soln30 - The Hong Kong Polytechnic University Department of...

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P. 1 / 3 The Hong Kong Polytechnic University Department of Mechanical Engineering 2009/10 Semester 2 ME4209 Product Mechatronics Assignment 2 Solutions 1. a) Consider a system with the following transfer function: ) 2 )( 1 ( 1 ) ( s s s T Analyze the frequency response of the system if s = j for = 0, 0.5, 1.0, 2.0, 4.0 and 8.0. (3 marks) Solution: The system frequency response is usually considered using the transfer function T(s) with two items: Magnitude ) ( j T ) ( arg j T when putting s = j . e.g, for = 0.5, then s = 0.5 j , the magnitude and phase angle of T (0.5 j ) can be found from its graph in s -plane. 4339 . 0 25 . 1 25 . 4 1 ) 5 . 0 ( j T o o o j T 61 . 40 57 . 26 04 . 14 ) 5 . 0 ( arg Similarly, a table of other values of can be obtained as follows: 0 0.5 1.0 2.0 4.0 8.0 ) ( j T 0.5 0.434 0.316 0.158 0.054 0.015 ) ( arg j T -40.6° -71.6° -108.5° -139.4° -158.9° b) Comment with explanation on the system stability. (2 marks)
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This note was uploaded on 04/06/2010 for the course ME ME4209 taught by Professor Dr.f.y.kwan during the Spring '10 term at NYU Poly.

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soln30 - The Hong Kong Polytechnic University Department of...

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