My $0.02....Is it just me that finds it impossible to understand math notation?
No! I have trouble too. It is because the books/instructors are not consistent in the symbols they use for certain variables all the time. Math has a language all its own. Often there are no worked examples. I like examples.
Not exactly new to motion control, I was Galil's first machine-control customer back in the mid-80's and I had Jacob Tal on speed-dial
I went to a Jacob Tal seminar back in the late 80s or early 90s. I still have to book from the seminar. I learned few significant things. I remember twisting the motor that he had for a demo to get a "real feel" of what the P, I and D do. I learned the strengths and weakness of the Galil controllers.
I believe that many engineers remain ignorant of how this stuff works because they have the same problem and don't want to admit it.
Craig
They must have had the math, calculus, differential equations and linear algebra in college. The problem is that they forget what they learned or almost learned and consider themselves lucky to survived the course. The problem is there is a "Use it or lose it" factor. So many forgot what they were taught. Some we NEVER taught very well. Many professors have NEVER had to solve these problems in real life. Some have trouble applying what they know.
I remembered Runge-Kutta, calculus, differential equations, and linear algebra from college. The rest I had to learn on my own. PIDs, the closed loop part is easy compared to the target generator that controls the motion.
Back on topic. The problem is that the OPs don't even say what their application is and what they are trying to do. It is almost like the don't think anyone has done something like it before.