State feedback control

 

• consider the state feedback configuration with r = 0

 

• Problem: find a state gain K so that y decays to zero at a desired rate

 

• apply u = −Kx, so the closed loop dynamic matrix is A − BK

 

• design K such that λ(A − BK) is stable and lies in a desired region

 

Pole placement - Ackermann’s formular

Example

 

 

Optimal regulator system

 

 

 

Algebraic Riccati equation