Exam Solutions 61-70

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

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ....
View Full Document

## 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.

### Page1 / 10

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online