PID 参数整定公式参考

以 \(K_p\) 的更新为例，

\[ E=\frac{1}{2}(y-r)^2 \]

\[ \begin{align} \frac{\partial{E}}{\partial{K_p}}&=\frac{\partial{E}}{\partial{y}}\frac{\partial{y}}{\partial{(ku)}}\frac{\partial{(ku)}}{\partial{u}}\frac{\partial{u}}{\partial{K_p}} \\&=(y-r)sgn(n)K (r-y) \end{align} \]

\[ \Delta K_p=-\eta \frac{\partial{E}}{\partial{K_p}} \]

\[ K_p'=K_p+\Delta K_p \]