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MATLAB_ASSIGNMENT_5_Spring_2009_upd ated

# MATLAB_ASSIGNMENT_5_Spring_2009_upd ated - (a t y = t 5...

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MATLAB ASSIGNMENT # 5 ECSE-2410 Signals & Systems – Spring 2009 Wed 04/29/09 1(25). For the circuits shown, (A) (B). (a). Find ) ( s H , where R 1 = 1 Ω, R 2 = 2 Ω, C = ½ F (b). Use Matlab to plot the Bode magnitude and phase diagrams. (c). As in HW 14, state whether the phase shift is leading (positive) or lagging (negative). 2(25). Given the RLC circuit shown, (a). Find ) ( s H by hand. (b). Use MATLAB to plot pole zero diagram. (hint: use pzplot or rlocus command) (c). Use MATLAB to find n ϖ ζ , . (hint, use grid command, and use the data cursor to mark where a pole is. (d). Now find find n ϖ ζ , by hand. Do your results match part c? (d). Use MATLAB to plot the Bode magnitude and phase diagrams. Do you observe resonant peak in the magnitude plot? Comment on why you see this (hint: it has something to do with ζ ) (e). Use the MATLAB instruction, step(num,den) , to plot the step response. 3(15 pts). Using the symbolic toolbox, take the Laplace transforms of the following:

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Unformatted text preview: (a). ) ( t y = t 5 u(t) (b). ) ( t y = e 2t u(t) (c). ) ( t y = sin(wt)u(t) (d). ) ( t y = cos(wt)u(t) Do your answers agree with those listed in the tables? 4) (15 pts). Using the symbolic toolbox, take the inverse Laplace transforms of the following: (a). ) ( t y = 1 1-s (b). ) ( t y = 1 1 2 + s (c). ) ( t y = 4 2 + s s (d). ) ( t y = 4 1 2 + s R =2 L =2 H C =F x(t) y(t) Do your answers agree with those listed in the tables? 5(20 pts). Given the control system below, with plant 2 2 2 6 2 ( ) 3 4 s s + G s = s s + + + and controller 4( 3) ( ) 12 s + H s = s + (a). Plot the open loop step response G(s) (b). Using Matlab, find the closed loop transfer function of this system. Hint: use feedback command. (c). Plot the closed loop step response (d). Compare the results from parts a and c....
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