Ibrahim Ahmed

Electrical Engineering @ Vanderbilt University

Modern control: State space equations

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.

Classical control: Transfer functions

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.

Classical control: Transforms

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.

Control Systems: Overview

Monday, Sep 10, 2018 | 4 min read
A primer for classical control theory.

Hugo and Jupyter Notebooks

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. I use Hugo for my site.