pid的差分方程为
U（n）=U（n-1）+Kp(En-E(n-1)+Ki*En+Kd(En-2E(n-1)+E(n-2)))
Un为输出
En为输入
简单些就是
u(k)=u(k-1)+a*e(k)-b*e(k-1)+c*e(k-2)
u(k)是当前要输出的duty cycle
e(k)是当前误差。
a b c是控制参数，
其实可以用查表法，这样就不用耗时的乘法了，查表一加就得下一个dutycycle的值。

　　＃i nclude <stdio.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++;
　　
　　 }
　　
　　}

自己调试过，希望你能看得明白