[Tex/LaTex] Adding text line in Equation Environment

equations

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

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

Best Answer

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}
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