Critically Stable - Control Theory

[Delber]

I am preparing for my control theory exam, but I have come across that I am struggling. I have a third order system and its asking to me determine when a value of an adjustable parameter, K for when the system is critically stable.

I just don't know what this corresponds two for a third order system. I know for a second order system it is when the dampening ratio is equal to one. Do I need to just find the value of K that places all the poles on the negative real axis?

Any help would be appreciated thanks.

 

[viscousflow]

Could you post the denominator of this transfer function? The number of terms in the Tx function can make a huge difference in the analysis. I almost suspect the function is of the form

$$s^3+s^2+s$$

which in that case you can factor out an s and all will be clear.

 

[anggavi]

Can you define critically stable? is it associated with eigenvalue? when can i say the stability becomes crytically stable? i hope someone can help me to explain it, Thank You :)