PID控制算法的C语言实现(完整版).doc

PID控制算法的C语言实现一 PID算法原理 最近两天在考虑一般控制算法的C语言实现问题，发现网络上尚没有一套完整的比较体系的讲解。于是总结了几天，整理一套思路分享给大家。 在工业应用中PID及其衍生算法是应用最广泛的算法之一，是当之无愧的万能算法，如果能够熟练掌握PID算法的设计与实现过程，对于一般的研发人员来讲，应该是足够应对一般研发问题了，而难能可贵的是，在我所接触的控制算法当中，PID控制算法又是最简单，最能体现反馈思想的控制算法，可谓经典中的经典。经典的未必是复杂的，经典的东西常常是简单的，而且是最简单的，想想牛顿的力学三大定律吧，想想爱因斯坦的质能方程吧，何等的简单！简单的不是原始的，简单的也不是落后的，简单到了美的程度。先看看PID算法的一般形式： PID的流程简单到了不能再简单的程度，通过误差信号控制被控量，而控制器本身就是比例、积分、微分三个环节的加和。这里我们规定（在t时刻）： 1.输入量为rin(t); 2.输出量为rout(t); 3.偏差量为err(t)=rin(t)-rout(t); pid的控制规律为 理解一下这个公式，主要从下面几个问题着手，为了便于理解，把控制环境具体一下： 1.规定这个流程是用来为直流电机调速的; 2.输入量rin(t)为电机转速预定值; 3.输出量rout(t)为电机转速实际值; 4.执行器为直流电机; 5.传感器为光电码盘，假设码盘为10线; 6.直流电机采用PWM调速 转速用单位 转/min 表示; 不难看出以下结论： 1.输入量rin（t）为电机转速预定值（转/min）; 2. 输出量rout(t)为电机转速实际值（转/min）; 3.偏差量为预定值和实际值之差（转/min）; 那么以下几个问题需要弄清楚： 1.通过PID环节之后的U(t)是什么值呢？ 2.控制执行器（直流电机）转动转速应该为电压值（也就是PWM占空比）。 3.那么U(t)与PWM之间存在怎样的联系呢？/user1/3407/archives/2006/33541.html（见附录1）这篇文章上给出了一种方法，即，每个电压对应一个转速，电压和转速之间呈现线性关系。但是我考虑这种方法的前提是把直流电机的特性理解为线性了，而实际情况下，直流电机的特性绝对不是线性的，或者说在局部上是趋于线性的，这就是为什么说PID调速有个范围的问题。具体看一下/component/article90249.htm（见附录2）这篇文章就可以了解了。所以在正式进行调速设计之前，需要现有开环系统，测试电机和转速之间的特性曲线（或者查阅电机的资料说明），然后再进行闭环参数整定。这篇先写到这，下一篇说明连续系统的离散化问题。并根据离散化后的特点讲述位置型PID和增量型PID的用法和C语言实现过程。PID控制算法的C语言实现二 PID算法的离散化 上一节中，我论述了PID算法的基本形式，并对其控制过程的实现有了一个简要的说明，通过上一节的总结，基本已经可以明白PID控制的过程。这一节中先继续上一节内容补充说明一下。 1.说明一下反馈控制的原理，通过上一节的框图不难看出，PID控制其实是对偏差的控制过程; 2.如果偏差为0,则比例环节不起作用，只有存在偏差时，比例环节才起作用。 3.积分环节主要是用来消除静差，所谓静差，就是系统稳定后输出值和设定值之间的差值，积分环节实际上就是偏差累计的过程，把累计的误差加到原有系统上以抵消系统造成的静差。 4.而微分信号则反应了偏差信号的变化规律，或者说是变化趋势，根据偏差信号的变化趋势来进行超前调节，从而增加了系统的快速性。 好了，关于PID的基本说明就补充到这里，下面将对PID连续系统离散化，从而方便在处理器上实现。下面把连续状态的公式再贴一下： 假设采样间隔为T，则在第K T时刻：偏差err(K)=rin(K)-rout(K);积分环节用加和的形式表示，即err(K)+err(K+1)+;微分环节用斜率的形式表示，即err(K)-err(K-1)/T;从而形成如下PID离散表示形式：则u(K)可表示成为：至于说Kp、Ki、Kd三个参数的具体表达式，我想可以轻松的推出了，这里节省时间，不再详细表示了。其实到这里为止，PID的基本离散表示形式已经出来了。目前的这种表述形式属于位置型PID，另外一种表述方式为增量式PID，由U上述表达式可以轻易得到：那么：这就是离散化PID的增量式表示方式，由公式可以看出，增量式的表达结果和最近三次的偏差有关，这样就大大提高了系统的稳定性。需要注意的是最终的输出结果应该为u(K)+增量调节值;PID的离散化过程基本思路就是这样，下面是将离散化的公式转换成为C语言，从而实现微控制器的控制作用。PID控制算法的C语言实现三 位置型PID的C语言实现 上一节中已经抽象出了位置性PID和增量型PID的数学表达式，这一节，重点讲解C语言代码的实现过程，算法的C语言实现过程具有一般性，通过PID算法的C语言实现，可以以此类推，设计其它算法的C语言实现。 第一步：定义PID变量结构体，代码如下：struct _pid float SetSpeed; /定义设定值 float ActualSpeed; /定义实际值 float err; /定义偏差值 float err_last; /定义上一个偏差值 float Kp,Ki,Kd; /定义比例、积分、微分系数 float voltage; /定义电压值（控制执行器的变量） float integral; /定义积分值pid;控制算法中所需要用到的参数在一个结构体中统一定义，方便后面的使用。 第二部：初始化变量，代码如下：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; egral=0.0; pid.Kp=0.2; pid.Ki=0.015; pid.Kd=0.2; printf(PID_init end n);统一初始化变量，尤其是Kp,Ki,Kd三个参数，调试过程当中，对于要求的控制效果，可以通过调节这三个量直接进行调节。第三步：编写控制算法，代码如下：float PID_realize(float speed) pid.SetSpeed=speed; pid.err=pid.SetSpeed-pid.ActualSpeed; egral+=pid.err; pid.voltage=pid.Kp*pid.err+pid.Ki*egral+pid.Kd*(pid.err-pid.err_last); pid.err_last=pid.err; pid.ActualSpeed=pid.voltage*1.0; return pid.ActualSpeed;注意：这里用了最基本的算法实现形式，没有考虑死区问题，没有设定上下限，只是对公式的一种直接的实现，后面的介绍当中还会逐渐的对此改进。 到此为止，PID的基本实现部分就初步完成了。下面是测试代码：int main() printf(System begin n); PID_init(); int count=0; while(count1000) float speed=PID_realize(200.0); printf(%fn,speed); count+; return 0;下面是经过1000次的调节后输出的1000个数据（具体的参数整定过程就不说明了，网上这种说明非常多）：83.00000111.55500059.55967528.17540852.90742138.94415251.89169946.14165153.33905451.50999855.90845055.94463158.97068059.88293662.22500163.53725465.52770767.01105868.81064670.35531872.04204073.59565875.20762076.74544478.30152679.81213681.32192982.80030484.26890985.71310887.14345588.55300589.94696091.32207892.68099694.02223495.34718696.65524297.94718099.222808100.482601101.726572102.955049104.168125105.366066106.549019107.717187108.870756110.009898111.134811112.245652113.342615114.425860115.495564116.551897117.595029118.625116119.642331120.646826121.638767122.618307123.585603124.540813125.484079126.415549127.335383128.243715129.140691130.026459130.901149131.764909132.617870133.460162134.291942135.113308135.924419136.725382137.516332138.297401139.068697139.830352140.582499141.325237142.058701142.782985143.498218144.204509144.901969145.590726146.270843146.942486147.605718148.260674148.907425149.546109150.176794150.799612151.414626152.021959152.621696153.213951153.798781154.376315154.946626155.509812156.065958156.615146157.157471157.693012158.221871158.744097159.259826159.769078160.271991160.768588161.258996161.743264162.221494162.693737163.160075163.620593164.075347164.524422164.967877165.405795165.838235166.265257166.686967167.103377167.514610167.920681168.321682168.717670169.108719169.494862169.876198170.252740170.624605170.991799171.354406171.712487172.066080172.415265172.760077173.100594173.436838173.768895174.096796174.420594174.740352175.056096175.367915175.675818175.979886176.280136176.576656176.869444177.158600177.444121177.726087178.004510178.279458178.550967178.819094179.083860179.345315179.603504179.858466180.110241180.358866180.604388180.846849181.086262181.322699181.556172181.786733182.014396182.239222182.461226182.680475182.896971183.110768183.321881183.530369183.736239183.939545184.140301184.338555184.534321184.727651184.918558185.107080185.293243185.477080185.658625185.837886186.014930186.189745186.362382186.532859186.701207186.867437187.031605187.193713187.353802187.511884187.667997187.822151187.974384188.124700188.273148188.419728188.564488188.707429188.848592188.987995189.125644189.261576189.395801189.528364189.659258189.788528189.916170190.042233190.166702190.289633190.411007190.530867190.649236190.766119190.881544190.995531191.108087191.219243191.329005191.437382191.544428191.650111191.754504191.857565191.959350192.059857192.159119192.257135192.353919192.449511192.543890192.637105192.729137192.820032192.909776192.998410193.085920193.172360193.257700193.341993193.425214193.507408193.588568193.668715193.747847193.826004193.903175193.979391194.054643194.128963194.202349194.274828194.346393194.417073194.486854194.555777194.623820194.691027194.757390194.822919194.887626194.951536195.014633195.076965195.138496195.199273195.259270195.318547195.377060195.434856195.491918195.548283195.603919195.658886195.713145195.766734195.819654195.871912195.923517195.974472196.024791196.074478196.123558196.172016196.219859196.267115196.313778196.359851196.405363196.450296196.494672196.538492196.581753196.624494196.666678196.708363196.749493196.790138196.830267196.869889196.909019196.947656196.985803197.023493197.060701197.097449197.133733197.169558197.204940197.239872197.274378197.308436197.342089197.375309197.408125197.440523197.472520197.504114197.535309197.566127197.596546197.626594197.656258197.685546197.714486197.743047197.771265197.799113197.826629197.853799197.880631197.907131197.933284197.959122197.984629198.009823198.034705198.059275198.083520198.107481198.131129198.154493198.177566198.200349198.222843198.245062198.267001198.288662198.310059198.331178198.352049198.372645198.392982198.413066198.432911198.452499198.471846198.490953198.509819198.528439198.546842198.565003198.582945198.600648198.618147198.635415198.652474198.669313198.685955198.702378198.718611198.734625198.750448198.766067198.781497198.796736198.811776198.826628198.841303198.855788198.870087198.884218198.898162198.911943198.925538198.938970198.952229198.965320198.978257198.991033199.003643199.016092199.028390199.040542199.052536199.064373199.076067199.087617199.099019199.110280199.121407199.132381199.143240199.153940199.164511199.174957199.185270199.195457199.205514199.215440199.225262199.234930199.244503199.253928199.263275199.272468199.281571199.290541199.299421199.308165199.316815199.325345199.333789199.342115199.350336199.358462199.366479199.374396199.382228199.389943199.397586199.405110199.412555199.419891199.427152199.434307199.441389199.448363199.455264199.462073199.468802199.475442199.481995199.488475199.494857199.501183199.507404199.513578199.519639199.525656199.531579199.537437199.543230199.548936199.554583199.560149199.565647199.571073199.576436199.581730199.586961199.592118199.597220199.602260199.607218199.612132199.616974199.621764199.626486199.631156199.635757199.640316199.644808199.649249199.653636199.657959199.662246199.666457199.670635199.674752199.678815199.682833199.686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461199.999473PID控制算法的C语言实现四 增量型PID的C语言实现 上一节中介绍了最简单的位置型PID的实现手段，这一节主要讲解增量式PID的实现方法，位置型和增量型PID的数学公式请参见我的系列文PID控制算法的C语言实现二中的讲解。实现过程仍然是分为定义变量、初始化变量、实现控制算法函数、算法测试四个部分，详细分类请参加PID控制算法的C语言实现三中的讲解，这里直接给出代码了。#include#includestruct _pid float SetSpeed; /定义设定值 float ActualSpeed; /定义实际值 float err; /定义偏差值 float err_next; /定义上一个偏差值 float err_last; /定义最上前的偏差值 float Kp,Ki,Kd; /定义比例、积分、微分系数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(count1000) float speed=PID_realize(200.0); printf(%fn,speed); count+; return 0;运行后的1000个数据为：83.00000011.55500059.55967728.17540652.90742538.94414951.89170146.14165553.33905051.51000255.90844755.94463758.97067659.88294262.22499863.53724765.52770267.01104768.81063870.35530972.04202373.59564275.20760376.74543078.30151479.81212681.32191582.80029384.26889885.71309787.14344088.55299489.94694591.32206792.68097794.02222495.34717696.65523597.94717499.222801100.482597101.726562102.955040104.168114105.366058106.549004107.717178108.870743110.009888111.134796112.245636113.342598114.425842115.495552116.551880117.595009118.625099119.642311120.646812121.638756122.618294123.585594124.540794125.484062126.415535127.335365128.243698129.140671130.026443130.901138131.764893132.617859133.460159134.291931135.113297135.924408136.725372137.516327138.297394139.068695139.830353140.582489141.325226142.058685142