Page 241 - Modern Control Systems

Skills Check 215

"1 5/'
c ¢(/,0) =
.1 1 .
2
"l 5/ / ~
d. #(/,0) = 0 1 t
0 0 1 _
8. For the initial conditions x t (0) = .*2(0) = 1, the response x(t) for the zero-input response is:
a. x {(t) = (1 + t),x 2(t) = lfor/ > 0
b. x x(t) = (5 + t),x 2(t) = /for/ > 0
c. jci(f) = (5/ + 1),JC 2(/) = 1 for/ > 0
d. x x(t) = x 2(t) = for/ > 0
l
9. A single-input, single-output system has the state variable representation
0 1
x +
_ -5 -10
y = [0 I0]x
The transfer function of the system T(s) = Y(s)/U(s) is
TV ^ " 5 0
5 + 5s 2 + 50s
3
a. T{s) = -50
2
s + 10^ + 5
b. T(s) = -5
s + 5
c T(s) = -50
d. T(s) =
s 2 + 55 + 5
10. The differential equation model for two first-order systems in series is
x(t) + 4x{t) + 3x(t) = u(t),
where u(t) is the input of the first system and x(t) is the output of the second system.
The response x(t) of the system to a unit impulse «(/) is:
2
a. x(t) = e~' - 2e~ '
b. x(t) = -e~

, X l -t l ,-3/
c. x(t) = 2 ' - —e
—e
2
3
d. x(t) = e~' - e~ '
11. A first-order dynamic system is represented by the differential equation
Sx(t) + x(t) = u(t).
The corresponding transfer function and state-space representation are
x = -0.2* + 0.5«
rfc^ — and
G{S)
1 + 55 y = OAx
b. G W 10 and x = -0.2JC + u
= 1 + 5s y = x
x — — 5x + u
CI c\ and
C{S)
"'5 + 5 y = x
d. None of the above