| ECE 381: Laboratory 5 |
Winter 2006 |
| Analog system response using ODE solvers |
February 21 |
|
| Part II.
Assignment |
Preparatory
notes | Assignment |
|
Use Matlab, as explained in the preparatory notes, to numerically evaluate
the zero-state, zero-input, and total response for each of the analog systems
described by the following differential equations :
| |
System equation |
Excitation |
Initial Conditions |
Solve for |
| (a) |
y''(t) + 5y'(t) +
6y(t) = x(t); |
x(t) = 6u(t);
|
y(0) = 0, y'(0) = 1; |
0 ≤ t ≤ 10. |
| (b) |
y''(t) + 5y'(t) +
6y(t) = x(t); |
x(t) = 2e-tu(t);
|
y(0) = 0, y'(0) = 1; |
0 ≤ t ≤ 8. |
| (c) |
y''(t) + 4y'(t) +
3y(t) = x(t); |
x(t) = 36tu(t);
|
y(0) = 0, y'(0) = 1; |
0 ≤ t ≤ 2. |
| (d) |
y''(t) + 4y'(t) +
4y(t) = x(t); |
x(t) = 2e-2tu(t);
|
y(0) = 0, y'(0) = 1; |
0 ≤ t ≤ 5. |
| (e) |
y''(t) + 4y'(t) +
4y(t) = x(t); |
x(t) = 8cos(2t)u(t);
|
y(0) = 0, y'(0) = 1; |
0 ≤ t ≤ 10. |
| (f) |
y'''(t) + 4y''(t) +
5y'(t) + 2y(t) = x(t);
|
x(t) = e-2tu(t);
|
y(0) = 0, y'(0) = 1, y''(0) = 0;
|
0 ≤ t ≤ 10. |
In each case, obtain the three responses separately for the indicated
interval of time, and plot them in one figure, on the same time axis. Comment on
the results. In particular, can you verify the initial conditions from your
plots? Do the zero-state and zero-input responses seem to add up to the total
response? Can you identify the transient and steady-state responses in your
plots?
Turn in all plots, Matlab scripts and functions. Include your comments and
answers to questions.
School of Computing and Engineering
University of
Missouri - Kansas City |
Last updated: February 20, 2006
|