0195136047.pdf

826 BASIC CONTROL SYSTEMS

Figure P16.2.34, which uses proportional control.

WithTd(s)=0, if a unit-step function is applied

to the reference input, find the expression for the

time responseωc(t).

16.2.35Figure P16.2.35 shows a block diagram of a speed-
control system that uses proportional as well as
integral control action. Show that this will result
in the elimination of the steady-state system error
in response to a unit-step disturbance torque input.

16.2.36Consider two type-1 systems, as shown in Figures
P16.2.36(a) and (b), with the integrator located
in two different locations. Check whether both

systems eliminate the steady-state error for unit-

step function disturbance inputU(s).

16.2.37It is desirable to have an amplifier system of sev-

eral stages with an overall gain of 1000±20. The

gain of any one stage is given to drift from 10 to

20. Determine the required number of stages and
    the feedback function needed to meet the speci-
    fications. Consider the closed-loop system as one
    that has an initial value of 980 and a final value of
    1020, while each stage has an initial value of 10
    and a final value of 20.

G 1 G 2 G 3 G 4

+

+

+

+

+

−

H 0

H 1

H 3

H 2

Figure P16.2.28

G 1 G 2 C

R 1

R 2

++

+

−−

H 2

H 1

Figure P16.2.29

G 1 G 2 G 3 G 4 G 6

R ++

+

+

−

−

H 1

G 5

H 2

Figure P16.2.30