# hw2 - Homework 2 MAE143B Spring 2010 due Thursday April 15...

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Homework 2 - MAE143B Spring 2010: due Thursday April 15 Question 1 — State Variable Realization Consider the system from input, u ( t ) , to output, y ( t ) , described by the transfer function 4 s + 4 s 3 + 2 . 4 s 2 + 25 . 84 s + 50 . 08 . Provide a state-variable description of this system. That is, write down a ﬁrst-order vector ordinary differential equation together with an output equation which represents this relationship between u and y . Check your answer in matlab using the tf command. That is, create a system with your A , B , C and D matrices from your state-variable description via sys = ss(A,B,C,D), then compare matlab’s reverse computation to the above system via the command tf(sys). Plot the frequency response of the state-variable realization of this system using the matlab bode(sys) command. Label your plot well. Question 2 — Simulation with sinusoidal input Use the state-variable description of the system from Question 1 to construct a numerical simu- lation of the system with an input

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hw2 - Homework 2 MAE143B Spring 2010 due Thursday April 15...

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