# Digital Control Theory

ELE4 DCT

–

Digital Control Theory

Assignment 2

This assignment

is due by 2:00pm, Monday

1

9

October

2015

.

You must show all working clearly and neatly.

Late submissions will not be assessed.

(Total: 25

marks)

Question 1

.

For the

sampled

–

data system in

Figure 1

, express the output C(z)

as a

function of the input and the transfer functions shown

.

(5

marks)

H

(

s

)

G

(

s

)

R

(

s

)

C

(

s

)

T

E

2

(

s

)

E

1

(

s

)

T

Figure

1

Question 2

.

A discrete

–

time system is described by the signal

–

flow graph in

Figure

2

.

The state variables are

labeled

as

)

(

1

k

x

and

)

(

2

k

x

in Figure 1

.

(a)

Write th

e

state

–

space

equation

of the system

.

(

5

marks)

(b)

D

erive the pulse transfer function

)

(

)

(

z

U

z

Y

of the system in Figure 1

.

(5 marks)

u(k)

–

0.4

–

0.8

y(k)

1

2

1

1

z

–

1

z

–

1

x

1

(k)

x

2

(k)

Figure

2

Question 3

.

A discrete

–

time system is given by

)

(

0

1

)

(

0

1

0

5

.

0

)

1

(

k

u

k

k

ïƒº

ïƒ»

ïƒ¹

ïƒª

ïƒ«

ïƒ©

ï€«

ïƒº

ïƒ»

ïƒ¹

ïƒª

ïƒ«

ïƒ©

ï€

ï€½

ï€«

x

x

)

(

]

5

.

0

5

.

0

[

)

(

k

k

y

x

ï€½

(a)

Design a full

–

state feedback controller of the form

)

(

)

(

k

k

u

Kx

ï€

ï€½

to place the

two closed

–

loop poles at

,

5

.

0

1

ï€½

z

8

.

0

2

ï€½

z

.

(5 marks)

(b)

With the full

–

state feedback controller designed in (a), write the closed

–

loop

state equation

.

(5 marks)

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**Category**: Sample Questions