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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=0.8//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',75/(s+1)*(s+3)*(s+8))//given tranfer function G(s)
+//find magnitude and phase of G(s) at s=sd
+a=75/((1+sd)*(3+sd)*(8+sd))
+ad=abs(a)
+disp(ad,'the value of ad is')
+phid=phasemag(a)
+disp(phid,'the value of phid is')
+ess=0.08//steady state error
+kv=1/ess//velocity error constant
+//the transfer function of PID controller is Gc(s)=kp+kd*s+ki/s
+//by definition of velocity error constant applying s=0 in S*Gc(s)*G(s)
+ki=12.5/3.125//integeral constant
+kd=sind(phid)/(d*ad*sind(betaa))+(ki/(d^2)) //derivative constant
+disp(kd,'the derivative  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', 0.68*(s^2+4.26*s+5.88)/s)//transfer function of PID 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 ')