ECE535_10S_hw6

ECE535_10S_hw6 - 1 s 2 0 2 s 1(a Convert G s to its...

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ECE 535 DISCRETE TIME SYSTEMS SPRING 2010 HOMEWORK ASSIGNMENT #6 Due: 7 April 2010 (corrected version, posted 4 April 2010) 1. (Text problem 8.4, corrected) For the open loop system x ( k + 1) = " 1 1 0 1 # x ( k ) + " 1 2 1 # u ( k ) y ( t ) = h 1 0 i x ( k ) ﬁnd the estimator equations and the value of the gain matrix L for (a) a predictor estimator whose poles are at z = 0 . 6 ± j 0 . 3, (b) a current estimator whose poles are at z = 0 . 6 ± j 0 . 3, and (c) a reduced order estimator with its pole at z = 0 . 6. Do all your calculations by hand . 2. (Text problem 8.5, corrected) For the open-loop system with transfer function G ( s ) = Y ( s ) U ( s ) =
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Unformatted text preview: 1 s 2 + 0 . 2 s + 1 , (a) Convert G ( s ) to its ZOH-equivalent with T = 0 . 1, and ﬁnd a state space descrip-tion for this system in observable canonical form. (b) Find the predictor estimate equations that estimate the state of the system in part (a), together with the value of the gain L p , so that the estimation error is less than 1% within 0.5 seconds (that is, t s < . 5 sec). (c) Verify that t s is satisﬁed by plotting the response of ˜ x 1 (which is ˜ y ) to an initial value....
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