Download chapter_1

MESB 374
Modeling and Analysis of
Dynamic System
Introduction
1
Example
Vehicle speed control

Inertia force
Traction: input, excitation
Friction: damping
Mv  f e ( t )  Bv  Mg sin
MODEL:
Mv  Bv  f e ( t )  Mg 
ANALYSIS:
Gravitation: disturbance
linearization
Desired
v
Actual
Increasing grade speed
speed
t
Gravity / incline
Desired
CONTROL:
speed
+
-
force
Controller
+
Actual
speed
-
Vehicle
output
input
states
2
Course Overview
One of the most important and multi-disciplinary
courses you’ll ever take
Physics
Kinematics
Mathematics
Time and frequency response analysis
Engineering judgment
Leveraging previous coursework and preparing for future
coursework
Mechanics, electrical, electromechanical
Fluid-thermal
Remember these?
Calculus, differential equations, complex algebra
Measurements/instrumentation understanding
Emphasize combination of theoretical and conceptual
understanding i.e. Can you explain the basic concepts
to other people?
3
Basic Concepts
System
A combination of components acting
together to perform a specific objective
Modeling
A procedure to obtain a model describing
important characteristics of system
Analysis
Investigation of performance of system, whose
model is known, under specified conditions
4
Motivation for MESB 374
Pervasiveness
Why should we care about
modeling and analysis?
Explaining
interesting
Phenomenon
Component and
Machine Design
Feedback Control
Design and
Adding Intelligence
5
Definitions Related to System
Input
A variable that excites a system
Inputs are not always known beforehand
Inputs are always responsible for problems in systems
Output
A variable that we observe and consider important
Measurements/instrumentation
Not necessary what we want to know
State
A variable that is used to describes the internal
system dynamics
A set of states can be used to fully describe
system’s current situation.
With two identical sets of initial values of states,
performance of a system is the same
Do you get all the states of system ?
6
Different Systems/System
Descriptions
Distributed System
A System with infinitely many state variables
Continuous elastic structures (beams, shells, and plates)
Fluid systems (ocean and atmosphere)
Can often be approximately described with lumped models (FEM, AMM)
Lumped System
A System with a finite number of state variables
Lumped parameter/ discrete system
Usually an artificial/modeling concept
Continuous-time System
All the signals are continuous in time
Everything is defined at each instant time
Also called Analog systems
Discrete-time Systems
Variables are only defined at discrete times
Also called sampled data systems
Hybrid System
Continuous-time + discrete-time
7
More Different
Systems/System Descriptions
Time-varying System (in practice)
The characteristics of system changes with time going
time-varying parameters
time-varying dynamics
Time-invariant System (ideal)
The features of system never ever changes
Usually a good approximation for most engineering application
A good starting point to obtain main features of system
Relatively easy to analyze
Linear System
Equations describing system are linear
Principle of superposition
Nonlinear System
Linearize it near a operating condition to obtain a linear approximation
8
Interdisciplinary and System Nature of MESB 374
Analogous systems
Models are the same regardless of the physical domain of interest
=
=
=
y  Charge
y  Transl. displ.
y  Angular displ.
y  Volume
u  Voltage
u  Force
u  Torque
u  Pressure
u
y  y  y  u (t )
y
We only need to understand how to analyze one model, but the
results are applicable for four seemingly different types of
physical systems!
9
Big Picture
Physical System
Develop Idea
Model
Modeling
Not Good
Verify
Model
No
OK
Simulation
Study
Yes
Feedback/
Feedforward
Not So
Control Design
great
Meet
Performance
Spec.
Analysis
Design
Good
Build Actual
System and
Verify Design
Implement on
Actual System
No
Predict
Performance
Yes
GET
PAID !!
Yes
Meet
Performance
Spec.
Implementation
Test
No
10
Course Outline
Introduction
Components/
elements
Connections/
interconnects
Mechanical
Hydraulic
Electrical
Thermal
Electromech
Input/output Vs.
state-variable
models
Time-frequency
tools of
systems analysis
Feedback and
system design
11