hw_prj_2

# Hw_prj_2 - Dr Atilla Dogan MAE 4310 Automatic Control Fall 2006 Homework2(Due date Thursday Textbook Readings 53 54 1 Consider the system y(t 8y(t

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Dr. Atilla Dogan MAE 4310 Automatic Control – Fall 2006 Homework–2 (Due date: Thursday, Sep 21, 2006) Textbook Readings: Sections 5–1, 5–2, 5–3, 5–4 1. Consider the system ... y ( t ) + 8 ˙ y ( t ) + 25 y ( t ) = 2 ˙ u ( t ) + u ( t ) with y (0) = 1, ˙ y (0) = 0 and ¨ y (0) = 0 (i) Determine the transient and steady-state response to the inputs (a) u ( t ) = 3 × 1(t) (b) u ( t ) = t 2 (c) u ( t ) = cos 3 t by using Laplace transforms and partial fraction expansions. You may use the table of Laplace transforms ( pp. 17-18) of the text and MATLAB for the partial fraction expansions. (iv) Determine whether lim t →∞ y ( t ) exits for inputs a–c, and if so, use the Final Value Theorem to evaluate it. 2. Consider the system shown below Use the Final Value Theorem to ﬁnd lim t →∞ y ( t ), if it exits, for the following cases: (i) G ( s ) = 1 2 s 2 + s +4 , U ( s ) = 1 s (ii) G ( s ) = 1 s 3 +3 s - 4 , U ( s ) = 1 (iii) G ( s ) = s +2 4 s 2 +2 , U ( s ) = 1 s 2 (iv) G ( s ) = 4 s - 1 , U ( s ) = 1 s 2 (v) G ( s ) = 1 s +2 , U ( s ) = s s 2 +4 3. Find the DC gain and time–constant τ of the following ﬁrst-order systems: (i) G ( s ) = 9 s +3 (ii) G ( s ) = 1 s +0 . 5 (iii) G ( s ) = 14 s +1 Mechanical and Aerospace Engineering - UTA 1 of 4

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Dr. Atilla Dogan MAE 4310 Automatic Control – Fall 2006 4. MATLAB (i) Create pole-zero maps for the systems in Problem 3. to do this, type >> num = numerator of G(s),den = denominator of G(s) ; >> sys1=tf(num,den) >> pzmap(sys1) >>
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## This note was uploaded on 06/15/2009 for the course MAE 4310 taught by Professor Staff during the Fall '08 term at UT Arlington.

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Hw_prj_2 - Dr Atilla Dogan MAE 4310 Automatic Control Fall 2006 Homework2(Due date Thursday Textbook Readings 53 54 1 Consider the system y(t 8y(t

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