Another typical control problem: balancing a ball on a beam

Balancing a ball on a beam is not a common problem you may face during your everyday life, however, this simple example of engineering can be extended to more complex problems and, in general, to other more interesting control problems such as

• Control of temperature in a room
• Control of robots
• Control of automated cars
• Control of industrial processes

The main problem tackled in this article is the design and implementation of a basic PID based controller to control the position of a ping pong ball on a beam. Ideally the controller should be able to set the position to whatever value of the x axis the user decides to apply. This is a simple scheme of the physical system

Modelling a DC motor using LTspice, Simulink and Matlab

Electrically speaking, a permanent magnet DC motor can be modelled as follows:

applying LKT we obtain the following differential equation

$$v = Ri+L\frac{di}{dt}+e$$

where $R$ is the equivalent resistance of the brushes plus the windings, $L$ is the inductance as seen from the external terminals of the motor and $e$ is the back EMF. Usually R is very small and can be difficult to measure with a multimeter. The back EMF can be expressed as a function of the speed of the motor $e = k\phi\omega$.

Taylor series with Python and Sympy: Revised

More than 2 years ago I wrote a short post on Taylor series. The post featured a simple script that took a single variable function (a sine in the example), printed out the Taylor expansion up to the nth term and plotted the approximation along with the original function. As you can see on the right on the “Popular posts” bar, that post is one of the most popular and I’m told it appears among the first results on Google.

The script I wrote originally was a bit clunky, and there surely was room for improvement. Last week I received an email from a reader, Josh, who sent me an improved version of the original post.