Problems for home work (no.4)
1. . The forward path transfer function is given by G(s) = 9/s(s+6). Obtain an expression for
unit step response of the system.
a) 1+3te-t+e-2t
c) 1-e-t+3e-2t
b) 1-e-3t-3te-3t
d) 1-2te-2t+e+2t
3. Which of the following transfer function will have the greatest maximum overshoot?
a) 9/(s2+2s+9)
c) 25/(s2+2s+25)
b) 16/(s2+2s+16)
d) 36/(s2+2s+36)
4. Consider a system with transfer function G(s) = s+6/ Ks2+s+6. Its damping ratio will be
0.5 when the values of k is:
a) 2/6
b) 3
c) 1/6
d) 6
5. A system with transfer function 1/Ts+1, subjected to a unit step input to reach 63.2% of
final value, The value of t is :
a) T
b) T/2
c) 3T
d. 4T
6. The block diagram of a closed loop control system is given by figure. The values of K and
P such that the system has a damping ratio of 0.7 and an undamped natural frequency ωn
of 5 rad/sec, are respectively equal to:
a. 20 and 0.3
c. 25 and 0.3
b. 20 and 0.2
d. 25 and 0.2
7. Which of the following transfer functions represent under damped second order
systems?
a) 1/(s² + s + 1).
b) 4/(s² + 2s + 4).
c) 2/(s² + 2s + 2).
d) all of the above.
8. A second order control system is defined by the following equation:
4 d²c(t)/dt² + 8 dc(t)/dt + 16 c(t) = 16 r(t) .The damping ratio and natural frequency
for this system are respectively 0.25 and 2 rad/s
a. true
b. flus
9.
Given the unity feedback control system with open loop transfer function
G(s)=K/s(s+a) . Find the value of K & a to yield Kv =1000 and ζ=0.5
10. The transfer function of a system given by , 100 / ( s2 + 20s + 100 ) the system is
a) an over damped.
b) an under damped
c) a unstable..
d) a critically damped.