Instructor: Chen-Hsiung Yang
Dynamic System Modeling Analysis and Control
動態系統建模分析與控制
Lecture1
Introduction to System Dynamics
Outline
1-1. Introduction
1-2. Mathematical Modeling of Dynamic Systems
1-3. Analysis and Design of Dynamic Systems
1-4. Summary
3
1-1. Introduction
Systems
A system is a combination of components acting together to perform a specific objective.
A component is a single functioning unit of a system.
Dynamic
if its present output depends on past input;
<Note>
if its current output depends only on current input,
the system is known as static.
4
1-1. Introduction(Cont.)
Linear and nonlinear differential equations.
linear, time-invariant differential equation
linear, time-varying differential equation
A differential equation is called nonlinear if it is not linear.
0 10
2
5
2
x
dt dx dt
x d
0 )
2 cos 1
2
(
2
t x
dt x d
) sin(
0 )
1 (
3 2
2
2 2
2
wt x
dt x dx dt
x d
dt x x dx
dt x d
5
1-1. Introduction(Cont.)
Continuous-time systems and discrete-time systems
Continuous-time systems are systems in
which the signals involved are continuous in
time.
6
1-2. Mathematical Modeling of Dynamic Systems
Mathematical modeling.
Mathematical modeling involves descriptions of important system characteristics by sets of equations.
By applying physical laws to a specific
system, it may be possible to develop a
mathematical model that describes the
dynamics of the system.
7
1-2. Mathematical Modeling of Dynamic Systems(Cont.)
Mathematical modeling procedure.
1.
Draw a schematic diagram of the system, and define variables.
2.
Using physical laws, write equations for each component, combine them according to the system diagram, and obtain a mathematical model.
3.
To verify the validity of the model, its predicted
performance, obtained by solving the
equations of the model, is compared with
experimental results.
8
1-3. Analysis and Design of Dynamic Systems
Analysis.
Means the investigation, under specified conditions, of the performance of a system whose mathematical model is known.
Design.
Refers to the process of finding a system that accomplishes a given task. In general, the design procedure is not straightforward and will require trial and error.
Synthesis.
Using of an explicit procedure to find a system that
will perform in a specified way.
9
1-4. Summary
The objective of this book is to enable the reader
1.
To build mathematical models that closely represent behaviors of physical systems
2.
