hw6 - H ( s ) = k 1 s 2 + ( k 1 + k 2 ) s + k 1 k 2 where k...

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ASE 330M Linear System Analysis Unique Number: 12495, Spring 2006 Homework #6 Date Given: April 11, 2006 Due Date: April 18, 2006 For this homework, unless otherwise indicated, you are permitted use of MATLAB and/or calculator in evaluating roots of polynomials order higher than 2. 1. Determine all the poles and zeros of: (a) X ( s ) = (2 s + 3) / ( s 2 + 5 s + 6) (b) X ( s ) = ( s 2 + s - 3) / ( s 4 + 2 s 2 + 6) (c) X ( s ) = (4 s 2 + 6) / ( s 3 + s 2 - 2) (d) X ( s ) = ( s - 1) / ( s 2 + s - 2) Hand sketch a separate pole-zero diagram for each of the above systems and comment on BIBO stability. 2. The transfer function of an LTI causal system is given by H ( s ) = 4 s 2 + 8 s + 10 2 s 3 + 8 s 2 + 18 s + 20 Use the Routh test to determine if this system is BIBO stable. 3. An LTI causal system with zero initial energy is subjected to an input signal x ( t ) = e - 3 t cos(2 t ) u ( t ) . The resulting output is given by y ( t ) = t 3 e - 2 t sin( t ) u ( t ) . Calculate the pole locations and thereby determine if this system is BIBO stable. 4. The transfer function of an LTI system is described by
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Unformatted text preview: H ( s ) = k 1 s 2 + ( k 1 + k 2 ) s + k 1 k 2 where k 1 and k 2 are some system specic real constant parameters. Your tasks are the following: (a) Derive conditions on parameters k 1 and k 2 so that the system is BIBO stable. (b) Evaluate the system impulse response. Make sure you pay careful attention to the possibility k 1 = k 2 . 5. Use the Routh test to determine the range of parameter k values that ensure stability of the following system: H ( s ) = s 2 + 3 s-2 s 3 + s 2 + ( k + 3) s + 3 k-5 6. The transfer function of an LTI causal system is given by H ( s ) = 20 s ( s + 1) 3 + 8 Use the Routh test to demonstrate the existence of two poles for this system that have zero real parts. Further, using the entries of the Routh array, determine (without use of calculator), the two purely imaginary poles of this system....
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This note was uploaded on 09/25/2011 for the course ASE 18510 taught by Professor Jeannefalcon during the Spring '10 term at University of Texas at Austin.

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