1. 디지털제어 강의실 : 211 담당교수 : 고경철(기계공학부) 사무실 : 산학협력관 105B 면담시간 : 수시
강의실 : 211
담당교수 : 고경철(기계공학부)
사무실 : 산학협력관 105B
면담시간 : 수시
홈페이지:

2. 강의진도 참고문헌 [1주] 1장 서론 [2주] 2장 Z 변환 [3주] 3장 역z변환
[1] 고경철외 3인, “디지털 제어 시스템”, 홍릉과학출판사, 2005
[2] Ogata, Discrete-Time Control System,
[3] Dorf, Modern Control Systems, Wesley, 1998
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3. 3. Inverse Z transform Inverse Z transform
z domain
discrete time domain
5 methods for Inverse Z transform
(1) direct division method
(2) difference equation method
(3) computational method
(4) Z-transform table method
(5) partial-fraction expansion method
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4. Three kinds of representations of Z transformed function
3.1 Direct division method
Three kinds of representations of Z transformed function
(1) z’s polynomial representation
(2) pole-zero factorized representation
(3) ’s polynomial representation
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5. Three kinds of representations of Z transformed function
3.1 Direct division method
Three kinds of representations of Z transformed function
Representation: example
i) Z’s polynomial representation
iI) Poles and zeros representation
iii) ’s polynomial representation
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6. 3.1 Direct division method
- expanding a infinite series of X(z)
by direct division
example)
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7. 3.1 Direct division method
문제3.1(1) 풀이
ex)
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8. 3.1 Direct division method
문제3.1(3) ~(5)
ex2)Unit step function
ex3)unit ramp function
ex3)unit parabolic function
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9. 3.1 Direct division method
예제3.3
ex ) Fibonacci
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10. 3.2 Difference equation method
If u(k) is Kronecker delta input or
Then,
Thus,
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11. 3.2 Difference equation method
if G(z) is given by the z inverse representation form as
We can derive the following difference equation by using delay shifting theorem
It can be rewritten as ARMA(Auto Regressive Moving Average) form by
Auto Regressive
Moving Average
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12. 3.2 Difference equation method
예제3.4
ex)
We can get difference equation
Where
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13. 3.3 Computational method
We can get difference equation
Where
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14. 3.3 Computational method
list3-1_Difference_eq cpp
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15. 3.3 Computational method list3-1_Difference_eqFileOut090315.cpp
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16. 3.3 Computational method We can get difference equation as Where
문제3.3 (3) 풀이
We can get difference equation as
Where
(i) k=0 ; x(0) =0
(ii) k=1; x(1)=10
(iii) x(2)=17
(iv) x(3)=18.4
(v) x(4)= 18.68
…….
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17. 3.3 Computational method We can get difference equation as Where
list3-1_Difference_eq_para cpp
We can get difference equation as
Where
(i) k=0 ; x(0) =0
(ii) k=1; x(1)=10
(iii) x(2)=17
(iv) x(3)=18.4
(v) x(4)= 18.68
…….
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18. 3.4 Z-transform table method
Using Z-transform Table of Tab.2-1
ex)
let
where
referring the table 2-1,
Then,
Since,
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19. 3.5 Partial fraction expansion method
Thus,
where,
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20. 3.6 Z transform for solving the difference equation
for a linear time-invariant discrete time system
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21. 3.6 Z transform for solving the difference equation
(ex) solve the following difference equation using z-transform
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22. 3.7 Summary direct division method for inverse z transformation
as well as
difference equation method,
computational method using c-programming,
Z transform table method,
and partial fraction method.
finally, solved difference equation using Z transform and inverse
Z transform
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23. HW#3
Solve Pr.3.1, 3.3,3.5,3.7,3.9,3.11,3.13,3.15
Due: Next week this time
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