# MODERN CONTROL FINAL EXAM 2005/1/12

```MODERN CONTROL FINAL EXAM
1. Derive state models for the following system G ( s) 
2005/1/12
1
s  3s  5s  1
3
2
and design the full-state feedback gain matrix K to place the
closed-loop pole at –2+2j.
2. Consider the linear system described by

1
0
0 
X (t )  
X (t )   U (t )

  1  2
1
Y (t )  1 0X (t )  1  U (t )

If we change the state variables to obey the relationship X 1  X 1  X 2 and


X 2  X 1  X 2 what is the state-space representation in the state X ?
3. A dc motor control system has the form shown in Fig(1). The three
state variables are available for measurement (X1 is position; X2 is
velocity and X3 is field current); the output position is X1(t). Select
the feedback gains so that the system has damping ratio 0.8 with 2
second settling time. Furthermore, if we consider designing a
compensator that provides asymptotic tracking of a reference input
with zero steady-state error, what should we do?
 1  1 0 
1


X (t )   1  3 0  X (t )  0U (t )
4.
Determine and explain this state
 0
1
0  4
Y (t )  1 0 0X (t )

model is uncontrollable or unobservable ?
5. Please explain the observer design procedure as possible as you can.
GOOD LUCK AV8D !!
,
Name :
No :
```