第七章作业

G(s)=Ks(s+2)(s2+4s+5)

(a) Sketch a root locus for K, and show that the dominant roots are s=-0.35±j0.80 when K=6.5.

(b) For the dominant roots of part (a), calculate the settling time and overshoot for a step input.

E7.7 The elevator in a modem office building travels at a top speed of 25 feet per second and is still able to stop within one-eighth of an inch of the floor outside. The transfer function of the unity feedback elevator position control is

G(s)=K(s+10)s(s+1)(s+20)(s+50)

Determine the gain K when the complex roots have a ς equal to 0.8. E7.12 A unity feedback system has a loop transfer function

KG(s)K(s1)

s(s26s18)(a) Sketch the root locus for K>0. (b) Find the roots when K=10 and 20.

(c) Computer the 0-100% rise time, percent overshoot, and setting time(with a 2% criterion) of the system for a unit step input when K=10 and 20. E7.16 A negative unity feedback system has a loop transfer function

KesTGc(s)G(s)

s1Where T=0.1 second, Show that an approximation for the time delay is

e-sT2(-s)@T2(+s)T

Using

e-0.1s=(20-s)(20+s)

Obtain the root locus for the system for K>0. Determine the range of K for which the system is stable.

E7.20 A unity feedback system has a loop transfer function

G(s)K(s1)

s(s1)(s4)(a) Determine the range of K for stability. (b) Sketch the root locus.

(c) Determine the maximum ς of the stable complex roots. P7.3 A unity feedback system has the loop transfer function

G(s)=Ks(s+2)(s+5)

Find

(a) the breakaway point on the real axis and the gain K for this point, (b) the gain and the roots when two toots lie on the imaginary axis, (c) the roots when K=6. (d) sketch the root locus.