ECED 4601 Digital Control Systems
Assignment #5
http://myweb.dal.ca/~jgu/4601/assignments.html
Due date: November 25 2014. Late submission will not be accepted.
Assignment #5 contains the following problems:
1) Problem B-6-1: Consider the system defined by
xk  1  Gxk   Hu k 
y k   Cxk 
a b 
1
, H   , C  1 0,

c d 
1
Where G  
Determine the conditions on a,b,c, and d for complete state controllability and complete
observability.
2) B-6-8 consider the pulse transfer function system.


Y z 
z 1 1  z 1

U  z  1  0.5 z 1 1  0.5 z 1



Obtain the state-space representation of the system in the following forms
a) controllable canonical form
b) observable canonical form
c) diagonal canonical form
3) B-6-12 consider the system defined by
1
0  x1 k  1
 x1 k  1  0
 x k  1   0
0
1  x2 k   1u k 
 2
 
 x3 k  1  0.16 0.84 0  x3 k  1
Determine the state feedback gain matrix such that when the control signal is given by
u k    Kxk 
The closed loop system will exhibit the deadbeat response to any initial state x0
4) B-6-16 consider the system defined by:
xk  1  Gxk   Hu k 
y k   Cxk 
0  0.16
0 
, H   , C  0 1,

1 
1
1
Where G  
Using MATLAB, determine the observer feedback gain matrix K e such that the desired eigenvalues
for the observer matrix are
u1  0.5  j 0.5 , u2  0.5  j 0.5
Assume that the system consifuration is identical to that shown in figure. Using Ackermann’s formula,
write a MATLAB program.
Observed state feedback control system

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