ME 4183 Chapter : Exam 1 2009
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Me 4183 theory and design of mechanical control systems. Find the transfer function x2(s)/f (s) for the mechanical system below, where fvi denotes a linear viscous friction coe cient. S2 + 3s + 1 x1(s) (3s + 1) x2(s) = f (s) (3s + 1) x1(s) + s2 + 4s + 1 x2(s) = 0. Solving for x2(s) using, for example, cramer"s rule, Hence, s2 + 3s + 1 f (s) (3s + 1) s2 + 3s + 1 (3s + 1) 0 s2 + 4s + 1 (3s + 1) f (s) s (s3 + 7s2 + 5s + 1) Y (s) = s + 2 + s + 3 s2 + 3s + 2. Thus, s + 3 s2 + 3s + 2 s + 3. = 1. y(t) = (t) + 2 (t) + 2e t e 2t. The electrical circuit below contains a nonlinear resistor whose voltage-current relationship is given by vr = 10 ln 1.
