Investigation and Control of Linearizable, Dynamical systems
EE550 Course Project
Dr. Ahmad A. Masoud, Electrical Engineering, KFUPM, 2012-1
The objective of this project is to explore the use of linear systems in understanding and controlling practical s
Linear Control Systems, HW-2
Dr. Ahmad A. Masoud, Posting date: Friday Sept. 21 2012, Due date: Saturday Sept. 29, 2012
Q1-
Q2-
Q3-
Q4-
Q5-
Q6-
Q7-
Q8-
X 1
Consider the under-constrained linear system: [1 2 3] X 2 = [6]
X 3
0
A particular solution of the system is: Xp = 0
2
Lets now construct the general solution using vectors that are only independent of [1 2 3]T
X = Xp + 1 N 1 + 2 N 2
EE 550-1 Take home Quiz-3
Dr. Ahmad A. Masoud, Due Sunday October 30, 2013
All of you know by now that system stability is important it is the minimum requirement a system must satisfy
for it to be useful. Also all of you know that one famous test of asym
EE 550-1 Take home Quiz-2
Dr. Ahmad A. Masoud, Due Sunday October 27, 2013
Name:
Number:
Consider a SISO system with transfer function shown below
1
H ( s) = n
s + a n 1 s n 1 +.+ a1 s + a 0
Consider the A matrix in the controller canonical form realizati
EE 550-1 Take home Quiz-1
Dr. Ahmad A. Masoud, Due Tuesday October 8, 2013
Name:
Number:
This is the first take home quiz. It is optional and its mark is a bonus ( 5 marks = half the mark of a regular quiz). It is due next Tuesday on which the
second regu
Linear Control Systems-1, HW-6
Dr. Ahmad A. Masoud, Posting date: Friday December 6 2013, Due date: Sunday December 14, 2013
Q1: Given a system with transfer function:
S 1
( S 1)( S + 2)
2
find a three dimensional controllable realization and check its ob
Linear Control Systems-2, HW-5
Dr. Ahmad A. Masoud, Posting date: Monday November 18 2013,
2
1
1
x=
x + u,
y = [1 2]x
2 4
2
1- Find the rank of the matrix [ A I , B] for each eigenvalue of the A matrix
Q1: Consider the ss system:
A I
for each eige
Linear Control Systems , HW-3
Dr. Ahmad A. Masoud, Posting date: Wednesday, Oct. 2nd, 2013, Due date: Tuesday Oct. 8 2013
2 1
2 3
Q1: Consider a state space system with an A matrix A =
find the homogeneous response to the initial conditions X1(0)=1
X2
Linear Control Systems-2, HW-4
Dr. Ahmad A. Masoud, Posting date: Monday October 29 2013,
Q1- Find whether the system defined by the ss equations shown below is BIBO (show full details)
1 10
2
x=
x + u,
0 1
0
y = [ 2 4] x
Q2- Find whether the state e
Linear Control Systems , HW-2
Dr. Ahmad A. Masoud, Posting date: Wednesday, Sept. 18, 2013, Due date: Monday Sept. 23, 2013
Q1: Use the Gram-Schmidt procedure to construct orthogonal set of vectors from the set of independent
vectors
0
1
X 1 = ,
1
1
1
0
Copyrighted Material
LECTURE 1
State-Space Linear Systems
CONTENTS
This lecture introduces state-space linear systems, which are the main focus of this course.
1. State-Space Linear Systems
2. Block Diagrams
3. Exercises
1.1 STATE-SPACE LINEAR SYSTEMS
A c
2.14 Analysis and Design of Feedback Control Systems
State-Space Representation of LTI Systems
Derek Rowell October 2002
1
Introduction
The classical control theory and methods (such as root locus) that we have been using in class to date are based on a s
1
State-Space Canonical Forms
For any given system, there are essentially an innite number of possible state
space models that will give the identical input/output dynamics. Thus, it
is desirable to have certain standardized state space model structures:
ME2025 Digital Control
Z Transform in State Space
Jee-Hwan Ryu
School of Mechanical Engineering
Korea University of Technology and Education
State-Space Representations of
Discrete-time Systems
Many ways to realize state-space
representation
Controllable
Chapter 6
Eigenvalues and Eigenvectors
6.1 Introduction to Eigenvalues
Linear equations Ax D b come from steady state problems. Eigenvalues have their greatest importance in dynamic problems. The solution of d u=dt D Au is changing with time- growing or d
MEEN 364
Parasuram August 3, 2001
HANDOUT A.5 - LINEARIZATION OF NONLINEAR DYNAMICS
Introduction The dynamics of a physical system can be expressed in the following general form x(t ) = f (x(t ), u (t ) ) y (t ) = h(x(t ), u (t ) )
.
(1) (2)
where the fun
ECE311 - Dynamic Systems and Control Linearization of Nonlinear Systems
Objective
This handout explains the procedure to linearize a nonlinear system around an equilibrium point. An example illustrates the technique.
1
State-Variable Form and Equilibrium
numerical methods - 17.1
17. LAPLACE TRANSFORMS
Topics: Laplace transforms Using tables to do Laplace transforms Using the s-domain to find outputs Solving Partial Fractions Objectives: To be able to find time responses of linear systems using Laplace tra