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Unformatted text preview: ASE 330M Homework #6 – Due December 5th, 2008 Reading Assignment: Sections 4.5, 4.7, and 4.8 Problem #1, For the unity feedback system below, identify the following quantities: (a) The plant transfer function, Y s / U s (b) The controller transfer function, U s / E s (c) The closed loop transfer function, Y s / R s Problem #2 Find the characteristic equation of the closed loop transfer function (CLTF) identified in problem #1. Express your answer as a function of K . The roots of the characteristic equation are guaranteed to have negative real parts for K K cr . Find K cr . Problem #3 For the characteristic equation and the range of K identified in problem 2, write a MATLAB script that finds the poles of the CLTF for K cr K K cr . Include at least 50 sample values of K within this range. In a single figure, plot the real and imaginary parts of the poles for each value of K considered. [Hint: the following MATLAB commands will be useful: roots, real, imag] Problem #4 For K = 10, plot the step response of the closed loop system using the MATLAB step command. [Hint: Use the MATLAB tf command to upload the closed loop transfer function into MATLAB, then use the step command on the resulting transfer function to generate a plot of the step response.] Problem #5 Use the final value theorem and the CLTF to identify the steady state value of Y s for K 10 . Does your answer match the steady state value from the plot in problem #4? Should it? How far did the solution overshoot the steady state value? ...
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