Midterm Solution

Identify the a b c and d matrices of the model x ax bu

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Unformatted text preview: t − t2 ) − 2 exp − (t2 − t2 ) 0 0 2 t 0 1( t − t 0 ) Problem 7 Find the A(t) matrix for the system that has the following transition matrix exp 2(t − t0 ) 0 φ(t, t0 ) = − exp − (t − t0 ) cos(t0 ) − 3 sin(t0 ) exp − (t − t0 ) + exp 2(t − t0 ) cos(t) − 3 sin(t) Solution: A(t) = d φ(t, t0 ) dt t 0 =t 2 exp 2(t − t0 ) 0 = exp − (t − t0 ) cos(t0 ) − 3 sin(t0 ) + 2 exp 2(t − t0 ) cos(t) − 3 sin(t) − exp − (t − t0 ) + exp 2(t − t0 ) − sin(t) − 3 cos(t) = t 0 =t 2 0 −10 sin(t) −1 Problem 8 a) Write the state differential and output equations for the following circuit, where x1 is the current through the inductor, x2 is the voltage across the capacitor, u1 (t) 6 (voltage source) and u2 (t) (...
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This document was uploaded on 03/23/2014 for the course EL 6253 at NYU Poly.

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