# Very stiff state space matrices after linearizing my Simscape model

I want to simulate and build a furuta pendulum from scratch as a project. Currently I´m having some difficulties with the simulation of my model in Simscape and I can´t figure out what´s wrong with it.

Here is a Link to a Git repository where I´ve uploaded my current model in case you wanna have a closer look: https://github.com/Joo234/Furuta_pendulum

My first goal is to set up a state feedback controller. As you can see from my model, the state feedback control (without an observer) basically works fine. However, I actually can´t really explain or understand why it works, because the A matrix is actually very stiff and therefore the rank of the controllability matrix is only 1. According to my books full controllability is necessary for state feedback control to work. So why is it, that the pendulum is still balanced out despite of the low rank of my controllability matrix? In general I´m very confused that one of the Eigenvalues in the A matrix is 5 decimals smaller than all other Eigenvalues. I feel like there´s something wrong with my model or the way I linearized it but I can´t figure out what it is.

I´d highly appretiate any help on that!


A =

1.0e+05 *

-0.0000   -0.0015    0.0000   -0.0000
0         0    0.0000         0
0.0000    0.0046   -0.0001    0.0000
0.0001         0         0   -3.2500

>> Rank_ctrb

Rank_ctrb =

1


• Please edit your question to show how you're computing the rank of your controllability matrix, and show us your input matrix. – TimWescott Jul 27 '20 at 21:06