Description

Homework should be submitted via Canvas before the beginning of the class. Late submission is not accepted.
Professor Milad Siami
Problem 1
Problem 1
(a) Find e(0), e(1), and e(10) for

using the inversion formula.
(b) Check the value of e(0) using the initial-value property.
(c) Check the values calculated in part (a) using partial fractions.
(d) Find e(k) for k = 0,1,2,3,4 if Z[e(k)] is given by

(e) A continuous time function e(t), when sampled at a rate of 10 Hz (T = 0.1s), has the following ztransform . Find function e(t).
(f) Repeat part (e) for .
(g) From parts (e) and (f), what is the effect on the inverse z-transform of changing the sign on a real pole?
Problem 2
Problem 2
Consider the system described by
,
(a) Find the transfer function
(b) Using any similarity transformation, find a different state model for this system.
(c) Find the transfer function of the system from the transformed state equations.
Problem 3
Problem 3
Given the MATLAB program

that solves the difference equation of a digital controller.
(a) Find the transfer function of the controller from input e(.) to output m(.).
(b) Find the z-transform of the controller input .
(c) Use the results of parts (a) and (b) to find the inverse z-transform of the controller output. (d) Run the program to check the results of part (c). Please attach your MATLAB code/result (from the command window) to your report.
Problem 4
Problem 4
Problem 3.7-7 of the textbook (page 113).