Getting Started With Control Systems

[dvscrobe]

I am in my 4th year in a Bachelor of Science Electrical Engineering Technology (BSEET) program that leans toward electrical transmission and distribution. I have had two courses in calculus, so have briefly covered differential equations. Unfortunately, my course curriculum does not cover control systems, which I have started to have a great interest in knowing about. As an employee for a transmission owner company, there is great application to understanding control theory. For example, a power transformer with a Beckwith controller will attempt to regulate its low side voltage with the use of a load tap changer. The only problem is that the math is very complicated! My school offers a course on control systems and I plan to take it as an elective but I got extremely lost when I got to the chapter on explaining the math formulas. I have found an online book at Cal-Tech's website (link below) to be the best online source. It is written very well and it doesn't dive into the math too quickly. I am hoping that a few on the boards here can help me with a few questions I have to help get me on my feet. I am using the damped spring system as my example to learn.

1) What the heck is state space? My understanding of state space is that your control formula takes into consideration real time states of a system, the inputs to it, and the system's output. But, a damped spring mass system has actually three states, position, velocity, and acceleration. Is the goal of writing a state space formula to always to ensure that there is only a 1st order ordinary differential equation?

Thanks, Dan

http://www.cds.caltech.edu/~murray/books/AM08/pdf/am08-complete_04Mar10.pdf

 

[scottdave]

It's been awhile for me, but I believe state space is a matrix of the eigenvectors. There are some advantages to having in that format. I'm on my phone right now, but I'll come back. I did find this article which you may like. http://lpsa.swarthmore.edu/Representations/SysRepTransformations/TF2SS.html

 

[256bits]

What the heck is state space

a little rusty also I must declare.

Exactly what is shown in Fig 2.
The plot on the left has a plot of a function y = f(t), where y is either position or velocity - ie the time domain.
( One can also produce a plot of the frequency domain. )

The plot on the right has position and velocity, and how they relate to one another.
Take for example any value of position. There is a series of velocities corresponding to that position is state space.
Note that there is no mention of time - you have to do some fancy algebraic footwork, as @scottdave has mentioned.

While you mention that there are three states - position, velocity, acceleration - the number of states that one writes down corresponds the number of energy storing components - in this case one has the mass storing energy due to its velocity, and the spring storing energy due to its position.

 

[dvscrobe]

scottdave, That link to swarthmore is very interesting. I was able to navigate to its home section. Very good stuff in here. Good tip! Thanks. Dan.