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Unformatted text preview: G * c ( s ) using a ﬁrst-order ﬁlter f ( s ) = 1 τ c s +1 . Specify the closed-loop transfer function Y ( s ) R ( s ) . Derive the closed-loop response y ( t ) for a unit step change in the setpoint r ( t ) when τ c = 2. Problem 3. Consider the following state-space system: dx dt = ±-1 4 1-1 ² x + ± 1-1 ² u = Ax + Bu y = ( 1 0 ) u = Cx 1. Compute the eigenvalues of the system and determine if the system is stable. Use the controllability and observability matrices to determine if the system is controllable and/or observable. 1 2. Compute the state feedback controller gains k 1 and k 2 such that the closed-loop character-istic equation is equal to ( λ + 3) 2 = 0. 3. Compute the observer gains l 1 and l 2 such that the characteristic equation of the observer error dynamics is equal to ( λ + 10) 2 = 0. 2...
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This document was uploaded on 02/06/2011.
- Spring '09