Page 159 - Modern Control Systems

Skills Check 133

10. The closed-loop unit step response is:
20 20 _, 5' _ t2 e-5t
a. y{t) = i r +
25 25
b. y{t) = 1 + 20re~ ' 5
, s 20 20 5t 5t
- 3 M = 2 5 - 2 5 e °~ - 4te~
5
d. y(t) = 1 - 2e~ ' - Ate' ' 5
11. The final value of y(t) is:
a. y„ = lim y(t) = 0.8
r-*oo
b. y w = lim y(f) = 1.0
f-»oo
c. y„ = Kmy(t) = 2.0
/->oo
d. y ss = lim y(t) = 1.25
/—»00
12. Consider the differential equation
y + 2y + y = u
where y(0) = y(0) = 0 and u(t) is a unit step. The poles of this system are:
a. s-i = -1,¾ = - 1
b. 5! = 1/, 5 2 = 1 ;
-
C S-i = - 1 , 5 2 = —2
d. None of the above
13. A cart of mass m = 1000 kg is attached to a truck using a spring of stiffness
k = 20,000 N/m and a damper of constant 6 = 200 Ns/m, as shown in Figure 2.81.
2
The truck moves at a constant acceleration of a = 0.7 m/s .

FIGURE 2.81 Truck pulling a cart of mass m.

The transfer function between the speed of the truck and the speed of the cart is:
50
a. T(s) = 2
55 + s + 100
20 + s
b. T(s) -
^ + 105 + 25
100 + 5
c. T(s) = 2
5s + s + 100
d. None of the above