EE5307Fall07

# EE5307Fall07 - ). 3 ( x 2 (6 points) Solution : x 2 x 1 y u...

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EE5307 EXAM I October 11, 2007 Name (Print): ___________________________ (Last) (First) I.D.: ___________________________ Solve ALL THREE problems. Time: 1 hr. 30 min. Maximum Score: 36 points. Problem 1 (a) Set up the state-variable description for the following circuit with input u, output y and state variables x 1 and x 2 . (8 points) (b) Can x 1 be deduced from a measurement of u and x 2 over finite time? If not, when is this impossible? (3 points) Solution : Current x 2 u(t) L R 1 R 2 C y(t) x 1

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Problem 2 Consider the following system with input u and output y: (a) The relation between u and y can be expressed as u b u b u b y a y a y 2 1 0 2 1 Determine the coefficients a’s and b’s in terms of the parameter k. (6 points) (b) Suppose k=0. Let , 5 t , 1 ) t ( u and let . 0 ) 5 ( x , 2 ) 5 ( x 2 1 Calculate the value of
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Unformatted text preview: ). 3 ( x 2 (6 points) Solution : x 2 x 1 y u s 1 s 1 k 2 4 -1 Problem 3 Convert the following system with input u and output y u 3 1 1 y u 1 1 4 x x x into an equivalent description u d y u z T z z z z c b z A z ( z A is a diagonal matrix) using the transformation Vz x where the (1,1) and (2,2) elements of V are chosen to be unity. (a) Calculate T z z z , , , c b A V and d z . (8 points) (b) Let the input u be identically zero. Determine all points on the unit circle in the figure below such that if the system starts from these points, the system trajectory will converge to the origin. (5 points) Solution 2 x 1 x-1 -1 1 1...
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## This note was uploaded on 04/11/2011 for the course EE 5307 taught by Professor Staff during the Spring '08 term at UT Arlington.

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EE5307Fall07 - ). 3 ( x 2 (6 points) Solution : x 2 x 1 y u...

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