20 files changed, 339 insertions, 0 deletions

diff --git a/1151/CH6/EX6.1/example1.sce b/1151/CH6/EX6.1/example1.sce
new file mode 100755
index 000000000..de96b9368
--- /dev/null
+++ b/1151/CH6/EX6.1/example1.sce
@@ -0,0 +1,17 @@
+s=%s;

+m=s^4+2*s^3+6*s^2+4*s +1;

+disp (m)

+r= coeff (m)

+n= length (r)

+routh = routh_t (m) // Thi s Func t ion g e n e r a t e s the Routht a b l e

+disp (routh ," r o u t h s t a b u l a t i o n=")

+c =0;

+for i =1: n

+if ( routh (i ,1) <0)

+c=c+1;

+end

+end

+if(c >=1)

+printf (" sys t em i s u n s t a b l e ")

+else printf (" sys t em i s s t a b l e ")

+end

diff --git a/1151/CH6/EX6.10/example10.sce b/1151/CH6/EX6.10/example10.sce
new file mode 100755
index 000000000..69ada3df0
--- /dev/null
+++ b/1151/CH6/EX6.10/example10.sce
@@ -0,0 +1,17 @@
+s=%s;

+m=s ^5+2*s ^4+24*s^3+48*s^2-25*s-50;

+disp (m)

+r= coeff (m)

+n= length (r)

+routh = routh_t (m)

+disp (routh ," r o u t h s t a b u l a t i o n s=")

+c =0;

+for i =1: n

+ if ( routh (i ,1) <0)

+c=c+1;

+ end

+ end

+if(c >=1)

+printf (" sys t em i s u n s t a b l e ")

+else printf (" sys t em i s ma r g i n a l l y s t a b l e ")

+ end

diff --git a/1151/CH6/EX6.11/example11.sce b/1151/CH6/EX6.11/example11.sce
new file mode 100755
index 000000000..d2e3bdec6
--- /dev/null
+++ b/1151/CH6/EX6.11/example11.sce
@@ -0,0 +1,23 @@
+// d e t e rmi n i n g c r i t i c a l v a l u e o f K

+s=%s

+syms K

+m=s ^3+6.5* s ^2+10* s +10* K

+cof_a_0 = coeffs (m, ' s ' ,0);

+cof_a_1 = coeffs (m, ' s ' ,1);

+cof_a_2 = coeffs (m, ' s ' ,2);

+cof_a_3 = coeffs (m, ' s ' ,3);

+ r=[ cof_a_0 cof_a_1 cof_a_2 cof_a_3 ]

+ n= length (r);

+ routh =[r ([4 ,2]) ;r ([3 ,1]) ];

+routh =[ routh ;- det ( routh )/ routh (2 ,1) ,0];

+t= routh (2:3 ,1:2) ; // e x t r a c t i n g the s qu a r e sub b l o c ko f r outh mat r ix

+ routh =[ routh ;- det (t)/t(2 ,1) ,0]

+disp (routh ," r o u t h s t a b u l a t i o n=")

+routh (3 ,1) =0 // For ma r g ina ly s t a b l e sys t em

+sys = syslin ( ' c ' ,10/(s ^3+6.5* s ^2+10* s ))

+k= kpure ( sys )

+disp (k,"K( ma r g ina l )=")

+disp ( '=0 ' ,routh (2 ,1) *(s^2) +1.5*10^7*k," a u x i l l a r y e q u a t i o n ")

+p= poly ([ 10* K,0 ,6.5] , ' s ' , ' c o e f f ' )

+s= roots (p)

+disp (s," Fr equency o f o s c i l l a t i o n ( i n rad / s e c )=")

diff --git a/1151/CH6/EX6.12/example12.sce b/1151/CH6/EX6.12/example12.sce
new file mode 100755
index 000000000..ff846183c
--- /dev/null
+++ b/1151/CH6/EX6.12/example12.sce
@@ -0,0 +1,17 @@
+s=%s;

+m=s^3+7*s^2+25*s+39;

+disp (m)

+r= coeff (m)

+n= length (r)

+routh = routh_t (m) // Thi s Func t ion g e n e r a t e s the Routht a b l e

+disp (routh ," r o u t h s t a b u l a t i o n=")

+c =0;

+for i =1: n

+if ( routh (i ,1) <0)

+c=c+1;

+end

+end

+if(c >=1)

+printf (" sys t em i s u n s t a b l e ")

+else printf (" sys t em i s s t a b l e ")

+end

diff --git a/1151/CH6/EX6.13/example13.sce b/1151/CH6/EX6.13/example13.sce
new file mode 100755
index 000000000..ce50f5449
--- /dev/null
+++ b/1151/CH6/EX6.13/example13.sce
@@ -0,0 +1,17 @@
+s=%s;

+m=s^4+2*s^3+8*s^2+4*s +3;

+disp (m)

+r= coeff (m)

+n= length (r)

+routh = routh_t (m) // Thi s Func t ion g e n e r a t e s the Routht a b l e

+disp (routh ," r o u t h s t a b u l a t i o n=")

+c =0;

+for i =1: n

+if ( routh (i ,1) <0)

+c=c+1;

+end

+end

+if(c >=1)

+printf (" system is unstable ")

+else printf (" system is stable ")

+end

diff --git a/1151/CH6/EX6.14/example14.sce b/1151/CH6/EX6.14/example14.sce
new file mode 100755
index 000000000..7407ef0aa
--- /dev/null
+++ b/1151/CH6/EX6.14/example14.sce
@@ -0,0 +1,34 @@
+ s=%s;

+ syms K

+ p=s^2 -(K +2) *s +((2* K) +5)

+cof_a_0 = coeffs (p, ' s ' ,0);

+ cof_a_1 = coeffs (p, ' s ' ,1);

+ cof_a_2 = coeffs (p, ' s ' ,2);

+ r=[ cof_a_0 cof_a_1 cof_a_2 ]

+ n= length (r);

+routh =[r ([3 ,1]) ;r (2) ,0];

+routh =[ routh ;- det ( routh )/ routh (2 ,1) ,0];

+ disp (routh ," r outh=")

+// f o r sys t em to be s t a b l e

+ routh (2 ,1) >0

+

+ K < -2;

+ routh (3 ,1) >0

+K > -2.5;

+disp ("For s t a b l e sys tem , 􀀀2>K>􀀀2.5")

+ // f o r l imi t e d s t a b i l i t y

+routh (2 ,1) =0

+ K=-2

+ routh (3 ,1) =0

+ K= -2.5

+ disp ("For l imt e d s t a b l e sys t em K=􀀀2 and K=􀀀2.5")

+ // f o r u n s t a b l e sys t em

+ disp ("For u n s t a b l e sys t em K<􀀀2 or K>􀀀2.5")

+ roots (p) // g i v e s the r o o t s o f the po l ynomi a l m

+// f o r c r i t i c a l l y damped c a s e

+28 g=(K+2) ^2 -4*((2* K) +5)

+ roots (g)

+ // f o r s t a b l i t y K=6.47 i s u n s t a b l e

+ // f o r c r i t i c a l damping K=􀀀2.47

+ disp ("For underdamded cas e , 􀀀2>K>􀀀2.47")

+disp (" f o r overdamped cas e , 􀀀2.47>K>􀀀2.5")

diff --git a/1151/CH6/EX6.15/example15.sce b/1151/CH6/EX6.15/example15.sce
new file mode 100755
index 000000000..99f283036
--- /dev/null
+++ b/1151/CH6/EX6.15/example15.sce
@@ -0,0 +1,29 @@
+s=%s;

+ syms K a

+ p=s ^4+10* s ^3+32* s ^2+( K +32) *s+(K*a)

+cof_a_0 = coeffs (p, ' s ' ,0);

+cof_a_1 = coeffs (p, ' s ' ,1);

+ cof_a_2 = coeffs (p, ' s ' ,2);

+cof_a_3 = coeffs (p, ' s ' ,3);

+ cof_a_4 = coeffs (p, ' s ' ,4);

+r=[ cof_a_0 cof_a_1 cof_a_3 cof_a_4 ]

+ n= length (r);

+ routh =[r ([5 ,3 ,1]) ;r ([4 ,2]) ,0]

+routh =[ routh ;- det ( routh (1:2 ,1:2) )/ routh (2 ,1) ,-det (routh (1:2 ,2:3) )/ routh (2 ,2) ,0];

+routh =[ routh ;- det ( routh (2:3 ,1:2) )/ routh (3 ,1) ,-det (routh (2:3 ,2:3) )/ routh (3 ,2) ,0];

+routh =[ routh ;- det ( routh (3:4 ,1:2) )/ routh (4 ,1) ,0 ,0];

+disp (routh ," r outh=")

+// f o r the g i v e n sys t em to be s t a b l e

+routh (3 ,1) >0

+K <288;

+routh (4 ,1) >0

+(288 -K)*(K +32) -100(K*a) >0

+// l e t K=200

+K =200;

+a =((288 - K)*(K +32) ) /(100* K)

+// v e l o c i t y e r r o r

+Kv =(K*a) /(4*2*4) ;

+// % v e l o c i t y e r r o r

+Kvs =100/ Kv

+disp (a," c o n t r o l parame t e r=")

+disp (K,"Gain=")

diff --git a/1151/CH6/EX6.16/example16.sce b/1151/CH6/EX6.16/example16.sce
new file mode 100755
index 000000000..ce50f5449
--- /dev/null
+++ b/1151/CH6/EX6.16/example16.sce
@@ -0,0 +1,17 @@
+s=%s;

+m=s^4+2*s^3+8*s^2+4*s +3;

+disp (m)

+r= coeff (m)

+n= length (r)

+routh = routh_t (m) // Thi s Func t ion g e n e r a t e s the Routht a b l e

+disp (routh ," r o u t h s t a b u l a t i o n=")

+c =0;

+for i =1: n

+if ( routh (i ,1) <0)

+c=c+1;

+end

+end

+if(c >=1)

+printf (" system is unstable ")

+else printf (" system is stable ")

+end

diff --git a/1151/CH6/EX6.17/example17.sce b/1151/CH6/EX6.17/example17.sce
new file mode 100755
index 000000000..ce50f5449
--- /dev/null
+++ b/1151/CH6/EX6.17/example17.sce
@@ -0,0 +1,17 @@
+s=%s;

+m=s^4+2*s^3+8*s^2+4*s +3;

+disp (m)

+r= coeff (m)

+n= length (r)

+routh = routh_t (m) // Thi s Func t ion g e n e r a t e s the Routht a b l e

+disp (routh ," r o u t h s t a b u l a t i o n=")

+c =0;

+for i =1: n

+if ( routh (i ,1) <0)

+c=c+1;

+end

+end

+if(c >=1)

+printf (" system is unstable ")

+else printf (" system is stable ")

+end

diff --git a/1151/CH6/EX6.18/example18.sce b/1151/CH6/EX6.18/example18.sce
new file mode 100755
index 000000000..79714d001
--- /dev/null
+++ b/1151/CH6/EX6.18/example18.sce
@@ -0,0 +1,17 @@
+s=%s;

+m=s^4+2*s^3+s^2+4*s +2;

+disp (m)

+r= coeff (m)

+n= length (r)

+routh = routh_t (m) // Thi s Func t ion g e n e r a t e s the Routht a b l e

+disp (routh ," r o u t h s t a b u l a t i o n=")

+c =0;

+for i =1: n

+if ( routh (i ,1) <0)

+c=c+1;

+end

+end

+if(c >=1)

+printf (" system is unstable ")

+else printf (" system is stable ")

+end

diff --git a/1151/CH6/EX6.19/exmple19.sce b/1151/CH6/EX6.19/exmple19.sce
new file mode 100755
index 000000000..065bf8141
--- /dev/null
+++ b/1151/CH6/EX6.19/exmple19.sce
@@ -0,0 +1,18 @@
+ // e l eme n t s i n one row o f r o u t h s t a b u l a t i o n s a r e a l lz e r o

+s=%s;

+m=s^6+3*s ^5+5* s ^4+9* s ^3+8* s ^2+6* s +4;

+disp (m)

+ r= coeff (m)

+ n= length (r)

+ routh = routh_t (m)

+ disp (routh ," r o u t h s t a b u l a t i o n s=")

+ c =0;

+for i =1: n

+ if ( routh (i ,1) <0)

+ c=c+1;

+end

+ end

+ if(c >=1)

+printf (" sys t em i s u n s t a b l e ")

+else printf("system is marginally stable")

+end

diff --git a/1151/CH6/EX6.2/example2.sce b/1151/CH6/EX6.2/example2.sce
new file mode 100755
index 000000000..1c16de6eb
--- /dev/null
+++ b/1151/CH6/EX6.2/example2.sce
@@ -0,0 +1,17 @@
+s=%s;

+m=2+3*s+s^2+2*s^3+2*s^4;

+disp (m)

+r= coeff (m)

+n= length (r)

+routh = routh_t (m) // Thi s Func t ion g e n e r a t e s the Routht a b l e

+disp (routh ," r o u t h s t a b u l a t i o n=")

+c =0;

+for i =1: n

+if ( routh (i ,1) <0)

+c=c+1;

+end

+end

+if(c >=1)

+printf (" sys t em i s u n s t a b l e ")

+else printf (" sys t em i s s t a b l e ")

+end

diff --git a/1151/CH6/EX6.20/example20.sce b/1151/CH6/EX6.20/example20.sce
new file mode 100755
index 000000000..e87195501
--- /dev/null
+++ b/1151/CH6/EX6.20/example20.sce
@@ -0,0 +1,7 @@
+s=%s; 

+num=1; 

+den=s*(s+2)*(s^2+6*s+25); 

+t=syslin('c',num/den); 

+clf; 

+evans(t); 

+mtlb_axis([-5 5 -5 5]);

diff --git a/1151/CH6/EX6.3/example3.sce b/1151/CH6/EX6.3/example3.sce
new file mode 100755
index 000000000..80a4e32da
--- /dev/null
+++ b/1151/CH6/EX6.3/example3.sce
@@ -0,0 +1,17 @@
+s=%s;

+m=1+2*s+5*s^2+5*s^3+2*s^4;

+disp (m)

+r= coeff (m)

+n= length (r)

+routh = routh_t (m) // Thi s Func t ion g e n e r a t e s the Routht a b l e

+disp (routh ," r o u t h s t a b u l a t i o n=")

+c =0;

+for i =1: n

+if ( routh (i ,1) <0)

+c=c+1;

+end

+end

+if(c >=1)

+printf (" sys t em  i s  u n s t a b l e ")

+else printf (" sys t em  i s  s t a b l e ")

+end

diff --git a/1151/CH6/EX6.4/example4.sce b/1151/CH6/EX6.4/example4.sce
new file mode 100755
index 000000000..160608b2c
--- /dev/null
+++ b/1151/CH6/EX6.4/example4.sce
@@ -0,0 +1,17 @@
+s=%s;

+m=s^4+2*s^3+3*s^2+4*s +5;

+disp (m)

+r= coeff (m)

+n= length (r)

+routh = routh_t (m) // Thi s Func t ion g e n e r a t e s the Routht a b l e

+disp (routh ," r o u t h s t a b u l a t i o n=")

+c =0;

+for i =1: n

+if ( routh (i ,1) <0)

+c=c+1;

+end

+end

+if(c >=1)

+printf (" system is unstable ")

+else printf (" system is stable ")

+end

diff --git a/1151/CH6/EX6.5/example5.sce b/1151/CH6/EX6.5/example5.sce
new file mode 100755
index 000000000..e0de7a8cf
--- /dev/null
+++ b/1151/CH6/EX6.5/example5.sce
@@ -0,0 +1,17 @@
+clc;s=%s;

+m=s^3+4.5*s^2+3.5*s +1.5;

+disp (m)

+r= coeff (m)

+n= length (r)

+routh = routh_t (m) // Thi s Func t ion g e n e r a t e s the Routht a b l e

+disp (routh ," r o u t h s t a b u l a t i o n=")

+c =0;

+for i =1: n

+if ( routh (i ,1) <0)

+c=c+1;

+end

+end

+if(c >=1)

+printf (" system is unstable ")

+else printf (" system is stable ")

+end

diff --git a/1151/CH6/EX6.6/example6.sce b/1151/CH6/EX6.6/example6.sce
new file mode 100755
index 000000000..faa5ef468
--- /dev/null
+++ b/1151/CH6/EX6.6/example6.sce
@@ -0,0 +1,17 @@
+clc;s=%s;

+m=s^5+6*s^4+3*s^3+2*s^2+s+1;

+disp (m)

+r= coeff (m)

+n= length (r)

+routh = routh_t (m) // Thi s Func t ion g e n e r a t e s the Routht a b l e

+disp (routh ," r o u t h s t a b u l a t i o n=")

+c =0;

+for i =1: n

+if ( routh (i ,1) <0)

+c=c+1;

+end

+end

+if(c >=1)

+printf (" system is unstable ")

+else printf (" system is stable ")

+end

diff --git a/1151/CH6/EX6.7/example7.sce b/1151/CH6/EX6.7/example7.sce
new file mode 100755
index 000000000..c634a2606
--- /dev/null
+++ b/1151/CH6/EX6.7/example7.sce
@@ -0,0 +1,8 @@
+// f i r s t e l ement i n any row o f r o u t h s t a b u l a t i o n i s z e r o

+clc;s=%s

+m=s^4+s ^3+2* s ^2+2* s+3

+r= coeff (m); // Ex t r a c t s the c o e f f i c i e n t o f the po l ynomi a l

+n= length (r);

+routh = routh_t (m)

+disp (routh ," r outh=")

+printf (" since there are two sign changes the system is unstable")

diff --git a/1151/CH6/EX6.8/example8.sce b/1151/CH6/EX6.8/example8.sce
new file mode 100755
index 000000000..fbb5ce9f5
--- /dev/null
+++ b/1151/CH6/EX6.8/example8.sce
@@ -0,0 +1,8 @@
+// f i r s t e l ement i n any row o f r o u t h s t a b u l a t i o n i s z e r o

+clc;s=%s

+m=s^5+2*s^4+2*s^3+4*s^2+11*s+10;

+r= coeff (m); // Ex t r a c t s the c o e f f i c i e n t o f the po l ynomi a l

+n= length (r);

+routh = routh_t (m)

+disp (routh ," r outh=")

+printf (" since there are two sign changes the system is unstable")

diff --git a/1151/CH6/EX6.9/example9.sce b/1151/CH6/EX6.9/example9.sce
new file mode 100755
index 000000000..4b2bd1854
--- /dev/null
+++ b/1151/CH6/EX6.9/example9.sce
@@ -0,0 +1,8 @@
+// f i r s t e l ement i n any row o f r o u t h s t a b u l a t i o n i s z e r o

+clc;s=%s

+m=s^3+s+1;

+r= coeff (m); // Ex t r a c t s the c o e f f i c i e n t o f the po l ynomi a l

+n= length (r);

+routh = routh_t (m)

+disp (routh ," r outh=")

+printf (" since there are two sign changes the system is unstable")