Question

Consider the following transfer function of a linear control system

$\frac{Y(s))}{U(s))}=\frac{1}{}{(s+1)(s^2+0.7s+2)}$

1- Determine the state feedback gain matrix that places the closed system at s=-32, -3.234 ± j3.3.

2- Design a full order observer which produces a set of desired closed loop poles at s=-16, -16.15±j16.5

3-Assume X1 is measurable, design a reduced order observer with desired closed loop poles at -16.15±j16.5

1 Y(s) U(s) (s+1)(s2+0.7s+2) Consider the following transfer function of a linear control system (a) Determine the state feedback gain matrix that places the closed system poles at s- -32, -3.234+j3.3. (b) Design a full order observer which produces a set of desired closed loop poles at s=-16,-16.15 ± j16.5 | (c) Assurmex, is measurable, design a reduced order observer with desired closed loop poles at-16.15 ±j165.

Answer 1

Given "(s) (a) elosed loop soften poles s--3,-3.234 ± iss are celsech temp systern. Te-Hatt 8 l+G,H = (St3)//cat 3.23 l/)_+. (3.3) " b of3.3 6 ,46 , s + 19.40t+

(b) closed loop poles at s=%, -! 6-1sti 165 closed loop poles ot 16 1t it6.S s-16.15+ 32.3 s+16.5 3