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| author | prashantsinalkar | 2017-10-10 12:27:19 +0530 |
|---|---|---|
| committer | prashantsinalkar | 2017-10-10 12:27:19 +0530 |
| commit | 7f60ea012dd2524dae921a2a35adbf7ef21f2bb6 (patch) | |
| tree | dbb9e3ddb5fc829e7c5c7e6be99b2c4ba356132c /1430/CH15/EX15.7/exa15_7.sce | |
| parent | b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (diff) | |
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initial commit / add all books
Diffstat (limited to '1430/CH15/EX15.7/exa15_7.sce')
| -rw-r--r-- | 1430/CH15/EX15.7/exa15_7.sce | 33 |
1 files changed, 33 insertions, 0 deletions
diff --git a/1430/CH15/EX15.7/exa15_7.sce b/1430/CH15/EX15.7/exa15_7.sce new file mode 100644 index 000000000..9c0177269 --- /dev/null +++ b/1430/CH15/EX15.7/exa15_7.sce @@ -0,0 +1,33 @@ +// Example 15.7
+// Calculating the Zero-Input Response
+t=0:0.01:10;
+s=%s;
+n=2;
+r=2;
+A=[-8,-5;3,0];
+C=[6,10;0,-2];
+q_1_bef=2; //q_1(0^-)
+q_2_bef=-4;//q_2(0^-)
+q_bef=[2;-4]; // q(0^-)
+I=eye(2,2)
+W=s*I-A;
+// Taking adjoint of W i.e. adj[s*I-A]
+W_adj=[s,-5;3 ,s+8]
+P_s=det(W);
+phi_s=W_adj/P_s // Resolvent matrix
+// Transform of the state vector
+Q_s=phi_s*q_bef;
+// Writing down two elements of Q_s
+Q_s1=(2*s+20)/P_s;
+q_1=7*exp(-3*t)-5*exp(-5*t);// inverse laplace transform of Q_s1
+Q_s2=(-4*s-26)/P_s;
+q_2=-7*exp(-3*t)+3*exp(-5*t); // inverse laplace transform of Q_s2
+// y=C*q=[6,10;0,-2]*[q_1;q_2]=[6*q1+10*q2;-2*q2]
+y_1=6*q_1+10*q_2;
+y_2=-2*q_2;
+plot(t,y_1,'-g',t,y_2,'-r')
+xlabel('t');
+ylabel('y');
+title('Signal Waveform')
+h1=legend(['y_1';'y_2']);
+
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