x
B
=
Laplace transform
+ x
V=
ax + x + x(x
)2[y(t)3
>
-
EF
ma
=
properties
,
(y(t)e d+ Y(s)
+
=
=
:
EM I %
,
& (a + (+) bg(+)3
EMo
To
2[x(t)3
=
2 [x(t)3
=
=
[Mp Ip2 Fap
=
+
Ip I
=
+
m
X
mac
sX(s)
s2X(s) sx(0) x(0)
(KE PE)
52(x(+)]
S[x(+ D)u (+ x)3 e X(s)
S Setx( +)3 X(s a)
KE
PE
P
=
=
+
+
myh
=
M w
Period
:
T
=
zkx2
+
Fv
or
.
,
)
(
=
-
z(mv [w])
=
=
,
Pin-Port
=
-
=
-
+
x(0)
-
-
2 [dox(+)a+ 3
r
.
aS[f(+3 + b2[g2+)3
=
+
=
:
Zor
E 2zWn
=
=w
Wa
=
Wn
Time constant t
:
Linearization
1 find
2.
ve
,
point where
y j, ..., n
,
veby + uedy +... =
Sy
=
Stability
imaginary
4- Yea
Sy
,
realcO
,
real
real = O
,
=
eve
,
i,
z2
zon eot t to
or
,
=
and is
.
.
0
ye ,
Su
+
...
-Yea
internally stable
BIBO stable
,
internally neutrally stable
,
,
Gain=
=
.
Su +
real > O internally rustable
DC
-
:
ear
.
=
1
the
,
steady-state
BIBO unstable
BIBO unstable
ratio of output to input for
a
constant input
Time
Laplace
GJH
1
Jt)
↳
Power P
=
E
=
=
Impulse
:
Step
:
Ramp
:
u,
E
i <R =
Series & Paralle Impedance
S Pat
=
Jirdt
7 (s)
,
=
⑤
z(vz = Li
+
zu
V(s)
=
z (s) [(s) + zy(s) [()
,
⑤
It = 63 %
45
Impedance division
98 %
=
Mp(%)
tr =
100e))
=
=
w
5
z(
1 - 33
- z
1
-
=
-
=
Masoris
Rule : from lecture notes
I
Rule of thumb
Tz
:
G
P
dominant
slow T is
,
-
Time to get
,
to
,
Integral Realization
-
misus
block diagram
guin
,
+
-
,
=
+
-
+
V
a summation
=
IR
,
(V
J
-
+
-
H
63 % T+ Tz
ys) clis Ys)
(s(ys yn)) k 1z yu) ((y) yrs)
k (y
=
integrators
use
<PSHs)
-t
T FTz
mys
=
⑮
-tan") 1Wn
+p
·
1-
Ein
-
-
=
L
i
=
v
/
S
.
L
Vm = kw
State
X
y
-
=
=
representations
space
Ax + Bu
A
(x + Du
X = nx)
Ts)
CCSI-A)" B
=
=
B
myn
,
State space to TF
,
=
y
=
nxm
Px)
(
,
,
=
v =
pxn
D
,
=
Tm
pxm
mx
:
+
D
Enverse
:
A
=
[i]
=>
A
=
adoc
input
T(s)
=
[In ] output
TF to state
-
:
must
space :
be strictly proper
:
#zeros
<#poles
(order of num order of denom)
.+
TIs) =Su
*
)
+a
,
S" +... an + S + An
A B D
it
,
strictly
proper
=
ki
S 6023