From b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b Mon Sep 17 00:00:00 2001
From: priyanka
Date: Wed, 24 Jun 2015 15:03:17 +0530
Subject: initial commit / add all books

---
 29/CH7/EX7.24.2/exa7_24_2.sce | 51 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 51 insertions(+)
 create mode 100755 29/CH7/EX7.24.2/exa7_24_2.sce

(limited to '29/CH7/EX7.24.2/exa7_24_2.sce')

diff --git a/29/CH7/EX7.24.2/exa7_24_2.sce b/29/CH7/EX7.24.2/exa7_24_2.sce
new file mode 100755
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--- /dev/null
+++ b/29/CH7/EX7.24.2/exa7_24_2.sce
@@ -0,0 +1,51 @@
+//caption:root_locus_description
+//example 7.24.2
+//page 296
+s=%s;
+syms K;
+GH=K/(s*(s+1)*(s+3))
+zeta=0.5
+//from given data 
+disp("the characterstics eq. is determined as:")
+CH=(s*(s+1)*(s+3))+K
+CH=sym('(s*(s+1)*(s+3))+K');
+disp('=0',CH,"characterstics_eq,CH=")
+c0=coeffs(CH,'s',0);
+c1=coeffs(CH,'s',1);
+c2=coeffs(CH,'s',2);
+c3=coeffs(CH,'s',3);
+b=[c0 c1 c2 c3]
+n=4;
+routh=[b([4,2]);b([3,1])];
+routh=[routh;-det(routh)/routh(2,1),0]
+t=routh(2:3,1:2)
+routh=[routh;-det(t)/t(2,1),0]
+K=sym('-(s^3+4*s^2+3*s)')
+d=diff(K,s)
+e=-3*s^2-8*s-3 
+r1=roots(e)
+disp(r1,"roots=")
+disp("-0.45 is break away point since it lies on root locus")
+disp(routh,"routh=")
+disp("for given system to be marginally stable:");
+disp("(12-K)=0 ");
+disp("which gives:");
+disp("K=12, for margianl stability");
+K=12;
+k=12
+a=4*s^2+k//intersection of root locus with imaginary plane
+r=roots(a)
+g=k/(s*(s+1)*(s+3))
+G=syslin('c',g)
+evans(g,8)
+xgrid(2)
+disp("the line theta=acos(zeta)=60 intersects root locus at sa=(-0.35+i0.6)")
+disp("the value of K at s=sa is find to be 1.66 ")
+disp("the value of K at s=-4")
+disp("K=12")
+disp("at K=1.66")
+k=1.66
+H=1
+G=k/(s*(s+1)*(s+3))
+CL=G/(1+G*H)
+disp(CL,"C(s)/R(s)=")
\ No newline at end of file
-- 
cgit