# # $Id: controls.demo 3.38.2.6 1992/11/14 02:25:21 woo 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 # # 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