The transfer function $(H(s))$ of a system (usually defined by a differential equation) can be thought of as the dynamic gain of a system.
The DC Gain occurs when $s=0$.
The Multiplier Gain is the constant in the zero-pole form.
This document is a compilation of my notes for ELE 639: Control Systems at TMU. All information comes from my professor’s lectures, as well as the course textbook Control Systems Engineering by Norman S.
Adam Szava - 2tor.ca
W2023
The transfer function $(H(s))$ of a system (usually defined by a differential equation) can be thought of as the dynamic gain of a system.
The DC Gain occurs when $s=0$.
The Multiplier Gain is the constant in the zero-pole form.
<aside> ➕ Initial Value Theorem
This theorem is used to determine the value of the time function when $t=0$, without finding the inverse Laplace, by:
$$ \lim_{t\to 0 }x(t)=\lim_{s\to\infty}s\cdot X(s) $$
</aside>
<aside> ➕ Final Value Theorem
This theorem is used to determine the value of the time function when $t=\infty$ (steady-state), without finding the inverse Laplace, by:
$$ \lim_{t\to \infty }x(t)=\lim_{s\to 0}s\cdot X(s) $$
</aside>
A system is an object which possesses all three of the following properties:
Control is an action that has the following properties: