Solution_problem_4.5 - Solution to problem 4.5 We have two...

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4.5 – 1 Solution to problem 4.5 We have two coupled differential equations relating two outputs ( 1 2 , y y ) with two inputs ( 1 2 , u u ): 1 1 2 1 2 1 2 1 2 2 2 3 2 (1) 4 6 2 4 (2) dy y y u dt dy y y u u dt = - - + = - + + The objective of the exercise is to obtain the four transfer functions relating the outputs to the inputs, in other words, we must find: 1 1 2 2 11 12 21 22 1 2 1 2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Y s Y s Y s Y s G s G s G s G s U s U s U s U s = = = = To save time, we will from now on write 1 Y instead of 1 ( ) Y s , etc. In order to find these relations, we must solve 1 Y and 2 Y as a function of 1 U and 2 U . Since our model is defined in the time-domain, the first step is to perform Laplace Transform: 1 1 1 2 1 2 2 1 2 1 2 2 (0) 2 3 2 (3) (0) 4 6 2 4 (4) sY y Y Y U sY y Y Y U U - = - - + - = - + + Note that 1 (0) y and 2 (0) y are zero because 1 y and 2 y are deviation variables, as indicated in the problem description of this exercise. Now we have a set of two equations with two unknowns, which can be solved algebraically
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This note was uploaded on 11/20/2009 for the course CHME DTU-abroad taught by Professor Rafiqulgani during the Spring '09 term at Rensselaer Polytechnic Institute.

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Solution_problem_4.5 - Solution to problem 4.5 We have two...

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