PracticeProblemsMidterm_solu

57 s reaches the peak value 2 135 27 at t 46 and

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: state value in 0.57 s, reaches the peak value 2 ⇥ 1.35 = 2.7 at t = 4.6, and settles down within 1% of the final value in 4.6 s. You should sketch it and compare with the matlab plot. 3. For each of the following three systems: (a) pendulum without friction (b) inverted pendulum (c) mass-spring-dashpot system choose the corresponding transfer function from: (A) s2 1 + 2s + 10 (B) s2 1 +4 (C) 1 s2 5 (D) 1 s+1 Solution: A pendulum without friction would oscillate indefinitely, so its transfer function would have a pair of poles on the imaginary axis. An inverted pendulum would be unstable and diverge without oscillation, so it should have at least one real positive pole. A mechanical system with mass, spring, and dashpot would be stable, and of order at least two. Therefore, (a) B (b) C (c) A 4. Consider the system described by 3¨ + ✓ = u, z¨ ˙ z + 2✓ = 10✓. ¨ Find the transfer function from u to ✓. Solution: Taking the Laplace transform of the differential equations, (3Z +...
View Full Document

Ask a homework question - tutors are online