#

# $Id: controls.dem,v 1.2 1999/08/17 15:31:54 lhecking Exp $

#

# warning:  this demo is SLOW on PCs without math coprocessors!

#

# From _Automatic_Control_Systems_, fourth ed., figure 6-14

# transient response of a second-order system to a unit step input function

#

damp(t) = exp(-s*wn*t)/sqrt(1.0-s*s)

per(t) = sin(wn*sqrt(1.0-s**2)*t - atan(-sqrt(1.0-s**2)/s))

c(t) = 1-damp(t)*per(t)

#

#	wn is natural undamped frequency

#	s is damping factor

#

wn = 1.0

set xrange [0:13]

set samples 50

set dummy t

set key box

#

# plot c(t) for several different damping factors s

#

plot s=.1,c(t),s=.3,c(t),s=.5,c(t),s=.7,c(t),s=.9,c(t),s=1.0,c(t),s=1.5,c(t),s=2.0,c(t)

pause -1 "Hit return to continue"

reset