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hmwk2 - u i and y i n are used where n is additive white...

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University of California, Santa Barbara Department of Electrical & Computer Engineering ECE 147c: Digital Control Spring 2009 Homework 2. Due 5.00pm Tuesday, 5th May, 2009 in the homework boxes on the 3rd floor of Harold Frank Hall. Consider the following continuous time system, H ( s ) = 100 s 2 + 4 s + 100 . In this problem, you will use discrete time signals to excite this system through a sample and hold and will use the data collected to identify its frequency response. 1. Perform a discretization of H using c2d using the zoh option, and a sampling period of 0.05 seconds. Generate a zero mean white random noise signal using randn and use it as an input to the discretized system using lsim . Take the resulting output over 10000 and 100000 time samples and name them as y 1 and y 2 respectively. Name the corresponding parts of the input u 1 and u 2 respectively. 2. Consider two cases for both y 1 and y 2 (four cases in total). The first is where u i and y i ( i = 1 , 2) are used to identify the frequency response. The second is where
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Unformatted text preview: u i and y i + n are used, where n is additive white gaussian noise of variance 1 (this can be generated using randn ). In all four cases, estimate the frequency response using etfe . Generate four bode plots each having one of the identi²ed responses together with the original frequency response of H . Comment on the mismatches and their possible sources. 3. This part should be done with input and output signals of length 100000 time steps. The output should have additive noise of variance of 1. Instead of using white noise as input, use as input a colored noise signal, ˆ u . This signal is generated from a white noise signal u by passing it through a ²rst order highpass ²lter with a cuto³ frequency of 8 rad/sec. Plot the identi²ed frequency response together with the real response and comment on the mismatches and their possible. 1...
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