CON2 - Chapter 2 Mathematical Modelling Electrical Systems...

Info iconThis preview shows pages 1–58. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 2 Mathematical Modelling Electrical Systems R L C Voltage (e), Current (i)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
i R = e / R i C = C de / dt i L = (1/L) e dt
Background image of page 2
Mechanical Systems M K B velocity ( v) force ( f )
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
f K = K v dt f M = M dv/dt f B = Bv
Background image of page 4
Force - current analogy C M 1/L K 1/R B
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Integro - differential equations by analogy approach free body diagram approach
Background image of page 6
Electro mechanical example + - R L M K B + f i e S v
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
current i force f velocity v back emf e b voltage source e S
Background image of page 8
e s
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
e s i f
Background image of page 10
e s i v f
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
e s i v f e b
Background image of page 12
(e s - e b ) - + e s e b i f v
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Equations (e s -e b ) = Ri + L di/dt K 1 i = f f = M dv/dt+Bv+K vdt e b = K 2 v
Background image of page 14
input output x y y = K x K
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
In our example i f K 1 v e b K 2
Background image of page 16
How do we represent (e s - e b ) = Ri + L di / dt + - e s e b e Let e s - e b = e Then
Background image of page 17

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Take Laplace Transform of e = Ri + L di/dt ? Now e i
Background image of page 18
E (s) = R I (s) + Ls I (s) = (R + Ls) I(s) assuming ?
Background image of page 19

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Assuming Initial Conditions to be Ignored/zero
Background image of page 20
? E I I(s)/E(s) = 1 /( R + Ls) = G 1 (s) (say)
Background image of page 21

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Similarly F ? v
Background image of page 22
Mechanical Components M + f B K
Background image of page 23

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon