pid.h File Reference

proportional integral derivative controller More...

#include "a.h"

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Data Structures
struct	a_pid
	instance structure for PID controller More...

Macros
#define	a_pid_init(ctx)
	initialize for PID controller

Typedefs
typedef struct a_pid	a_pid
typedef struct a_pid	a::pid

Functions
void	a_pid_set_kpid (a_pid *ctx, a_real kp, a_real ki, a_real kd)
	set proportional integral derivative constant for PID controller
a_real	a_pid_run (a_pid *ctx, a_real set, a_real fdb)
	compute for PID controller
a_real	a_pid_pos (a_pid *ctx, a_real set, a_real fdb)
	compute for positional PID controller
a_real	a_pid_inc (a_pid *ctx, a_real set, a_real fdb)
	compute for incremental PID controller
void	a_pid_zero (a_pid *ctx)
	zeroing for PID controller

Detailed Description

proportional integral derivative controller

A proportional integral derivative controller (PID controller or three-term controller) is a control loop mechanism employing feedback that is widely used in industrial control systems and a variety of other applications requiring continuously modulated control.

$$u(t)=K_p[e(t)+\frac{1}{T_i}\int e(t)\text{dt}+T_d\frac{\text{d}e(t)}{\text{d}t}]$$

$$u(k)=K_p[e(k)+\frac{T}{T_i}\sum _{i=0}^{k}e(i)+\frac{T_d}{T}[e(k)-e(k-1)]]$$

• positional PID controller

  $$\begin{array}{rl}u(k)& =K_{p}e(k)+q\sum _{i=0}^k{K}_{i}e(i)+K_d[e(k)-e(k-1)]\\ & =(K_p+K_d)e(k)+q\sum _{i=0}^k{K}_{i}e(i)+(-K_d)e(k-1)\\ & \{\begin{array}{ll}q=0& |\sum _{i=0}^{k-1}{K}_{i}e(i)|>E\bigvee [\sum _{i=0}^{k-1}{K}_{i}e(i)]K_{k}e(k)>0\\ q=1\end{array}\end{array}$$

• incremental PID controller

  $$\begin{array}{rl}\mathrm{\Delta }u(k)& =K_p[e(k)-e(k-1)]+K_{i}e(k)+K_d[e(k)+e(k-2)-2e(k-1)]\\ & =(K_p+K_i+K_d)e(k)+(-K_p-2K_i)e(k-1)+K_{d}e(k-2)\end{array}$$

  https://en.wikipedia.org/wiki/PID_controller