*Monday, Sep 24, 2018* | 4 min read

In modern control approaches, systems are analyzed in time domain as a set of differential equations. Higher order differential equations are decomposed into sets of first order equations of state variables that represent the system internally. This produces three sets of variables:
Input variables are stimuli given to the system. Denoted by $u$. Output variables are the result of the current system state and inputs. Denoted by $y$. State variables represent the internal state of a system which may be obscured in the output variables.

*Friday, Sep 21, 2018* | 4 min read

A transfer function relates the output of a system to its input when it is represented in the Laplace domain. An assumption is made that initial steady-state response is 0. If $Y(s)$ is the output of a system, $X(s)$ is the input, then the transfer function is:
$$ H(s) = \frac{Y(s)}{X(s)} $$
Example - A Car A car as a system: The input is the acceleration. The output is the total distance travelled.

*Monday, Sep 10, 2018* | 5 min read

Classical control methods simplify handling of a complex system by representing it in a different domain. The equations governing system dynamics are transformed into a different set of variables. A for a function $f(t)$ in the $t$ domain, an oft used transformation is of the form:
$$ \mathcal{T}(f(t)) = F(s) = \int_{Domain} f(t) \cdot g(s, t)\; dt $$
Mathematically, the integral removes the $t$ variable and only leaves $s$, thus converting from the $t$ domain to the $s$ domain.

*Monday, Sep 10, 2018* | 4 min read

A primer for classical control theory.

*Monday, Apr 30, 2018* | 6 min read

Hugo is a static site generator. It takes a bunch of markdown files and renders them to HTML. It is fast and simple.
Jupyter Notebooks are an interactive front-end for python (with support for other languages too). They execute code, display its output, and render markdown all in a browser window. The notebooks are a neat compilation of formatted code and text generated as HTML.
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