How to find the point on the root locus with a certain damping in Octave
May 13, 2023 at 12:03 pm
I don't have MatLab installed on my computer (and I don't know how to install it), so I am trying to do a laboratory exercise in Control Engineering in Octave. In that laboratory exercise, I am supposed to find the gain at the point on the root locus where damping is equal to 0.7. Octave does support the `rlocus` command, however, in the window where the root locus is opened, in the "Tools" menu, there is no "Data Tips" option (that the instructions for the laboratory exercise advise us to use). So, how can I find the point on the root locus where the damping is equal to 0.7 in Octave? Are you supposed to somehow get an array of the coordinates of all the points on the root locus and find the one for which the cos(atan(y/x)) (I think that's how the formula goes, but I am not sure) is the closest to 0.7, or?
I am not very familiar with the MatLab/Octave programming language. I was thinking about attempting to do that in the language I am familiar with, such as JavaScript. Finding a pair of numbers from some list (the coordinates of points on the root locus) for which the damping (if damping associated with some point on root locus is indeed equal to cos(atan(y/x))) is the closest to 0.7 is trivial in JavaScript. So is telling the gain associated with that point. The formula for that involves absolute diffences between complex numbers, but those can trivially be replaced by Pythagorean Theorem. But telling whether some randomly chosen point indeed belongs to the root locus is not trivial to do in JavaScript. It is not obvious how to implement those formulas (the amplitude and phase condition) in a language that doesn't support complex numbers.
In all seriousness, this university is killing me. I am considering dropping out even if I only have two tests left to the diploma. What do you think, by deciding not to drop out, am I committing the Sunk Cost Fallacy?
I am not very familiar with the MatLab/Octave programming language. I was thinking about attempting to do that in the language I am familiar with, such as JavaScript. Finding a pair of numbers from some list (the coordinates of points on the root locus) for which the damping (if damping associated with some point on root locus is indeed equal to cos(atan(y/x))) is the closest to 0.7 is trivial in JavaScript. So is telling the gain associated with that point. The formula for that involves absolute diffences between complex numbers, but those can trivially be replaced by Pythagorean Theorem. But telling whether some randomly chosen point indeed belongs to the root locus is not trivial to do in JavaScript. It is not obvious how to implement those formulas (the amplitude and phase condition) in a language that doesn't support complex numbers.
In all seriousness, this university is killing me. I am considering dropping out even if I only have two tests left to the diploma. What do you think, by deciding not to drop out, am I committing the Sunk Cost Fallacy?
