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HW_3_sol

# HW_3_sol - HW 3 From Lindner's notes 10.5.1(10(10(10 ECE...

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DKL:2/16/07 HW 3 1/4 HW 3 ECE 3704 Due 2-16-07 From Lindner’s notes 10.5.1 Consider the block diagram in Figure P10.5.1. (10) (a) Find the transfer function by block diagram reduction. (10) (b) Assign state variables to the block diagram and write the state equations. (10) (c) Enter the state space model into Matlab and computer the transfer function. Show your code. Show that this answer match part (a). 1 s 1 s 1 s 4 3 + - + - + + X ( s ) Y ( s ) Figure P10.5.1 Solution This problem illustrates block diagram reduction and the construction of state space models from an all-integrator block diagram, Procedure 10.5.9. (a) The first step is to reduce the inner feedback loop as shown in Figure P10.5.1a. 1 s 1 + 3 s = 1 s + 3 Figure P10.5.1a Continuing, the next feedback loop is reduced as shown in Figure P10.5.1b.

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DKL:2/16/07 HW 3 2/4 1 s ( s + 3) 1 + (4) 1 s ( s + 3) ( ) = 1 s ( s + 3) + 4 = 1 s 2 + 3 s + 4 Figure P10.5.1b Finally, the parallel combination is reduced to obtain the transfer function Y ( s ) X ( s ) = 1 s 2 + 3 s + 4 + 1 s = s 2 + 4 s + 4 s s 2 + 3 s + 4 ( )
DKL:2/16/07 HW 3 3/4 (b) First, assign state variables to the output signals of the integrators as shown in Figure P10.5.1c. Figure P10.5.1c Next the derivative of the state variable is assigned to the input signal of the integrator.

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HW_3_sol - HW 3 From Lindner's notes 10.5.1(10(10(10 ECE...

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