Control Systems MEC709
Lab 1
Submit lab report to your TA at the beginning of your next lab: Sections 2, 4 the week of Feb. 14 Sections 1, 3, 5 the week of Feb. 28 Submit the report in groups of 3 students from a same section (you can choose the same grou
Electrical Network Transfer Functions Electrical Network Transfer Functions
Example (cont.):
(Step 4) sum voltages around each mesh through which the currents, I1(s) and I2(s), flow:
Mesh 1, where I1(s) flows Mesh 2, where I2(s) flows
by combining term
Transfer Functions For Systems With Gears Transfer Functions For Systems With Gears
Most rotational mechanical systems have gear trains associated with them; especially those driven by motors Gears provide mechanical advantage to rotational systems The l
Modeling
Chapter 2
Laplace Transform Review Laplace Transform Review
Why?
Many engineering systems are represented mathematically by differential equations. Differential equations are difficult to model as a block diagram. But we prefer system represent
Chapter Chapter 6 Stability
(c) 2010 Farrokh Sharifi
Objectives Objectives
To learn: learn: How to determine the stability of a LTI system using Routh-Hurwitz criterion How to determine system parameters to yeild stability
(c) 2010 Farrokh Sharifi
Introdu
Special Cases Special Cases
Auxiliary polynomial with reciprocal roots: Original Polynomial: n n 1
s an 1s
n
. a1s a0 0
1 . a1 a0 0 d
Replacing s by 1/d:
1 1 an 1 d d
n 1
1 d
n
1 (1 n ) n 1 1 1 1 an 1 . a1 a0 d d d n
1 1 an 1d . a1d n 1 a0 d n 0 d
S
Time Response Time Response
CHAPTER 4
(c)2010FarrokhSharifi
1
Poles, Zeros
(section 4.2 in the book)
Goal of this chapter Analysis of system transient response of system transient response Poles of a Transfer Function (1)The values of the Laplace transfo
Project for MEC709 Control Systems Winter semester 2011
Control of an overhead crane
Goal To provide a complete system modeling, analysis and control design experience.
Objective The objective of this project is to model a system mathematically, analyze i
AER509 Control System
Assignment 3
Due on Feb. 22, 2016
Problem 1: For the unity feedback system shown below, specify the gain K of the feedback controller so that
the output y(t) has an overshoot of no more than 10% in response to the unit step input.
Pr
AER509 Control System
Assignment 4
Due on March 14 (Thursday), 2016
1. Given a unity positive feedback system with open-loop transfer function G ( s )
18
s s 7 s 3 7 s 2 18s
5
4
Using the Routh table, tell how many poles are in the right half-plane, in t
AER509 Control System
Assignment 2
Due on Feb. 12, 2016
Problem 1: Using Masons rule, find the transfer function T(s)=Y(s)/R(s).
Problem 2: Using Masons rule or reducing the block diagram to find the transfer function T(s)=Y(s)/U(s).
Problem 3:
Problem 4:
AER509 Control System
Assignment 1 Solution Due on Jan. 29, 2016
1. Solution the following different equations using Laplace transform.
a)
dx
7 x 5cos(2t )
dt
b)
d 2x
dx
d 2x
dx
6
8
x
5sin(3
t
)
c)
8 25 x 10u(t )
2
2
dt
dt
dt
dt
2. Find the transfer fun
Laplace Transform Review (Tutorial 1) Laplace Transform Review (Tutorial 1)
1. For the following transfer functions, find the equivalent differential equation: (problem 8.c)
X (s) s2 3 F ( s ) s 8s 2 9 s 15
2. (skill assessment) Find inverse Laplace trans
Control Systems MEC709
Lab 0
Note: No report needed to be submitted for this lab.
Lab problems:
Problem 1. Using MATLAB find: a) the product of matrices A and B, i.e. A*B, b) determinants of the matrices A, B and A*B, c) inverse of the matrices A, B, and
PROBELM #1 DONE.CHECK FILE AT SCHOOL
PROBLEM #2
a)
> numf=[1 0 3]
numf =
1 0 3
> denf=[1 -4 -9 36]
denf =
1 -4 -9 36
> [K,p,k]=residue(numf,denf)
K =
2.7143
-2.0000
0.2857
p =
4.0000
3.0000
-3.0000
k =
[]
EXPLAINATION
The K values are called the
MEC709 Fall 2007 Control Systems Course Outline Instructor Siyuan He
Ryerson University Department of Mechanical and Industrial Engineering
COURSE OUTLINE MEC709 CONTROL SYSTEMS Prerequisite: Compulsory Text: EES512 Automatic Control Systems Benjamin C. K
Control Systems MEC709 Midterm Exam
b1 Problem
1.
(10 marks)
Consider the following Transfer Function: Gs=10s(s+1)
a) Represent the poles of G(s) in the
plane jw) and specify the following:
b) Draw an approximate polar plot for G(
limw0|Gjw| , limw|Gjw| ,
Control Systems MEC709 Midterm Exam
Problem 1.
Obtain the inverse Laplace Transform of
(10 marks)
Control Systems MEC709 Midterm Exam
Problem 2. Find the solution x(t) of the differential equation
(10 marks)
Control Systems MEC709 Midterm Exam
Problem 3.
ONE
Introduction
ANSWERS TO REVIEW QUESTIONS
1. Guided missiles, automatic gain control in radio receivers, satellite tracking antenna
2. Yes - power gain, remote control, parameter conversion; No - Expense, complexity
3. Motor, low pass filter, inertia s
Modeling
Chapter 2
Laplace Transform Review Laplace Transform Review
Why?
Many engineering systems are represented mathematically by differential equations. Differential equations are difficult to model as a block diagram. But we prefer system represent
Reduction of Multiple Reduction of Multiple Subsystems
Chapter 6
Introduction
(section 5.1 from the book)
Objective: to reduce a system composed of block-diagram of multiple subsystems into representation of a single inputoutput bock diagram. We want to
APPENDIX D: MATLABS GUI TOOLS TUTORIAL
D.1
INTRODUCTION
Readers who are studying MATLAB may want to explore the convenience of MATLABs LTI Viewer, the Simulink LTI Viewer, and the SISO Design Tool. SISO is an acronym for single-input single-output. Before
AER509 Control System
Assignment 5 Due on April 8, 2016 Before 5 pm
1. Given the unity feedback system with G ( s ) =
K ( s 2 + 130s + 200)
( s + 30)( s 2 20s + 200)
Do the following:
a). Sketch the root locus by finding the angle of departure, imaginary-