MESB374 System Modeling and Analysis

Introduction

ExampleVehicle speed control

MgtfBvvM

MgBvtfvM

e

e

)(

sin)(

MODEL:MODEL:

ANALYSIS:ANALYSIS:t

v speed

Desired

speed

Actual Increasing grade

Vehicle

speed

Actual

-+speed

Desired

Controller +force

incline/Gravity

-CONTROL:CONTROL:

input output

states

linearization

Inertia forceTraction: input, excitation

Gravitation: disturbanceFriction: damping

Course OverviewOne of the most important and multi-disciplinary

courses you’ll ever take

Physics

Kinematics

Mathematics

Time and frequency response analysis

Engineering judgment

Remember these?

i.e. Can you explain the basic conceptsto other people?

Leveraging previous coursework and preparing for future

coursework

Mechanics, electrical, electromechanical

Fluid-thermal

Calculus, differential equations, complex algebra

Measurements/instrumentation understanding

Emphasize combination of theoretical and conceptual

understanding

Basic Concepts

System

Modeling

Analysis

A combination of components acting together to perform a specific objective

A procedure to obtain a model describing important characteristics of system

Investigation of performance of system, whose model is known, under specified conditions

Motivation for MESB 374Pervasiveness

Why should we care aboutmodeling and analysis?

Why should we care aboutmodeling and analysis?

Explaining interesting

Phenomenon

Explaining interesting

Phenomenon

Component and Machine Design

Component and Machine Design

Feedback Control Design and

Adding Intelligence

Feedback Control Design and

Adding Intelligence

Definitions Related to System

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 ?

Input A variable that excites a system

Inputs are not always known beforehand

Inputs are always responsible for problems in systems

Lumped System A System with a finite number of state variables Lumped parameter/ discrete system

Usually an artificial/modeling concept

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)

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

More Different Systems/System Descriptions

Time-varying System (in practice)

The characteristics of system changes with time going

time-varying parameters

time-varying dynamics

Linear System

Equations describing system are linear

Principle of superposition

Nonlinear System

Linearize it near a operating condition to obtain a linear approximation

Time-invariant System (ideal) The features of system never ever changesUsually a good approximation for most engineering applicationA good starting point to obtain main features of systemRelatively easy to analyze

Interdisciplinary and System Nature of ME 375Analogous systems

Models are the same regardless of the physical domain of interest

We only need to understand how to analyze one model, but the results are applicable for four seemingly different types of physical systems!

u y

= = =

)(tuyyy

Voltage

Charge

u

y

Force

displ. Transl.

u

y

Torque

displ.Angular

u

y

Pressure

Volume

u

y

Big Picture Physical System

Develop Idea Model

Verify Model

GETPAID !!

Predict Performance

Build Actual System and Verify Design

MeetPerformance

Spec.

MeetPerformance

Spec.

Feedback/ Feedforward

Control Design

SimulationStudy

Implement on Actual System

No Yes

No

Yes

Not So great Good

OK

No

Not Good

Yes

Modeling

AnalysisDesign

ImplementationTest

Course Outline

Introduction

Components/elements

Connections/interconnects

Mechanical

Thermal

Electrical

ElectromechHydraulic

Input/output Vs.state-variable

models

Time-frequencytools of

systems analysis

Feedback andsystem design