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+//Caption:time_response_and_peak_overshoot
+//example 12.8
+//page 521
+s=%s;
+syms t;
+num=sym('8*(s+1)');
+den=sym('(s^2+2*s+2)');
+CL=num/den;
+disp(CL,"C(s)/R(s)=");
+//for unit step response R(s)=1/s; 
+d=CL*(1/s);
+disp(d,"C(s)=");
+c=ilaplace(d,s,t);
+disp(c,"c(t)=");
+//for peak time we get tp=%pi/2
+t=%pi/2
+a=s*d;
+a=simple(a)
+Cmax=4*(1+1.414*exp(-t)*sin(t-(%pi/4)))
+Css=limit(a,s,0);
+disp(Css,"Css=");
+Mp=((Cmax-Css)/Css)*100
+Mp=float(Mp)
+disp(Mp,"peak_overshoot=")