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| author | priyanka | 2015-06-24 15:03:17 +0530 |
|---|---|---|
| committer | priyanka | 2015-06-24 15:03:17 +0530 |
| commit | b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (patch) | |
| tree | ab291cffc65280e58ac82470ba63fbcca7805165 /842/CH9 | |
| download | Scilab-TBC-Uploads-b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b.tar.gz Scilab-TBC-Uploads-b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b.tar.bz2 Scilab-TBC-Uploads-b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b.zip | |
initial commit / add all books
Diffstat (limited to '842/CH9')
29 files changed, 329 insertions, 0 deletions
diff --git a/842/CH9/EX9.1/Example9_1.sce b/842/CH9/EX9.1/Example9_1.sce new file mode 100755 index 000000000..3cc48f678 --- /dev/null +++ b/842/CH9/EX9.1/Example9_1.sce @@ -0,0 +1,8 @@ +//clear//
+//Example9.1:Lapalce Transform x(t) = exp(-at).u(t)
+syms t s;
+a = 3;
+y =laplace('%e^(-a*t)',t,s);
+disp(y)
+//Result
+//1/(s+a)
diff --git a/842/CH9/EX9.10/Example9_10.sce b/842/CH9/EX9.10/Example9_10.sce new file mode 100755 index 000000000..e2246733f --- /dev/null +++ b/842/CH9/EX9.10/Example9_10.sce @@ -0,0 +1,12 @@ +//clear//
+//Example9.10:Inverse Lapalce Transform
+//X(S) = 1/((s+1)(s+2)) Re(s)< -1,Re(s)< -2
+s =%s ;
+syms t ;
+[A]=pfss(1/((s+1)*(s+2))) //partial fraction of F(s)
+F1 = ilaplace(A(1),s,t)
+F2 = ilaplace(A(2),s,t)
+F = -F1-F2;
+disp(F,"f(t)=")
+//Result
+// %e^-(2*t)-%e^-t
diff --git a/842/CH9/EX9.11/Example9_11.sce b/842/CH9/EX9.11/Example9_11.sce new file mode 100755 index 000000000..af99b5f11 --- /dev/null +++ b/842/CH9/EX9.11/Example9_11.sce @@ -0,0 +1,12 @@ +//clear//
+//Example9.11:Inverse Lapalce Transform
+//X(S) = 1/((s+1)(s+2)) -2< Re(s)< -1
+s =%s ;
+syms t ;
+[A]=pfss(1/((s+1)*(s+2))) //partial fraction of F(s)
+F1 = ilaplace(A(1),s,t)
+F2 = ilaplace(A(2),s,t)
+F = -F1+F2;
+disp(F,"f(t)=")
+//Result
+// -(%e^-t)-(%e^-(2*t))
diff --git a/842/CH9/EX9.12/Example9_12.sce b/842/CH9/EX9.12/Example9_12.sce new file mode 100755 index 000000000..876152dbc --- /dev/null +++ b/842/CH9/EX9.12/Example9_12.sce @@ -0,0 +1,7 @@ +//clear//
+//Example9.12:Inverse Lapalce Transform
+//X(S) = 1/(s+(1/2)) Re(s)> -1/2
+s =%s ;
+G =syslin('c',(1/(s+0.5)))
+disp(G,"G( s )=")
+plzr(G)
diff --git a/842/CH9/EX9.13/Example9_13.sce b/842/CH9/EX9.13/Example9_13.sce new file mode 100755 index 000000000..97c9faa64 --- /dev/null +++ b/842/CH9/EX9.13/Example9_13.sce @@ -0,0 +1,19 @@ +//clear//
+//Example9.13
+//Inverse Lapalce Transform
+//X1(S) = 1/(s+1) Re(s)> -1
+//X2(S) = 1/((s+1)(s+2)) Re(s)>-1
+s =%s ;
+syms t ;
+G1 =syslin('c',(1/(s+1)));
+disp(G1,"G( s )=")
+figure
+plzr(G1)
+G2 =syslin('c',(1/((s+1)*(s+2))));
+disp(G2,"G( s )=")
+figure
+plzr(G2)
+G3 = syslin('c',(1/(s+1))-(1/((s+1)*(s+2))));
+disp(G3,"G( s )=")
+figure
+plzr(G3)
diff --git a/842/CH9/EX9.14/Example9_14.sce b/842/CH9/EX9.14/Example9_14.sce new file mode 100755 index 000000000..b7da6a7d6 --- /dev/null +++ b/842/CH9/EX9.14/Example9_14.sce @@ -0,0 +1,14 @@ +//clear//
+//Example9.14:Lapalce Transform
+//x(t) = t.exp(-at), t>0
+//x(t) = (t^2)/2.exp(-at), t>0
+s =%s ;
+syms t ;
+a =10;
+x1 = laplace('t*%e^(-10*t)',t,s);
+disp(x1)
+x2 = laplace('((t^2)/2)*%e^(-10*t)',t,s);
+disp(x2)
+//Result
+//1/((s+10)^2)
+// 1/((s+10)^3)
diff --git a/842/CH9/EX9.15/Example9_15.sce b/842/CH9/EX9.15/Example9_15.sce new file mode 100755 index 000000000..7c86a11d1 --- /dev/null +++ b/842/CH9/EX9.15/Example9_15.sce @@ -0,0 +1,13 @@ +//clear//
+//Example9.15:Inverse Lapalce Transform
+//X(S) = (2s^2+5s+5)/((s+1)^2)(s+2)) Re(s)>-1
+s =%s ;
+syms t ;
+[A]=pfss((2*(s^2)+5*s+5)/(((s+1)^2)*(s+2))); //partial fraction of F(s)
+F1 = ilaplace(A(1),s,t)
+F2 = ilaplace(A(2),s,t)
+//F3 = ilaplace(A(3),s,t)
+F = F1+F2;
+disp(F,"f(t)=")
+//Result
+//(2*t*(%e^-t))-(%e^-t)+(3*%e^-(2*t))
diff --git a/842/CH9/EX9.16/Example9_16.sce b/842/CH9/EX9.16/Example9_16.sce new file mode 100755 index 000000000..28fe8e4de --- /dev/null +++ b/842/CH9/EX9.16/Example9_16.sce @@ -0,0 +1,12 @@ +//clear//
+//Example9.16:Initial Value Theorem of Lapalace Transform
+syms s;
+num =poly([12 5 2],'s','coeff')
+den =poly([20 14 4 1],'s','coeff')
+X = num/den
+disp (X,"X(s)=")
+SX = s*X;
+Initial_Value =limit(SX,s,%inf);
+disp(Initial_Value,"x(0)=")
+//Result
+//(2*%inf^3+5*%inf^2+12*%inf)/(%inf^3+4*%inf^2+14*%inf+20) =2
diff --git a/842/CH9/EX9.17/Example9_17.sce b/842/CH9/EX9.17/Example9_17.sce new file mode 100755 index 000000000..0b8d044ec --- /dev/null +++ b/842/CH9/EX9.17/Example9_17.sce @@ -0,0 +1,8 @@ +//clear//
+//Example9.17:Analysis and Characterization of LTI System
+//Lapalce Transform h(t) = exp(-t).u(t)
+syms t s;
+h =laplace('%e^(-t)',t,s);
+disp(h)
+//Result
+//1/(s+1)
diff --git a/842/CH9/EX9.18/Example9_18.sce b/842/CH9/EX9.18/Example9_18.sce new file mode 100755 index 000000000..0ecf9e867 --- /dev/null +++ b/842/CH9/EX9.18/Example9_18.sce @@ -0,0 +1,9 @@ +//clear//
+//Example9.18:Analysis and Characterization of LTI System
+//Lapalce Transform x(t) = exp(-abs(t))
+//x(t) = exp(-t).u(t)+exp(t).u(-t)
+syms t s;
+y = laplace('%e^(-t)-%e^(t)',t,s);
+disp(y)
+//Result
+// (1/(s+1))-(1/(s-1))
diff --git a/842/CH9/EX9.19/Example9_19.sce b/842/CH9/EX9.19/Example9_19.sce new file mode 100755 index 000000000..654f41b7c --- /dev/null +++ b/842/CH9/EX9.19/Example9_19.sce @@ -0,0 +1,12 @@ +//clear//
+//Example9.19:Analysis and Characterization of LTI System
+//Inverse Lapalce Transform
+//X(S) = (e^s)/(s+1)
+syms s t ;
+h1 = exp(-1);//Inverse Laplace Transform of exp(s)
+H2 =1/(s+1);
+h2 = ilaplace(H2,s,t)
+h = h1*h2;
+disp(h,"h(t)=")
+//Result
+// (18089*(%e^-t))/49171 = 0.3678794(%e^-t)
diff --git a/842/CH9/EX9.2/Example9_2.sce b/842/CH9/EX9.2/Example9_2.sce new file mode 100755 index 000000000..27042029e --- /dev/null +++ b/842/CH9/EX9.2/Example9_2.sce @@ -0,0 +1,8 @@ +//clear//
+//Example9.2:Lapalce Transform x(t) = -exp(-at).u(-t)
+syms t s;
+a =3;
+y = laplace('%e^(a*-t)',t,s);
+disp(y)
+//Result
+//1/(s+a)
diff --git a/842/CH9/EX9.20/Example9_20.sce b/842/CH9/EX9.20/Example9_20.sce new file mode 100755 index 000000000..12fad35e3 --- /dev/null +++ b/842/CH9/EX9.20/Example9_20.sce @@ -0,0 +1,17 @@ +//clear//
+//Example9.20:Inverse Lapalce Transform
+//X(S) = ((s-1)/((s+1)*(s-2)))
+s =%s ;
+syms t ;
+[A] = pfss(s/((s+1)*(s-2)));
+[B] = pfss(1/((s+1)*(s-2)));
+F1 = ilaplace(A(1),s,t)
+F2 = ilaplace(A(2),s,t)
+F3 = ilaplace(B(1),s,t)
+F4 = ilaplace(B(2),s,t)
+F = F1+F2-F3-F4;
+disp(F,"f(t)=")
+//Result
+//f(t)= 33333329999999*exp(2*t)/99999970000000+6666664*%e^-t/9999997
+//i.e. f(t) =0.3333334*exp(2*t)+0.6666666*%e^(-t)
+//Refer equation 9.120. (1/3)=0.3333 and (2/3) = 0.66666
diff --git a/842/CH9/EX9.21/Example9_21.sce b/842/CH9/EX9.21/Example9_21.sce new file mode 100755 index 000000000..a485b6e3b --- /dev/null +++ b/842/CH9/EX9.21/Example9_21.sce @@ -0,0 +1,8 @@ +//clear//
+//Example9.21:Analysis and Characterization of LTI System
+//Lapalce Transform h(t) = exp(2t)u(t), Re(s)>2
+syms t s;
+X = laplace('%e^(2*t)',t,s);
+disp(X)
+//Result
+//1/(s-2)
diff --git a/842/CH9/EX9.25/Example9_25.sce b/842/CH9/EX9.25/Example9_25.sce new file mode 100755 index 000000000..81296cda7 --- /dev/null +++ b/842/CH9/EX9.25/Example9_25.sce @@ -0,0 +1,13 @@ +//clear//
+//Example9.25:LTI Systems Characterized by Linear Constant
+//Coefficient differential Equation
+//Finding Transfer function H(S) of LTI system
+//x(t) = exp(-3t).u(t)
+//y(t) = [exp(-t)-exp(-2t)].u(t)
+syms t s;
+X = laplace('%e^(-3*t)',t,s);
+Y = laplace('%e^(-t)-%e^(-2*t)',t,s);
+H = Y/X;
+disp(H)
+//Result
+//(s+3)*(1/(s+1)-1/(s+2))
diff --git a/842/CH9/EX9.3/Example9_3.sce b/842/CH9/EX9.3/Example9_3.sce new file mode 100755 index 000000000..978f199ab --- /dev/null +++ b/842/CH9/EX9.3/Example9_3.sce @@ -0,0 +1,7 @@ +//clear//
+//Example9.3:Lapalce Transform x(t) = 3exp(-2t)u(t)-2exp(-t)u(t)
+syms t s;
+y = laplace('3*%e^(-2*t)-2*%e^(-t)',t,s);
+disp(y)
+//Result
+//(3/(s+2))-(2/(s+1))
diff --git a/842/CH9/EX9.31/Example9_31.sce b/842/CH9/EX9.31/Example9_31.sce new file mode 100755 index 000000000..cdb6d63cc --- /dev/null +++ b/842/CH9/EX9.31/Example9_31.sce @@ -0,0 +1,19 @@ +//clear//
+//Example9.31:Causal LTI Systems described by differential equations
+//and Rational System functions
+//Partial Fraction
+//H(S) = ((s-1)/((s+1)*(s-2)))
+s =%s ;
+syms t ;
+[A] = pfss((2*s^2+4*s-6)/(s^2+3*s+2));
+disp(A,"H(S)=")
+//Result H(S)=
+//// - 8
+// -----
+// 1 + s
+// 6
+// -----
+// 2 + s
+//
+// 2
+
diff --git a/842/CH9/EX9.33/Example9_33.sce b/842/CH9/EX9.33/Example9_33.sce new file mode 100755 index 000000000..54c9c3785 --- /dev/null +++ b/842/CH9/EX9.33/Example9_33.sce @@ -0,0 +1,9 @@ +//clear//
+//Example9.33:Unilateral Laplace Transform:Time Shifting Property
+//x(t) = exp(-a(t+1)).u(t+1)
+syms t s;
+a = 2;
+X = laplace('%e^(-a*(t+1))',t,s);
+disp(X)
+//Result
+//%e^-a/(s+a)
diff --git a/842/CH9/EX9.34/Example9_34.sce b/842/CH9/EX9.34/Example9_34.sce new file mode 100755 index 000000000..cf25b8f11 --- /dev/null +++ b/842/CH9/EX9.34/Example9_34.sce @@ -0,0 +1,11 @@ +//clear//
+//Example9.34:Unilateral Laplace Transform
+//x(t) = s(t)+2u(t)+e^t.u(t)
+syms t s;
+a = 2;
+X = laplace('2+%e^(t)',t,s);
+Y = 1+X;
+disp(X)
+disp(Y)
+//Result
+// (2/s)+(1/(s-1))+1
diff --git a/842/CH9/EX9.35/Example9_35.sce b/842/CH9/EX9.35/Example9_35.sce new file mode 100755 index 000000000..7f926cfe8 --- /dev/null +++ b/842/CH9/EX9.35/Example9_35.sce @@ -0,0 +1,11 @@ +//clear//
+//Example9.35:Unilateral Inverse Laplace Transform
+//X(S) = 1/((s+1)(s+2))
+s = %s;
+syms t;
+X = 1/((s+1)*(s+2));
+x = ilaplace(X,s,t);
+disp(X)
+disp(x)
+//Result
+// (%e^-t)-(%e^-(2*t))
diff --git a/842/CH9/EX9.36/Example9_36.sce b/842/CH9/EX9.36/Example9_36.sce new file mode 100755 index 000000000..88c213281 --- /dev/null +++ b/842/CH9/EX9.36/Example9_36.sce @@ -0,0 +1,7 @@ +//clear//
+//Example9.36:Unilateral Laplace Transform
+//X(S) = ((s^2)-3)/(s+2)
+s = %s;
+syms t;
+[X] = pfss(((s^2)-3)/(s+2));
+disp(X)
diff --git a/842/CH9/EX9.37/Example9_37.sce b/842/CH9/EX9.37/Example9_37.sce new file mode 100755 index 000000000..7b0300cce --- /dev/null +++ b/842/CH9/EX9.37/Example9_37.sce @@ -0,0 +1,14 @@ +//clear//
+//Example9.37:Unilateral Laplace Transform:Solving Differential Equation
+//Y(S) = alpha/(s(s+1)(s+2))
+s = %s;
+syms t;
+alpha = 1; //Alpha value assigned as some constant one
+[A] = pfss(alpha/(s*(s+1)*(s+2)));
+F1 = ilaplace(A(1),s,t)
+F2 = ilaplace(A(2),s,t)
+F3 = ilaplace(A(3),s,t)
+F = F1+F2+F3
+disp(F)
+//result
+// (-%e^-t)+((%e^-(2*t))/2)+(1/2 )
diff --git a/842/CH9/EX9.38/Example9_38.sce b/842/CH9/EX9.38/Example9_38.sce new file mode 100755 index 000000000..aeeb74e95 --- /dev/null +++ b/842/CH9/EX9.38/Example9_38.sce @@ -0,0 +1,17 @@ +//clear//
+//Example9.38:Unilateral Laplace Transform:Solving Differential Equation
+//Y(S)=[beta(s+3)/((s+1)(s+2))]+[gamma/((s+2)(s+2))]+[alpha/(s(s+1)(s+2))]
+s = %s;
+syms t;
+alpha = 2; //input constant
+beta_B = 3; //intial condition
+gamma_v = -5; //initial condition
+Y1 = 1/s;
+Y2 = 1/(s+1);
+Y3 = 3/(s+2);
+Y = Y1-Y2+Y3;
+disp(Y)
+y = ilaplace(Y,s,t)
+disp(y)
+//result
+// ( -%e^(-t))+3*(%e^(-(2*t)))+1
diff --git a/842/CH9/EX9.4/Example9_4.sce b/842/CH9/EX9.4/Example9_4.sce new file mode 100755 index 000000000..dc9f05e86 --- /dev/null +++ b/842/CH9/EX9.4/Example9_4.sce @@ -0,0 +1,8 @@ +//clear//
+//Example9.4:Lapalce Transform x(t) = exp(-2t)u(t)+exp(-t)(cos3t)u(t)
+syms t s;
+y = laplace('%e^(-2*t)+%e^(-t)*cos(3*t)',t,s);
+disp(y)
+//Result
+//[(s+1)/(s^2+2*s+10)]+[1/(s+2)] refer equation 9.29
+//Equivalent to (2*s^2+5*s+12)/((s^2+2*s+10)*(s+2)) refer equation 9.30
diff --git a/842/CH9/EX9.5/Example9_5.sce b/842/CH9/EX9.5/Example9_5.sce new file mode 100755 index 000000000..9a5f6e4e7 --- /dev/null +++ b/842/CH9/EX9.5/Example9_5.sce @@ -0,0 +1,8 @@ +//clear//
+//Example9.5:Lapalce Transform of x(t)=s(t)-(4/3)exp(-t)u(t)+(1/3)exp(2t)u(t)
+syms t s;
+y = laplace('-(4/3)*%e^(-t)+(1/3)*%e^(2*t)',t,s);
+y = 1+y;
+disp(y)
+//Result
+//[-4/(3*(s+1))]+[1/(3*(s-2))]+1
diff --git a/842/CH9/EX9.6/Example9_6.sce b/842/CH9/EX9.6/Example9_6.sce new file mode 100755 index 000000000..0b6b570d6 --- /dev/null +++ b/842/CH9/EX9.6/Example9_6.sce @@ -0,0 +1,11 @@ +//clear//
+//Example9.6
+//Lapalce Transform x(t) = exp(-at)u(t), 0<t<T
+syms t s;
+a = 3;
+T = 10;
+//t = T;
+y = laplace('%e^(-a*t)-%e^(-a*t)*%e^(-(s+a)*T)',t,s);
+disp(y)
+//Result
+// [1/(s+a)]-[(exp((-s-a)*T))/(s+a)]
diff --git a/842/CH9/EX9.7/Example9_7.sce b/842/CH9/EX9.7/Example9_7.sce new file mode 100755 index 000000000..9abac173f --- /dev/null +++ b/842/CH9/EX9.7/Example9_7.sce @@ -0,0 +1,10 @@ +//clear//
+//Example9.7
+//Lapalce Transform x(t) = exp(-b.abs(t)).u(t), 0<t<T
+//x(t) = exp(-bt).u(t)+exp(bt).u(-t)
+syms t s;
+b = 3;
+y = laplace('%e^(-b*t)-%e^(b*t)',t,s);
+disp(y)
+//Result
+// [1/(s+b)]-[1/(s-b)]
diff --git a/842/CH9/EX9.8/Example9_8.sce b/842/CH9/EX9.8/Example9_8.sce new file mode 100755 index 000000000..c44b7ebf1 --- /dev/null +++ b/842/CH9/EX9.8/Example9_8.sce @@ -0,0 +1,13 @@ +//clear//
+//Example9.8:Inverse Lapalce Transform
+//X(S) = 1/((s+1)(s+2))
+s =%s ;
+G =syslin('c',(1/((s+1)*(s+2)))) ;
+disp(G,"G( s )=")
+plzr(G)
+x=denom(G) ;
+disp(x,"Ch a r a c t e r i s t i c s Polynomial=" )
+y = roots(x) ;
+disp(y,"Poles of a system=" )
+//Result
+// -1 and -2
diff --git a/842/CH9/EX9.9/Example9_9.sce b/842/CH9/EX9.9/Example9_9.sce new file mode 100755 index 000000000..1b27379ae --- /dev/null +++ b/842/CH9/EX9.9/Example9_9.sce @@ -0,0 +1,12 @@ +//clear//
+//Example9.9:Inverse Lapalce Transform
+//X(S) = 1/((s+1)(s+2))
+s =%s ;
+syms t ;
+[A]=pfss(1/((s+1)*(s+2))) //partial fraction of F(s)
+F1 = ilaplace(A(1),s,t)
+F2 = ilaplace(A(2),s,t)
+F=F1+F2;
+disp(F,"f(t)=")
+//Result
+// (%e^-t)-(%e^-(2*t))
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