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, double kp, double ki, double kd)
	set proportional integral derivative constant for PID controller
double	a_pid_run (a_pid *ctx, double set, double fdb)
	calculate for PID controller
double	a_pid_pos (a_pid *ctx, double set, double fdb)
	calculate for positional PID controller
double	a_pid_inc (a_pid *ctx, double set, double fdb)
	calculate 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.

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

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

• positional PID controller

  \begin{aligned} u(k) &= K_p e(k) + q\sum^k_{i=0} K_i e(i) + K_d [e(k)-e(k-1)] \\ &= (K_p+K_d) e(k) + q\sum^k_{i=0}K_i e(i) + (-K_d) e(k-1) \\ &\begin{cases}q=0&|\sum\limits^{k-1}_{i=0}K_ie(i)|>E \bigvee [\sum\limits^{k-1}_{i=0}K_ie(i)]K_ke(k)>0 \\ q=1\end{cases} \end{aligned}

• incremental PID controller

  \begin{aligned} \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{aligned}

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