question 4

The effect when described for a 2^nd order system:

Consider the second-order system

Poles are s = –p1 & s = –p2. When we add zero at s = –z1 to the controller, the open-loop transfer function will change to:

We can put zero at 3 different positions with respect to the poles:

1. To the right of s = –p1 Fig (b)

2. Between s = –p2 & s = –p1 Fig(c)

3. To the left of s = –p2 Fig (d)

The effect of changing the gain K on the position of closed-loop poles and type of responses:

(a) The zero s = –z1 is not present.

Over, critically or under damped

(b) The zero s = –z1 is located to the right of s = – p2 & s = –p1.

Over damped

(c) The zero s = –z1 is located between s = –p2 & s = –p1.

Over damped

(d) The zero s = –z1 is located to the left of s = –p2.

Flexible configuration

Since there is a relationship between position of closed-loop poles and system time domain performance, we can modify the behaviour of closed-loop system by introducing appropriate zeros in the controller.

Reference:

ü Web.mit.edu

ü www.wikipedia.com

ü www.palgrave.com

ü Applied control theory- James r Leigh-1987