# HW4s - MEEN 651 Control System Design Homework 4 Frequency...

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Unformatted text preview: MEEN 651 Control System Design Homework 4: Frequency Response, Bode Plots, Nyquist Diagrams Solution Assigned: Tuesday, 23 Sept. 2008 Due: Tuesday, 30 Sept. 2008, 5:00 pm Problem 1) Given a linear time invariant (LTI) state space system described by: Cx y Bu Ax x = + = & with ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = γ β 1 A , ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − = 1 α β B , and [ ] 1 = C , a. Derive the transfer function from u to y (Note the slight difference from the system given in the in previous HW) b. Sketch the Bode plot for the following cases (please sketch magnitude and phase response, and be sure to label all pertinent information): i. < < < γ β α Example Plot for 1 , 10 , 100 − = − = − = γ β α-80-60-40-20 20 Magnitude (dB) 10-2 10-1 10 10 1 10 2 10 3 10 4-180-135-90-45 Phase (deg) ↓ α ↓ β ↓ γ Bode Diagram Frequency (rad/sec) ii. < < < γ α β Example Plot for 1 , 100 , 10 − = − = − = γ β α-80-70-60-50-40-30-20 Magnitude (dB) 10-2 10-1 10 10 1 10 2 10 3 10 4-90-45...
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HW4s - MEEN 651 Control System Design Homework 4 Frequency...

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