自動(dòng)化專業(yè)外文翻譯--PID控制器

1、.中文譯文PID控制器比例積分微分控制器（PID調(diào)節(jié)器）是一個(gè)控制環(huán)，廣泛地應(yīng)用于工業(yè)控制系統(tǒng)里的反饋機(jī)制。PID控制器通過調(diào)節(jié)給定值與測(cè)量值之間的偏差，給出正確的調(diào)整，從而有規(guī)律地糾正控制過程。PID控制器算法涉及到三個(gè)部分：比例，積分，微分。比例控制是對(duì)當(dāng)前偏差的反應(yīng)，積分控制是基于新近錯(cuò)誤總數(shù)的反應(yīng)，而微分控制則是基于錯(cuò)誤變化率的反應(yīng)。這三種控制的結(jié)合可用來調(diào)節(jié)過程系統(tǒng)，例如調(diào)節(jié)閥的位置，或者加熱系統(tǒng)的電源調(diào)節(jié)。根據(jù)具體的工藝要求，通過PID控制器的參數(shù)整定，從而提供調(diào)節(jié)作用?？刂破鞯捻憫?yīng)可以被認(rèn)為是對(duì)系統(tǒng)偏差的響應(yīng)。注意一點(diǎn)的是，PID算法不一定就是系統(tǒng)或系統(tǒng)穩(wěn)定性的最佳控制。一些應(yīng)用

2、可能只需要運(yùn)用一到兩種方法來提供適當(dāng)?shù)南到y(tǒng)控制。這是通過把不想要的控制輸出置零取得。在控制系統(tǒng)中存在P,PI,PD,PID調(diào)節(jié)器。PI調(diào)節(jié)器很普遍，因?yàn)槲⒎挚刂茖?duì)測(cè)量噪音非常敏感。積分作用的缺乏可以防止系統(tǒng)根據(jù)控制目標(biāo)而達(dá)到它的目標(biāo)值。注釋：由于控制理論和應(yīng)用領(lǐng)域的差異，很多相關(guān)變量的命名約定是常用的?？刂骗h(huán)基礎(chǔ) 一個(gè)關(guān)于控制環(huán)類似的例子就是保持水在理想溫度，涉及到兩個(gè)過程，冷、熱水的混合。人可以憑觸覺估測(cè)水的溫度。基于此他們?cè)O(shè)計(jì)一個(gè)控制行為：用冷水龍頭調(diào)整過程。重復(fù)這個(gè)過程，調(diào)節(jié)熱水流直到溫度處于期望的穩(wěn)定值。感覺水溫就是對(duì)過程值或變量的測(cè)量。期望得到的溫度稱為給定值?？刂破鞯妮敵鰧?duì)象和過程

3、的輸入對(duì)象稱為控制參數(shù)。測(cè)量值與給定值之間的差就是偏差值，太高、太低或正常。作為一個(gè)控制器，在確定溫度給定值后，就可以粗略決定改變閥門位置多少，以及怎樣改變偏差值。首次估計(jì)即是PID控制器的比例度的確定。當(dāng)它幾乎正確時(shí)，PID控制器的積分作用就是起著逐漸調(diào)整溫度的作用。微分作用就是根據(jù)水溫變得更熱、更冷，以及變化速率來決定什么時(shí)候、怎樣調(diào)整那些閥門。當(dāng)偏差小時(shí)而做了一個(gè)大變動(dòng)，相當(dāng)于一個(gè)大的調(diào)整控制器，會(huì)導(dǎo)致超調(diào)。如果控制器反復(fù)進(jìn)行大的變動(dòng)并且反復(fù)越過給定值的改變，控制環(huán)將會(huì)不穩(wěn)定。輸出值將在期望值或一常量周圍擺動(dòng)，甚至破壞系統(tǒng)穩(wěn)定性。人不會(huì)這樣做，因?yàn)槲覀兪怯兄腔鄣目刂迫藛T，可以從歷史經(jīng)驗(yàn)中

4、學(xué)習(xí)，但PID控制器沒有學(xué)習(xí)能力，必須正確的設(shè)定。為有效的控制系統(tǒng)選擇正確的參數(shù)被稱為整定控制器。如果控制器在零偏差從穩(wěn)定開始，然后進(jìn)一步的變化將導(dǎo)致其它一些影響過程的能測(cè)量、不能測(cè)量值的變化，并且作用于偏差值上。除主過程以外，其他的對(duì)擾動(dòng)有影響的過程可以用來抑制擾動(dòng)或?qū)崿F(xiàn)對(duì)目標(biāo)值的改變。供給水溫的變化就構(gòu)成了對(duì)過程的一個(gè)擾動(dòng)。理論上，控制器能用來控制可測(cè)量對(duì)象，以及可以影響偏差的輸出、輸入標(biāo)準(zhǔn)值的所有過程參數(shù)。控制器在工業(yè)中被用來調(diào)節(jié)溫度，壓力，流速，化學(xué)組成，速度以及其它任何存在可測(cè)量的對(duì)象。汽車游覽控制就是一個(gè)自動(dòng)化的過程控制的例子。由于它們悠久的歷史，簡(jiǎn)易，良好的理論基礎(chǔ)以及簡(jiǎn)單的設(shè)置

5、、維護(hù)要求，PID控制器被許多應(yīng)用實(shí)踐所采納。2.PID控制器理論注釋：這部分描述PID控制器理想平行或非相互作用的形式。關(guān)于其他形式，請(qǐng)看“其它的表達(dá)式和PID形式”這部分。PID控制是根據(jù)它的三個(gè)參數(shù)而命名的，三參數(shù)結(jié)合起來就形成控制參數(shù)。因此： Pout，Iout和Dout是控制器的三個(gè)參數(shù)，下面分別予以確定。2.1比例度比例度是根據(jù)當(dāng)前的錯(cuò)誤值而做出的變動(dòng)。比例度可以通過恒定的Kp增加來調(diào)整，稱為比例增益。比例度計(jì)算如下： Pout:比例度Kp：比例系數(shù)，協(xié)調(diào)參數(shù)。e:偏差=SP-PVt:時(shí)間或瞬時(shí)時(shí)間（當(dāng)前的）一個(gè)高的比例增益產(chǎn)生于一種輸出值的大的變化。如果比例增益太高，系統(tǒng)將變得不

6、穩(wěn)定。響應(yīng)地，一個(gè)小的調(diào)整產(chǎn)生于一小的輸出變化，而如果比例增益太低，當(dāng)對(duì)系統(tǒng)振蕩作出反映時(shí)，控制作用可能太小。缺少擾動(dòng)的情況下，純粹的比例控制不能完全解決問題，但是將保留從過程中獲得的具有比例增益的功能的穩(wěn)態(tài)偏差。盡管有穩(wěn)態(tài)補(bǔ)償，理論和工業(yè)實(shí)踐都表明比例度在輸出控制中起到大部分的作用。2.2積分值積分值的大小與偏差的大小及持續(xù)時(shí)間成正比。根據(jù)即時(shí)的超時(shí)的錯(cuò)誤改正，進(jìn)行積累補(bǔ)償。積累的誤差通過積分調(diào)節(jié)后再作用于輸出。對(duì)總的控制作用的積分大小由積分時(shí)間常數(shù)來決定，即Ki，積分值計(jì)算如下： Iout：積分值Ki:積分時(shí)間常數(shù)，協(xié)調(diào)參數(shù)e:偏差=SP-PV：積分時(shí)間積分值加速面向設(shè)定值的過程運(yùn)動(dòng)并且消

7、除殘余的只與控制器發(fā)生作用的穩(wěn)態(tài)偏差。然而，因?yàn)榉e分從過去的積累誤差作出反應(yīng)，引起當(dāng)前的值越過設(shè)定值（跨過設(shè)定值向其它方向改變）。想了解更多的關(guān)于積分和控制器穩(wěn)定度的知識(shí)，請(qǐng)參見關(guān)于環(huán)路調(diào)諧的部分。2.3微分值過程偏差的變化率通過超時(shí)錯(cuò)誤的斜率來計(jì)算（即它第一個(gè)關(guān)于調(diào)節(jié)的微分），并增加由微分時(shí)間常數(shù)Kd引起的變化的速率。對(duì)整個(gè)控制行為的微分作用的大小稱為微分值Kd。微分值計(jì)算如下： Dout:微分輸出值Kd:微分時(shí)間常數(shù)，協(xié)調(diào)參數(shù)e:偏差=SP-PVt:時(shí)間或瞬時(shí)時(shí)間（當(dāng)前的）微分作用減緩了控制器輸出的變化率，這種效果最接近于控制器的給定值。因此，微分控制用來降低由積分部分產(chǎn)生的因素并改進(jìn)控制

8、器過程控制的穩(wěn)定度。但是，信號(hào)噪音對(duì)偏差值非常敏感，而且如果噪音和微分度足夠大的話，將使系統(tǒng)變得不穩(wěn)定。2.4摘要 三種參數(shù)控制的輸出值，比例，積分和微分綜合起來能夠計(jì)算出PID調(diào)節(jié)器的輸出，計(jì)算控制器輸出時(shí)，PID算法的最終形式u(t)為：協(xié)調(diào)參數(shù)分別是：Kp:比例增益偏差愈大時(shí)，Kp也愈大，比例期補(bǔ)償更大。過大的比例增益會(huì)導(dǎo)致系統(tǒng)的不穩(wěn)定乃至崩潰。Ki:積分，Ki越大時(shí)，穩(wěn)態(tài)偏差會(huì)更迅速地被消除。在達(dá)到穩(wěn)態(tài)之前，在瞬態(tài)響應(yīng)期間組合的任何誤差必須分開。Kd：微分。Kd越大時(shí)，越容易超調(diào)，但是不同擾動(dòng)區(qū)域的信號(hào)噪音的瞬態(tài)響應(yīng)可能導(dǎo)致系統(tǒng)的不穩(wěn)定。3.環(huán)路調(diào)諧如果PID控制器參數(shù)選擇的不正確，控

9、制過程輸入可能是不穩(wěn)定的，即：它的輸出有分歧，有或沒有動(dòng)搖，并且只通過飽和或者機(jī)械破損是有限的?？刂骗h(huán)的協(xié)調(diào)根據(jù)那些期望控制過程的最佳值來調(diào)整它的控制參數(shù)。最佳控制行為就是過程能根據(jù)應(yīng)用作出相應(yīng)的變化。一些過程不允許在設(shè)定值以外易變的過程超限，如果發(fā)生了，將是不安全的。其它過程必須在達(dá)到新設(shè)定值過程前把用掉的能量減到最小。通常，過程要求穩(wěn)定，不可因?yàn)檫^程條件和給定值的任何變化而擺動(dòng)。一些過程有一定的非線性，因此在系統(tǒng)滿負(fù)荷下正常工作的參數(shù)在系統(tǒng)零負(fù)荷下將停止工作。這部分為環(huán)路調(diào)諧描述了一些傳統(tǒng)的手工方法。PID環(huán)的調(diào)節(jié)有幾種方法。最有效的方法一般與某種形式的過程模型的發(fā)展有關(guān)，然后選擇的P,I

10、和基于動(dòng)態(tài)模型參數(shù)的D。手工協(xié)調(diào)方法相對(duì)來說可能沒有效率。方法的選擇基本依賴于控制環(huán)是否可以協(xié)調(diào)，以及系統(tǒng)的響應(yīng)時(shí)間。如果系統(tǒng)可被離線工作，最好的協(xié)調(diào)方法經(jīng)常與輸入的階躍變化系統(tǒng)有關(guān)，輸出值的測(cè)量作為一個(gè)時(shí)間函數(shù)，并用來確定控制參數(shù)。3.1 手工調(diào)節(jié)如果系統(tǒng)必須保持在線，一種協(xié)調(diào)方法把積分和微分時(shí)間常數(shù)置零。增加P值直到環(huán)的輸出值擺動(dòng)，然后，P值應(yīng)該大約被設(shè)為標(biāo)準(zhǔn)值的四分之一。 然后增加D直到過程補(bǔ)償在足夠的時(shí)間內(nèi)是正確的。不過，D值太大將引起不穩(wěn)定。最后，增加I值，如果需要的話，直到那些環(huán)在負(fù)荷擾動(dòng)之后可迅速到達(dá)給定值。不過，I值太大將引起過度的反應(yīng)并且超調(diào)?？焖貾ID環(huán)路調(diào)諧通常越過微小擾

11、動(dòng)并且能更迅速地達(dá)到給定值；但是，一些系統(tǒng)不能承受超調(diào)，這時(shí)，采用超調(diào)閉環(huán)系統(tǒng)是有必要的，這個(gè)要求P值確定為引起系統(tǒng)擺動(dòng)的P值的一半。3.2 ZieglerNichols 方法 另一種調(diào)節(jié)方式方法正式被稱為 ZieglerNichols方法，由約翰·G.齊格勒和納撒尼爾·B.尼科爾斯發(fā)明。如同在上面的方法內(nèi)，I和D常數(shù)開始時(shí)先被置零。P值增加直至達(dá)到Kc值，此時(shí)閉環(huán)輸出值穩(wěn)定。Kc和Pc用來象顯示的那樣設(shè)定目標(biāo)值： 3.3 PID調(diào)節(jié)軟件 現(xiàn)在大多數(shù)的現(xiàn)代工業(yè)設(shè)備自動(dòng)控制環(huán)不再使用以上介紹的各種手工計(jì)算方法。相應(yīng)地，PID協(xié)調(diào)和循環(huán)優(yōu)化軟件被用來保證結(jié)果的確定。這些軟件自動(dòng)

12、收集數(shù)據(jù)，構(gòu)建過程模型，并且建立最佳的調(diào)節(jié)方式。一些軟件包甚至能根據(jù)參考值的變化規(guī)律來開發(fā)數(shù)據(jù)庫。數(shù)學(xué)PID環(huán)路調(diào)節(jié)在系統(tǒng)里引起一個(gè)推動(dòng)，然后根據(jù)被控制的系統(tǒng)的頻率響應(yīng)設(shè)計(jì)PID 環(huán)標(biāo)準(zhǔn)值。在有幾分鐘響應(yīng)時(shí)間的環(huán)、數(shù)學(xué)環(huán)路調(diào)諧中被推薦，因?yàn)榉磸?fù)試驗(yàn)要花費(fèi)數(shù)天，而僅僅是為了找到一套穩(wěn)定的環(huán)價(jià)值。 而最佳的控制值更難以發(fā)現(xiàn)。一些數(shù)字環(huán)控制器提供非常小的特征值變化，被送入系統(tǒng)自動(dòng)控制過程，使控制器本身實(shí)現(xiàn)最佳控制。 根據(jù)不同的性能準(zhǔn)則環(huán)，還有其他公式對(duì)系統(tǒng)是可提供的。 4.對(duì)PID算法的修改基于PID算法給PID控制應(yīng)用提出了一些挑戰(zhàn)。關(guān)于理想PID實(shí)施的一個(gè)普遍問題不可缺少的終了。這可以被處理通過

13、：初始化控制器對(duì)期望值不可缺少。整定函數(shù)，知道PV已經(jīng)進(jìn)入可控制的區(qū)域。限制不可缺少的偏差被計(jì)算的時(shí)間段。避免不可缺少的時(shí)間段高于或低于預(yù)設(shè)值。許多PID循環(huán)控制一個(gè)機(jī)械設(shè)備（如一個(gè)閥門）。機(jī)械維護(hù)可能是主要的費(fèi)用，并在對(duì)輸入信號(hào)的機(jī)械反應(yīng)里以某些形式抑制擾動(dòng)。機(jī)械的比率主要是一個(gè)設(shè)備變動(dòng)一次的函數(shù)。PID能產(chǎn)生一輸出值，減小系統(tǒng)輸出的頻率。如果變化緩慢，修改控制器使其輸出穩(wěn)定是可以的。實(shí)際輸出值改變之前，被計(jì)算的輸出值必須保持穩(wěn)定。當(dāng)系統(tǒng)偏差值增加時(shí)，比例、微分控制能產(chǎn)生積極的變動(dòng)，例如設(shè)定值的變動(dòng)。就微分而言，取決于對(duì)錯(cuò)誤的積分。5.PID控制的限制當(dāng)PID控制器適用于很多控制問題時(shí)，它在

14、一些應(yīng)用過程中不好使用。當(dāng)單獨(dú)使用并且必須降低PID環(huán)路增益時(shí)，PID控制器會(huì)給出劣質(zhì)的控制性能。因此，控制系統(tǒng)不超調(diào)。在給定值附近擺動(dòng)?？刂葡到y(tǒng)可以通過結(jié)合PID控制器與前饋控制來進(jìn)行改進(jìn)。關(guān)于系統(tǒng)的知識(shí)，可以用前饋和PID輸出來改進(jìn)總的系統(tǒng)性能。單獨(dú)的前饋控制經(jīng)常能提供主要控制器輸出值的部分。PID控制器還能對(duì)在SP和PV的實(shí)際值之間的偏差作出反應(yīng)。因?yàn)榍梆伾a(chǎn)沒被過程反饋影響，它永遠(yuǎn)不能引起控制系統(tǒng)擺動(dòng)，且有助于改進(jìn)系統(tǒng)的穩(wěn)定性。例如，在大多數(shù)運(yùn)動(dòng)控制系統(tǒng)中，為了在控制一機(jī)械負(fù)荷，需要更多的來自電動(dòng)機(jī)、發(fā)動(dòng)機(jī)或作動(dòng)器的力量或者力矩。如果一速度PID控制器被用來控制負(fù)荷的速度，并驅(qū)動(dòng)被原動(dòng)

15、力使用的力或者力矩，它有利于賦予負(fù)荷所需的加速度，恰當(dāng)估價(jià)并且給PID速度環(huán)控制器的輸出添加給定值。這表明每當(dāng)負(fù)荷被加速或者被降速時(shí)，成比例的力量從那些原動(dòng)力產(chǎn)生而不受反饋值影響任何導(dǎo)致輸出增加或減少的因素，為了降低給定值與反饋值的差值。同時(shí)工作時(shí)，結(jié)合的開環(huán)前饋控制器和封閉環(huán)PID控制器能提供一個(gè)更敏感、可靠的控制系統(tǒng)。面臨PID 控制器的另一個(gè)問題是他們是在線的。 因此，在非線性系統(tǒng)(象空調(diào)系統(tǒng)那樣)內(nèi)的PID 控制器的工作是易變的。經(jīng)常PID 控制器通過各種方法獲得PID值或者模糊邏輯來進(jìn)一步提高。 更進(jìn)一步的實(shí)際應(yīng)用問題起因于連接控制器的檢測(cè)儀表。保證足夠高的取樣率，測(cè)量精密和測(cè)量準(zhǔn)確

16、度以使控制器取得足夠的控制性能。 一個(gè)關(guān)于微分方面的問題是少量測(cè)量或者過程噪音能引起輸出的大量改變。 為了除去高頻率的噪音組成部分，用低通濾波器過濾測(cè)量數(shù)據(jù)是經(jīng)常有幫助的。 不過，低通濾波器和微分控制能互相消除，那么以檢測(cè)儀表方法降低噪音是更好的選擇。 或者，這些不同的因素可以被很多系統(tǒng)避免。這相當(dāng)于使用PID 控制器作為一個(gè)PI控制器。 6. 串級(jí)控制 PID 控制器的一個(gè)特別的優(yōu)勢(shì)是兩個(gè)PID 控制器可以一同被使用以產(chǎn)生更好的動(dòng)態(tài)特性。 這被稱作串聯(lián)PID 控制。 在串級(jí)控制，有二個(gè)PID控制器控制另一個(gè)參數(shù)值。 一個(gè)PID 控制器擔(dān)任外環(huán)控制器，例如易流動(dòng)物體或者速度控制主要物質(zhì)參數(shù)。另

17、一控制器擔(dān)任內(nèi)環(huán)控制器，讀取外環(huán)控制器的輸出， 通?？刂埔桓淖兏杆俚膮?shù)。數(shù)學(xué)上可以證明，通過使用串聯(lián)的PID 控制器，控制器的工作頻率被增加，目標(biāo)的時(shí)間常數(shù)被降低。 7. PID控制的物理實(shí)現(xiàn) 在早期自動(dòng)化過程控制的的歷史上，PID 控制器被用作一個(gè)機(jī)械設(shè)備實(shí)現(xiàn)。這些機(jī)械控制器經(jīng)常使用一根杠桿 , 曲軸和活塞由壓縮空氣提供能量。這些氣動(dòng)控制器曾經(jīng)是工業(yè)標(biāo)準(zhǔn)。電子模擬控制器可以一固態(tài)或者成管狀 放大器構(gòu)成，例如一個(gè)電容器和一個(gè)電感。 電子模擬PID 控制環(huán)經(jīng)常在更復(fù)雜的電子系統(tǒng)內(nèi)被發(fā)現(xiàn)，例如，頭一個(gè)磁盤驅(qū)動(dòng)器位置的確定，動(dòng)力電源的限制或者甚至一臺(tái)現(xiàn)代地震儀的運(yùn)動(dòng)?，F(xiàn)在，用microcontr

18、ollers或者FPGAs實(shí)現(xiàn)的數(shù)字控制器已經(jīng)基本上替換電子控制器。 大多數(shù)現(xiàn)代PID 工業(yè)控制器被可編程序邏輯控制器里的軟件實(shí)現(xiàn)或者作為數(shù)字控制器。軟件實(shí)現(xiàn)有優(yōu)勢(shì)，即他們相對(duì)便宜，并且關(guān)于PID 算法的實(shí)施是靈活的。 外文原文PID controllerA proportionalintegralderivative controller (PID controller) is a generic .control loop feedback mechanism widely used in industrial control systems. A PID controller attem

19、pts to correct the error between a measured process variable and a desired setpoint by calculating and then outputting a corrective action that can adjust the process accordingly.The PID controller calculation (algorithm) involves three separate parameters; the Proportional, the Integral and Derivat

20、ive values. The Proportional value determines the reaction to the current error, the Integral determines the reaction based on the sum of recent errors and the Derivative determines the reaction to the rate at which the error has been changing. The weightedsum of these three actions is used to adjus

21、t the process via a control element such as the position of a control valve or the power supply of a heating element.By "tuning" the three constants in the PID controller algorithm the PID can provide control action designed for specific process requirements. The response of the controller

22、 can be described in terms of the responsiveness of the controller to an error, the degree to which the controller overshoots the setpoint and the degree of system oscillation. Note that the use of the PID algorithm for control does not guarantee optimal control of the system or system stability.Som

23、e applications may require using only one or two modes to provide the appropriate system control. This is achieved by setting the gain of undesired control outputs to zero. A PID controller will be called a PI, PD, P or I controller in the absence of the respective control actions. PI controllers ar

24、e particularly common, since derivative action is very sensitive to measurement noise, and the absence of an integral value may prevent the system from reaching its target value due to the control action.Note: Due to the diversity of the field of control theory and application, many naming conventio

25、ns for the relevant variables are in common use.1.Control loop basicsA familiar example of a control loop is the action taken to keep one's shower water at the ideal temperature, which typically involves the mixing of two process streams, cold and hot water. The person feels the water to estimat

26、e its temperature. Based on this measurement they perform a control action: use the cold water tap to adjust the process. The person would repeat this input-output control loop, adjusting the hot water flow until the process temperature stabilized at the desired value.Feeling the water temperature i

27、s taking a measurement of the process value or process variable (PV). The desired temperature is called the setpoint (SP). The output from the controller and input to the process (the tap position) is called the manipulated variable (MV). The difference between the measurement and the setpoint is th

28、e error (e), too hot or too cold and by how much.As a controller, one decides roughly how much to change the tap position (MV) after one determines the temperature (PV), and therefore the error. This first estimate is the equivalent of the proportional action of a PID controller. The integral action

29、 of a PID controller can be thought of as gradually adjusting the temperature when it is almost right. Derivative action can be thought of as noticing the water temperature is getting hotter or colder, and how fast, and taking that into account when deciding how to adjust the tap.Making a change tha

30、t is too large when the error is small is equivalent to a high gain controller and will lead to overshoot. If the controller were to repeatedly make changes that were too large and repeatedly overshoot the target, this control loop would be termed unstable and the output would oscillate around the s

31、etpoint in either a constant, growing, or decaying sinusoid. A human would not do this because we are adaptive controllers, learning from the process history, but PID controllers do not have the ability to learn and must be set up correctly. Selecting the correct gains for effective control is known

32、 as tuning the controller.If a controller starts from a stable state at zero error (PV = SP), then further changes by the controller will be in response to changes in other measured or unmeasured inputs to the process that impact on the process, and hence on the PV. Variables that impact on the proc

33、ess other than the MV are known as disturbances and generally controllers are used to reject disturbances and/or implement setpoint changes. Changes in feed water temperature constitute a disturbance to the shower process.In theory, a controller can be used to control any process which has a measura

34、ble output (PV), a known ideal value for that output (SP) and an input to the process (MV) that will affect the relevant PV. Controllers are used in industry to regulate temperature, pressure, flow rate, chemical composition, speed and practically every other variable for which a measurement exists.

35、 Automobile cruise control is an example of a process which utilizes automated control.Due to their long history, simplicity, well grounded theory and simple setup and maintenance requirements, PID controllers are the controllers of choice for many of these applications.2.PID controller theoryNote:

36、This section describes the ideal parallel or non-interacting form of the PID controller. For other forms please see the Section "Alternative notation and PID forms".The PID control scheme is named after its three correcting terms, whose sum constitutes the manipulated variable (MV). Hence:

37、 where Pout, Iout, and Dout are the contributions to the output from the PID controller from each of the three terms, as defined below.2.1. Proportional termThe proportional term makes a change to the output that is proportional to the current error value. The proportional response can be adjusted b

38、y multiplying the error by a constant Kp, called the proportional gain.The proportional term is given by: WherePout: Proportional output Kp: Proportional Gain, a tuning parameter e: Error = SP PV t: Time or instantaneous time (the present) Change of response for varying KpA high proportional gain re

39、sults in a large change in the output for a given change in the error. If the proportional gain is too high, the system can become unstable (See the section on Loop Tuning). In contrast, a small gain results in a small output response to a large input error, and a less responsive (or sensitive) cont

40、roller. If the proportional gain is too low, the control action may be too small when responding to system disturbances.In the absence of disturbances, pure proportional control will not settle at its target value, but will retain a steady state error that is a function of the proportional gain and

41、the process gain. Despite the steady-state offset, both tuning theory and industrial practice indicate that it is the proportional term that should contribute the bulk of the output change.2.2.Integral termThe contribution from the integral term is proportional to both the magnitude of the error and

42、 the duration of the error. Summing the instantaneous error over time (integrating the error) gives the accumulated offset that should have been corrected previously. The accumulated error is then multiplied by the integral gain and added to the controller output. The magnitude of the contribution o

43、f the integral term to the overall control action is determined by the integral gain, Ki.The integral term is given by: Iout: Integral output Ki: Integral Gain, a tuning parameter e: Error = SP PV : Time in the past contributing to the integral response The integral term (when added to the proportio

44、nal term) accelerates the movement of the process towards setpoint and eliminates the residual steady-state error that occurs with a proportional only controller. However, since the integral term is responding to accumulated errors from the past, it can cause the present value to overshoot the setpo

45、int value (cross over the setpoint and then create a deviation in the other direction). For further notes regarding integral gain tuning and controller stability, see the section on loop tuning.2.3 Derivative termThe rate of change of the process error is calculated by determining the slope of the e

46、rror over time (i.e. its first derivative with respect to time) and multiplying this rate of change by the derivative gain Kd. The magnitude of the contribution of the derivative term to the overall control action is termed the derivative gain, Kd.The derivative term is given by: Dout: Derivative ou

47、tput Kd: Derivative Gain, a tuning parameter e: Error = SP PV t: Time or instantaneous time (the present) The derivative term slows the rate of change of the controller output and this effect is most noticeable close to the controller setpoint. Hence, derivative control is used to reduce the magnitu

48、de of the overshoot produced by the integral component and improve the combined controller-process stability. However, differentiation of a signal amplifies noise and thus this term in the controller is highly sensitive to noise in the error term, and can cause a process to become unstable if the no

49、ise and the derivative gain are sufficiently large.2.4 SummaryThe output from the three terms, the proportional, the integral and the derivative terms are summed to calculate the output of the PID controller. Defining u(t) as the controller output, the final form of the PID algorithm is: and the tun

50、ing parameters areKp: Proportional Gain - Larger Kp typically means faster response since the larger the error, the larger the Proportional term compensation. An excessively large proportional gain will lead to process instability and oscillation. Ki: Integral Gain - Larger Ki implies steady state e

51、rrors are eliminated quicker. The trade-off is larger overshoot: any negative error integrated during transient response must be integrated away by positive error before we reach steady state. Kd: Derivative Gain - Larger Kd decreases overshoot, but slows down transient response and may lead to inst

52、ability due to signal noise amplification in the differentiation of the error. 3. Loop tuningIf the PID controller parameters (the gains of the proportional, integral and derivative terms) are chosen incorrectly, the controlled process input can be unstable, i.e. its output diverges, with or without

53、 oscillation, and is limited only by saturation or mechanical breakage. Tuning a control loop is the adjustment of its control parameters (gain/proportional band, integral gain/reset, derivative gain/rate) to the optimum values for the desired control response.The optimum behavior on a process chang

54、e or setpoint change varies depending on the application. Some processes must not allow an overshoot of the process variable beyond the setpoint if, for example, this would be unsafe. Other processes must minimize the energy expended in reaching a new setpoint. Generally, stability of response (the

55、reverse of instability) is required and the process must not oscillate for any combination of process conditions and setpoints. Some processes have a degree of non-linearity and so parameters that work well at full-load conditions don't work when the process is starting up from no-load. This sec

56、tion describes some traditional manual methods for loop tuning.There are several methods for tuning a PID loop. The most effective methods generally involve the development of some form of process model, then choosing P, I, and D based on the dynamic model parameters. Manual tuning methods can be re

57、latively inefficient.The choice of method will depend largely on whether or not the loop can be taken "offline" for tuning, and the response time of the system. If the system can be taken offline, the best tuning method often involves subjecting the system to a step change in input, measur

58、ing the output as a function of time, and using this response to determine the control parameters. Choosing a Tuning Method MethodAdvantagesDisadvantages Manual TuningNo math required. Online method.Requires experienced personnel. ZieglerNicholsProven Method. Online method.Process upset, some trial-and-error, very aggressive tuning. Software ToolsConsistent tuning. Online or offline method. May include valve and sensor analysis. Allow simulation before downloading.Some cost and training involved. Cohen-CoonG