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Unformatted text preview: G * c ( s ) using a ﬁrstorder ﬁlter f ( s ) = 1 τ c s +1 . Specify the closedloop transfer function Y ( s ) R ( s ) . Derive the closedloop response y ( t ) for a unit step change in the setpoint r ( t ) when τ c = 2. Problem 3. Consider the following statespace system: dx dt = ±1 4 11 ² x + ± 11 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 closedloop characteristic 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

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