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2001quiz2 - [4’10:1‘9:3 was 275 cf“ 16.060 Quiz 1...

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Unformatted text preview: [4’10 :1‘9/ :3 was 275: cf“ 16.060 Quiz November 20, 2001 ._. __., 1. Develop a state space model and determine the A, B, C and D matrices for each of the 8 following systems ' I Q . " 1 - a G s = m ) ( ) (s2 + s + 4) - ("t l ‘1' ”it I H L ;. a 5-. '9) 6(3) :"EEL E I U (s + 3 +4) ' . (52 +1) I C) 0(5) = “2—“ (s + s + 4) 2. Given the fountains, state space system / fl fl '5’ A— "'3 _1 3-1 C—2 3 0"[0] I . — _2 __ 4 —' 1 _ [ ] _ 3) Determine its stability b). Determine its inputfoutput transfer function-~ - 3. Determine the state transition matrix for a state space system with the folloWing A // matrix _‘__H Mm... F a: a] 4. For the following state space system . \R‘ - _ A=[g _12] B=[?] C=[l 1] D=[0] " //{) detennine the ontp'ut response to a unit step input and the following initial conditions .310) = [3] _. . A second-order open-loop system is subjected to a unity step input. The response is shown 3: below. The percentage overshoot is 16.3% and the time to peak is 0.9083. (0 a) Calculate _ _ i. The damping ratio, C (hint: use the data on the following page) ii. The damped natural fiequency, (0d — b) What are the open-loop poles of the system? 3 n a a 0) Design a PD compensator which, when used in a unity feedback closed-100p system will yield closed-100p poles at s=——3.46:t has ,1. #0 ,q 0é / ' "' 6. What value(s) of the constant c 1will make following state space system (1 uncontrollable? . _ 3a. C cit-ll his] i ' // . '7. Determine a full state feedback matrix K for the following system l3 lei—lg 1 ll B-l-gl c—rhl 3] 0-131 . _l:1 3 Ol _l1l lo 0 ll l0l so that the closed loop system has poles at +3j.-3j, and -4 ...
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