System Identification Homework for Mechanical and Aerospace Engineering Students at UF, Fa, Assignments of Electrical and Electronics Engineering

Download System Identification Homework for Mechanical and Aerospace Engineering Students at UF, Fa and more Assignments Electrical and Electronics Engineering in PDF only on Docsity! EML 4930 Fall 2008 System Identification University of Florida Mechanical and Aerospace Engineering HW #2 Issued: September 19, 2008 Due : in class on September 26, 2008 Problem 1. 1. Download the MATLAB function F sim system1.p from the class website that produces noisy output signal for a 1st order linear discrete time system y[k + 1] = ay[k] + bu[k], for a given initial condition and an input signal {u[k]}. Read the “readme.txt” for help on using the function. Use the function to gather measurements of the output of the system. Estimate the parameters a and b by choosing an appropriate input signal type (step, sinusoidal, etc.), length of the signal N , and an initial condition. 2. Choose a few values of N and plot the least squares estimates a and b obtained as a function of “data length” N . What conclusion do you draw from this plot? 3. Repeat the above, but now with the MATLAB function F sim system2.p, which simulates a different first order system. Problem 2. The function F sim system3.p (available from the class website) also simulates a first order system, but now you can’t specify the initial condition. Instead the function chooses the initial condition. Obtain least squares estimates of a and b. Problem 3. We know that the Laplace transform of the signal y(t) = eζt1(t), where ζ ∈ C, is Y (s) = 1/(s − ζ), with the ROC specified by Re(s) > Re(ζ). Compute the Laplace transform for a large number of values of s in the region specified by 0 < Re(s) < 50 and −50 < Imag(s) < 50. Provide a surface plot of |Y (s)| and ∠(Y (s)) for the values of s in this region. Prabir Barooah 1