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+//control systems by Nagoor Kani A
+//Edition 3
+//Year of publication 2015
+//Scilab version 6.0.0
+//operating systems windows 10
+// Example 3.9
+
+clc;
+clear; 
+s=poly(0,'s')
+// the input is 12 unit step signal
+h=syslin('c',10/(s^2+2*s+10))
+disp(h,'the closed loop transfer function')
+//standard form od second order system is w^2/s^2+2*zeta*w*s+w^2
+//compaing h with the standard form
+w=3.162//natural frequency of oscillation
+disp(w,'natural frequency of oscillation in rad/sec')
+zeta=2/(2*w)
+disp(zeta,' damping ratio is')
+mp=exp((-zeta*%pi)/sqrt(1-(zeta)^2))*100//percentage peak overshoot 
+disp(mp,'percentage peak overshoot in percentage') 
+po=(mp/100)*12//peak over shoot for 12 units
+disp(po,'peak over shoot for 12 units')
+tp=%pi/(w*sqrt(1-(zeta)^2))
+disp(tp,'peak time in seconds')
+//constructing a right angle triangle with zeta and sqrt(1-zeta^2)
+theta=atan(0.866/0.5)//(1-zeta^2)/zeta
+disp(theta,'the value of theta is')
+tr=(%pi- theta)/(w*sqrt(1-(zeta)^2))
+disp(tr,'the rise time in seconds')
+t=1/(zeta*w)//time constant
+ts1=3*t//settling time for 5% error
+disp(ts1,'settling time for 5% error in seconds')
+ts2=4*t//settling time for 2% error
+disp(ts2,'settling time for 2% error in seconds')