PID控制算法的C語(yǔ)言實(shí)現(xiàn)一PID算法原理

PID控制算法的C語(yǔ)言實(shí)現(xiàn)一PID算法原理

最近兩天在考慮?般控制算法的c語(yǔ)言實(shí)現(xiàn)問(wèn)題，發(fā)現(xiàn)網(wǎng)絡(luò)上尚沒(méi)有?套

完整的比較體系的講解。于是總結(jié)了幾天,整理一套思路分享給大家。

在工業(yè)應(yīng)用中P1D及其衍生算法是應(yīng)用最廣泛的算法之一,是當(dāng)之無(wú)愧的

萬(wàn)能算法,如果能夠熟練掌握PID算法的設(shè)計(jì)與實(shí)現(xiàn)過(guò)程,對(duì)于一般的研發(fā)人員

來(lái)講,應(yīng)該是足夠應(yīng)對(duì)一般研發(fā)問(wèn)題了，而難能可貴的是,在我所接觸的控制算法

當(dāng)中,P1D控制算法乂是最簡(jiǎn)單,最能體現(xiàn)反饋思想的控制算法,可謂經(jīng)典中的經(jīng)

典。經(jīng)典的未必是復(fù)雜的，經(jīng)典的東西常常是簡(jiǎn)單的，而且是最簡(jiǎn)單的，想想牛頓

的力學(xué)三大定律吧,想想愛(ài)因斯坦的質(zhì)能方程吧，何等的簡(jiǎn)單！簡(jiǎn)單的不是原始的,

簡(jiǎn)單的也不是落后的,簡(jiǎn)單到了美的程度。先看看P1D算法的一般形式：

PID的流程簡(jiǎn)單到了不能再簡(jiǎn)單的程度,通過(guò)誤差信號(hào)控制被控量,而控制

器本身就是比例、積分、微分三個(gè)環(huán)節(jié)的加和。這里我們規(guī)定（在t時(shí)刻：

1.輸入量為rin<t>;

2.輸出量為rout〈t》;

3.偏差量為err<t>=rin<t>-rout<t>;

pid的控制規(guī)律為

理解一下這個(gè)公式,主要從下面幾個(gè)問(wèn)題著手,為了便于理解,把控制環(huán)境

具體一下：

1.規(guī)定這個(gè)流程是用來(lái)為直流電機(jī)調(diào)速的；

2.輸入量rin<t>為電機(jī)轉(zhuǎn)速預(yù)定值；

3.輸出量rout<t>為電機(jī)轉(zhuǎn)速實(shí)際值；

4.執(zhí)行器為直流電機(jī)；

5.傳感器為光電碼盤(pán)，假設(shè)碼盤(pán)為10線；

6.直流電機(jī)采用PWM調(diào)速轉(zhuǎn)速用單位轉(zhuǎn)/min表示；

不難看出以下結(jié)論：

1.輸入量rin（t為電機(jī)轉(zhuǎn)速預(yù)定值（轉(zhuǎn)/min;

2.輸出量roul<t>為電機(jī)轉(zhuǎn)速實(shí)際值（轉(zhuǎn)/min;

3.偏差量為預(yù)定值和實(shí)際值之差（轉(zhuǎn)/min;

那么以下幾個(gè)問(wèn)題需要弄清楚：

1.通過(guò)PID環(huán)節(jié)之后的U〈t>是什么值呢？

2.控制執(zhí)行器（直流電機(jī)轉(zhuǎn)動(dòng)轉(zhuǎn)速應(yīng)該為電壓值（也就是PWM占空比。

3.那么（Kt>與PWM之間存在怎樣的聯(lián)系呢？

（見(jiàn)附錄1這篇文章上給出了一種方法，即，每個(gè)電壓對(duì)應(yīng)一個(gè)轉(zhuǎn)速，電壓和轉(zhuǎn)速

之間呈現(xiàn)線性關(guān)系。但是我考慮這種方法的前提是把直流電機(jī)的特性理解為線性

（見(jiàn)附錄2這篇文章就可以了解了。所以在正式進(jìn)行調(diào)速設(shè)計(jì)之前，需要現(xiàn)有開(kāi)

環(huán)系統(tǒng),測(cè)試電機(jī)和轉(zhuǎn)速之間的特性曲線（或者查閱電機(jī)的資料說(shuō)明，然后再進(jìn)行

閉環(huán)參數(shù)整定。這篇先寫(xiě)到這，下一篇說(shuō)明連續(xù)系統(tǒng)的離散化問(wèn)題。并根據(jù)離散

化后的特點(diǎn)講述位置型PID和增量型PID的用法和C語(yǔ)言實(shí)現(xiàn)過(guò)程。

PID控制算法的C語(yǔ)言實(shí)現(xiàn)二PID算法的離散化

上一節(jié)中，我論述rPID算法的基本形式,并對(duì)其控制過(guò)程的實(shí)現(xiàn)有了一個(gè)

簡(jiǎn)要的說(shuō)明，通過(guò)上一節(jié)的總結(jié)，基本已經(jīng)可以明白P1D控制的過(guò)程。這一節(jié)中先

繼續(xù)上一節(jié)內(nèi)容補(bǔ)充說(shuō)明一下。

1.說(shuō)明一下反饋控制的原理,通過(guò)上一節(jié)的框圖不難看出，PID控制其實(shí)是

對(duì)偏差的控制過(guò)程；

2.如果偏差為0,則匕例環(huán)節(jié)不起作用，只有存在偏差時(shí)，比例環(huán)節(jié)才起作

用。

3.積分環(huán)節(jié)主要是用來(lái)消除靜差,所謂靜差,就是系統(tǒng)穩(wěn)定后輸出值和設(shè)定

值之間的差值,積分環(huán)節(jié)實(shí)際上就是偏差累計(jì)的過(guò)程,把累計(jì)的誤差加到原有系

統(tǒng)上以抵消系統(tǒng)造成的靜差。

4.而微分信號(hào)則反應(yīng)了偏差信號(hào)的變化規(guī)律,或者說(shuō)是變化趨勢(shì),根據(jù)偏差

信號(hào)的變化趨勢(shì)來(lái)進(jìn)行超前調(diào)節(jié),從而增加了系統(tǒng)的快速性。

好了，關(guān)于PID的基本說(shuō)明就補(bǔ)充到這里,下面將對(duì)PID連續(xù)系統(tǒng)離散化，

從而方便在處理器上實(shí)現(xiàn)。下面把連續(xù)狀態(tài)的公式再贓一下：

假設(shè)采樣間隔為T(mén),則在第KT時(shí)刻：

偏差err<K>=rin<K>-rout<K>;

積分環(huán)節(jié)用加和的形式表示，即err<K>+err<K+l>+........;

微分壞節(jié)用斜率的形式表示，即［err<K>-err<K-l>］/T;

從而形成如下P1D離散表示形式：

則u<K>可表示成為：

至于說(shuō)Kp、Ki、Kd三個(gè)參數(shù)的具體表達(dá)式，我想可以輕松的推出了，這里節(jié)省時(shí)

間，不再詳細(xì)表示了。

其實(shí)到這里為止,PID的基本離散表示形式已經(jīng)出來(lái)了。目前的這種表述形式屬

于位置型PH),另外一種表述方式為增量式P1I),由U上述表達(dá)式可以輕易得到：

那么：

這就是離散化P1D的增量式表示方式，由公式可以看出，增量式的表達(dá)結(jié)果和最

近三次的偏差有關(guān),這樣就大大提高了系統(tǒng)的穩(wěn)定性。需要注意的是最終的輸出

結(jié)果應(yīng)該為

u〈K>+增量調(diào)節(jié)值；

PID的離散化過(guò)程基本思路就是這樣，下面是將離散化的公式轉(zhuǎn)換成為C語(yǔ)言，從

而實(shí)現(xiàn)微控制器的控制作用。

PID控制算法的C語(yǔ)言實(shí)現(xiàn)三位置型PID的C語(yǔ)言實(shí)

現(xiàn)

上一節(jié)中已經(jīng)抽象出了位置性PID和增量型P1D的數(shù)學(xué)表達(dá)式,這一節(jié),重

點(diǎn)講解C語(yǔ)言代碼的實(shí)現(xiàn)過(guò)程,算法的C語(yǔ)言實(shí)現(xiàn)過(guò)程具有一般性,通過(guò)PTD算法

的C語(yǔ)言實(shí)現(xiàn),可以以此類(lèi)推,設(shè)計(jì)其它算法的C語(yǔ)言實(shí)現(xiàn)。

第一步：定義PID變量結(jié)構(gòu)體，代碼如下：

struct_pid(

floatSetSpeed;〃定義設(shè)定值

floatActualSpeed;〃定義實(shí)際值

floaterr;〃定義偏差值

floaterr_last;〃定義上一個(gè)偏差值

floatKp,Ki,Kd;〃定義比例、積分、微分系數(shù)

floatvoltage;〃定義電壓值［控制執(zhí)行器的變量

floatintegral;〃定義積分值

}pid;

控制算法中所需要用到的參數(shù)在一個(gè)結(jié)構(gòu)體中統(tǒng)一定義，方便后面的使用。

第二部：初始化變量，代碼如下：

voidPIDinit<>{

printf<^PID_initbegin\n”>;

pid.SetSpeed=O.0;

pid.ActualSpeed-O.0;

pid.err=0.0;

pid.err_last=0.0;

pid.voltage=0.0;

pid.integral=0.0;

pid.Kp=0.2;

pid.Ki=0.015;

pid.Kd=0.2;

printf<*PID_initend\n”》;

)

統(tǒng)一初始化變量,尤其是Kp,Ki,Kd三個(gè)參數(shù),調(diào)試過(guò)程當(dāng)中，對(duì)于要求的控制效

果,可以通過(guò)調(diào)節(jié)這三個(gè)量直接進(jìn)行調(diào)節(jié)。

第三步：編寫(xiě)控制算法，代碼如下：

floatPID_realize<floatspeed>{

pid.SctSpeed=spced;

pid.err=pid.SetSpeed-pid.ActualSpeed;

pid.integral+=pid.err;

pid.voltagc=pid.Kp*pid.err+pid.Ki*pid.integral+pid.Kd*<pid.err-pi

d.errlast>;pid.err_last=pid.err;

pid.ActualSpeed=pid.voltage*1.0;

returnpid.ActualSpeed;

)

注意：這里用了最基本的算法實(shí)現(xiàn)形式，沒(méi)有考慮死區(qū)問(wèn)題，沒(méi)有設(shè)定上下限，只

是對(duì)公式的一種直接的實(shí)現(xiàn)，后面的介紹當(dāng)中還會(huì)逐漸的對(duì)此改進(jìn)。

到此為止,PID的基本實(shí)現(xiàn)部分就初步完成了。下面是測(cè)試代碼：

intmainO{

printf<，/Systembegin\n〃>;

PID.initO;

intcount=0;

whilc<count<1000>

floatspeed=PIDrealize<200.0>;

printf<"%f\n",speed>;

count++;

}

return0;

)

下面是經(jīng)過(guò)1000次的調(diào)節(jié)后輸出的1000個(gè)數(shù)據(jù)(具體的參數(shù)整定過(guò)程就不說(shuō)明

了，網(wǎng)上這種說(shuō)明非常多：

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PID控制算法的C語(yǔ)言實(shí)現(xiàn)四增量型PID的C語(yǔ)言實(shí)

現(xiàn)

上一節(jié)中介紹了最簡(jiǎn)單的位置型PID的實(shí)現(xiàn)手段，這一節(jié)主要講解增量式

P1D的實(shí)現(xiàn)方法，位置型和增量型P1D的數(shù)學(xué)公式請(qǐng)參見(jiàn)我的系列文《P1D控制算

法的C語(yǔ)言實(shí)現(xiàn)二》中的講解。實(shí)現(xiàn)過(guò)程仍然是分為定義變量、初始化變量、實(shí)

現(xiàn)控制算法函數(shù)、算法測(cè)試四個(gè)部分，詳細(xì)分類(lèi)請(qǐng)參加《PID控制算法的C語(yǔ)言

實(shí)現(xiàn)三》中的講解，這里直接給出代碼了。

#include<stdio.h>

#include<stdlib.h>

struct_pid(

floatSetSpeed;〃定義設(shè)定值

floatActualSpeed;〃定義實(shí)際值

floaterr;〃定義偏差值

floaterr_next;〃定義上一個(gè)偏差值

floaterrlast;〃定義最上前的偏差值

floatKp,Ki,Kd;〃定義比例、積分、微分系數(shù)

}pid;

voidPIDinitO{

pid.SetSpeed=O.0;

pid.ActualSpeed-O.0;

pid.err=0.0;

pid.err_last=0.0;

pid.err_next=O.0：

pid.Kp=O.2;

pid.Ki=0.015;

pid.Kd=O.2;

)

floatPID_realize<floatspeed>{

pid.SetSpeed=speed;

pid.err=pid.SctSpeed-pid.ActualSpeed;

float

incrementSpeed=pid.Kp*<pid.err-pid.err_next>+pid.Ki*pid.err+pid.Kd*<p

id.err-2*pid.err_ncxt+pid.err_last>;

pid.ActualSpeed+=incrementSpeed;

pid.err_last=pid.errnext;

pid.err_next=pid.err;

returnpid.ActualSpeed;

)

intmain<>{

PlD_init<>;

intcount=0;

while<count