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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 6.15

+

+clc;

+clear; 

+s=poly(0,'s')

+//dominent pole sd=-zeta*w=%i*w*sqrt(1-zeta^2)

+zeta=0.9//damping ratio

+w=2.5//natural frequency of osciilation in rad/sec

+sd=(-zeta*w)+((%i*w)*sqrt(1-zeta^2))

+disp(sd,'the dominennt pole is')

+d=abs(sd)

+disp(d,'the value of d is ')

+betaa=phasemag(sd)

+disp(betaa,'the value of betaa is;')

+h=syslin('c',4/(s+1)*(s+5))//given tranfer function G(s)

+//find magnitude and phase of G(s) at s=sd

+a=4/((1+sd)*(5+sd))

+ad=abs(a)

+disp(ad,'the value of ad is')

+phid=phasemag(a)

+disp(phid,'the value of phid is')

+ki=-(d*sind(phid))/(ad*sind(betaa))//integral  constant

+disp(ki,'the integral   constant is')

+kp=(-sind(betaa+phid))/(ad*sind(betaa))-(2*ki*cosd(betaa))/d //proportional constant

+disp(kp,'the proportional  constant is')

+hc=syslin('c', 2.02*(s+1.19)/s)//transfer function of PD controller is kpof +kd*s

+disp(hc,'transfer function of PI controller is')

+hcmp=syslin('c',h*hc)//transfer function   compensated system 

+disp(hcmp,'transfer function   compensated system ')