Chapter 6. Frequency Response
Methods
6.1 Introduction
Fundamental fact:
r(t)
Let r(t) = sint,
t 0,
frequancy:
rad/s
y(t)
G(S)
The steadystate output:
yss(t) = M () sin[t + ()]
M (): magnitude freq. response
(): phase
freq. response
M and are used to cha
University of Victoria
Department of Mechanical Engineering
MECH 380 Automatic Control Engineering
CRN: 12317
Instructor: Dr. Yang Shi
Sample Final Examination
Dec. 2015
Name:
ID: V00
_
Instructions:
1. This is a threehour test starting from 2PM. You may
University of Victoria
Department of Mechanical Engineering
MECH 380 Automatic Control Engineering
CRN: 12317
Instructor: Dr. Yang Shi
Sample Final Examination
Dec. 2015
Name:
ID: V00
_
Instructions:
1. This is a threehour test starting from 2PM. You may
Chapter 5. Root Locus Method
5.1 Introduction
Root locus: A way to study the eect of one parameter on the locations
of closedloop pols
Setup:
(or F(s)=1);
K:
Study the closedloop pols as K varies from 0 to .
Example 5.1.1:
Ch. eqn:
1 + K S+5
S+1 = 0
S
MECH 380: Automatic Control Engineering
Solution to Homework set 7
1. Objective
To understand the root locus method.
2. Solutions
Question 1.
1
(c)
Figure 1. The root locus for Question 1.
2
Question 2.
Figure 2. The root locus for Question 2.
3
Question
Comparing Class Notes and Textbook
Class Notes
Textbook (6th Edition)
Ch 1 Intro
Ch 1
Ch2 Systems and System Modeling
2.1 Linear Systems
2.2 Laplace Transform
2.3 Modeling
Ch2: 2.1, Ch3
Ch2: 2.3
Ch3: 2.2
Ch2, Ch3
Ch3 Block Diagram Reduction
3.1 BDR Based
MECH 380: Automatic Control Engineering
Homework set 7
Due: 5:00pm, Friday, December 4th
Question 1: Consider a unity feedback system with
() =
(+1)
2 +4+5
G (s)

a. Find the angle of departure of the root locus from the complex poles
b. Find the entry