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Unformatted text preview: y ( t ) is in this case the input force, while x 1 ( t ) and x 2 ( t ) are the unknown output displacements. Rewrite the system equations in state-space form using matrices. Figure 1: Left-hand ﬁgure corresponds to Problem 1. Right-hand ﬁgure corresponds to Problem 2. 3. A system is described by the following ODE plus output equation: 7 d 3 y ( t ) dt 3-21 cos( y ( t )) d 2 y ( t ) dt 2 + 7 dy ( t ) dt + 14 y ( t ) = U ( t ) , z ( t ) = sin( y ( t )-π ) . Here U ( t ) is the input signal, y ( t ) is a system unknown, and z ( t ) is the system output. (a) Is the system linear? Write the system in state space form. (b) Consider the point ( y, ˙ y, ¨ y ) = ( π, , 0). Linearize the system around this point. 1...
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This note was uploaded on 04/26/2010 for the course MAE 101B 101B taught by Professor Rohr during the Summer '09 term at UCSD.
- Summer '09