#
# $Id: controls.demo,v 3.26 92/03/24 22:32:19 woo Exp Locker: woo $
#
#
# 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
#
# 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"
# undo what we have done
set xrange [-10:10]
set autoscale xy
set samples 160
set dummy x