Hi,
I am investigating a typical 'active' 1/4 car suspension system (one actuator). Along my studies of controls, I was told along the way that mechanical systems (or electrical) with symmetry sometimes end up being 'uncontrollable', (i.e. the matrix M = [B AB A^2B ... A^(n-1)B] is not full rank).
Conceptually, an active suspension with only one actuator should be uncontrollable. The states can not all be controlled by one actuator. So, is my concept of controllability incorrect? Or is it that all the states (x1-x4) can be taken to the next desired state in finite time, but not all states simultaneously??? When I perform rank(M), it equals 4, which means it is full rank. Shouldn't it be 3 revealing that it is not controllable?
I am not a state space expert (obviously!), but I am writing a paper that contains controllability and would like to get this bit correct. I have search all over the web for info on symmetrical controllable 2 Degree of Freedom Systems examples but had no luck. I figured if anyone can help it would be someone here.
Thanks!
--t