Modern Control Engineering

aa

240 Chapter 5 / Transient and Steady-State Response Analyses

Hence, the time response c(t)can be given by

The fact that the response curve is an exponential curve superimposed by damped sinusoidal

curves can be seen from Figure 5–56.

A–5–9. When the closed-loop system involves a numerator dynamics, the unit-step response curve

may exhibit a large overshoot. Obtain the unit-step response of the following system with

MATLAB:

Obtain also the unit-ramp response with MATLAB.

Solution.MATLAB Program 5–19 produces the unit-step response as well as the unit-ramp

response of the system. The unit-step response curve and unit-ramp response curve, together with

the unit-ramp input, are shown in Figures 5–57(a) and (b), respectively.

Notice that the unit-step response curve exhibits over 215%of overshoot. The unit-ramp

response curve leads the input curve. These phenomena occurred because of the presence of a large

derivative term in the numerator.

C(s)

R(s)

=

10s+ 4

s^2 +4s+ 4

• 0.4375e-2t-0.375te-2t+ 1

c(t)=-0.5626e-2tcos4t+0.3438e-2tsin4t

Amplitude

Time (sec)

Step Response

0.6

0.4

0.2

0.8

1

1.2

0

0 0.5 1 1.5 2 2.5 3

Figure 5–56

Unit-step response

curve.

Openmirrors.com