一文讀懂PID控制演算法（拋棄公式，從原理上真正理解PID控制）
PID控制演算法的C語言實現一 PID演算法原理
最近兩天在考慮一般控制演算法的C語言實現問題，發現網路上尚沒有一套完整的比較體系的講解。於是總結了幾天，整理一套思路分享給大家。
在工業應用中PID及其衍生演算法是應用最廣泛的演算法之一，是當之無愧的萬能演算法，如果能夠熟練掌握PID演算法的設計與實現過程，對於一般的研發人員來講，應該是足夠應對一般研發問題了，而難能可貴的是，在我所接觸的控制演算法當中，PID控制演算法又是最簡單，最能體現反饋思想的控制演算法，可謂經典中的經典。經典的未必是複雜的，經典的東西常常是簡單的，而且是最簡單的，想想牛頓的力學三大定律吧，想想愛因斯坦的質能方程吧，何等的簡單！簡單的不是原始的，簡單的也不是落後的，簡單到了美的程度。先看看PID演算法的一般形式：
PID的流程簡單到了不能再簡單的程度，通過誤差訊號控制被控量，而控制器本身就是比例、積分、微分三個環節的加和。這裡我們規定（在t時刻）：
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的控制規律為
理解一下這個公式，主要從下面幾個問題著手，為了便於理解，把控制環境具體一下：
1.規定這個流程是用來為直流電機調速的;
2.輸入量rin(t)為電機轉速預定值;
3.輸出量rout(t)為電機轉速實際值;
4.執行器為直流電機;
5.感測器為光電碼盤，假設碼盤為10線;
6.直流電機採用PWM調速 轉速用單位 轉/min 表示;
不難看出以下結論：
1.輸入量rin（t）為電機轉速預定值（轉/min）;
2. 輸出量rout(t)為電機轉速實際值（轉/min）;
3.偏差量為預定值和實際值之差（轉/min）;
那麼以下幾個問題需要弄清楚：
1.通過PID環節之後的U(t)是什麼值呢？
2.控制執行器（直流電機）轉動轉速應該為電壓值（也就是PWM佔空比）。
3.那麼U(t)與PWM之間存在怎樣的聯絡呢？
http://blog.21ic.com/user1/3407/archives/2006/33541.html（見附錄1）這篇文章上給出了一種方法，即，每個電壓對應一個轉速，電壓和轉速之間呈現線性關係。但是我考慮這種方法的前提是把直流電機的特性理解為線性了，而實際情況下，直流電機的特性絕對不是線性的，或者說在區域性上是趨於線性的，這就是為什麼說PID調速有個範圍的問題。具體看一下http://articles.e-works.net.cn/component/article90249.htm（見附錄2）這篇文章就可以瞭解了。所以在正式進行調速設計之前，需要現有開環系統，測試電機和轉速之間的特性曲線（或者查閱電機的資料說明），然後再進行閉環引數整定。這篇先寫到這，下一篇說明連續系統的離散化問題。並根據離散化後的特點講述位置型PID和增量型PID的用法和C語言實現過程。
PID控制演算法的C語言實現二 PID演算法的離散化
上一節中，我論述了PID演算法的基本形式，並對其控制過程的實現有了一個簡要的說明，通過上一節的總結，基本已經可以明白PID控制的過程。這一節中先繼續上一節內容補充說明一下。
1.說明一下反饋控制的原理，通過上一節的框圖不難看出，PID控制其實是對偏差的控制過程;
2.如果偏差為0,則比例環節不起作用，只有存在偏差時，比例環節才起作用。
3.積分環節主要是用來消除靜差，所謂靜差，就是系統穩定後輸出值和設定值之間的差值，積分環節實際上就是偏差累計的過程，把累計的誤差加到原有系統上以抵消系統造成的靜差。
4.而微分訊號則反應了偏差訊號的變化規律，或者說是變化趨勢，根據偏差訊號的變化趨勢來進行超前調節，從而增加了系統的快速性。
好了，關於PID的基本說明就補充到這裡，下面將對PID連續系統離散化，從而方便在處理器上實現。下面把連續狀態的公式再貼一下：
假設取樣間隔為T，則在第K T時刻：
偏差err(K)=rin(K)-rout(K);
積分環節用加和的形式表示，即err(K)+err(K+1)+……;
微分環節用斜率的形式表示，即[err(K)-err(K-1)]/T;
從而形成如下PID離散表示形式：
則u(K)可表示成為：
至於說Kp、Ki、Kd三個引數的具體表達式，我想可以輕鬆的推出了，這裡節省時間，不再詳細表示了。
其實到這裡為止，PID的基本離散表示形式已經出來了。目前的這種表述形式屬於位置型PID，另外一種表述方式為增量式PID，由U上述表示式可以輕易得到：
那麼：
這就是離散化PID的增量式表示方式，由公式可以看出，增量式的表達結果和最近三次的偏差有關，這樣就大大提高了系統的穩定性。需要注意的是最終的輸出結果應該為
u(K)+增量調節值;
PID的離散化過程基本思路就是這樣，下面是將離散化的公式轉換成為C語言，從而實現微控制器的控制作用。
PID控制演算法的C語言實現三 位置型PID的C語言實現
上一節中已經抽象出了位置性PID和增量型PID的數學表示式，這一節，重點講解C語言程式碼的實現過程，演算法的C語言實現過程具有一般性，通過PID演算法的C語言實現，可以以此類推，設計其它演算法的C語言實現。
第一步：定義PID變數結構體，程式碼如下：
struct _pid{ float SetSpeed; //定義設定值 float ActualSpeed; //定義實際值 float err; //定義偏差值 float err_last; //定義上一個偏差值 float Kp,Ki,Kd; //定義比例、積分、微分系數 float voltage; //定義電壓值（控制執行器的變數） float integral; //定義積分值 }pid;
控制演算法中所需要用到的引數在一個結構體中統一定義，方便後面的使用。
第二部：初始化變數，程式碼如下：
void PID_init(){ printf("PID_init begin \n"); pid.SetSpeed=0.0; pid.ActualSpeed=0.0; 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_init end \n"); }
統一初始化變數，尤其是Kp,Ki,Kd三個引數，除錯過程當中，對於要求的控制效果，可以通過調節這三個量直接進行調節。
第三步：編寫控制演算法，程式碼如下：
float PID_realize(float speed){ pid.SetSpeed=speed; pid.err=pid.SetSpeed-pid.ActualSpeed; pid.integral+=pid.err; pid.voltage=pid.Kp*pid.err+pid.Ki*pid.integral+pid.Kd*(pid.err-pid.err_last); pid.err_last=pid.err; pid.ActualSpeed=pid.voltage*1.0; return pid.ActualSpeed; }
注意：這裡用了最基本的演算法實現形式，沒有考慮死區問題，沒有設定上下限，只是對公式的一種直接的實現，後面的介紹當中還會逐漸的對此改進。
到此為止，PID的基本實現部分就初步完成了。下面是測試程式碼：
int main(){ printf("System begin \n"); PID_init(); int count=0; while(count<1000) { float speed=PID_realize(200.0); printf("%f\n",speed); count++; } return 0; }
下面是經過1000次的調節後輸出的1000個數據（具體的引數整定過程就不說明了，網上這種說明非常多）：
83.000001 11.555000 59.559675 28.175408 52.907421 38.944152 51.891699 46.141651 53.339054 51.509998 55.908450 55.944631 58.970680 59.882936 62.225001 63.537254 65.527707 67.011058 68.810646 70.355318 72.042040 73.595658 75.207620 76.745444 78.301526 79.812136 81.321929 82.800304 84.268909 85.713108 87.143455 88.553005 89.946960 91.322078 92.680996 94.022234 95.347186 96.655242 97.947180 99.222808 100.482601 101.726572 102.955049 104.168125 105.366066 106.549019 107.717187 108.870756 110.009898 111.134811 112.245652 113.342615 114.425860 115.495564 116.551897 117.595029 118.625116 119.642331 120.646826 121.638767 122.618307 123.585603 124.540813 125.484079 126.415549 127.335383 128.243715 129.140691 130.026459 130.901149 131.764909 132.617870 133.460162 134.291942 135.113308 135.924419 136.725382 137.516332 138.297401 139.068697 139.830352 140.582499 141.325237 142.058701 142.782985 143.498218 144.204509 144.901969 145.590726 146.270843 146.942486 147.605718 148.260674 148.907425 149.546109 150.176794 150.799612 151.414626 152.021959 152.621696 153.213951 153.798781 154.376315 154.946626 155.509812 156.065958 156.615146 157.157471 157.693012 158.221871 158.744097 159.259826 159.769078 160.271991 160.768588 161.258996 161.743264 162.221494 162.693737 163.160075 163.620593 164.075347 164.524422 164.967877 165.405795 165.838235 166.265257 166.686967 167.103377 167.514610 167.920681 168.321682 168.717670 169.108719 169.494862 169.876198 170.252740 170.624605 170.991799 171.354406 171.712487 172.066080 172.415265 172.760077 173.100594 173.436838 173.768895 174.096796 174.420594 174.740352 175.056096 175.367915 175.675818 175.979886 176.280136 176.576656 176.869444 177.158600 177.444121 177.726087 178.004510 178.279458 178.550967 178.819094 179.083860 179.345315 179.603504 179.858466 180.110241 180.358866 180.604388 180.846849 181.086262 181.322699 181.556172 181.786733 182.014396 182.239222 182.461226 182.680475 182.896971 183.110768 183.321881 183.530369 183.736239 183.939545 184.140301 184.338555 184.534321 184.727651 184.918558 185.107080 185.293243 185.477080 185.658625 185.837886 186.014930 186.189745 186.362382 186.532859 186.701207 186.867437 187.031605 187.193713 187.353802 187.511884 187.667997 187.822151 187.974384 188.124700 188.273148 188.419728 188.564488 188.707429 188.848592 188.987995 189.125644 189.261576 189.395801 189.528364 189.659258 189.788528 189.916170 190.042233 190.166702 190.289633 190.411007 190.530867 190.649236 190.766119 190.881544 190.995531 191.108087 191.219243 191.329005 191.437382 191.544428 191.650111 191.754504 191.857565 191.959350 192.059857 192.159119 192.257135 192.353919 192.449511 192.543890 192.637105 192.729137 192.820032 192.909776 192.998410 193.085920 193.172360 193.257700 193.341993 193.425214 193.507408 193.588568 193.668715 193.747847 193.826004 193.903175 193.979391 194.054643 194.128963 194.202349 194.274828 194.346393 194.417073 194.486854 194.555777 194.623820 194.691027 194.757390 194.822919 194.887626 194.951536 195.014633 195.076965 195.138496 195.199273 195.259270 195.318547 195.377060 195.434856 195.491918 195.548283 195.603919 195.658886 195.713145 195.766734 195.819654 195.871912 195.923517 195.974472 196.024791 196.074478 196.123558 196.172016 196.219859 196.267115 196.313778 196.359851 196.405363 196.450296 196.494672 196.538492 196.581753 196.624494 196.666678 196.708363 196.749493 196.790138 196.830267 196.869889 196.909019 196.947656 196.985803 197.023493 197.060701 197.097449 197.133733 197.169558 197.204940 197.239872 197.274378 197.308436 197.342089 197.375309 197.408125 197.440523 197.472520 197.504114 197.535309 197.566127 197.596546 197.626594 197.656258 197.685546 197.714486 197.743047 197.771265 197.799113 197.826629 197.853799 197.880631 197.907131 197.933284 197.959122 197.984629 198.009823 198.034705 198.059275 198.083520 198.107481 198.131129 198.154493 198.177566 198.200349 198.222843 198.245062 198.267001 198.288662 198.310059 198.331178 198.352049 198.372645 198.392982 198.413066 198.432911 198.452499 198.471846 198.490953 198.509819 198.528439 198.546842 198.565003 198.582945 198.600648 198.618147 198.635415 198.652474 198.669313 198.685955 198.702378 198.718611 198.734625 198.750448 198.766067 198.781497 198.796736 198.811776 198.826628 198.841303 198.855788 198.870087 198.884218 198.898162 198.911943 198.925538 198.938970 198.952229 198.965320 198.978257 198.991033 199.003643 199.016092 199.028390 199.040542 199.052536 199.064373 199.076067 199.087617 199.099019 199.110280 199.121407 199.132381 199.143240 199.153940 199.164511 199.174957 199.185270 199.195457 199.205514 199.215440 199.225262 199.234930 199.244503 199.253928 199.263275 199.272468 199.281571 199.290541 199.299421 199.308165 199.316815 199.325345 199.333789 199.342115 199.350336 199.358462 199.366479 199.374396 199.382228 199.389943 199.397586 199.405110 199.412555 199.419891 199.427152 199.434307 199.441389 199.448363 199.455264 199.462073 199.468802 199.475442 199.481995 199.488475 199.494857 199.501183 199.507404 199.513578 199.519639 199.525656 199.531579 199.537437 199.543230 199.548936 199.554583 199.560149 199.565647 199.571073 199.576436 199.581730 199.586961 199.592118 199.597220 199.602260 199.607218 199.612132 199.616974 199.621764 199.626486 199.631156 199.635757 199.640316 199.644808 199.649249 199.653636 199.657959 199.662246 199.666457 199.670635 199.674752 199.678815 199.682833 199.686798 199.690715 199.694583 199.698409 199.702177 199.705905 199.709582 199.713209 199.716788 199.720339 199.723826 199.727276 199.730690 199.734054 199.737378 199.740657 199.743901 199.747111 199.750260 199.753393 199.756474 199.759526 199.762524 199.765490 199.768422 199.771314 199.774169 199.776992 199.779775 199.782527 199.785247 199.787938 199.790590 199.793204 199.795787 199.798338 199.800860 199.803343 199.805802 199.808225 199.810624 199.812986 199.815326 199.817642 199.819915 199.822175 199.824388 199.826587 199.828755 199.830902 199.833006 199.835097 199.837155 199.839194 199.841210 199.843191 199.845168 199.847096 199.849024 199.850905 199.852784 199.854621 199.856449 199.858238 199.860016 199.861757 199.863486 199.865199 199.866879 199.868549 199.870186 199.871813 199.873419 199.874997 199.876563 199.878109 199.879620 199.881136 199.882613 199.884088 199.885527 199.886971 199.888371 199.889783 199.891142 199.892518 199.893845 199.895180 199.896485 199.897783 199.899057 199.900322 199.901562 199.902797 199.904010 199.905222 199.906392 199.907576 199.908720 199.909875 199.910985 199.912108 199.913193 199.914287 199.915352 199.916423 199.917459 199.918505 199.919527 199.920526 199.921513 199.922496 199.923452 199.924415 199.925348 199.926275 199.927198 199.928108 199.929019 199.929903 199.930788 199.931653 199.932509 199.933353 199.934187 199.935002 199.935816 199.936617 199.937420 199.938195 199.938971 199.939733 199.940477 199.941228 199.941961 199.942685 199.943392 199.944111 199.944804 199.945491 199.946181 199.946854 199.947518 199.948165 199.948824 199.949456 199.950083 199.950714 199.951326 199.951930 199.952532 199.953125 199.953714 199.954290 199.954863 199.955424 199.955979 199.956538 199.957073 199.957623 199.958146 199.958671 199.959189 199.959693 199.960203 199.960689 199.961191 199.961665 199.962156 199.962619 199.963098 199.963543 199.964014 199.964448 199.964907 199.965330 199.965772 199.966201 199.966625 199.967046 199.967458 199.967868 199.968263 199.968664 199.969047 199.969437 199.969817 199.970193 199.970565 199.970943 199.971297 199.971668 199.972011 199.972363 199.972712 199.973047 199.973388 199.973726 199.974049 199.974379 199.974699 199.975014 199.975326 199.975645 199.975939 199.976249 199.976546 199.976832 199.977125 199.977414 199.977688 199.977969 199.978247 199.978525 199.978782 199.979061 199.979312 199.979576 199.979825 199.980077 199.980335 199.980569 199.980812 199.981053 199.981300 199.981522 199.981755 199.981984 199.982213 199.982427 199.982648 199.982860 199.983080 199.983298 199.983501 199.983704 199.983914 199.984114 199.984309 199.984500 199.984698 199.984887 199.985079 199.985262 199.985442 199.985623 199.985803 199.985984 199.986170 199.986327 199.986508 199.986668 199.986846 199.987006 199.987169 199.987321 199.987481 199.987633 199.987800 199.987948 199.988094 199.988237 199.988386 199.988526 199.988675 199.988815 199.988965 199.989090 199.989231 199.989359 199.989491 199.989629 199.989757 199.989889 199.990012 199.990133 199.990253 199.990373 199.990493 199.990614 199.990734 199.990854 199.990960 199.991072 199.991180 199.991289 199.991398 199.991507 199.991616 199.991718 199.991837 199.991922 199.992025 199.992123 199.992214 199.992314 199.992412 199.992503 199.992604 199.992701 199.992792 199.992878 199.992967 199.993047 199.993136 199.993216 199.993305 199.993385 199.993474 199.993554 199.993637 199.993726 199.993806 199.993881 199.993952 199.994024 199.994101 199.994170 199.994241 199.994313 199.994391 199.994459 199.994531 199.994602 199.994680 199.994748 199.994805 199.994868 199.994928 199.994989 199.995049 199.995109 199.995175 199.995226 199.995295 199.995346 199.995416 199.995466 199.995536 199.995593 199.995653 199.995713 199.995759 199.995811 199.995859 199.995902 199.995960 199.995999 199.996051 199.996100 199.996148 199.996191 199.996249 199.996288 199.996340 199.996389 199.996438 199.996480 199.996538 199.996578 199.996629 199.996678 199.996712 199.996746 199.996787 199.996824 199.996855 199.996896 199.996927 199.996967 199.997005 199.997036 199.997076 199.997113 199.997145 199.997185 199.997216 199.997256 199.997294 199.997325 199.997365 199.997403 199.997434 199.997474 199.997512 199.997543 199.997583 199.997614 199.997640 199.997669 199.997689 199.997711 199.997740 199.997760 199.997789 199.997809 199.997838 199.997858 199.997880 199.997909 199.997929 199.997958 199.997978 199.998007 199.998027 199.998049 199.998078 199.998098 199.998127 199.998147 199.998170 199.998199 199.998218 199.998247 199.998267 199.998296 199.998316 199.998339 199.998368 199.998387 199.998416 199.998436 199.998459 199.998488 199.998508 199.998537 199.998556 199.998585 199.998590 199.998605 199.998616 199.998634 199.998642 199.998654 199.998665 199.998676 199.998694 199.998702 199.998714 199.998725 199.998743 199.998745 199.998766 199.998774 199.998785 199.998803 199.998805 199.998826 199.998834 199.998845 199.998863 199.998871 199.998883 199.998894 199.998905 199.998923 199.998931 199.998943 199.998954 199.998972 199.998974 199.998995 199.999003 199.999014 199.999032 199.999034 199.999055 199.999063 199.999074 199.999092 199.999094 199.999115 199.999123 199.999135 199.999152 199.999161 199.999172 199.999183 199.999201 199.999203 199.999224 199.999232 199.999243 199.999261 199.999263 199.999284 199.999292 199.999304 199.999321 199.999323 199.999344 199.999352 199.999364 199.999381 199.999390 199.999401 199.999412 199.999430 199.999432 199.999453 199.999461 199.999473
PID控制演算法的C語言實現四 增量型PID的C語言實現
上一節中介紹了最簡單的位置型PID的實現手段，這一節主要講解增量式PID的實現方法，位置型和增量型PID的數學公式請參見我的系列文《PID控制演算法的C語言實現二》中的講解。實現過程仍然是分為定義變數、初始化變數、實現控制演算法函式、演算法測試四個部分，詳細分類請參加《PID控制演算法的C語言實現三》中的講解，這裡直接給出程式碼了。 #include<stdio.h> #include<stdlib.h> struct _pid{ float SetSpeed; //定義設定值 float ActualSpeed; //定義實際值 float err; //定義偏差值 float err_next; //定義上一個偏差值 float err_last; //定義最上前的偏差值 float Kp,Ki,Kd; //定義比例、積分、微分系數 }pid; void PID_init(){ pid.SetSpeed=0.0; pid.ActualSpeed=0.0; pid.err=0.0; pid.err_last=0.0; pid.err_next=0.0; pid.Kp=0.2; pid.Ki=0.015; pid.Kd=0.2; } float PID_realize(float speed){ pid.SetSpeed=speed; pid.err=pid.SetSpeed-pid.ActualSpeed; float incrementSpeed=pid.Kp*(pid.err-pid.err_next)+pid.Ki*pid.err+pid.Kd*(pid.err-2*pid.err_next+pid.err_last); pid.ActualSpeed+=incrementSpeed; pid.err_last=pid.err_next; pid.err_next=pid.err; return pid.ActualSpeed; } int main(){ PID_init(); int count=0; while(count<1000) { float speed=PID_realize(200.0); printf("%f\n",speed); count++; } return 0; } 執行後的1000個數據為：
83.000000 11.555000 59.559677 28.175406 52.907425 38.944149 51.891701 46.141655 53.339050 51.510002 55.908447 55.944637 58.970676 59.882942 62.224998 63.537247 65.527702 67.011047 68.810638 70.355309 72.042023 73.595642 75.207603 76.745430 78.301514 79.812126 81.321915 82.800293 84.268898 85.713097 87.143440 88.552994 89.946945 91.322067 92.680977 94.022224 95.347176 96.655235 97.947174 99.222801 100.482597 101.726562 102.955040 104.168114 105.366058 106.549004 107.717178 108.870743 110.009888 111.134796 112.245636 113.342598 114.425842 115.495552 116.551880 117.595009 118.625099 119.642311 120.646812 121.638756 122.618294 123.585594 124.540794 125.484062 126.415535 127.335365 128.243698 129.140671 130.026443 130.901138 131.764893 132.617859 133.460159 134.291931 135.113297 135.924408 136.725372 137.516327 138.297394 139.068695 139.830353 140.582489 141.325226 142.058685 142.782974 143.498199 144.204498 144.901962 145.590714 146.270844 146.942474 147.605713 148.260651 148.907410 149.546082 150.176773 150.799576 151.414597 152.021927 152.621674 153.213913 153.798752 154.376282 154.946594 155.509781 156.065918 156.615112 157.157440 157.692993 158.221848 158.744095 159.259811 159.769073 160.271973 160.768585 161.258987 161.743271 162.221481 162.693726 163.160065 163.620575 164.075333 164.524399 164.967865 165.405777 165.838226 166.265259 166.686951 167.103378 167.514587 167.920670 168.321671 168.717667 169.108704 169.494858 169.876175 170.252731 170.624588 170.991791 171.354401 171.712479 172.066086 172.415268 172.760086 173.100601 173.436844 173.768890 174.096786 174.420578 174.740326 175.056076 175.367889 175.675797 175.979858 176.280121 176.576630 176.869431 177.158569 177.444092 177.726044 178.004471 178.279419 178.550934 178.819046 179.083817 179.345276 179.603470 179.858429 180.110214 180.358841 180.604370 180.846817 181.086243 181.322662 181.556137 181.786682 182.014359 182.239182 182.461197 182.680435 182.896942 183.110733 183.321854 183.530334 183.736206 183.939514 184.140274 184.338531 184.534302 184.727631 184.918533 185.107056 185.293228 185.477066 185.658615 185.837891 186.014923 186.189743 186.362381 186.532852 186.701202 186.867432 187.031601 187.193710 187.353790 187.511871 187.667984 187.822128 187.974365 188.124680 188.273132 188.419724 188.564484 188.707428 188.848587 188.987976 189.125626 189.261566 189.395798 189.528351 189.659256 189.788513 189.916168 190.042221 190.166702 190.289627 190.411011 190.530884 190.649246 190.766144 190.881561 190.995544 191.108109 191.219254 191.329025 191.437408 191.544449 191.650146 191.754517 191.857590 191.959366 192.059875 192.159134 192.257141 192.353928 192.449509 192.543884 192.637085 192.729126 192.820007 192.909760 192.998383 193.085907 193.172333 193.257675 193.341965 193.425186 193.507385 193.588531 193.668686 193.747818 193.825974 193.903152 193.979370 194.054626 194.128952 194.202332 194.274811 194.346375 194.417053 194.486832 194.555756 194.623810 194.691010 194.757370 194.822906 194.887619 194.951523 195.014633 195.076950 195.138489 195.199265 195.259277 195.318542 195.377060 195.434845 195.491913 195.548264 195.603912 195.658859 195.713135 195.766724 195.819641 195.871902 195.923508 195.974472 196.024796 196.074493 196.123566 196.172028 196.219879 196.267136 196.313797 196.359879 196.405380 196.450317 196.494690 196.538513 196.581787 196.624512 196.666702 196.708374 196.749512 196.790146 196.830261 196.869888 196.909012 196.947647 196.985809 197.023483 197.060699 197.097443 197.133728 197.169556 197.204941 197.239883 197.274384 197.308456 197.342102 197.375320 197.408127 197.440521 197.472519 197.504105 197.535309 197.566116 197.596542 197.626587 197.656250 197.685547 197.714478 197.743042 197.771255 197.799118 197.826630 197.853806 197.880630 197.907120 197.933289 197.959122 197.984634 198.009827 198.034698 198.059265 198.083527 198.107483 198.131134 198.154495 198.177567 198.200348 198.222839 198.245056 198.266998 198.288666 198.310059 198.331177 198.352036 198.372635 198.392975 198.413071 198.432907 198.452499 198.471848 198.490952 198.509811 198.528442 198.546829 198.565002 198.582932 198.600647 198.618134 198.635406 198.652466 198.669312 198.685944 198.702377 198.718597 198.734619 198.750443 198.766068 198.781494 198.796722 198.811768 198.826614 198.841278 198.855759 198.870056 198.884186 198.898132 198.911911 198.925507 198.938934 198.952194 198.965286 198.978226 198.990997 199.003616 199.016068 199.028366 199.040512 199.052505 199.064346 199.076050 199.087601 199.099014 199.110275 199.121399 199.132385 199.143234 199.153946 199.164520 199.174973 199.185287 199.195465 199.205521 199.215454 199.225266 199.234955 199.244522 199.253967 199.263290 199.272507 199.281601 199.290588 199.299454 199.308212 199.316864 199.325409 199.333847 199.342178 199.350403 199.358521 199.366547 199.374466 199.382294 199.390015 199.397644 199.405167 199.412613 199.419952 199.427200 199.434357 199.441422 199.448410 199.455307 199.462112 199.468842 199.475479 199.482040 199.488510 199.494904 199.501221 199.507462 199.513611 199.519699 199.525696 199.531631 199.537476 199.543259 199.548965 199.554611 199.560181 199.565674 199.571106 199.576462 199.581757 199.586990 199.592148 199.597244 199.602280 199.607254 199.612167 199.617020 199.621811 199.626541 199.631210 199.635818 199.640366 199.644867 199.649307 199.653687 199.658020 199.662292 199.666519 199.670685 199.674805 199.678864 199.682877 199.686844 199.690750 199.694626 199.698441 199.702209 199.705933 199.709610 199.713242 199.716827 199.720367 199.723862 199.727310 199.730713 199.734085 199.737411 199.740692 199.743942 199.747147 199.750305 199.753433 199.756516 199.759567 199.762573 199.765549 199.768478 199.771378 199.774231 199.777054 199.779846 199.782593 199.785309 199.787994 199.790649 199.793259 199.795853 199.798401 199.800919 199.803406 199.805862 199.808289 199.810684 199.813049 199.815384 199.817688 199.819962 199.822220 199.824432 199.826630 199.828796 199.830933 199.833054 199.835144 199.837204 199.839233 199.841248 199.843231 199.845200 199.847137 199.849045 199.850937 199.852798 199.854645 199.856461 199.858261 199.860031 199.861786 199.863510 199.865219 199.866898 199.868561 199.870209 199.871826 199.873428 199.875015 199.876572 199.878113 199.879639 199.881149 199.882629 199.884094 199.885544 199.886978 199.888397 199.889786 199.891174 199.892532 199.893875 199.895203 199.896515 199.897812 199.899094 199.900360 199.901611 199.902847 199.904068 199.905273 199.906464 199.907639 199.908798 199.909943 199.911072 199.912186 199.913284 199.914368 199.915436 199.916489 199.917526 199.918564 199.919571 199.920578 199.921570 199.922546 199.923523 199.924469 199.925415 199.926346 199.927261 199.928177 199.929077 199.929962 199.930832 199.931702 199.932556 199.933395 199.934235 199.935059 199.935867 199.936676 199.937469 199.938248 199.939026 199.939789 199.940536 199.941284 199.942017 199.942749 199.943466 199.944168 199.944870 199.945557 199.946243 199.946915 199.947586 199.948242 199.948883 199.949524 199.950150 199.950775 199.951385 199.951996 199.952591 199.953186 199.953766 199.954346 199.954910 199.955475 199.956024 199.956573 199.957108 199.957642 199.958176 199.958694 199.959213 199.959717 199.960220 199.960724 199.961212 199.961700 199.962173 199.962646 199.963120 199.963577 199.964035 199.964478 199.964920 199.965363 199.965790 199.966217 199.966644 199.967056 199.967468 199.967880 199.968277 199.968674 199.969070 199.969452 199.969833 199.970215 199.970581 199.970947 199.971313 199.971664 199.972015 199.972366 199.972717 199.973053 199.973389 199.973724 199.974045 199.974380 199.974701 199.975021 199.975327 199.975632 199.975937 199.976242 199.976532 199.976822 199.977112 199.977402 199.977676 199.977966 199.978241 199.978516 199.978790 199.979050 199.979309 199.979568 199.979828 199.980072 199.980331 199.980576 199.980820 199.981064 199.981293 199.981537 199.981766 199.981995 199.982224 199.982437 199.982666 199.982880 199.983093 199.983307 199.983521 199.983719 199.983932 199.984131 199.984329 199.984528 199.984726 199.984909 199.985107 199.985291 199.985474 199.985657 199.985840 199.986023 199.986191 199.986374 199.986542 199.986710 199.986877 199.987045 199.987213 199.987366 199.987534 199.987686 199.987839 199.987991 199.988144 199.988297 199.988449 199.988586 199.988739 199.988876 199.989014 199.989151 199.989288 199.989426 199.989563 199.989685 199.989822 199.989944 199.990067 199.990189 199.990311 199.990433 199.990555 199.990677 199.990799 199.990906 199.991028 199.991135 199.991257 199.991364 199.991470 199.991577 199.991684 199.991791 199.991898 199.992004 199.992096 199.992203 199.992294 199.992401 199.992493 199.992584 199.992676 199.992767 199.992859 199.992950 199.993042 199.993134 199.993225 199.993301 199.993393 199.993469 199.993561 199.993637 199.993713 199.993790 199.993866 199.993942 199.994019 199.994095 199.994171 199.994247 199.994324 199.994400 199.994476 199.994537 199.994614 199.994675 199.994751 199.994812 199.994873 199.994934 199.994995 199.995056 199.995117 199.995178 199.995239 199.995300 199.995361 199.995422 199.995483 199.995544 199.995605 199.995667 199.995712 199.995773 199.995819 199.995880 199.995926 199.995987 199.996033 199.996094 199.996140 199.996185 199.996231 199.996277 199.996323 199.996368 199.996414 199.996460 199.996506 199.996552 199.996597 199.996643 199.996689 199.996735 199.996780 199.996826 199.996872 199.996902 199.996948 199.996979 199.997025 199.997055 199.997101 199.997131 199.997177 199.997208 199.997253 199.997284 199.997314 199.997345 199.997375 199.997406 199.997437 199.997467 199.997498 199.997528 199.997559 199.997589 199.997620 199.997650 199.997681 199.997711 199.997742 199.997772 199.997803 199.997833 199.997864 199.997894 199.997925 199.997955 199.997986 199.998016 199.998047 199.998077 199.998093 199.998123 199.998138 199.998169 199.998184 199.998215 199.998230 199.998260 199.998276 199.998306 199.998322 199.998352 199.998367 199.998398 199.998413 199.998444 199.998459 199.998489 199.998505 199.998520 199.998535 199.998550 199.998566 199.998581 199.998596 199.998611 199.998627 199.998642 199.998657 199.998672 199.998688 199.998703 199.998718 199.998734 199.998749 199.998764 199.998779 199.998795 199.998810 199.998825 199.998840 199.998856 199.998871 199.998886 199.998901 199.998917 199.998932 199.998947 199.998962 199.998978 199.998993 199.999008 199.999023 199.999039 199.999054 199.999069 199.999084 199.999100 199.999115 199.999130 199.999146 199.999161 199.999176 199.999191 199.999207 199.999222 199.999237 199.999252 199.999268 199.999283 199.999298 199.999298 199.999313 199.999313 199.999329 199.999329 199.999344 199.999344 199.999359 199.999359 199.999374 199.999374 199.999390 199.999390 199.999405 199.999405 199.999420 199.999420 199.999435 199.999435 199.999451 199.999451 199.999466 199.999466 199.999481 199.999481 199.999496 199.999496 199.999512 199.999512
PID控制演算法的C語言實現五 積分分離的PID控制演算法C語言實現
通過三、四兩篇文章，基本上已經弄清楚了PID控制演算法的最常規的表達方法。在普通PID控制中，引入積分環節的目的，主要是為了消除靜差，提高控制精度。但是在啟動、結束或大幅度增減設定時，短時間內系統輸出有很大的偏差，會造成PID運算的積分積累，導致控制量超過執行機構可能允許的最大動作範圍對應極限控制量，從而引起較大的超調，甚至是震盪，這是絕對不允許的。
為了克服這一問題，引入了積分分離的概念，其基本思路是 當被控量與設定值偏差較大時，取消積分作用; 當被控量接近給定值時，引入積分控制，以消除靜差，提高精度。其具體實現程式碼如下：
pid.Kp=0.2; pid.Ki=0.04; pid.Kd=0.2; //初始化過程
if(abs(pid.err)>200) { index=0; }else{ index=1; pid.integral+=pid.err; } pid.voltage=pid.Kp*pid.err+index*pid.Ki*pid.integral+pid.Kd*(pid.err-pid.err_last); //演算法具體實現過程
其它部分的程式碼參見《PID控制演算法的C語言實現三》中的講解，不再贅述。同樣採集1000個量，會發現，系統到199所有的時間是原來時間的1/2,系統的快速性得到了提高。
199.003571 199.036804 199.068924 199.099960 199.129974 199.158981 199.187012 199.214111 199.240311 199.265640 199.290115 199.313797 199.336655 199.358795 199.380157 199.400818 199.420792 199.440109 199.458771 199.476807 199.494263 199.511124 199.527420 199.543182 199.558426 199.573135 199.587372 199.601120 199.614426 199.627289 199.639694 199.651718 199.663315 199.674561 199.685410 199.695908 199.706039 199.715851 199.725311 199.734482 199.743332 199.751907 199.760162 199.768173 199.775894 199.783371 199.790588 199.797577 199.804337 199.810867 199.817154 199.823257 199.829147 199.834839 199.840347 199.845673 199.850815 199.855789 199.860596 199.865234 199.869736 199.874069 199.878281 199.882324 199.886261 199.890045 199.893707 199.897263 199.900665 199.903992 199.907181 199.910278 199.913284 199.916168 199.918976 199.921677 199.924286 199.926804 199.929245 199.931610 199.933884 199.936081 199.938217 199.940277 199.942276 199.944183 199.946045 199.947830 199.949585 199.951248 199.952896 199.954437 199.955963 199.957428 199.958847 199.960205 199.961548 199.962830 199.964066 199.965271 199.966431 199.967545 199.968628 199.969666 199.970673 199.971649 199.972595 199.973511 199.974380 199.975235 199.976074 199.976852 199.977631 199.978378 199.979095 199.979797 199.980453 199.981125 199.981735 199.982361 199.982925 199.983505 199.984055 199.984604 199.985107 199.985611 199.986069 199.986557 199.987000 199.987442 199.987869 199.988281 199.988663 199.989044 199.989395 199.989761 199.990097 199.990417 199.990753 199.991058 199.991348 199.991653 199.991913 199.992203 199.992447 199.992706 199.992950 199.993179 199.993408 199.993607 199.993835 199.994034 199.994232 199.994431 199.994598 199.994797 199.994965 199.995132 199.995285 199.995453 199.995605 199.995743 199.995895 199.996017 199.996155 199.996277 199.996414 199.996521 199.996643 199.996750 199.996872 199.996964 199.997070 199.997162 199.997269 199.997360 199.997437 199.997528 199.997604 199.997681 199.997772 199.997849 199.997910 199.997986 199.998047 199.998108 199.998169 199.998245 199.998306 199.998352 199.998398 199.998459 199.998489 199.998550 199.998596 199.998642 199.998703 199.998734 199.998795 199.998825 199.998856 199.998886 199.998917 199.998962 199.998978 199.999023 199.999054 199.999084 199.999115 199.999146 199.999191 199.999207 199.999252 199.999283 199.999298 199.999313 199.999329 199.999344 199.999359 199.999374 199.999390 199.999405 199.999435 199.999435 199.999466 199.999466 199.999496 199.999512 199.999527 199.999542 199.999557 199.999573 199.999588 199.999603 199.999619 199.999634 199.999649 199.999680 199.999680 199.999710 199.999710 199.999741 199.999756 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771 199.999771
PID控制演算法的C語言實現六 抗積分飽和的PID控制演算法C語言實現
所謂的積分飽和現象是指如果系統存在一個方向的偏差，PID控制器的輸出由於積分作用的不斷累加而加大，從而導致執行機構達到極限位置，若控制器輸出U(k)繼續增大，執行器開度不可能再增大，此時計算機輸出控制量超出了正常執行範圍而進入飽和區。一旦系統出現反向偏差，u(k)逐漸從飽和區退出。進入飽和區越深則退出飽和區時間越長。在這段時間裡，執行機構仍然停留在極限位置而不隨偏差反向而立即做出相應的改變，這時系統就像失控一樣，造成控制性能惡化，這種現象稱為積分飽和現象或積分失控現象。
防止積分飽和的方法之一就是抗積分飽和法，該方法的思路是在計算u(k)時，首先判斷上一時刻的控制量u(k-1)是否已經超出了極限範圍： 如果u(k-1)>umax，則只累加負偏差; 如果u(k-1)<umin，則只累加正偏差。從而避免控制量長時間停留在飽和區。直接貼出程式碼，不懂的看看前面幾節的介紹。
struct _pid{ float SetSpeed; //定義設定值 float ActualSpeed; //定義實際值 float err; //定義偏差值 float err_last; //定義上一個偏差值 float Kp,Ki,Kd; //定義比例、積分、微分系數 float voltage; //定義電壓值（控制執行器的變數） float integral; //定義積分值 float umax; float umin; }pid; void PID_init(){ printf("PID_init begin \n"); pid.SetSpeed=0.0; pid.ActualSpeed=0.0; pid.err=0.0; pid.err_last=0.0; pid.voltage=0.0; pid.integral=0.0; pid.Kp=0.2; pid.Ki=0.1; //注意，和上幾次相比，這裡加大了積分環節的值 pid.Kd=0.2; pid.umax=400; pid.umin=-200; printf("PID_init end \n"); } float PID_realize(float speed){ int index; pid.SetSpeed=speed; pid.err=pid.SetSpeed-pid.ActualSpeed; if(pid.ActualSpeed>pid.umax) //灰色底色表示抗積分飽和的實現 { if(abs(pid.err)>200) //藍色標註為積分分離過程 { index=0; }else{ index=1; if(pid.err<0) { pid.integral+=pid.err; } } }else if(pid.ActualSpeed<pid.umin){ if(abs(pid.err)>200) //積分分離過程 { index=0; }else{ index=1; if(pid.err>0) { pid.integral+=pid.err; } } }else{ if(abs(pid.err)>200) //積分分離過程 { index=0; }else{ index=1; pid.integral+=pid.err; } } pid.voltage=pid.Kp*pid.err+index*pid.Ki*pid.integral+pid.Kd*(pid.err-pid.err_last); pid.err_last=pid.err; pid.ActualSpeed=pid.voltage*1.0; return pid.ActualSpeed; }
最終的測試程式運算結果如下，可以明顯的看出系統的穩定時間相對前幾次來講縮短了不少。
100.000000 30.000000 95.000000 65.500000 103.750000 92.175003 115.237503 112.173752 126.794380 127.653938 137.468842 139.967911 146.934479 149.954224 155.144211 158.157745 162.174561 164.953079 168.149734 170.611786 173.205124 175.339691 177.470551 179.298065 181.063431 182.616440 184.086655 185.400513 186.628952 187.737457 188.766006 189.699692 190.561951 191.347580 192.071030 192.731674 193.338928 193.894257 194.404160 194.870834 195.299072 195.691193 196.050888 196.380341 196.682465 196.959244 197.213043 197.445572 197.658768 197.854111 198.033203 198.197311 198.347763 198.485626 198.612015 198.727829 198.834000 198.931290 199.020477 199.102219 199.177139 199.245804 199.308746 199.366425 199.419296 199.467758 199.512161 199.552872 199.590179 199.624390 199.655716 199.684464 199.710785 199.734924 199.757034 199.777298 199.795883 199.812912 199.828537 199.842834 199.855972 199.867981 199.879013 199.889099 199.898361 199.906845 199.914612 199.921753 199.928268 199.934280 199.939743 199.944794 199.949371 199.953629 199.957474 199.961029 199.964279 199.967270 199.969986 199.972504 199.974792 199.976898 199.978821 199.980591 199.982208 199.983688 199.985062 199.986298 199.987442 199.988495 199.989441 199.990326 199.991135 199.991867 199.992554 199.993179 199.993744 199.994263 199.994751 199.995178 199.995590 199.995941 199.996292 199.996582 199.996887 199.997116 199.997391 199.997574 199.997803 199.997971 199.998154 199.998291 199.998444 199.998581 199.998703 199.998810 199.998917 199.999008 199.999084 199.999176 199.999237 199.999298 199.999359 199.999405 199.999466 199.999496 199.999542 199.999588 199.999619 199.999649 199.999680 199.999710 199.999725 199.999756 199.999771 199.999786 199.999817 199.999817 199.999847 199.999847 199.999863 199.999863 199.999878 199.999893 199.999893 199.999908 199.999924 199.999924 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939 199.999939
PID控制演算法的C語言實現七 梯形積分的PID控制演算法C語言實現
先看一下梯形演算法的積分環節公式
作為PID控制律的積分項，其作用是消除餘差，為了儘量減小余差，應提高積分項運算精度，為此可以將矩形積分改為梯形積分，具體實現的語句為：
pid.voltage=pid.Kp*pid.err+index*pid.Ki*pid.integral/2+pid.Kd*(pid.err-pid.err_last); //梯形積分
其它函式請參見本系列教程六中的介紹
最後運算的穩定資料為：199.999878，較教程六中的199.9999390而言，精度進一步提高。
PID控制演算法的C語言實現八 變積分的PID控制演算法C語言實現
變積分PID可以看成是積分分離的PID演算法的更一般的形式。在普通的PID控制演算法中，由於積分系數ki是常數，所以在整個控制過程中，積分增量是不變的。但是，系統對於積分項的要求是，系統偏差大時，積分作用應該減弱甚至是全無，而在偏差小時，則應該加強。積分系數取大了會產生超調，甚至積分飽和，取小了又不能短時間內消除靜差。因此，根據系統的偏差大小改變積分速度是有必要的。
變積分PID的基本思想是設法改變積分項的累加速度，使其與偏差大小相對應：偏差越大，積分越慢; 偏差越小，積分越快。
這裡給積分系數前加上一個比例值index：
當abs(err)<180時，index=1;
當180<abs(err)<200時，index=（200-abs(err)）/20;
當abs(err)>200時，index=0;
最終的比例環節的比例係數值為ki*index;
具體PID實現程式碼如下：
pid.Kp=0.4; pid.Ki=0.2; //增加了積分系數 pid.Kd=0.2;
float PID_realize(float speed){ float index; pid.SetSpeed=speed; pid.err=pid.SetSpeed-pid.ActualSpeed; if(abs(pid.err)>200) //變積分過程 { index=0.0; }else if(abs(pid.err)<180){ index=1.0; pid.integral+=pid.err; }else{ index=(200-abs(pid.err))/20; pid.integral+=pid.err; } pid.voltage=pid.Kp*pid.err+index*pid.Ki*pid.integral+pid.Kd*(pid.err-pid.err_last); pid.err_last=pid.err; pid.ActualSpeed=pid.voltage*1.0; return pid.ActualSpeed; }
最終結果可以看出，系統的穩定速度非常快（測試程式參見本系列教程3）：
120.000000 64.000000 148.800003 96.959999 165.632004 120.934395 177.300476 139.081223 185.469742 152.898834 191.139313 163.452988 195.022278 171.538986 197.635025 177.753738 199.350967 182.546188 200.439255 186.254608 201.093094 189.134460 201.450439 191.379044 201.609268 193.135010 201.638611 194.513870 201.586670 195.600708 201.486694 196.460571 201.361328 197.143387 201.225632 197.687561 201.089340 198.122787 200.958511 198.472076 200.836655 198.753296 200.725555 198.980423 200.625870 199.164398 200.537506 199.313843 200.459900 199.435547 200.392258 199.534912 200.333679 199.616211 200.283203 199.682877 200.239899 199.737640 200.202866 199.782700 200.171295 199.819855 200.144470 199.850525 200.121704 199.875870 200.102432 199.896851 200.086136 199.914230 200.072372 199.928635 200.060776 199.940582 200.051010 199.950500 200.042801 199.958755 200.035904 199.965622 200.030090 199.971344 200.025223 199.976105 200.021118 199.980057 200.017700 199.983353 200.014832 199.986099 200.012421 199.988403 200.010391 199.990326 200.008698 199.991928 200.007263 199.993256 200.006088 199.994370 200.005081 199.995300 200.004257 199.996063 200.003555 199.996719 200.002975 199.997253 200.002487 199.997711 200.002075 199.998077 200.001740 199.998398 200.001465 199.998657 200.001221 199.998886 200.001007 199.999084 200.000839 199.999237 200.000702 199.999359 200.000580 199.999451 200.000488 199.999542 200.000397 199.999619 200.000336 199.999680 200.000275 199.999725 200.000229 199.999756 200.000198 199.999802 200.000168 199.999832 200.000137 199.999863 200.000107 199.999893 200.000092 199.999908 200.000076 199.999924 200.000061 199.999939 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.999954 200.000046 199.9999