2319/12 Recap
LEC 1
tracking error
* Controller
↓
Yoite
reference
">
Plant
Basic Feedback Control
Short-term
control (decisions
n=
A
y variable
-Ye Outph
-
Signal
·
input
control
+
variable
we measure
=
Loop
obj.=
Examples
ExIS
0
of
control
Be
x
A
=
=
u
Applying
Newton's law Mx u-Bx
=
In terms
of
-(B/N)- (1/M)[x
+
1
+
Mi
=
itas in
e.st.
↳
Fig. 1
(W n
=
ref speed
X-
Voltage
of
control
RLC
mis
1
R
u
-
MgsinO
of
B0
MgsinO
+
math model
car.
d disturbance
=
de
Parallel yct t > Asin (Wt+P(
i
kUL:K-Ri-LIdi/dt
y 0,
->
[cdy/dte.
-RCcdy/dth-18 AY y 0
=
-
=
=
:22
+
R2j +4
"2nd order linear
into
of
system
y (voltages
a
lut order ODES
:x
SX1=
=
complex form
Let
x
(2]
=
x
=>
=
(1)
-
R1.i u))
=
+
-
~Bu
An
11m 11: I 1x+ 1iI
S
x
=
y
7101X
=
active
prosthesis
u input
torque, d: disturbance torque
Rotation about fixed axis:
=
a
x10
x
=
mgsinO
+
moment problem:make y
W
as a state
-
+Id
"2nd order nonlinear ODE".
0
e
=
space model (system of 1st order ODES):
Let:X1 0iX2 0
=
=
x =8EYgL/1)
15
I
y
[1
=
x/rRix+ws
linear time-invariantmodel" (LTi).
-
Let's write it
y)
RLC circuit:
-
ugline at
↓
11III
-
ODE
of
11
C-
Ex33 stance control for
motor
=
model
1st order ODESC.
=
=
State variables
I
coefficient
i12 Xr12
y
-
↑
"Stable-space
const
12 Such
=
input-output
=h
=
=
Xi i
x2 I (current
=
More
ODE"
=
-
Convertis
co-efficient
"Istorder linear const
V,
y=
cl
circuitin-input voltage, y-capacitor voltage
=y
2
-
Set
Y
=
+
usbur,
+
Ex2)
m
=
d
vd, 0 escontroller
+
=
no]=
Put
x
car,
=
=
MgV
I
n-force imparted by engine, y-speed of
x y v x =v is velocity (speeds.
car;
=
so,
(1)
a
01X
cannotwrite as
sincXl
mer
+11/1).n+11/I) Id
nowlinear state
me
-
siA+BU,
space model
asRLC, ButWrite
as
f(x, h
9x=
y
h(X,u)
=