pid 公式

1. 离散位置式 PID 公式：

u(k) = k_{p}(error(k) + \frac{T}{T_{i}}\sum_{j = 0}^{k}error(j) + \frac{^{T_{d}}}{T}(error(k) - error(k - 1))) 
= k_{p}error(k) + k_{i}\sum_{j = 0}^{k}error(j)T + k_{d}\frac{error(k) - error(k - 1)}{T}

其中

k_{i} = \frac{k_{p}}{T_{i}}, k_{d} = \frac{k_{p}}{T_{d}}

2. 增量式 PID 公式

\triangle u(k) = k_{p}(error(k) - error(k - 1)) + k_{i}error(k) + k_{d}(error(k) - 2error(k - 1) + error(k - 2))

备注：

PID 调参可以参考以下网页： https://www.cnblogs.com/qsyll0916/p/8580211.html https://www.cnblogs.com/sasasatori/p/11672918.html https://www.moz8.com/thread-36004-1-1.html https://www.cirmall.com/bbs/thread-32321-1-3.html https://www.stmcu.org.cn/module/forum/thread-601133-1-1.html https://wenku.baidu.com/view/558921c7d5bbfd0a79567351.html https://blog.csdn.net/zhaoyuaiweide/article/details/54572569 https://www.cnblogs.com/dustinzhu/p/3892128.html https://www.amobbs.com/thread-5575823-1-1.html?_dsign=b5dd56b7 https://blog.csdn.net/guanjianhe/article/details/76438219 https://www.arduino.cn/forum.php?mod=viewthread&tid=12813&highlight=pid https://www.arduino.cn/forum.php?mod=viewthread&tid=94294&extra=&highlight=pid&page=1 还有电机的说明和编码器的说明。