Adding text line in Equation Environment

Question

I am a new user in LaTex. 1. Can someone please help me what wrong is with this code.

\begin{equation*}
T_{Loop Filter}(s)=K_{p}+\frac{K_{i}}{s}\\
The overall transfer function of given PLL can be given as\\
\frac{{\phi}_{c}(s)}{{\phi}(s)}=\frac{T_{Loop Filter}(s)*\frac{1}{s}}{1+\frac{T_{Loop Filter}(s)*\frac{1}{s}}\\
\frac{\phi_{c}(s)}{\phi(s)}=\frac{K_{p}(s)+K_{i}}{s^{2}+K_{p}(s)+K_{i}}\\
In general transfer function for a second order closed loop control system is given as\\
T_{second order}=\frac{{\omega}^2+{2{\delta}{\omega}s}{s_{2}+2{\delta}{\omega}s+{\omega}^{2}}\\
On comparing {\omega}={sqrt{K_i}}  {\delta}=\frac{K_p}{2\sqrt{K_{i}}}
\end{equation*}

I am getting following error

"Runaway argument? {1+\frac {T_{Loop Filter}(s)*\frac {1}{s}}\ \frac {\phi _{c}(s)}{\phi \ETC. ! File ended while scanning use of \frac

2. What is the professional way to write equations for research paper(\begin{equation} or \begin{eqnarray} or $$ or \begin{OtherStyle}
3. Can we add text line directly in inside \begin{equation} environment without any commands
4. How to use center aligned(Under \begin{equation}) as well as align with respect to particular character(\begin{Align}) in equation environment.

Answer 1

I think flalign* and \intertext{} are very good for you.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{flalign*}
& & T_{Loop Filter}(s)&=K_{p}+\frac{K_{i}}{s} & & \\
\intertext{The overall transfer function of given PLL can be given as}
& & \frac{{\phi}_{c}(s)}{{\phi}(s)}&=\frac{T_{Loop Filter}(s)*\frac{1}{s}}{1+\frac{T_{Loop Filter}}(s)*\frac{1}{s}} & & \\
& & \frac{\phi_{c}(s)}{\phi(s)}&=\frac{K_{p}(s)+K_{i}}{s^{2}+K_{p}(s)+K_{i}} & & 
\intertext{In general transfer function for a second order closed loop control system is given as}
& & T_{second order}&=\frac{{\omega}^2+{2{\delta}}{\omega}s}{s_{2}+2{\delta}{\omega}s+{\omega}^{2}} & & \\
& \rlap{\text{On comparing}} & {\omega}&={sqrt{K_i}}  {\delta}=\frac{K_p}{2\sqrt{K_{i}}} & &
\end{flalign*}
\end{document}

Answer 2

You have a misssing } in your code.

This should work:

\[
T_{Loop Filter}(s)=K_{p}+\frac{K_{i}}{s}
\]
The overall transfer function of given PLL can be given as
\[
\frac{{\phi}_{c}(s)}{{\phi}(s)}=\frac{T_{Loop Filter}(s)*\frac{1}{s}}{1+\frac{T_{Loop Filter}}(s)*\frac{1}{s}}
\]
\[
\frac{\phi_{c}(s)}{\phi(s)}=\frac{K_{p}(s)+K_{i}}{s^{2}+K_{p}(s)+K_{i}}
\]
In general transfer function for a second order closed loop control system is given as
\[
T_{second order}=\frac{{\omega}^2+{2{\delta}}{\omega}s}{s_{2}+2{\delta}{\omega}s+{\omega}^{2}}
\]
On comparing
\[ 
{\omega}={sqrt{K_i}}  {\delta}=\frac{K_p}{2\sqrt{K_{i}}}
\]

I don't try all } so some could be added.

Answer 3

Can i use $ Equation $ inside and outside \intertext{} under flalign{} environment .Because of these two lines my all equations got justified to left.Please help in this regard Before adding it is properly justified wrt center \begin{flalign*} & & \frac{Y(s)}{R(s)}&=\frac{{\omega}^2+{2{\delta}}{\omega}{s}}{s^{2}+2{\delta}{\omega}{s}+{\omega}^{2}} & & \ \end{flalign*} After adding bellow text, instead of center it is justified toward left {\intertext{On comparing}} ${\omega}={\sqrt{K_i}}$ \quad ${\delta}=\frac{K_p}{2\sqrt{K_{i}}}$\