Numerical 125:305 Modeling in Biomedical Systems Homework Assignment #4 Due Tuesday, 10/5/2010 1) Prob. 2.6.4 a-e (pg. 68) Provide all answers in terms of k1, k2, and . For Part c, ignore Comment on the result. Selected Answer: Part e,
Fall, 2010 Dr. Shoane
1 k2t x4 (t ) = (1 ) At + e k2
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2) Prob. 2.8.1 a and b only (pg. 91) Note: Select only 3 state variable x1, x2, and x3, so that A is a 3x3 matrix.
In the simulation diagram, the connection at z needs to be moved to r, before the summing junction. (This because is the output c cannot be written in terms of z , or x3 , but must be in terms of x1, x2, x3, and r).
Hint: Use Fig. 3.5.8 on pg. 119 as a reference.
Selected Answers:
b a b C = 0 0 23 a3 a3
b1 a1b3 a3 a32
b2 a2b3 a3 a32
D=
b3 , where the D matrix serves as the gain for direct connection from r to c. a3
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