Modern Control Engineering

Section 8–7 / Zero-Placement Approach to Improve Response Characteristics 613

With this controller the closed-loop transfer function Y(s)/R(s)becomes

The response to the unit-step reference input becomes as shown in Figure 8–43(a).

Y(s)

R(s)

=

12.6051s^2 +52.63s+85.8673

s^3 +12.6051s^2 +52.63s+85.8673

Gc2(s),

(a)

yr

(t)

t (sec)

Response to Unit-Step Reference Input

0.6

0.8

1

1.2

1.4

0.4

0.2

0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Figure 8–43
(a) Response to unit-
step reference input;
(b) response to unit-
ramp reference
input; (c) response to
unit-acceleration
reference input. (b)

yr

(t)

t (sec)

Response to Unit-Ramp Reference Input

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0.4

0.2

0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Input

Output