Exam Solutions 61-70

Exam Solutions 61-70 - Part I: theory (Closed Book)...

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Unformatted text preview: Part I: theory (Closed Book) Question 1 (weight:2) Given: The transfer function of a system G ( s ) is: G ( s ) = ( s + 2) ( s + 1) · (3 s + 1) Asked: 1. Sketch the Nyquist plot of G ( s ) ( Be precise about the shape of the Nyquist plot around the origin ! ) 2. Give the value of the gain margin of G ( s ) . 3. Show graphically in your sketch the phase margin of G ( s ) . Part II: exercises (Open Book) Question 2 (weight:2) Given: The mass-spring system is illustrated below F k 1 k 2 k 3 x 1 x 2 m 1 m 2 b where F is the input force, the force of friction b is described as F b = b 1 v + b 2 v 3 , and the energy function of the spring k 2 is E 2 (Δ x 2 ) = 1 2 k 21 Δ x 2 2 + 1 4 k 22 Δ x 4 2 . The springs k 1 and k 3 are linear. Asked: 1. Draw a bond-graph of the system considering F as the input force ( Note : The walls are modelled as a flow source of zero velocity). The structure of the bond-graph can be simplified to the structure illustrated below. 1 1 S e : F C :: E 2 (Δ x 2 ) v 1 I : m 2 R : b 2. Annotate the bond-graph and calculate from it the state space differential equation of the form ˙ x = f ( x ,F ) describing the dynamics of the system. 3. Linearize the system around the equilibrium x and u = F . Question 3 (weight:2) Given: The following system in state space form is given: ˙ x = parenleftbigg- 1- 3- 3 / 2 parenrightbigg x + parenleftbigg 2 2 b parenrightbigg u (1) y = ( 1 2 c ) x (2) Asked: 1. Calculate for what values of b and c the system is controllable. 2. Calculate for what values of b and c the system is observable. 3. Sketch the amplitude frequency response of the system system for b = 0 and c = 3 / 4 ....
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This note was uploaded on 08/13/2010 for the course EE EE 302 taught by Professor Taufik during the Spring '10 term at Cal Poly.

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Exam Solutions 61-70 - Part I: theory (Closed Book)...

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