I have an issue with aligning some math expressions. Is it possible to make some expressions aligned to "&" sign and some to the center of the page with align? I've done it as seen in the screenshot but there are some empty lines in between. I would like to align the first and the second last line to center and the rest to "&" sign without the empty spaces. Thank you in advance
\begin{gather}
|e(t)| \leq e_{lim} \Rightarrow t \in \left\langle t_{set}; \infty\right) \label{eq:settling_time}
\end{gather}
\begin{align}
\left|\frac{1}{K_p\cdot K_s - p_1}\cdot \left[K_p\cdot K_s\cdot e^{(p_1 - K_p\cdot K_s)\cdot t} - p_1\right]\right| &\leq e_{lim} \nonumber \\
\frac{1}{K_p\cdot K_s - p_1}\cdot \left[K_p\cdot K_s\cdot e^{(p_1 - K_p\cdot K_s)\cdot t} - p_1\right] &> 0; \quad t \in \mathbb{R}_0^+ \nonumber \\
\frac{1}{K_p\cdot K_s - p_1}\cdot \left[K_p\cdot K_s\cdot e^{(p_1 - K_p\cdot K_s)\cdot t} - p_1\right] &\leq e_{lim} \nonumber \\
K_p\cdot K_s\cdot e^{(p_1 - K_p\cdot K_s)\cdot t} - p_1 &\leq e_{lim}\cdot (K_p\cdot K_s - p_1) \nonumber \\
K_p\cdot K_s\cdot e^{(p_1 - K_p\cdot K_s)\cdot t} &\leq e_{lim}\cdot (K_p\cdot K_s - p_1) + p_1 \nonumber \\
e^{(p_1 - K_p\cdot K_s)\cdot t} &\leq \frac{e_{lim}\cdot (K_p\cdot K_s - p_1) + p_1}{K_p\cdot K_s} \nonumber \\
(p_1 - K_p\cdot K_s)\cdot t &\leq \ln \left[\frac{e_{lim}\cdot (K_p\cdot K_s - p_1) + p_1}{K_p\cdot K_s}\right] \nonumber \\
t &\geq \frac{\displaystyle \ln \left[\frac{\displaystyle e_{lim}\cdot (K_p\cdot K_s - p_1) + p_1}{\displaystyle K_p\cdot K_s}\right]}{\displaystyle p_1 - K_p\cdot K_s} \nonumber
\end{align}
\begin{gather}
t \in \Bigg \langle \frac{\displaystyle \ln \left[\frac{\displaystyle e_{lim}\cdot (K_p\cdot K_s - p_1) + p_1}{\displaystyle K_p\cdot K_s}\right]}{\displaystyle p_1 - K_p\cdot K_s}; \infty \Bigg) \in \left\langle t_{set}; \infty \right) \nonumber \\
t_{set} = \frac{\displaystyle \ln \left[\frac{\displaystyle e_{lim}\cdot (K_p\cdot K_s - p_1) + p_1}{\displaystyle K_p\cdot K_s}\right]}{\displaystyle p_1 - K_p\cdot K_s} \label{eq:settling_time_1st_order_P_reg}
\end{gather}
2 Answers
You can set the aligned components within the gather using aligned:
\documentclass{article}
\usepackage{amsmath,amssymb}
\begin{document}
\begin{gather}
| e(t) | \leq e_{\text{lim}} \Rightarrow t \in \langle t_{\text{set}}; \infty ) \\
\begin{aligned}
\biggl| \frac{1}{K_p \cdot K_s - p_1} \cdot \bigl[ K_p \cdot K_s \cdot e^{(p_1 - K_p \cdot K_s) \cdot t} - p_1 \bigr] \biggr| &
\leq e_{\text{lim}} \\
\frac{1}{K_p \cdot K_s - p_1} \cdot \bigl[ K_p \cdot K_s \cdot e^{(p_1 - K_p \cdot K_s) \cdot t} - p_1 \bigr] &
> 0; \quad t \in \mathbb{R}_0^+ \\
\frac{1}{K_p \cdot K_s - p_1} \cdot \bigl[ K_p \cdot K_s \cdot e^{(p_1 - K_p \cdot K_s) \cdot t} - p_1 \bigr] &
\leq e_{\text{lim}} \\
K_p \cdot K_s \cdot e^{(p_1 - K_p \cdot K_s) \cdot t} - p_1 &
\leq e_{\text{lim}} \cdot (K_p \cdot K_s - p_1) \\
K_p \cdot K_s \cdot e^{(p_1 - K_p \cdot K_s) \cdot t} &
\leq e_{\text{lim}} \cdot (K_p \cdot K_s - p_1) + p_1 \\
e^{(p_1 - K_p \cdot K_s) \cdot t} &
\leq \frac{e_{\text{lim}} \cdot (K_p \cdot K_s - p_1) + p_1}{K_p \cdot K_s} \\
(p_1 - K_p \cdot K_s) \cdot t &
\leq \ln \biggl[ \frac{e_{\text{lim}} \cdot (K_p \cdot K_s - p_1) + p_1}{K_p \cdot K_s} \biggr] \\
t &
\geq \frac{\ln \biggl[ \dfrac{e_{\text{lim}} \cdot (K_p \cdot K_s - p_1) + p_1}{K_p \cdot K_s} \biggr]}{p_1 - K_p \cdot K_s}
\end{aligned} \nonumber \\
t \in \Bigg \langle \frac{ \ln \biggl[ \dfrac{e_{\text{lim}} \cdot (K_p \cdot K_s - p_1) + p_1}{K_p \cdot K_s} \biggr]}{p_1 - K_p \cdot K_s}; \infty \Bigg) \in \langle t_{\text{set}}; \infty ) \nonumber \\
t_{\text{set}} = \frac{\ln \biggl[ \dfrac{e_{\text{lim}} \cdot (K_p \cdot K_s - p_1) + p_1}{K_p \cdot K_s} \biggr]}{p_1 - K_p \cdot K_s}
\end{gather}
\end{document}
I would suggest using the \IEEEeqnarray environment. If you use the * version of this, you can get rid of all the \nonumber commands (9 in this case) and insert \yesnumber commands (2 in this case) where equation no is necessary.
\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{IEEEtrantools}
%-------Shows page layout-------------------
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.15pt}
\renewcommand*\ShowFrameColor{\color{red}}
%-------------------------------------------
\begin{document}
\begin{IEEEeqnarray*}{rcl}
\IEEEeqnarraymulticol{3}{c}{|e(t)| \leq e_{lim} \Rightarrow t \in \left\langle t_{set}; \infty\right)} \yesnumber \label{eq:settling_time}\\
\left|\frac{1}{K_p\cdot K_s - p_1}\cdot \left[K_p\cdot K_s\cdot e^{(p_1 - K_p\cdot K_s)\cdot t} - p_1\right]\right| & \leq & e_{lim} \\
\frac{1}{K_p\cdot K_s - p_1}\cdot \left[K_p\cdot K_s\cdot e^{(p_1 - K_p\cdot K_s)\cdot t} - p_1\right] & > & 0; \quad t \in \mathbb{R}_0^+ \\
\frac{1}{K_p\cdot K_s - p_1}\cdot \left[K_p\cdot K_s\cdot e^{(p_1 - K_p\cdot K_s)\cdot t} - p_1\right] & \leq & e_{lim} \\
K_p\cdot K_s\cdot e^{(p_1 - K_p\cdot K_s)\cdot t} - p_1 & \leq & e_{lim}\cdot (K_p\cdot K_s - p_1) \\
K_p\cdot K_s\cdot e^{(p_1 - K_p\cdot K_s)\cdot t} & \leq & e_{lim}\cdot (K_p\cdot K_s - p_1) + p_1 \\
e^{(p_1 - K_p\cdot K_s)\cdot t} & \leq & \frac{e_{lim}\cdot (K_p\cdot K_s - p_1) + p_1}{K_p\cdot K_s} \\
(p_1 - K_p\cdot K_s)\cdot t & \leq & \ln \left[\frac{e_{lim}\cdot (K_p\cdot K_s - p_1) + p_1}{K_p\cdot K_s}\right] \\
t & \geq & \frac{\displaystyle \ln \left[\frac{\displaystyle e_{lim}\cdot (K_p\cdot K_s - p_1) + p_1}{\displaystyle K_p\cdot K_s}\right]}{\displaystyle p_1 - K_p\cdot K_s} \\
\IEEEeqnarraymulticol{3}{c}{t \in \Bigg \langle \frac{\displaystyle \ln \left[\frac{\displaystyle e_{lim}\cdot (K_p\cdot K_s - p_1) + p_1}{\displaystyle K_p\cdot K_s}\right]}{\displaystyle p_1 - K_p\cdot K_s}; \infty \Bigg) \in \left\langle t_{set}; \infty \right)} \\
\IEEEeqnarraymulticol{3}{c}{t_{set} = \frac{\displaystyle \ln \left[\frac{\displaystyle e_{lim}\cdot (K_p\cdot K_s - p_1) + p_1}{\displaystyle K_p\cdot K_s}\right]}{\displaystyle p_1 - K_p\cdot K_s}} \yesnumber \label{eq:settling_time_1st_order_P_reg}
\end{IEEEeqnarray*}
\end{document}
Appendix F of this document covers the use of the IEEEeqnarray commands.
As mentioned in the comment, you may find quicker responses in TEX.SE
