https://rootloc.us/posts/ Recent content in Posts on rootloc.us Hugo -- gohugo.io en-us © FL Sat, 12 Nov 2022 00:00:00 +0000 https://rootloc.us/posts/nyquist/ Sat, 12 Nov 2022 00:00:00 +0000 https://rootloc.us/posts/nyquist/ The Nyquist criterion is one of the most powerful tools in classical Control Theory, but if not properly understood it might be “hard” to remember, at least, it was for me. Let’s look at the formula: $$\boxed{N=Z-P}$$ Where: $N$ is the number encirclement of the critical point $-1$. We count positively the clockwise encirclement and negatively the counterclockwise encirclements. $P$ is the number of poles in the right half plane of the open loop transfer function. https://rootloc.us/posts/mass_spring_damper_101/ Mon, 01 Jan 0001 00:00:00 +0000 https://rootloc.us/posts/mass_spring_damper_101/ The model of the Mass-Spring-Damper system is a very simple (and yet useful) one. It can be used to understand a lot of concepts in Dynamical Systems, and to model more complex systems (like car suspensions) in a pretty accurate way. According to Newton’s second law we can write the equation of forces in this way: $$ m\textbf{a}=\Sigma \textbf{F} $$ The acceleration is the second derivative of our state variable x(t), $\Sigma \textbf{F}$ is the sum of the elastic force imposed by the linear spring (Hooke’s law), the viscous damping force imposed by the linear damper and the input force u(t).