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Unformatted text preview: Dr. Atilla Dogan MAE 4310 Automatic Control – Fall 2006 Homework–3 (Due date: Thursday, Sep 28, 2006) Textbook Readings: Sections 5–5, 5–6 1. Consider the following second-order systems: (a) G ( s ) = 3 s 2 +5 s +4 (b) G ( s ) = 4 s 2 +2 s +2 (c) G ( s ) = 3 s 2- 4 s +13 (d) G ( s ) = 1 s 2 +4 s +13 (i) Calculate the damping ratio, ζ ,the natural frequency, ω n , the damped natural frequency, ω d and the DC gain, K 2 , for the systems a-d. (ii) Classify these systems as underdamped, critically damped, overdamped or unstable systems. (iii) Calculate the rise time, T r , and the % overshoot of the underdamped systems and plot their step responses in MATLAB. (See Homework 3 for commands). Mark the rise time and peak overshoot on the plots. 2. A third-order system G ( s ) is analyzed as the sum of a first-order system G 1 ( s ) and a second-order system G 2 ( s ). G 1 ( s ) has the following specifications....
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- Fall '08
- Natural Frequency, DC gain, Dr. Atilla Dogan