Control System Requirements

$$\frac{1}{1-\frac{1}{\left(1+\mathit{TD}\right)}}=\frac{\left(1+\mathit{TD}\right)}{D}.$$

$$\left(\frac{K_{\mathrm{I}}}{D}+K_{\mathrm{P}}\right)=\frac{K_I\left(1+\frac{K_{\mathrm{P}}}{K_{\mathrm{I}}}D\right)}{D}\text{or}\frac{K_{\mathrm{I}}\left(1+\mathit{TD}\right)}{D}$$