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Unformatted text preview: MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Aeronautics and Astronautics 16.060: Principles of Automatic Control Fall 2003 PROBLEM SET 5 Solutions Problem 1 11.9(a) Define the states as shown b elow: D R � + �� � �� �- � + X1��� � +�� 5 s+1 X3 10 s+10 2 s+2 X2 � C � The input, output, and state vectors are: �� r �= u d y=c � ⎡ x1 � = �x2 ⎣ x x3 From the block diagram, we can write down the state equations and the output equation: x1 = 5(r − x3 ) − x1 = −x1 − 5x3 + r ˙ x2 = 2(x1 + d) − 2x2 = 2x1 − 2x2 + 2d ˙ x3 = 10x2 − 10x3 ˙ y = x2 In matrix form: � −1 ˙ x � = �2 0 ⎦ y= 01 ⎡ � ⎡ 0 −5 10 −2 0 ⎣ � + �0 2 ⎣ � x u 10 −10 00 � ⎦ � 0 �+ 0 0 � x u 1 11.9(b) Define the states as shown b elow: R1 2 s+1 � 0.5 s+6 � R2 � 1 s+10 � 4 s X1 � 1 s+2 X2 ��� � + C1 �� + � �� 3 X �� � �� ��� �� ��� �� �� �� � �� X4 X5 � 1 s+4 + � X6 �...
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This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.

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