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Unformatted text preview: CONTINUOUS-THVIE SYSTEM RESPONSE s2+l6 (d) T(S) = T = —— (a) (s) 2s2 + 6s + 20 Ans. (a) 5, 0.4, 2, 4.58; (c) 1.82, 0.09, 0.16, 1.8 5. Find a controller transmittance G(s) such that the overall system of Figure P25 ,7 is second-order and critically damped. A solution to this problem is not unique. Controller GCs) Figure P25 6. For the system of Figure P2.6 find the constant value of gain, K, for which the}, damping ratio of the overall system is 0.7. For this value of K, what is the system’s} undamped natural frequency? Figure P2.6 Ans. 17.87, 8.57 7. For the system of Figure P2.7 find a gain K for which the natural component 0 the output decays at least as rapidly as eXp(—10t). A solution to this problem i not unique. + S K 2 _ s + 2s + 300 4 Figure P2.7 “C: 8. Draw “block” diagrams to represent the transfer function m) : 10(s — l)(s + 4) (s + 2)(s + 3)(s + 6) as follows: (a) In terms of cascaded (end—to-end connection) first—order blocks. (b) In terms of tandem (same input, outputs summed) first—order blocks. (c) As a nonuival combination of cascaded and tandem first-order blocks. ...
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