From 7f60ea012dd2524dae921a2a35adbf7ef21f2bb6 Mon Sep 17 00:00:00 2001
From: prashantsinalkar
Date: Tue, 10 Oct 2017 12:27:19 +0530
Subject: initial commit / add all books

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+// Example 9.12
+// Step Response with variable damping
+V_s1=0; // Voltage source value for t<0
+V_s2=30;//Voltage source value for t>0 
+L=0.1;
+C=1/640;
+omega_0=sqrt(1/(L*C));
+v_C_aft=0; // v_C(0^+)=0;
+v_C_aft_d=0; // v_C'(0^+)=0;
+V_ss=30;
+// for Overdamped Response
+// Let
+R=34;
+alpha=R/(2*L);
+p1=-alpha+sqrt(alpha^2-omega_0^2)
+p2=-alpha-sqrt(alpha^2-omega_0^2)
+P=[1,1;p1,p2];// coefficients of A's matrix
+V=[v_C_aft-V_ss;v_C_aft_d];// initial conditions and excitations
+A=P\V;
+A_1=A(1);
+A_2=A(2);
+t=0:0.001:0.5
+v_C=V_ss+A_1*exp(p1*t)+A_2*exp(p2*t);// t>0
+// for Underdamped Response
+// Let
+R1=5;
+alpha1=R1/(2*L);
+p3=-alpha1+sqrt(alpha1^2-omega_0^2);
+p4=-alpha1-sqrt(alpha1^2-omega_0^2);
+omega_d=sqrt(omega_0^2-alpha1^2);
+P1=[1,1;p3,p4];
+V1=[v_C_aft-V_ss;v_C_aft_d];
+A1=P1\V1
+A_3=A1(1);
+v_C1=V_ss+2*abs(A_3)*exp(-alpha1*t).*cos(omega_d*t+atan(imag(A_3),real(A_3)));
+// for Critically Damped Response
+R2=sqrt(6400/25);
+alpha2=R2/(2*L);
+A_4=v_C_aft-V_ss;
+A_5=v_C_aft_d+alpha2*A_4;
+v_C2=V_ss+A_4*exp(-alpha2*t)+A_5*t.*exp(-alpha2*t);
+plot(t,v_C,t,v_C1,t,v_C2)
+xlabel('t')
+ylabel('v_c(t)')
+title('Step Response with variable damping')
+h1=legend(['Overdamped';'Underdamped';'Critically damped'])
-- 
cgit