1. Warmup
Open Loop System
Closed Loop System
The A matrix of an open-loop system is of full rank with eigenvalues 𝜆 1 and 𝜆 2 . The system is placed into closed-loop feedback such that the new closed-loop A matrix has 𝐴 𝐶𝐿 = 𝜆 1 − 𝐾 1 𝐾 𝜆 2 .
Set up the characteristic equation for the eigenvalues 𝜆 𝐶𝐿 of 𝐴 𝐶𝐿 in terms of 𝜆 1 , 𝜆 2 , 𝐾 1 , 𝐾 2 . (Do not solve the equation.)
If 𝜆 1 = 𝜆 2 =1, find 𝐾 1 and 𝐾 2 to place both 𝜆 𝐶𝐿 at 0.25.
(Recall: Set the actual and desired characteristic equations equal…)