diff options
Diffstat (limited to '3889/CH5')
23 files changed, 225 insertions, 0 deletions
diff --git a/3889/CH5/EX5.1/Ex5_1.sce b/3889/CH5/EX5.1/Ex5_1.sce new file mode 100644 index 000000000..bf716c150 --- /dev/null +++ b/3889/CH5/EX5.1/Ex5_1.sce @@ -0,0 +1,22 @@ +//Example 5.1
+//page 318
+//Control Systems: Principles and Design
+//M Gopal, Second Edition, Tata McGraw-Hill
+//Chapter: Concepts of Stability: Routh Stability Array
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//transfer function
+s=%s;
+P=s^4 + 8* s^3 +18*s^2 +16*s +5;
+//routh array
+disp('Routh Array')
+r=routh_t(P)
+disp(r)
+[r,num]=routh_t(1/P,20)
+if num==0
+ disp("As all the elements in first column are positive, system is stable")
+else
+ mprintf("There is %g sign changes in entries of first column.\nTherefore, system is unstable.", num)
+end
diff --git a/3889/CH5/EX5.1/Ex5_1output.PNG b/3889/CH5/EX5.1/Ex5_1output.PNG Binary files differnew file mode 100644 index 000000000..14e95bcaa --- /dev/null +++ b/3889/CH5/EX5.1/Ex5_1output.PNG diff --git a/3889/CH5/EX5.10/Ex5_10.sce b/3889/CH5/EX5.10/Ex5_10.sce new file mode 100644 index 000000000..c5aecdcfe --- /dev/null +++ b/3889/CH5/EX5.10/Ex5_10.sce @@ -0,0 +1,21 @@ +//Example 5.10
+//page 327
+//Control Systems: Principles and Design
+//M Gopal, Second Edition, Tata McGraw-Hill
+//Chapter:Concepts of Stability: Routh Stability Array
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//transfer function
+s=poly(2,'s');
+//substitution of s-2 for s
+
+P=(1+(5/s))*((s+3)/(s^2+2*s+2));
+k=poly(0,'k')
+//routh array
+r=routh_t(P,k)
+disp(r,"Routh Array")
+kval=kpure(P)
+mprintf('%g <K , is range of gain for closed loop poles to satisfy Re(s)<-2',kval(1))
+
diff --git a/3889/CH5/EX5.10/Ex5_10output.PNG b/3889/CH5/EX5.10/Ex5_10output.PNG Binary files differnew file mode 100644 index 000000000..4338c03b8 --- /dev/null +++ b/3889/CH5/EX5.10/Ex5_10output.PNG diff --git a/3889/CH5/EX5.2/Ex5_2.sce b/3889/CH5/EX5.2/Ex5_2.sce new file mode 100644 index 000000000..4ff2369c1 --- /dev/null +++ b/3889/CH5/EX5.2/Ex5_2.sce @@ -0,0 +1,22 @@ +//Example 5.2
+//page 318
+//Control Systems: Principles and Design
+//M Gopal, Second Edition, Tata McGraw-Hill
+//Chapter: Concepts of Stability: Routh Stability Array
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//transfer function
+s=%s;
+P=3*s^4 + 10* s^3 +5*s^2 +5*s +2;
+//routh array
+disp('Routh Array')
+r=routh_t(P)
+disp(r)
+[r,num]=routh_t(1/P,20)
+if num==0
+ disp("As all elements of first row are positive,system is stable")
+else
+ mprintf("There are %g sign changes in entries of first column.\nTherefore, system is unstable.", num)
+end
diff --git a/3889/CH5/EX5.2/Ex5_2output.PNG b/3889/CH5/EX5.2/Ex5_2output.PNG Binary files differnew file mode 100644 index 000000000..b7e2bad6c --- /dev/null +++ b/3889/CH5/EX5.2/Ex5_2output.PNG diff --git a/3889/CH5/EX5.3/Ex5_3.sce b/3889/CH5/EX5.3/Ex5_3.sce new file mode 100644 index 000000000..d9e06917b --- /dev/null +++ b/3889/CH5/EX5.3/Ex5_3.sce @@ -0,0 +1,22 @@ +//Example 5.3
+//page 319
+//Control Systems: Principles and Design
+//M Gopal, Second Edition, Tata McGraw-Hill
+//Chapter: Concepts of Stability: Routh Stability Array
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//transfer function
+s=%s;
+P=s^6+4*s^5+3*s^4 + 2* s^3 +s^2 +4*s +4;
+//routh array
+disp('Routh Array')
+r=routh_t(P)
+disp(r)
+[r,num]=routh_t(1/P,20)
+if num==0
+ disp("As all elements of first row are positive system is stable")
+else
+ mprintf("There are %g sign changes in entries of first column.\nTherefore, system is unstable.", num)
+end
diff --git a/3889/CH5/EX5.3/Ex5_3output.PNG b/3889/CH5/EX5.3/Ex5_3output.PNG Binary files differnew file mode 100644 index 000000000..a93ca399c --- /dev/null +++ b/3889/CH5/EX5.3/Ex5_3output.PNG diff --git a/3889/CH5/EX5.4/Ex5_4.sce b/3889/CH5/EX5.4/Ex5_4.sce new file mode 100644 index 000000000..ed4f4911a --- /dev/null +++ b/3889/CH5/EX5.4/Ex5_4.sce @@ -0,0 +1,22 @@ +//Example 5.4
+//page 321
+//Control Systems: Principles and Design
+//M Gopal, Second Edition, Tata McGraw-Hill
+//Chapter: Concepts of Stability: Routh Stability Array
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//transfer function
+s=%s;
+P=s^5+s^4 + 4* s^3 +24*s^2 +3*s +63;
+//routh array
+disp('Routh Array')
+r=routh_t(P)
+disp(r)
+[r,num]=routh_t(1/P,20)
+if num==0
+ disp("System is stable")
+else
+ mprintf("There are %g sign changes in entries of first column.\nTherefore, system is unstable.", num)
+end
diff --git a/3889/CH5/EX5.4/Ex5_4output.PNG b/3889/CH5/EX5.4/Ex5_4output.PNG Binary files differnew file mode 100644 index 000000000..42e2fb354 --- /dev/null +++ b/3889/CH5/EX5.4/Ex5_4output.PNG diff --git a/3889/CH5/EX5.5/Ex5_5.sce b/3889/CH5/EX5.5/Ex5_5.sce new file mode 100644 index 000000000..e94a985f3 --- /dev/null +++ b/3889/CH5/EX5.5/Ex5_5.sce @@ -0,0 +1,26 @@ +//Example 5.5
+//page 321
+//Control Systems: Principles and Design
+//M Gopal, Second Edition, Tata McGraw-Hill
+//Chapter:Concepts of Stability: Routh Stability Array
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//transfer function
+s=%s;
+P=s^6+2*s^5+8*s^4 + 12* s^3 +20*s^2 +16*s +16;
+//routh array
+disp('Routh Array')
+r=routh_t(P)
+disp(r)
+[r,num]=routh_t(P)
+disp('As there are no sign changes,there is no root on right half of s plane')
+disp('However as two rows are having same values, we decide stability on basis of auxiliary equation')
+//Extracting and finding roots of auxiliary polynomial
+a=flipdim(r(2,:),2)
+b=kron(a(1:$), [1 zeros(1,1)])
+P1=roots(poly(coeff(b),"x","coeff"))
+disp(P1,"Roots of auxiliary equation=")
+disp("As roots of auxiliary equation are purely imaginary, system is marginally stable")
+
diff --git a/3889/CH5/EX5.5/Ex5_5output.PNG b/3889/CH5/EX5.5/Ex5_5output.PNG Binary files differnew file mode 100644 index 000000000..dcd9026fb --- /dev/null +++ b/3889/CH5/EX5.5/Ex5_5output.PNG diff --git a/3889/CH5/EX5.6/Ex5_6.sce b/3889/CH5/EX5.6/Ex5_6.sce new file mode 100644 index 000000000..58642a3a4 --- /dev/null +++ b/3889/CH5/EX5.6/Ex5_6.sce @@ -0,0 +1,23 @@ +//Example 5.6
+//page 323
+//Control Systems: Principles and Design
+//M Gopal, Second Edition, Tata McGraw-Hill
+//Chapter:Concepts of Stability: Routh Stability Array
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//transfer function
+s=%s;
+P=s^5+3*s^4 + 2* s^3 +6*s^2 +6*s +9;
+//routh array
+
+r=routh_t(P)
+disp(r,"Routh Array")
+[r,num]=routh_t(1/P,20)
+disp("We know, eps tends to zero")
+if num==0
+ disp("System is stable")
+else
+ mprintf("There are %g sign changes in entries of first column.\nTherefore, system is unstable.", num)
+end
diff --git a/3889/CH5/EX5.6/Ex5_6output2.PNG b/3889/CH5/EX5.6/Ex5_6output2.PNG Binary files differnew file mode 100644 index 000000000..6b337768e --- /dev/null +++ b/3889/CH5/EX5.6/Ex5_6output2.PNG diff --git a/3889/CH5/EX5.6/Ex5_6outputarray.PNG b/3889/CH5/EX5.6/Ex5_6outputarray.PNG Binary files differnew file mode 100644 index 000000000..47696faa3 --- /dev/null +++ b/3889/CH5/EX5.6/Ex5_6outputarray.PNG diff --git a/3889/CH5/EX5.7/Ex5_7.sce b/3889/CH5/EX5.7/Ex5_7.sce new file mode 100644 index 000000000..e3d541ae2 --- /dev/null +++ b/3889/CH5/EX5.7/Ex5_7.sce @@ -0,0 +1,22 @@ +//Example 5.7
+//page 324
+//Control Systems: Principles and Design
+//M Gopal, Second Edition, Tata McGraw-Hill
+//Chapter:Concepts of Stability: Routh Stability Array
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//transfer function
+s=%s;
+P=s^6+s^5+3*s^4 + 3* s^3 +3*s^2 +2*s +1;
+//routh array
+r=routh_t(P)
+disp(r,"Routh Array")
+[r,num]=routh_t(1/P,20)
+disp("We know, eps tends to zero")
+if num==0
+ disp("System is stable")
+else
+ mprintf("There are %g sign changes in entries of first column.\nTherefore, system is unstable.", num)
+end
diff --git a/3889/CH5/EX5.7/Ex5_7output2.PNG b/3889/CH5/EX5.7/Ex5_7output2.PNG Binary files differnew file mode 100644 index 000000000..b8af86186 --- /dev/null +++ b/3889/CH5/EX5.7/Ex5_7output2.PNG diff --git a/3889/CH5/EX5.7/Ex5_7outputarray.PNG b/3889/CH5/EX5.7/Ex5_7outputarray.PNG Binary files differnew file mode 100644 index 000000000..3693f9b04 --- /dev/null +++ b/3889/CH5/EX5.7/Ex5_7outputarray.PNG diff --git a/3889/CH5/EX5.8/Ex5_8.sce b/3889/CH5/EX5.8/Ex5_8.sce new file mode 100644 index 000000000..ddc724253 --- /dev/null +++ b/3889/CH5/EX5.8/Ex5_8.sce @@ -0,0 +1,22 @@ +//Example 5.8
+//page 326
+//Control Systems: Principles and Design
+//M Gopal, Second Edition, Tata McGraw-Hill
+//Chapter:Concepts of Stability: Routh Stability Array
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//transfer function
+//substitution of s-1 for s
+s=poly(1,'s');
+P= s^3 +7*s^2 +25*s +39;
+//routh array
+r=routh_t(P)
+disp(r,"Routh Array")
+[r,num]=routh_t(1/P,20)
+if num==0
+ disp("As all the elements in first column are positive,roots of characteristic polynomial are more negative than -1 ")
+else
+ mprintf("There is %g sign changes in entries of first column.\nTherefore, characteistic polynomial has some roots relatively unstable with respect to s=-1", num)
+end
diff --git a/3889/CH5/EX5.8/Ex5_8output.PNG b/3889/CH5/EX5.8/Ex5_8output.PNG Binary files differnew file mode 100644 index 000000000..bcea18cc9 --- /dev/null +++ b/3889/CH5/EX5.8/Ex5_8output.PNG diff --git a/3889/CH5/EX5.9/Ex5_9.sce b/3889/CH5/EX5.9/Ex5_9.sce new file mode 100644 index 000000000..f24448eb1 --- /dev/null +++ b/3889/CH5/EX5.9/Ex5_9.sce @@ -0,0 +1,23 @@ +//Example 5.9
+//page 327
+//Control Systems: Principles and Design
+//M Gopal, Second Edition, Tata McGraw-Hill
+//Chapter:Concepts of Stability: Routh Stability Array
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//transfer function
+s=%s;
+P=s*(s^2+s+1)*(s+4);
+k=poly(0,'k')
+//routh array
+disp('Routh Array')
+r=routh_t(1/P,k)
+disp(r)
+disp('Solving for positive values,')
+disp(r($-1,1))
+mprintf('%g >K >0, for stability',kpure(1/P))
+
+
+
diff --git a/3889/CH5/EX5.9/Ex5_9output2.PNG b/3889/CH5/EX5.9/Ex5_9output2.PNG Binary files differnew file mode 100644 index 000000000..5ef4be740 --- /dev/null +++ b/3889/CH5/EX5.9/Ex5_9output2.PNG diff --git a/3889/CH5/EX5.9/Ex5_9outputarray.PNG b/3889/CH5/EX5.9/Ex5_9outputarray.PNG Binary files differnew file mode 100644 index 000000000..87dcfd7f2 --- /dev/null +++ b/3889/CH5/EX5.9/Ex5_9outputarray.PNG |
