Have fun with Automatic Control

I recently kicked off a new project on the design of a Virtual Lab on Automatic Control. Some first experiments are already running online at vlab.mooo.info. Visitors of the web site will be able to play and experiment with closed and open loop systems involving a PID controller and a dynamical system with a time-delay. I have endeavoured to provide full configurability of the framework and allow the user to explore in depth the dynamics of a PID controller in a closed loop. The Bode and Nyquist Diagrams for the open loop system can be generated as well. The project is still in alpha phase (testing) but soon it will be released with more running virtual experiments (with animation and surprises). So... stay tuned (follow @isToxic on twitter for more news).

Notes on Set Convergence

Sequences of sets over a topological space define analogous convergence and boundness notions as sequences of vectors or numbers. Set convergence in the Painleve-Kuratowski sense provides a rigorous framework for the study of sequences of sets and the basis for the study of convergence properties of sequences of extended-real-valued functions and multi-valued mappings. In these notes we define the notions of inner and outer limits and we characterize them in the light of the underlying topology.