Description
Problem 1
- Find e(0), e(1), and e(10) for
using the inversion formula.
- Check the value of e(0) using the initial-value property.
- Check the values calculated in part (a) using partial fractions.
- Find e(k) for k = 0,1,2,3,4 if Z[e(k)] is given by
- 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).
- Repeat part (e) for .
- 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
,
- Find the transfer function
- Using any similarity transformation, find a different state model for this system.
- 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.
- Find the transfer function of the controller from input e(.) to output m(.).
- Find the z-transform of the controller input .
- 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).
