PID算法

          在过程控制中，按偏差的比例（P）、积分（I）和微分（D）进行控制的PID控制器（亦称PID调节器）是应用最为广泛的一种自动控制器。它具有原理简单，易于实现，适用面广，控制参数相互独立，参数的选定比较简单等优点；而且在理论上可以证明，对于过程控制的典型对象──“一阶滞后＋纯滞后”与“二阶滞后＋纯滞后”的控制对象，PID控制器是一种最优控制。PID调节规律是连续系统动态品质校正的一种有效方法，它的参数整定方式简便，结构改变灵活（PI、PD、…）。
参数的选择：
     ①比例系数P对系统性能 的影响：比例系数加大，使系统的动作灵敏，速度加快，稳态误差减小；P偏大，振荡次数加多，调节时间加长；P太大时，系统会趋于不稳定；P太小，又会使系 统的动作缓慢。P可以选负数，这主要是由执行机构、传感器以及控制对象的特性决定的。如果P的符号选择不当对象测量值就会离控制目标的设定值越来越远，如 果出现这样的情况P的符号就一定要取反。同时要注意的是，力控的策略控制器的PID控制块的P参数是PID控制中的增益。
②积分控制I对系统性能的影响：积分作用使系统的稳定性下降，I小（积分作用强）会使系统不稳定，但能消除稳态误差，提高系统的控制精度。
③微分控制D对系统性能的影响：微分作用可以改善动态特性，D偏大时，超调量较大，调节时间较短；D偏小时，超调量也较大，调节时间也较长；只有D合适，才能使超调量较小，减短调节时间。

[转贴]C语言实现PID算法：
#include <stdio.h>
#include<math.h>

struct _pid {
int pv; /*integer that contains the process value*/
int sp; /*integer that contains the set point*/
float integral;
float pgain;
float igain;
float dgain;
int deadband;
int last_error;
};

struct _pid warm,*pid;
int process_point, set_point,dead_band;
float p_gain, i_gain, d_gain, integral_val,new_integ;;

/*------------------------------------------------------------------------
pid_init

DESCRIPTION This function initializes the pointers in the _pid structure
to the process variable and the setpoint. *pv and *sp are
integer pointers.
------------------------------------------------------------------------*/
void pid_init(struct _pid *warm, int process_point, int set_point)
{
struct _pid *pid;

pid = warm;
pid->pv = process_point;
pid->sp = set_point;
} 　　
/*------------------------------------------------------------------------
pid_tune

DESCRIPTION Sets the proportional gain (p_gain), integral gain (i_gain),
derivitive gain (d_gain), and the dead band (dead_band) of
a pid control structure _pid.
------------------------------------------------------------------------*/

void pid_tune(struct _pid *pid, float p_gain, float i_gain, float d_gain, int dead_band)
{
pid->pgain = p_gain;
pid->igain = i_gain;
pid->dgain = d_gain;
pid->deadband = dead_band;
pid->integral= integral_val;
pid->last_error=0;
}

/*------------------------------------------------------------------------
pid_setinteg

DESCRIPTION Set a new value for the integral term of the pid equation.
This is useful for setting the initial output of the
pid controller at start up.
------------------------------------------------------------------------*/
void pid_setinteg(struct _pid *pid,float new_integ)
{
pid->integral = new_integ;
pid->last_error = 0;
}

/*------------------------------------------------------------------------
pid_bumpless

DESCRIPTION Bumpless transfer algorithim. When suddenly changing
setpoints, or when restarting the PID equation after an
extended pause, the derivative of the equation can cause
a bump in the controller output. This function will help
smooth out that bump. The process value in *pv should
be the updated just before this function is used.
------------------------------------------------------------------------*/
void pid_bumpless(struct _pid *pid)
{ 　　
pid->last_error = (pid->sp)-(pid->pv); 　　
}

/*------------------------------------------------------------------------
pid_calc 　　
DESCRIPTION Performs PID calculations for the _pid structure *a. This function uses the positional form of the pid equation, and incorporates an integral windup prevention algorithim. Rectangular integration is used, so this function must be repeated on a consistent time basis for accurate control.

RETURN VALUE The new output value for the pid loop. 　　
USAGE #include "control.h"*/ 　　
float pid_calc(struct _pid *pid)
{
int err;
float pterm, dterm, result, ferror;

err = (pid->sp) - (pid->pv);
if (abs(err) > pid->deadband)
{
ferror = (float) err; /*do integer to float conversion only once*/
pterm = pid->pgain * ferror;
if (pterm > 100 || pterm < -100)
{
pid->integral = 0.0;
}
else
{
pid->integral += pid->igain * ferror;
if (pid->integral > 100.0)
{
pid->integral = 100.0;
}
else if (pid->integral < 0.0) pid->integral = 0.0;
}
dterm = ((float)(err - pid->last_error)) * pid->dgain;
result = pterm + pid->integral + dterm;
}
else result = pid->integral;
pid->last_error = err;
return (result);
}

void main(void)
{
float display_value;
int count=0;

pid = &warm;

// printf("Enter the values of Process point, Set point, P gain, I gain, D gain \n");
// scanf("%d%d%f%f%f", &process_point, &set_point, &p_gain, &i_gain, &d_gain);　　
process_point = 30;
set_point = 40;
p_gain = (float)(5.2);
i_gain = (float)(0.77);
d_gain = (float)(0.18);

dead_band = 2;
integral_val =(float)(0.01);

printf("The values of Process point, Set point, P gain, I gain, D gain \n");
printf(" %6d %6d %4f %4f %4f\n", process_point, set_point, p_gain, i_gain, d_gain);

printf("Enter the values of Process point\n");

while(count<=20)
{　　
scanf("%d",&process_point);　　
pid_init(&warm, process_point, set_point);
pid_tune(&warm, p_gain,i_gain,d_gain,dead_band);
pid_setinteg(&warm,0.0); //pid_setinteg(&warm,30.0);

//Get input value for process point
pid_bumpless(&warm);

// how to display output
display_value = pid_calc(&warm);
printf("%f\n", display_value);
//printf("\n%f%f%f%f",warm.pv,warm.sp,warm.igain,warm.dgain);
count++; 　
}

Karl Erik Arzen--PID Control:from argorithm to code