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Unformatted text preview: 16.06 QUIZ 2
November 19, 2003
Each question is worth an equal number of points. Problem 1 Given the following system A=t333l W €101] M01 La) Determine the system state transition matrix Lb) If the initial condition for the system state vector is _f0l
5—H and the input is a unit step function, determine the output by using convolution integrals.  $43 ~t
(a) SI'A' [o s] _.  r
q ! u I _ 9 i 7 :  573 M543);
‘> ‘5 l 0 543‘}: O 5 L 5 9
_ J. 13.. ’3‘
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t _:._ :15 (a: More)? ~.zt Ji
I 6 3 3 L— o t j Problem 2 You are to design the attitude control system for a boost vehicle with a large and massive rocket
motor. The transfer function relating 6(1), the pitch angle of the boost vehicle, to uﬂ), the input
command to the rocket motor actuator, is as follows— ®(s)_ 10 (32 +1) a [1(3)—(S+10) (st—1) where 8(3): Laplace Transform of the vehicle pitch angle
U(s)= Laplace Transform of the input to the rocket motor actuator 2.3,) Create a state space mode] of this system 2b) Develop a full state feedback control system so that the poles of the closed loop system are at
s=5
s=l+j
s=—l j (a) 8m we pairs at; 210m; ; ( DPSI'WJ CLGrﬁﬂLPG‘S'Ir'C €?um{r‘an f5:
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my; —I '2 © «2 H  :. 7 ( So (meld/Fr 35'. fl )U: (1C =2x, 43):? 40.313/ Problem 3 Consider the plant 2 6(3): s2 +1 3.3) To achieve a secondorder system that has a damping ratio of 0.707 and a time constant
of 0.53, where should the closedloop poles be located? 3.1)) Design a PD compensator which, when used in a unity feedback closedloop system will
meet the design speciﬁcations in 3.3). Be sure to state the ﬁnal transfer function for your
Gc(s). Problem 4
The plant (52 +2s+2) G“) 2 3(52 + s +0.5) has zeroes at s 2 1i j and poles at s = 0, s = —0.5 i 0.5}. Consider the root locus plot for unity feedback. 4.3) Calculate the angle of departure from the upper complex pole for K>O
4.1)) Calculate the angle of arrival at the upper complex zero for K>0 4.c) Sketch the root locus for K90. 4.d) On a separate plot, sketch the root locus for K<0. (q) We MfrW: [9 4 r0 Han’8‘] ‘ l 2’ 4902135] ~'  W 3/; 4340/ _..1' 3) r___.__... __ ._ . (L; AWL: (whim: [5 Jr $007 ._ m" M703 715(3) me] _~ J30" H <1 o
.xky ) ] (Ct/was o( Cé’fqrrhxe an! (I'mml 5%de $7 070”? ...
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 Fall '03
 willcox
 Aeronautics

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