diff options
Diffstat (limited to '104/CH8')
41 files changed, 215 insertions, 0 deletions
diff --git a/104/CH8/EX8.1/8_1.jpeg b/104/CH8/EX8.1/8_1.jpeg Binary files differnew file mode 100755 index 000000000..70d6f1e26 --- /dev/null +++ b/104/CH8/EX8.1/8_1.jpeg diff --git a/104/CH8/EX8.1/8_1.sce b/104/CH8/EX8.1/8_1.sce new file mode 100755 index 000000000..90dc6e766 --- /dev/null +++ b/104/CH8/EX8.1/8_1.sce @@ -0,0 +1,6 @@ +//poles and zeroes
+s=%s
+sys=syslin('c',(s+1)/(s*(s+2)*(s+3)))
+plzr(sys)
+printf("three points on the root loci at which K=0 and those at which K=inf are shown in fig")
+
diff --git a/104/CH8/EX8.10/8_10.jpeg b/104/CH8/EX8.10/8_10.jpeg Binary files differnew file mode 100755 index 000000000..736bfafad --- /dev/null +++ b/104/CH8/EX8.10/8_10.jpeg diff --git a/104/CH8/EX8.10/8_10.sce b/104/CH8/EX8.10/8_10.sce new file mode 100755 index 000000000..86c3eca4c --- /dev/null +++ b/104/CH8/EX8.10/8_10.sce @@ -0,0 +1,12 @@ +//intersection of root loci with real axis
+s=%s
+sys=syslin('c',1/(s*(s+3)*(s^2+2*s+2)))
+clf
+evans(sys)
+K=kpure(sys)
+disp(K,"value of K where RL crosses jw axis=")
+p=poly([K 6 8 5 1],'s','coeff')
+x=roots(p)
+x1=clean(x(1,1))
+x2=clean(x(2,1))
+disp(x2,x1,"crossover points on jw axis=")
\ No newline at end of file diff --git a/104/CH8/EX8.11/8_11.jpeg b/104/CH8/EX8.11/8_11.jpeg Binary files differnew file mode 100755 index 000000000..8693ab918 --- /dev/null +++ b/104/CH8/EX8.11/8_11.jpeg diff --git a/104/CH8/EX8.11/8_11.sce b/104/CH8/EX8.11/8_11.sce new file mode 100755 index 000000000..d10efd0d1 --- /dev/null +++ b/104/CH8/EX8.11/8_11.sce @@ -0,0 +1,16 @@ +//breakaway points
+s=%s
+sys=syslin('c',(s+4)/(s*(s+2)))
+evans(sys)
+syms s
+d=derivat(sys)
+n=numer(d)
+a=roots(n) //a=breakaway points
+disp(a,"breakaway points=")
+for i=1:2
+ K=-a(i,1)*(a(i,1)+2)/(a(i,1)+4)
+ disp(a(i,1),"s=")
+ disp(K,"K=")
+end
+printf("if K is positive breakaway point lies on RL or else on CRL")
+
diff --git a/104/CH8/EX8.12/8_12.jpeg b/104/CH8/EX8.12/8_12.jpeg Binary files differnew file mode 100755 index 000000000..58cb70671 --- /dev/null +++ b/104/CH8/EX8.12/8_12.jpeg diff --git a/104/CH8/EX8.12/8_12.sce b/104/CH8/EX8.12/8_12.sce new file mode 100755 index 000000000..98a39a6e9 --- /dev/null +++ b/104/CH8/EX8.12/8_12.sce @@ -0,0 +1,15 @@ +//breakaway points
+s=%s
+sys=syslin('c',(s+2)/(s^2+2*s+2))
+evans(sys)
+syms s
+d=derivat(sys)
+n=numer(d)
+a=roots(n) //a=breakaway points
+disp(a,"breakaway points=")
+for i=1:2
+ K=-(a(i,1)^2+2*a(i,1)+2)/(a(i,1)+2)
+ disp(a(i,1),"s=")
+ disp(K,"K=")
+end
+printf("if K is positive breakaway point lies on RL or else on CRL")
\ No newline at end of file diff --git a/104/CH8/EX8.13/8_13.jpeg b/104/CH8/EX8.13/8_13.jpeg Binary files differnew file mode 100755 index 000000000..a98ddaa7a --- /dev/null +++ b/104/CH8/EX8.13/8_13.jpeg diff --git a/104/CH8/EX8.13/8_13.sce b/104/CH8/EX8.13/8_13.sce new file mode 100755 index 000000000..d09a64a9b --- /dev/null +++ b/104/CH8/EX8.13/8_13.sce @@ -0,0 +1,16 @@ +//breakaway points
+s=%s
+sys=syslin('c',1/(s*(s+4)*(s^2+4*s+20)))
+evans(sys)
+syms s
+d=derivat(sys)
+n=numer(d)
+a=roots(n) //a=breakaway points
+disp(a,"breakaway points=")
+for i=1:3
+ K=-a(i,1)*(a(i,1)+4)*(a(i,1)^2+4*a(i,1)+20)
+ disp(a(i,1),"s=")
+ disp(K,"K=")
+end
+printf("if K is positive breakaway point lies on RL or else on CRL")
+
\ No newline at end of file diff --git a/104/CH8/EX8.14/8_14.jpeg b/104/CH8/EX8.14/8_14.jpeg Binary files differnew file mode 100755 index 000000000..edc7ea941 --- /dev/null +++ b/104/CH8/EX8.14/8_14.jpeg diff --git a/104/CH8/EX8.14/8_14.sce b/104/CH8/EX8.14/8_14.sce new file mode 100755 index 000000000..93a3f4988 --- /dev/null +++ b/104/CH8/EX8.14/8_14.sce @@ -0,0 +1,15 @@ +//breakaway points
+s=%s
+sys=syslin('c',1/(s*(s^2+2*s+2)))
+evans(sys)
+syms s
+d=derivat(sys)
+n=numer(d)
+a=roots(n) //a=breakaway points
+disp(a,"breakaway points=")
+for i=1:2
+ K=-a(i,1)^2+2*a(i,1)+2
+ disp(a(i,1),"s=")
+ disp(K,"K=")
+end
+printf("if K is complex then point is not a break away point")
\ No newline at end of file diff --git a/104/CH8/EX8.15/8_15.sce b/104/CH8/EX8.15/8_15.sce new file mode 100755 index 000000000..c06d5bca0 --- /dev/null +++ b/104/CH8/EX8.15/8_15.sce @@ -0,0 +1,13 @@ +//root sensitivity
+s=%s
+sys1=syslin('c',1/(s*(s+1)))
+evans(sys1)
+
+sys2=syslin('c',(s+2)/(s^2*(s+1)^2))
+evans(sys2)
+
+printf("root densitivity at breakaway points is infinite")
+
+
+
+
diff --git a/104/CH8/EX8.15/8_15a.jpeg b/104/CH8/EX8.15/8_15a.jpeg Binary files differnew file mode 100755 index 000000000..d1ed70cf0 --- /dev/null +++ b/104/CH8/EX8.15/8_15a.jpeg diff --git a/104/CH8/EX8.15/8_15b.jpeg b/104/CH8/EX8.15/8_15b.jpeg Binary files differnew file mode 100755 index 000000000..83947720d --- /dev/null +++ b/104/CH8/EX8.15/8_15b.jpeg diff --git a/104/CH8/EX8.16/8_16.jpeg b/104/CH8/EX8.16/8_16.jpeg Binary files differnew file mode 100755 index 000000000..58cb70671 --- /dev/null +++ b/104/CH8/EX8.16/8_16.jpeg diff --git a/104/CH8/EX8.16/8_16.sce b/104/CH8/EX8.16/8_16.sce new file mode 100755 index 000000000..026140ac2 --- /dev/null +++ b/104/CH8/EX8.16/8_16.sce @@ -0,0 +1,11 @@ +//calculation of K on root loci
+s=%s
+sys=syslin('c',(s+2)/(s^2+2*s+2))
+evans(sys)
+//value of K at s=0
+printf("K=A*B/C \n A and B are lenths of vectors drawn from poles of sys \n C is lenths of vector drawn from zero of sys")
+A=sqrt((-1)^2+1^2)
+B=sqrt((-1)^2+(-1)^2)
+C=-2
+K=A*B/C
+disp(K,"value of K at s=0 is")
\ No newline at end of file diff --git a/104/CH8/EX8.17/8_17.sce b/104/CH8/EX8.17/8_17.sce new file mode 100755 index 000000000..7d8a8b209 --- /dev/null +++ b/104/CH8/EX8.17/8_17.sce @@ -0,0 +1,19 @@ +//properties of root loci
+s=%s
+sys=syslin('c',(s+3)/(s*(s+5)*(s+6)*(s^2+2*s+2)))
+d=denom(sys)
+n=numer(sys)
+p=roots(d)
+z=roots(n)
+disp(p,"poles of sys=")
+disp(z,"zeroes of sys=")
+n=length(p)
+m=length(z)
+disp(n,"no of poles=")
+disp(m,"no of zeroes=")
+if (n>m) then
+ disp(n,"no of branches of RL=")
+else
+ disp(m,"no of branches of CRL=")
+end
+printf("the root loci are symmetrical with respect to the real axis of the plane")
diff --git a/104/CH8/EX8.18/8_18.sce b/104/CH8/EX8.18/8_18.sce new file mode 100755 index 000000000..56ba52184 --- /dev/null +++ b/104/CH8/EX8.18/8_18.sce @@ -0,0 +1,7 @@ +//effect of addition of poles to sys
+s=%s
+sys=syslin('c',1/(s*(s+1))) //a=1
+evans(sys)
+sys1=syslin('c',1/(s*(s+1)*(s+2))) //b=2
+evans(sys1)
+printf("adding a pole to sys has effect of pushing the root loci towards the RHP")
\ No newline at end of file diff --git a/104/CH8/EX8.18/8_18a.jpeg b/104/CH8/EX8.18/8_18a.jpeg Binary files differnew file mode 100755 index 000000000..d1ed70cf0 --- /dev/null +++ b/104/CH8/EX8.18/8_18a.jpeg diff --git a/104/CH8/EX8.18/8_18b.jpeg b/104/CH8/EX8.18/8_18b.jpeg Binary files differnew file mode 100755 index 000000000..3e5b2b1c5 --- /dev/null +++ b/104/CH8/EX8.18/8_18b.jpeg diff --git a/104/CH8/EX8.19/8_19.sce b/104/CH8/EX8.19/8_19.sce new file mode 100755 index 000000000..628a0ef13 --- /dev/null +++ b/104/CH8/EX8.19/8_19.sce @@ -0,0 +1,7 @@ +//effect of addition of zeroes to sys
+s=%s
+sys=syslin('c',1/(s*(s+1))) //a=1
+evans(sys)
+sys1=syslin('c',(s+2)/(s*(s+1))) //b=2
+//evans(sys1)
+printf("adding a LHP zero to sys has effect of moving and bending the root loci towards the LHP")
\ No newline at end of file diff --git a/104/CH8/EX8.19/8_19a.jpeg b/104/CH8/EX8.19/8_19a.jpeg Binary files differnew file mode 100755 index 000000000..d1ed70cf0 --- /dev/null +++ b/104/CH8/EX8.19/8_19a.jpeg diff --git a/104/CH8/EX8.19/8_19b.jpeg b/104/CH8/EX8.19/8_19b.jpeg Binary files differnew file mode 100755 index 000000000..7f09ab361 --- /dev/null +++ b/104/CH8/EX8.19/8_19b.jpeg diff --git a/104/CH8/EX8.2/8_2.jpeg b/104/CH8/EX8.2/8_2.jpeg Binary files differnew file mode 100755 index 000000000..590e299c2 --- /dev/null +++ b/104/CH8/EX8.2/8_2.jpeg diff --git a/104/CH8/EX8.2/8_2.sce b/104/CH8/EX8.2/8_2.sce new file mode 100755 index 000000000..b408b1c27 --- /dev/null +++ b/104/CH8/EX8.2/8_2.sce @@ -0,0 +1,5 @@ +//root locus
+s=%s
+sys=syslin('c',(s+1)/(s*(s+2)*(s+3)))
+evans(sys)
+printf("number of branches of root loci is 3 as equation is of 3rd order")
\ No newline at end of file diff --git a/104/CH8/EX8.20/8_20.sce b/104/CH8/EX8.20/8_20.sce new file mode 100755 index 000000000..ce764774d --- /dev/null +++ b/104/CH8/EX8.20/8_20.sce @@ -0,0 +1,13 @@ +//effect of moving pole near jw axis
+s=%s
+sys1=syslin('c',(s+1)/(s^2*(s+10))) //a=10 b=1
+evans(sys1)
+sys2=syslin('c',(s+1)/(s^2*(s+9))) //a=9
+evans(sys2)
+sys3=syslin('c',(s+1)/(s^2*(s+8))) //a=8
+evans(sys3)
+sys4=syslin('c',(s+1)/(s^2*(s+3))) //a=3
+evans(sys4)
+sys5=syslin('c',(s+1)/(s^2*(s+1))) //a=1
+evans(sys5)
+printf("as pole is moved towards jw axis RL also moves towards jw axis")
\ No newline at end of file diff --git a/104/CH8/EX8.20/8_20a.jpeg b/104/CH8/EX8.20/8_20a.jpeg Binary files differnew file mode 100755 index 000000000..9d8a45381 --- /dev/null +++ b/104/CH8/EX8.20/8_20a.jpeg diff --git a/104/CH8/EX8.20/8_20b.jpeg b/104/CH8/EX8.20/8_20b.jpeg Binary files differnew file mode 100755 index 000000000..4fe003793 --- /dev/null +++ b/104/CH8/EX8.20/8_20b.jpeg diff --git a/104/CH8/EX8.21/8_21.sce b/104/CH8/EX8.21/8_21.sce new file mode 100755 index 000000000..00f6ec7da --- /dev/null +++ b/104/CH8/EX8.21/8_21.sce @@ -0,0 +1,11 @@ +//effect of moving pole away from jw axis
+s=%s
+sys1=syslin('c',(s+2)/(s*(s^2+2*s+1))) //a=1
+evans(sys1)
+sys2=syslin('c',(s+1)/(s*(s^2+2*s+1.12))) //a=1.12
+evans(sys2)
+sys3=syslin('c',(s+1)/(s*(s^2+2*s+1.185))) //a=1.185
+evans(sys3)
+sys4=syslin('c',(s+1)/(s*(s^2+2*s+3))) //a=3
+evans(sys4)
+printf("as pole is moved away from jw axis RL also moves away from jw axis")
\ No newline at end of file diff --git a/104/CH8/EX8.21/8_21a.jpeg b/104/CH8/EX8.21/8_21a.jpeg Binary files differnew file mode 100755 index 000000000..6cbb018f1 --- /dev/null +++ b/104/CH8/EX8.21/8_21a.jpeg diff --git a/104/CH8/EX8.21/8_21b.jpeg b/104/CH8/EX8.21/8_21b.jpeg Binary files differnew file mode 100755 index 000000000..1ba1d4329 --- /dev/null +++ b/104/CH8/EX8.21/8_21b.jpeg diff --git a/104/CH8/EX8.3/8_3.jpeg b/104/CH8/EX8.3/8_3.jpeg Binary files differnew file mode 100755 index 000000000..88d069dac --- /dev/null +++ b/104/CH8/EX8.3/8_3.jpeg diff --git a/104/CH8/EX8.3/8_3.sce b/104/CH8/EX8.3/8_3.sce new file mode 100755 index 000000000..be18bd169 --- /dev/null +++ b/104/CH8/EX8.3/8_3.sce @@ -0,0 +1,6 @@ +//root locus
+s=%s
+sys=syslin('c',1/(s*(s+2)*(s+1)))
+clf
+evans(sys)
+printf("root loci is symmetical to both axis")
\ No newline at end of file diff --git a/104/CH8/EX8.4/8_4.jpeg b/104/CH8/EX8.4/8_4.jpeg Binary files differnew file mode 100755 index 000000000..82a24b68a --- /dev/null +++ b/104/CH8/EX8.4/8_4.jpeg diff --git a/104/CH8/EX8.4/8_4.sce b/104/CH8/EX8.4/8_4.sce new file mode 100755 index 000000000..ba78420b9 --- /dev/null +++ b/104/CH8/EX8.4/8_4.sce @@ -0,0 +1,6 @@ +//root locus
+s=%s
+sys=syslin('c',1/(s*(s+2)*(s^2+2*s+2)))
+clf
+evans(sys)
+printf("when pole zero configuration is symmetrical wrt a point in s plane,then root loci is symmetrical to that point")
\ No newline at end of file diff --git a/104/CH8/EX8.5/8_5.jpeg b/104/CH8/EX8.5/8_5.jpeg Binary files differnew file mode 100755 index 000000000..6c4c3f1bb --- /dev/null +++ b/104/CH8/EX8.5/8_5.jpeg diff --git a/104/CH8/EX8.5/8_5.sce b/104/CH8/EX8.5/8_5.sce new file mode 100755 index 000000000..8d6a092bd --- /dev/null +++ b/104/CH8/EX8.5/8_5.sce @@ -0,0 +1,24 @@ +//root locus
+s=%s
+sys=syslin('c',(s+1)/(s*(s+4)*(s^2+2*s+2)))
+clf
+evans(sys)
+n=4;
+disp(n,"no of poles=")
+m=1;
+disp(m,"no of poles=")
+//angle of asymptotes
+printf("angle of asymptotes of RL")
+for i=0:(n-m-1)
+ O=((2*i)+1)/(n-m)*180
+ disp(O,"q=")
+ end
+printf("angle of asymptotes of CRL")
+for i=0:(n-m-1)
+ O=(2*i)/(n-m)*180
+ disp(O,"q=")
+end
+//centroid
+printf("Centroid=((sum of all real part of poles of G(s)H(s))-(sum of all real part of zeros of G(s)H(s))/(n-m) \n")
+C=((0-4-1-1)-(-1))/(n-m);
+disp(C,"centroid=")
diff --git a/104/CH8/EX8.8/8_8.jpeg b/104/CH8/EX8.8/8_8.jpeg Binary files differnew file mode 100755 index 000000000..736bfafad --- /dev/null +++ b/104/CH8/EX8.8/8_8.jpeg diff --git a/104/CH8/EX8.8/8_8.sce b/104/CH8/EX8.8/8_8.sce new file mode 100755 index 000000000..3df597c43 --- /dev/null +++ b/104/CH8/EX8.8/8_8.sce @@ -0,0 +1,7 @@ +//angle of departure and angle of arrivals
+s=%s
+sys=syslin('c',1/(s*(s+3)*(s^2+2*s+2)))
+clf
+evans(sys)
+printf("angle of arrival and departure of root loci on the real axis are not affected by complex poles and zeroes of G(s)H(s)")
+
diff --git a/104/CH8/EX8.9/8_9.sce b/104/CH8/EX8.9/8_9.sce new file mode 100755 index 000000000..27b89197d --- /dev/null +++ b/104/CH8/EX8.9/8_9.sce @@ -0,0 +1,6 @@ +//multiple order pole
+s=%s
+sys=syslin('c',(s+3)/(s*(s+2)^3))
+clf
+evans(sys)
+printf("this shows that whole real axis is occupied by RL and CRL")
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