An RL circuit equation subject to a voltage source is given by: di L = +...

   

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An RL circuit equation subject to a voltage source is given by: di L = + Ri= v dt 1.a. Assuming v is constant and i(0) = lo, solve the differential equation and find an analytical expression for i(t). 1.b. Discretize the differential equation using the backward difference approximation and find and update law for i(k). Note that in BD: x(t)*(K)-x(k-1) At 1.c. Discretize the differential equation using the forward difference approximation and find and update law for i(k+1). Note that in FD: x(t) = x(k+1)-x(k) At 1.d. Using Matlab, plot the analytical solution for i(t) from Part 1.a vs. time for the following parameter values: L = 5 H R = 20 Ohm 10 = 0.5 A v=5 V t = [0:0.1:1] s 1.e. Write a Matlab script to compute i_bd(k) based on the obtained BD update law from 1.b inside a "for" loop, and i_fd(k+1) based on the FD update law from 1.c inside another "for" loop. Use the same parameter values as those listed in 1.d. Plot i(t),i_bd and i_fd vs. time on the same figure. Use different line types and legends to distinguish the three current trajectories (the analytical solution, the one obtained from the BD difference discretization, and the one obtained from the FD discretization). 1.f. Repeat exercise 1.e. for the following time vectors (use a separate figure for each time vector): t = [0:0.01:1] t = [0:0.001:1] What do you notice as time step decreases? An RL circuit equation subject to a voltage source is given by: di L = + Ri= v dt 1.a. Assuming v is constant and i(0) = lo, solve the differential equation and find an analytical expression for i(t). 1.b. Discretize the differential equation using the backward difference approximation and find and update law for i(k). Note that in BD: x(t)*(K)-x(k-1) At 1.c. Discretize the differential equation using the forward difference approximation and find and update law for i(k+1). Note that in FD: x(t) = x(k+1)-x(k) At 1.d. Using Matlab, plot the analytical solution for i(t) from Part 1.a vs. time for the following parameter values: L = 5 H R = 20 Ohm 10 = 0.5 A v=5 V t = [0:0.1:1] s 1.e. Write a Matlab script to compute i_bd(k) based on the obtained BD update law from 1.b inside a "for" loop, and i_fd(k+1) based on the FD update law from 1.c inside another "for" loop. Use the same parameter values as those listed in 1.d. Plot i(t),i_bd and i_fd vs. time on the same figure. Use different line types and legends to distinguish the three current trajectories (the analytical solution, the one obtained from the BD difference discretization, and the one obtained from the FD discretization). 1.f. Repeat exercise 1.e. for the following time vectors (use a separate figure for each time vector): t = [0:0.01:1] t = [0:0.001:1] What do you notice as time step decreases?

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1a Assuming v is constant and i0 io the differential equation for an RL circuit subject to a voltage ... View the full answer