu)設(shè)計(jì)，甚至無法設(shè)計(jì)出滿足性能要求的結(jié)構(gòu)。這種分離設(shè)計(jì)方法導(dǎo)致產(chǎn)品研制的周期長、成本高、性能差、結(jié)構(gòu)笨重。 3 雷達(dá)天線系統(tǒng)的結(jié)構(gòu)分析 結(jié)構(gòu)設(shè)計(jì)的目的旨在設(shè)計(jì)滿足伺服性能要求的機(jī)械結(jié)構(gòu)。為得到優(yōu)良的伺服跟蹤性能，一般要求機(jī)械結(jié)構(gòu)質(zhì)量小、剛性好，然而這些要求往往是矛盾的。為此，引入結(jié)構(gòu)優(yōu)化方法，即對(duì)質(zhì)量分布、傳動(dòng)形式和拓?fù)浣Y(jié)構(gòu)進(jìn)行優(yōu)化設(shè)計(jì)，在保證剛度要求的情況下達(dá)到總質(zhì)量或占用空間最小。在機(jī)構(gòu)的運(yùn)動(dòng)過程中，其構(gòu)型隨著時(shí)間不斷變化。為此，可將其提為一個(gè)多工況(不妨設(shè)為 n1 種工況)的結(jié)構(gòu)優(yōu)化問題(圖 1)。 圖1 雷達(dá)天線系統(tǒng)結(jié)構(gòu)優(yōu)化設(shè)計(jì) 求解 式中，d 為雷達(dá)伺服結(jié)構(gòu)的設(shè)計(jì)量， n2 為設(shè)計(jì)變量總數(shù)。 目標(biāo)函數(shù)為結(jié)構(gòu)的總質(zhì)量最小 式中，a、b 分別為簡單結(jié)構(gòu)參數(shù)(如主體尺寸、材料等)和依賴于控制的結(jié)構(gòu)設(shè)計(jì)要素(如驅(qū)動(dòng)力等)，n3 為雷達(dá)伺服結(jié)構(gòu)的構(gòu)件數(shù)， Vi 為第 i 個(gè)構(gòu)件的體積， ?i 為第 i 個(gè)構(gòu)件的材料密度。約束包括第一階固有頻率約束、應(yīng)力和位移約束 式中， frei 為第 i 個(gè)工況下的結(jié)構(gòu)基頻， f re1 為第一階固有頻率的最小容許值； ej 與工況下第 e 個(gè)單元應(yīng)力的實(shí)際值與最大容許值；ij與 i 分別為第 j 個(gè)工況下第 i 個(gè)位移約束的實(shí)際值與最大容許值。 同時(shí)，還必須滿足第 j 個(gè)工況下結(jié)構(gòu)的動(dòng)力微分方程 式中， m j 、 c j 、 k j 分別為結(jié)構(gòu)在第 j 個(gè)工況下對(duì)應(yīng)的質(zhì)量矩陣、阻尼矩陣和剛度矩陣。 求解此非線性規(guī)劃問題，可得設(shè)計(jì)變量的最優(yōu)取值和與之相對(duì)應(yīng)的依賴于結(jié)構(gòu)的控制設(shè)計(jì)要素A(包括 m、c、k、frel 等)，作為控制增益優(yōu)化設(shè)計(jì)的基礎(chǔ)。 4 雷達(dá)天線控制系統(tǒng)分系統(tǒng)設(shè)計(jì) 控制分系統(tǒng)設(shè)計(jì)的目的是在結(jié)構(gòu)給定的前提下設(shè)計(jì)滿足性能要求的控制系統(tǒng)。一般情況下，要求系統(tǒng)具有穩(wěn)、快、準(zhǔn)的性能，即所設(shè)計(jì)的控制器應(yīng)在保證穩(wěn)定的前提下，實(shí)現(xiàn)快速、準(zhǔn)確地跟蹤目標(biāo)。為此，可引入控制優(yōu)化設(shè)計(jì)方法，即對(duì)控制器增益p 進(jìn)行優(yōu)化設(shè)計(jì)，使系統(tǒng)具有優(yōu)異的伺服跟蹤性能，同時(shí)得到依賴于控制的結(jié)構(gòu)設(shè)計(jì)要素 B(如驅(qū)動(dòng)力等 )。于是該問題可描述為一個(gè)非線性規(guī)劃問題(圖 2)。 圖2 雷達(dá)天線伺服系統(tǒng)的最優(yōu)控制增益設(shè)計(jì) 求解 式中， pi 為第 i 個(gè)控制增益變量， n6 為增益設(shè)計(jì)變量總數(shù)。目標(biāo)函數(shù)為最小化累積跟蹤誤差 J ， J 反映了對(duì)跟蹤性能“快”與“準(zhǔn)”的要求 式中，T0 為一個(gè)運(yùn)動(dòng)周期， e(t) 為跟蹤誤差。 約束包括穩(wěn)定性約束、調(diào)節(jié)時(shí)間約束、超調(diào)量約束和力矩約束 式中，polei 為系統(tǒng)的第 i 個(gè)極點(diǎn)，n7 為極點(diǎn)總數(shù)，ts為調(diào)節(jié)時(shí)間， ò 為超調(diào)量， F (t) 為控制器在時(shí)域中的驅(qū)動(dòng)力或力矩。 5 雷達(dá)天線伺服系統(tǒng)的結(jié)構(gòu)與控制的集成設(shè)計(jì) 對(duì)于高性能的雷達(dá)伺服系統(tǒng)，即使分別對(duì)結(jié)構(gòu)和控制進(jìn)行優(yōu)化設(shè)計(jì)，往往仍然達(dá)不到要求的性能指標(biāo)，因?yàn)樯鲜龇椒ú荒鼙ＷC所設(shè)計(jì)的伺服系統(tǒng)在總體上是最優(yōu)的?？赡艿慕Y(jié)果是依據(jù)結(jié)構(gòu)優(yōu)化設(shè)計(jì)的結(jié)果進(jìn)行控制設(shè)計(jì)時(shí)，難以獲得滿足性能指標(biāo)的解，或者得到與結(jié)構(gòu)優(yōu)化設(shè)計(jì)相矛盾的設(shè)計(jì)要素 B。為此，有必要進(jìn)行結(jié)構(gòu)與控制的集成優(yōu)化設(shè)計(jì)，即將結(jié)構(gòu)優(yōu)化和控制優(yōu)化綜合起來。具體講，就是對(duì)于給定的結(jié)構(gòu)參數(shù) a 和控制參數(shù) u，通過尋求最優(yōu)的綜合性指標(biāo)H找到結(jié)構(gòu)設(shè)計(jì)變量d和控制增益P的最優(yōu)值。從而可將問題描述為非線性規(guī)劃問題（圖3）。 一般設(shè)計(jì)問題結(jié)合最小化結(jié)構(gòu)方面目標(biāo)構(gòu)成一個(gè)最優(yōu)設(shè)計(jì)問題。因?yàn)榭刂屏?力矩)都是控制增益 p 的函數(shù)，所以一般控制問題也可以描述為一個(gè)一般增益問題；一般增益問題結(jié)合最小化控制方面目標(biāo)構(gòu)成一個(gè)最優(yōu)增益問題。而最優(yōu)設(shè)計(jì)問題和最優(yōu)增益問題之間是相互耦合的，即求解最優(yōu)設(shè)計(jì)問題可得到依賴于結(jié)構(gòu)的控制設(shè)計(jì)要素 A(包括 m、c、k、frel 等)，作為最優(yōu)增益問題的基礎(chǔ)；而求解最優(yōu)增益問題可得到依賴于控制的結(jié)構(gòu)設(shè)計(jì)要素。 6 數(shù)值模擬與試驗(yàn) 為驗(yàn)證本文所提方法的可行性和有效性，特將其應(yīng)用于如下 3 個(gè)典型例子，取得了滿意的結(jié)果?？紤]到篇幅所限，第 1 個(gè)和第 3 個(gè)例子僅為數(shù)值試驗(yàn)結(jié)果，而第 2 個(gè)則同時(shí)具有數(shù)值試驗(yàn)和實(shí)物驗(yàn)證。 例 1：曲柄滑塊機(jī)構(gòu)式反射面天線(圖 4)。圖 4所示的曲柄滑塊機(jī)構(gòu)，在曲柄 OA 上施加控制力矩M，在連桿 AB 上選取某個(gè)位置 á 點(diǎn)安裝天線， áa對(duì)應(yīng)其指向。目的是通過調(diào)整控制力矩和結(jié)構(gòu)設(shè)計(jì)，使天線跟蹤目標(biāo)。角度的變化范圍為 10°～80°。 圖 4 曲柄連桿機(jī)構(gòu)式反射面天線 曲柄和連桿均為空心圓管，r1、r2 分別為曲柄和連桿的橫截面中徑，δa、δb 分別為壁厚。PID 控制器的比例、積分和微分增益參量分別為 p1、p2、p3。在動(dòng)力學(xué)建模中，視曲柄為剛體，連桿為彈性體，其彈性變形為簡支梁前 ne 階振形的疊加，本例取 ne =3。 集成與分離設(shè)計(jì)的結(jié)果對(duì)比如表 1 所示。圖 5、6 分別為前 0.2 s 的響應(yīng)和驅(qū)動(dòng)力矩的對(duì)比曲線，因?yàn)?0.2 s 以后兩者的差別不大?？梢姡稍O(shè)計(jì)的結(jié)果要明顯優(yōu)于分離優(yōu)化的結(jié)果，如調(diào)整時(shí)間 ts 減少了 13.5%(由 0.074 s 降到 0.064 s)，固有頻率 f re1 提高了 58.12%(由 11.52 Hz 提高到 18.2 Hz)，總質(zhì)量 m下降了 30.57% (由 0.268 9 kg 降到 0.186 7 kg)。 圖5 集成、分離設(shè)計(jì)的運(yùn)動(dòng)仿真對(duì)比圖 圖6 集成、分離設(shè)計(jì)的驅(qū)動(dòng)力矩對(duì)比圖 例 2：某伺服試驗(yàn)臺(tái)系統(tǒng)(圖 7)?？紤]由齒輪減速器構(gòu)成的伺服系統(tǒng)，設(shè)等效到電動(dòng)機(jī)軸上的轉(zhuǎn)動(dòng)慣量分別為 J1、J2 和 J3，相應(yīng)軸的扭轉(zhuǎn)剛度分別為 k1、k2，阻尼系數(shù)為 b1、b2，3 個(gè)軸承處的摩擦因數(shù)為1 、2 和3 。 設(shè)負(fù)載和電動(dòng)機(jī)已定，受外形幾何參數(shù)限制，電動(dòng)機(jī)軸和負(fù)載軸的軸距已定，控制器采用傳統(tǒng)的數(shù)字 PID 控制。要求設(shè)計(jì)相應(yīng)的結(jié)構(gòu)參數(shù)(包括負(fù)載軸長度 L、半徑 R、主動(dòng)軸半徑 r、減速比 i、PID控制增益 p1、p2 和 p3)，使系使系統(tǒng)在滿足所要求的性能指標(biāo)(單位階躍響應(yīng)下的超調(diào)量 ò ≤ 2% ，調(diào)節(jié)時(shí)間ts ≤ 0.3 s )的前提下具有總體最優(yōu)的性能。 采用相同的初始值 (伺服試驗(yàn)臺(tái)的初始設(shè)計(jì) )時(shí)，分別進(jìn)行分離設(shè)計(jì)和集成設(shè)計(jì)，并采用序列二次規(guī)劃法進(jìn)行了求解，結(jié)果如表 2 所示，相應(yīng)系統(tǒng)的單位階躍響應(yīng)如圖 8 所示。 圖8 系統(tǒng)的單位階躍響應(yīng)圖 為說明結(jié)果的正確性，特對(duì)初始參數(shù)下的數(shù)值結(jié)果在試驗(yàn)臺(tái)上進(jìn)行了實(shí)物驗(yàn)證。圖 9 為采用初始設(shè)計(jì)時(shí)，實(shí)測(cè)的單位階躍響應(yīng)和仿真結(jié)果的對(duì)比。由于未考慮電動(dòng)機(jī)和伺服放大器的動(dòng)態(tài)特性和制造精度，試驗(yàn)結(jié)果與仿真結(jié)果存在一定差異(最大誤差小于 5%)。需要指出的是，若要做針對(duì)優(yōu)化結(jié)果的試驗(yàn)，須特別定做齒輪、軸以及相應(yīng)的結(jié)構(gòu)，不太現(xiàn)實(shí)。不過，初始參數(shù)下的試驗(yàn)說明了模型建立的準(zhǔn)確性。 圖9 系統(tǒng)單位階躍響應(yīng)(初始設(shè)計(jì))的仿真與試驗(yàn)曲線 例 3：某 40 m 天線伺服系統(tǒng)(圖 10)。該 40 m天線座方位回轉(zhuǎn)系統(tǒng)如圖 10 所示。天線反射體通過支撐座安裝在叉臂上。方位伺服電動(dòng)機(jī)產(chǎn)生的驅(qū)動(dòng)力矩經(jīng)減速器、傳動(dòng)軸和齒圈作用在轉(zhuǎn)臺(tái)上，從而帶動(dòng)天線反射體繞方位軸旋轉(zhuǎn)。天線反射體質(zhì)量為65 t，要求其跟蹤精度為 30′′。假定方位回轉(zhuǎn)系統(tǒng)的減速比、叉臂的結(jié)構(gòu)形式和外部尺寸(包括叉臂截面長 La、寬 wa、內(nèi)腔長 Lb、內(nèi)腔寬 wb)以及轉(zhuǎn)臺(tái)的結(jié)構(gòu)形式已定。優(yōu)化設(shè)計(jì)的目的是通過調(diào)整控制力矩和結(jié)構(gòu)設(shè)計(jì)，使天線跟蹤性能提高，方位回轉(zhuǎn)系統(tǒng)的質(zhì)量降低。結(jié)構(gòu)設(shè)計(jì)變量包括：上、下支臂箱形結(jié)構(gòu)的外圈壁厚 δa，上、下支臂箱形結(jié)構(gòu)的內(nèi)圈壁厚 δb，轉(zhuǎn)臺(tái)結(jié)構(gòu)的壁厚 δc，天線支撐座的壁厚 δd，傳動(dòng)軸半徑 R；控制設(shè)計(jì)變量為 PID 增益系數(shù)(p1、p2 和 p3)。 在優(yōu)化中，取 M max = 18 kN m ，ts+ = 2.0 s ，òmax =2% ， f re1 = 5 Hz ，[ó ] = 30 MPa，結(jié)果對(duì)比如表 3 所示。表 3 為相應(yīng)的參數(shù)對(duì)比。由表 3 可知：通過集成優(yōu)化設(shè)計(jì)，調(diào)整時(shí)間 ts 減少了 14.3% (由 1.890 s 到1.620 s)，固有頻率 f re1 提高了 22.42% (由 6.870 Hz到 8.407 Hz)，累積跟蹤誤差減少了 16.12%(由 0.003 1到 0.002 6)，總質(zhì)量 m 略增加了 0.42% (由 77.905 t到 78.239 t)。可見，從整體上說，集成設(shè)計(jì)的結(jié)果優(yōu)于分離設(shè)計(jì)的結(jié)果。 上述數(shù)值模擬與實(shí)物驗(yàn)證說明，結(jié)構(gòu)與控制分離設(shè)計(jì)很難甚至無法獲得最優(yōu)的總體性能，集成設(shè)計(jì)可有效地解決此問題。集成設(shè)計(jì)尤其適用于伺服系統(tǒng)的方案設(shè)計(jì)。 7 結(jié)論 (1) 本文提出了雷達(dá)天線伺服系統(tǒng)的一種集成設(shè)計(jì)模型，可同時(shí)實(shí)現(xiàn)結(jié)構(gòu)的輕質(zhì)量和控制穩(wěn)、準(zhǔn)、快的目標(biāo)，解決了以往兩者分離設(shè)計(jì)所帶來的顧此失彼、很難甚至不能獲得系統(tǒng)的綜合性能最佳的問題。 (2) 研究了集成設(shè)計(jì)模型的非線性特點(diǎn)，并據(jù)此給出了求解的策略與方法，數(shù)值模擬結(jié)果，說明了模型與方法的可行性和有效性。但如果機(jī)構(gòu)模型更為復(fù)雜，設(shè)計(jì)變量更多時(shí)，用本文方法建模求解可能會(huì)比較困難。 (3) 為進(jìn)一步驗(yàn)證本文所提出的模型、方法及軟件的正確性和有效性，就某實(shí)際的伺服試驗(yàn)臺(tái)，進(jìn)行了實(shí)物驗(yàn)證，結(jié)果良好。為使該試驗(yàn)臺(tái)的結(jié)果更有說服力，應(yīng)考慮在下面的工作中，進(jìn)行離散變量的優(yōu)化設(shè)計(jì)，即在試驗(yàn)臺(tái)所給定參量可變范圍內(nèi)進(jìn)行，因?yàn)檫@個(gè)變化范圍往往僅是有限而離散的選擇。 (4) 本文所提出的模型與方法，對(duì)其他伺服系統(tǒng)的設(shè)計(jì)也具有一定的參考和借鑒價(jià)值。 參考資料 [1] TOUMI K Y. Modeling, design and control integration：Anecessary step in mechatronics[J]. IEEE/ASME Trans.Mechatronics, 1996, 1(1)：29-37. [2] ONODA J, HAFTKA R T. An approach to structure/control simultaneous optimization for large flexible spacecraft[J]. AIAA Journal, 1987, 25(8)：1133-1138. [3] RAO S S. Combined structural and control optimizationof flexible structures[J]. Engineering Optimization, 1988,13：1-16. [4] YAMAKAYA H. A unified method for combined struct-ural and control optimization of nonlinear mechanical andstructural systems[J]. Computer Aided Optimum Designof Structures, 1989, 287-298. [5] REYER J A, FATHY H K, PAPALAMBROS P Y.Comparison of combined embodiment design of control optimization strategies using optimality conditions[C]//]ASME Design Engineering Technical Conferences & Computers and Information in Engineering Conference,September 9-12, 2001, Pittsburgh, Pennsylvania. New York：ASME, 2001：1-10. [6] REYER J A, PAPALAMBROS P Y. Combined optimaldesign and control with application to an electric DC motor[J]. Journal of Mechanical Design, 2002, 124(6)：183-191. [7] WU F X, ZHANG W J, LI Q, et al. Integrated designand PD control of high-speed closed-loop mechanisms[J].Journal of Dynamic Systems, Measurement, and Control,2002, 124：522-528. 黃河科技學(xué)院畢業(yè)設(shè)計(jì)（外文資料） 第 13 頁 Structure And Control Radar Antenna Servo System Summary Radar antenna mainly depends on the level of its servo system design. Design of servo system design including design and control of two parts, interaction between these two parts are tightly coupled. General system design method is used to structure and control system design, respectively, and then adjusted according to the requirements, which often leads to long product development cycles, high cost, poor performance, structure of heavy, cannot ensure the overall performance of optimal servo system. For the radar antenna servo system design of structure and control design of phase separation problem, proposed a model of integrated optimization design of structure and control, gives the solution strategies and methods, and in turn, applied to the three typical examples, made satisfactory results. Numerical examples and real tests have verified the above radar antenna servo system integrated structure and control of the validity and correctness of the design models and methods. The model and method for other designs also have some reference of the servo system and its reference value. 1 Introduction Mechanical and electrical system is a body (or structure) and the control of two subsystems, integrated design of both is necessary. Structure and control integrated design of research since in the 1980 of the 20th century began yilai, both at home and abroad scholars for has fruitful of research, main set in is as follows 3 a area: ① space system structure and control of integrated design, especially flexible structure system, select structure rod pieces of cross section for design variable, structure of quality and control energy for target, but does not adaptation Yu variable structure (or institutions) problem; ② DC motor of structure and control of integrated design problem, to DC motor for cases, from state space model start, Study on coupling between the structure and control, pointed out the need for integrated design, but for complex institutions, its state space model are not easy to obtain; ③ system bodies and control integration (or collaborative, parallel) design problem, according to the concept of integrated design agency. Natural frequencies of these institutions was not considered, dynamic target tracking control of nonlinear constraints such as stability, accuracy and speed, is no lightweight and gives both the institution and tracking control for more integrated design model of stable, accurate and fast. 2 Ask a question Radar antenna pointing precision and fast response of performance depends on the level of its servo system design, design of servo system design including design and control of two parts. Realization of structure design affects performance, such as the realization of servo bandwidth depends on the natural frequency of the structure. In turn, the control will affect the structure of the design, such as driving force of servo system will affect the size of antenna pedestal structure design. Therefore, in order to achieve the "look" and "clearly" targets, structure design and controls must be integrated. Traditional radar antenna servo system design is the design of phase separation of design and control that individual design of mechanical structure and controlling system, adjusted to meet required targets. As a matter of fact, structure and control radar antenna servo system is coupled to each other, especially in the high-performance tracking and coupling of the two are very close. If you failed to fully consider the servo to control design structure characteristics, will cause a reduction in performance of servo tracking, even unable to meet the requirement of performance indicators on the other, who fails to fully consider the control at design time, you can't be optimal design, could not even designed to meet the performance requirements of the structure. This design method of separation results in long product development cycles, high cost, poor performance and structure of heavy. 3 Structural analysis of radar antenna systems Aims of structural design of mechanical structure design of servo performance requirements are met. To get a good servo to track performance, small quality general requirements for mechanical structure, good rigidity, however these requirements tend to be contradictory. To this end, the introduction of structural optimization, on quality and topology structure optimization design of distribution, transmission, stiffness requirements to achieve total quality guarantee or take up minimum space. In the body during exercise and its configuration changes over time. To this end, to mention it as a multiple-condition (it may be set to N1 indifferent conditions) of structure optimization problem (Figure 1). Figure 1 structure optimization design of radar antenna systems Solution In the d radar servo structure design, N2 is total number of design variables. Objective function for the total mass of the structure of the minimum Type a and b respectively for simple structural parameters (such as body size, material, and so on) and depends on the structure design of control elements (such as driving), N3 for radar servo number of members structure, Vi as a component volume I, I for the I component of the material density. Constraints include first-order natural frequency constraints and stress and displacement constraints In the structure under Frei as I pitch, f RE1 first-order natural frequencies of the smallest allowable value; e-unit under EJ and stress of actual value to the maximum allowable value; IJ I and j, respectively a condition I displacement under constraints of practical value to the maximum allowable value. At the same time, must also meet the j structure under a power differential equation M j, c j in j, k, j, respectively structure under a matrix, damping and stiffness matrix of corresponding quality. For this non-linear programming problem, design the optimal value of a variable and depends on the structure of the corresponding control design elements of a (including m, c, k, frel, etc), as a basis for optimization design of control gain. 4 System design of radar antenna control system Control system design in structure is the purpose of the given premise controlsystemdesigned to meet the performance requirements. Under normal circumstances,requires that the system has a stable, fast, accurate performance, the design of controller should be on the premise of ensuring stability, achieving fast, accurate tracking. To this end, the introduction of optimization design method for control, that is, to optimization design of the controller gain p, servo track system with excellent performance, and b at the same time are dependent on the structure design of control elements (such as drivers). So the problem can be described as a nonlinear programming problem (Figure 2). Figure 2 radar antenna servo system design of optimal control gain Solution In the PI as I gain control variable, N6 to gain total number of design variables. To minimize the objective function accumulate tracking errors j, j reflects on the track "fast" and "quasi" requirements Type, T0 is a motor cycle, e (t) for tracking errors. Constraints include the regulation stability constraints, time constraints,overshootand torque constraints Polei for System I, N7 is the total number of Poles, TS to adjust time, overshoot, f (t) to the controller in the field of driving force or torque. 5 Radar antenna servo system of integrated design of structure and control Radar servo system for high performance, even if separately for optimum design of structure and control for, often still do not meet the requirements of performance indicators, because this method does not guarantee that the overall design of servo system is optimal. Possible results are based on structure optimum design results of control design, solution of limited access to meet performance targets, or are b and contradicts the structure optimization design of design elements. To this end, there is a need for integrated optimization design of structure and control, optimization of structure and control together. Specifically, that is, for a given structure parameters of control parameter a and u, found by seeking optimal comprehensive index of h p d and control gain optimal structure design variable values. So problems can be described as a nonlinear programming problem (Figure 3). General design issues to minimize structural objectives constitute an optimal design problems. Because the control force (torque) is to control the gain function of p, so the average control can also be described as a general gain problem usually gain problem with minimized optimal gain control objectives constitute a problem. On the optimal design and optimal gain issues are coupled to each other, that for optimal design problems can be dependent on the structure of the design elements of a control (including m, c, k, frel, etc), as based on the optimal gain and optimal gain problem solving can be dependent on structure design of control elements. 6 Numerical simulation and experiment To verify the feasibility and effectiveness of the methods mentioned in this article, apply it to the following 3 example, made satisfactory results. Given the limited space, the 1th and the 3rd example are numerical test results only, and the 2nd one is both a numerical and physical verification. Example 1-reflector antenna with slider-crank mechanism (Figure 4). Crank-slider mechanism, as shown in Figure 4, m control torque applied to crank on OA, select a location to install the antenna on the connecting rod AB, corresponding to point to. Purpose and is controlled by adjusting the torque structure design, antenna tracking goals. Changes range from 10 ° from the angle of ~80 °. Figure 4 crank reflector antenna Crank and connecting rods are hollow tubes, R1 and R2, respectively in the cross section of the crank and connecting rod diameter, δ, δ b, respectively wall thickness. PID controller for proportional, integral and differential gain parameter P1, P2, P3, respectively. In dynamic modeling, crank for rigid body, connecting rod for elastomers, elastic deformation as the former ne-order vibration of simply-supported beam stack, take this example ne=3. Design integration and separation of the results as shown in table 1. Figures 5 and 6 respectively 0.2 s before responding and comparison of driving torque curve, because 0.2 s later there's little difference. Visible results to be significantly better than separation of the integrated design optimization results, such as reduced adjustment time TS by 13.5% (0.074 s down to 0.064 s), natural frequency f RE1 improves 58.12% (11.52 Hz up to 18.2 Hz), total mass m down 30.57% (0.268 9 kg down to 0.186 7 kg). Figure 5 integration, separation and design simulation comparison chart Figure 6 integration and isolation design of driving torque comparison chart Example 2: a servo test-bed system (Figure 7). Considering servo systems made up of gear reducer, set equivalent to the moment of inertia of the motor shaft, J1, J2 and J3, respectively, the torsional rigidity of the shaft respectively as K1, K2, damping coefficient for B1, B2,3 bearing friction factors are 1, 2, and 3. Load and motor has been established, overall geometry parameter limits, motor shaft and bearing axle wheelbase has been fixed, the digital PID controller using the traditional control. Requires the design of the structure parameters (including load axis radius r, length l, drive shaft radius r, I, PID control gain reduction ratio P1, P2 and P3), cause the system to meet the demands of performance indicators (under the unit step response overshoot ≤ 2%, adjusting time TS ≤ 0.3 s) has provided the overall best performance. Using the same initial values (initial design of servo test-bed), separate isolation design and integrated design, and sequential quadratic programming method for solving, results are shown in table 2, the unit step response of the system as shown in Figure 8. Figure 8 the unit step response of the system diagram To illustrate the correctness of results, under the initial physical validated numerical results on the test bench. Figure 9 to the initial design, measuring the unit step response and comparison of simulation results. Because of not considering dynamic characteristics of motor and servo amplifiers and manufacturing precision, experimental results and simulation results there is a difference (the maximum error is less than 5%). It is to be noted that, to optimize the results of tests shall be special made to order gears, shafts, as well as the corresponding structure, is not very realistic. However, under the initial description of the test the accuracy of the model. Figure 9 Unit step response of the system (initial design) simulation and experiment of curve Example 3: a 40 m antenna servo system (Figure 10). The 40 m antenna pedestal azimuth rotation system as shown in Figure 10. By supporting the installation of antenna on the fork arm. Direction of servo motor drive torque gearbox, drive shaft and the ring gear on the turn table, so as to drive the antenna azimuth rotation. Antenna weight to 65 t, its track in 30 ' precision '. Reduction ratio of the assumed position Rotary system, structure and the external dimension of the fork arm (including fork arm length in the section long La, w WA, Lb, cavity width WB) and table structures has been fixed. Purpose is controlled by adjusting the torque of the optimized design and structural design, the antenna tracking performance improvement, azimuth rotation system of reduced quality. Structural design variables include: upper and lower arm of box-shaped structure of the outer ring wall thickness δ a, upper and lower arm of box-shaped structure of inner wall thickness δ b, wall thickness δ c of table structure, antenna supporting wall thickness δ d, drive shaft radius r; for PID control design variable gain coefficient (P1, P2 and P3). In optimization, take the m-max 18 kN m, TS 2.0 s, Max 2%, f RE1 5 Hz, 30 MPa, results such as shown in table 3. Table 3 comparison for the corresponding parameter. Table 3: integrated optimization design, reduced the time TS 14.3% (1.890 s to 1.620 s), natural frequency f RE1 improves 22.42% (6.870 Hz to 8.407 Hz), reduced the cumulative tracking error 16.12% (from 0.003 to 0.002), total mass m increases 0.42% (from 77.905 t to 78.239 t). Visible, said on the whole, results than isolation design of integrated design results. Numerical simulation and physical verification of the above descriptions, separation of structure and control design is hard to even get the best overall performance, integrated design can be an effective solution to this problem. Integrated design especially suitable for servo-system design. 7 Conclusion (1) presented a radar antenna servo system of an integrated design model, at the light quality of the structure and control of stable, accurate and fast target, solved the design brought about by the separation of the two in the past have too many things to take care of at the same time, it's hard to even get the overall performance of the system the best question. (2) study on Nonlinear characteristics of integrated design model, and thus gives the solution to some of the strategies and methods, numerical simulation results, describes the feasibility and effectiveness of the models and methods. But if the agency model is more complex, more design variables, using this method of modeling to solve can be difficult. (3) to further verify this article's correctness and validity of models, methods and software, a practical servo test rig, physical verification, good results. To make the test results more convincing, should be taken into account in the work of the following, for discrete variable optimization design, that is, on the test bench the given parameters within the scope of a variable, because often only the scope of the change is limited and discrete choices. (4) models and methods proposed in this article, the other servo system design also has a certain reference and reference value. Reference materials [1] TOUMI K Y. Modeling, design and control integration：Anecessary step in mechatronics[J]. IEEE/ASME Trans.Mechatronics, 1996, 1(1)：29-37. [2] ONODA J, HAFTKA R T. An approach to structure/control simultaneous optimization for large flexible spacecraft[J]. AIAA Journal, 1987, 25(8)：1133-1138. [3] RAO S S. Combined structural and control optimizationof flexible structures[J]. Engineering Optimization, 1988,13：1-16. [4] YAMAKAYA H. 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