I have a fourth order system which is fully controllable and observable, which needs to satisfy certain design criteria.
I am trying to design a full-state feedback controller for the following system:
$$\frac{-0.00198s + 2}{s^4 + 0.1201s^3 + 12.22s^2 + 0.4201s + 2}$$
Design Requirements:
<5% Overshoot
<2s settling time
The schematic of this type of control system is shown below where \$K\$ is a matrix of control gains. Note that here we feedback all of the system's states, rather than using the system's outputs for feedback.
A related example, State-Space Methods for Controller Design.
While I am aware how to design second order systems using the above design requirements, I am struggling when it comes to higher order systems.
Below I present equations and working for finding poles for a second order system. Apologies if wording is hard to decipher.
Poles for 2nd order @ -2.6 +- i*2.39
One would then proceed to use MATLAB place
function as follows:
p2 = [-2.6 + 1i*2.39, -2.6 - 1i*2.39];
K = place(A,B,p2);
Acl = A - B*K;
mysys = ss(Acl,B,C,D);
Since this method only yields two poles, how can I satisfy my design requirements if I have a fourth order system?
This can also be thought of as designing a full state feedback controller to obtain the specific transient one requires. Closed loops dynamics and more specifically eigenvalues of matrix Acl have a lot to do with finding the desired poles. I am yet to fully understand how. Any suggestions would be appreciated.