(20110712)  Chapter 11 Solution of State Equations
Chapter 11 Solution of State Equations
 Sdomain
 Definitions
Note this approach introduces new definitions using known transform methods
Start with
We need
that statisfies [1]
Lets apply L to each s
SYDE 351 (20110503) Lecture 1
SYDE 351 System Models
Professor Gordon Savage
Important Notes
 Review linear algebra
 Will be using Maple
 For lectures, he calls inputs excitations, and outputs responses
A system has components which are interconnecte
Systems Design Engineering University of Waterloo
SYDE 351 Systems Models
Typos from Chapter 5.
Page 520
Case ii): In this setup = ho in (5.3.29) and we get two exponential terms and the head becomes
h (t ) = ho + 2ho e
1
t
RC
(5.3.31)
At t = 0, the hea
SYDE 351 (20110504) Chapter 2 Measurements and Variables
Relation
In engineering system (ie. real world), responses are represented by
1. Observations
2. Instruments
In math model (ie. computer), reponses are represented as real numbers
Both have to agr
SYDE 351 (20110504) Chapter 3 Linear Graph Theory
Linear graph theory helps sort out the precise number of equations we need in junction and loop
rules.
Linear graph theory essentials
 Linear means a sequence of lines
 System graph is an example of an
SYDE 351 (20110524) Chapter 5 Mathematical Models of Systems
5.3 Hydraulic systems
Pipe models (p511)
Laminar flow (p512,13)
 The condition for laminar flow is from Reynolds number,
May 31, 2011
Chap 5 more components
Chap 8 Dynamic systems
 Some la
SYDE 351 (20110524) Chapter 7 Tableaus and Formulations for SteadyState Systems
System model
 For a model with system graph G(n,e,p), there are 2e measurements (variables).
 We got np equations from fcutsets (from interconnection model)
 We got e
(20110531) SYDE 351 Chapter 8 Techniques for Analytical Solutions
Chapter 8 techniques for analytical solutions
Finding the analytical solution
For linear systems, we can apply the laplace transform
Two approaches
1. Formulate differential equations. Ap
(20110621) Chapter 6 <all the details of his lectures should be in his notes. This doc is more to document what was
covered in class>
Recap Transformers
 3TC, 1 process
 Ideal model (normally written in hybrid form)
Transducers
 4 tc, 2 process
 Ide
(20110628)  Chapter 9  Analytical Solutions of the System Equation
Transfer function
<example 9.2>
Standard excitations
 Step
o Delayed unit step
 Pulse
o Unit pulse
o Delayed unit pulse
o Unit impulse
 Application to sampleddata systems
o Pulse t
(20110629)  Chapter 10  Formulation of State Equations
<diagram for difference approaches>

State space approach is the foundation for modern control and stability studies.
Definition of state
The state of a system at time is the (minimum) amount of
SYDE 351  SYSTEMS MODELS I
Professor G.J. Savage DC 2619 Ext. 33941 [email protected]
Course Outline
In this course you will learn the principles for forming mathematical models of all engineering systems
and the methods needed to analyze their respo