Modern Control Engineering

Problems 647

B–8–14.Consider the system shown in Figure 8–81. The
plant is given by

Determine the controllers and such that, for
the step disturbance input, the response shows a small am-
plitude and approaches zero quickly (in a matter of 1 to
2 sec). For the response to the unit-step reference input, it is
desired that the maximum overshoot be 20%or less and the
settling time 1 sec or less. For the ramp reference input and
acceleration reference input, the steady-state errors should
be zero.

Gc1(s) Gc2(s)

Gp(s)=

2(s+1)

s(s+3)(s+5)

Gp(s)

B–8–15.Consider the two-degrees-of-freedom control

system shown in Figure 8–82. Design controllers and

such that the response to the step disturbance input

shows a small amplitude and settles to zero quickly (in 1 to

2 sec) and the response to the step reference input ex-

hibits 25%or less maximum overshoot and the settling time

is less than 1 sec. The steady-state error in following the ramp

reference input or acceleration reference input should be

zero.

Gc2(s)

Gc1(s)

Gc 1 (s) Gp(s)

R(s) U(s) Y(s)

D(s)

Gc 2 (s)

+ ++

+– –

Figure 8–81

Two-degrees-of-freedom control system.

1

C 1 (s) s 2

R(s) Y(s)

D(s)

C 2 (s)

+ ++

+

Figure 8–82

Two-degrees-of-freedom control system.