Introduction to DSC Laboratory

Introduction
Labs
Meas Systems
Experimentation
Modeling
Introduction to DSC Laboratory
Prof. R.G. Longoria
Department of Mechanical Engineering
The University of Texas at Austin
Fall 2014
ME 144L Dynamic Systems and Controls Lab (Longoria)
Computing
Summary
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
Introduction
This laboratory course aims to demonstrate and reinforce principles
and methods from the area of dynamic systems and controls.
Relatively simple yet practical systems are studied in the laboratory.
Experiment design and measurement system concepts are introduced
as needed.
The course provides hands-on experience in building mathematical
models, developing simulations, designing experiments, using
computer-based measurement hardware and software, and
implementing control systems.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
What is Dynamic Systems and Controls?
Dynamic systems and controls is concerned with the analysis, design, and
control of physical and engineering systems that change over time.
This subject area covers a broad range of system types, so there is a need
to model mechanical, fluid, electrical, and thermal systems, including
physical components that involve interactions between multiple physical
(energy) domains, as implied in the diagram below below.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
Example dynamic systems
A dynamic system can be as simple as
a solid projectile moving through the
atmosphere, maybe impacting the
ground. There may be interest in
determining conditions at impact, say,
to determine if the projectile
penetrates the ground, rebounds, or is
destroyed.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Alternatively, a dynamic system may
be complex, like a ground vehicle
comprised of many subsystems. Study
may focus on vehicle motion, or on
subsystems such as transmission,
suspension, steering, and so on.
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
DSC Course Topics
A course in DSC introduces modeling, analysis, and control of these types
of systems, thus supporting other activities such as design and
manufacturing of the systems themselves. Key areas of study include:
1
Modeling mechanical, electrical, fluid, and thermal systems
2
Deriving mathematical models as 1st order, 2nd order, as state space
equations, or as transfer functions
3
Analysis of mathematical models to determine response with and
without forcing
4
Basic concepts and methods for feedback control of systems
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
DSC laboratory approach
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This laboratory course presents DSC concepts and methods
independent of the related lecture course.
Laboratory experiments are designed to be challenging but allow
completion within a limited lab time, assuming pre-lab exercises are
completed.
Some basic knowledge in circuits and electronics is assumed, but
sensor and instrumentation concepts are introduced in each
laboratory.
Because experimentation is a key part of engineering, opportunities
are given to build skill and confidence in completing laboratory work
that supports theory and vice versa.
Computer-based methods for instrumentation, simulation, and control
are introduced and applied.
We teach and apply LabVIEW for measurement, simulation, and
control.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
Labs: compound pendulum experiment
The compound pendulum setup shown below introduces angular sensing,
modeling of rotational dynamics, and simulation of system equations.
This setup allows us to study nonlinear torques applied on the pendulum due to
gravitational force on the CG as well as friction at the pivot.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
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Meas Systems
Experimentation
Modeling
Computing
Summary
Labs: one- and two-can experiments
One- and two-can system experiments can be used to introduce pressure sensing
and use of models for designing experiments. Simulation is used to demonstrate
how well the models can predict different levels of filling.
This fluid system provides experience in experimental modeling of the relationship
between flow exiting the orifice and the associated pressure drop.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
Labs: beam sensor experiments
A cantilevered beam is instrumented with strain-gauges, forming a force sensor.
Strain-gauge instrumentation and usage is learned, and the beam sensor can be
used in additional experiments, such as measuring the response due to impact of
a clay ball, or studying beam vibration with attached accelerometer.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Labs: 2 DOF system; two-story building model
Modeling of systems with multiple
degrees of freedom (higher order
systems) can be studied using a
two-story building model, as shown
to the right.
We can monitor the motion of each
‘floor’ using accelerometers as
forces are applied or as the base is
moved.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Summary
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
Labs: vision measurement and feedback control
experiments
Study of feedback control is accomplished using LabVIEW to ‘close the feedback
loop’. In the example shown below, a USB webcam is used to monitor the
position of the needle on a simple analog meter (an electromechanical system).
The vision-based measurement of needle angular position and feedback control
algorithms for regulating needle position are all made using LabVIEW code.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
Working in the lab requires knowledge about measurement
systems
Measurement systems are essential knowledge for engineers. Selected topics are
introduced as needed due to time constraints.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
We apply experimental methods to systems of interest for
a given purpose
Some of these typical engineering experiments will be conducted in this course.
1
Determination of material properties and object dimensions
2
Determination of component parameters, variables, and performance indices
3
Determination of system parameters, variables and performance indices
4
Evaluation and improvement of theoretical models
5
Product/process improvement by testing
6
Exploratory experimentation
7
Acceptance testing
8
Use of physical models and analogues
9
Teaching/learning through experimentation
Sometimes intuition is sufficient to design experiments, but many times not. In
this course, we emphasize how system models should guide experiment design.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
Example: instrumenting an experiment
The compound pendulum setup is
relatively easy to instrument. With a
fixed-axis for rotation of the
pendulum, an angular sensor is used to
measure angle, θ.
For other systems, it may not be so
obvious where or why to make
measurements.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Until it is known what is to be found
out, it may be premature to decide on
what to measure, what data to collect,
and what should be done with data.
Example: For the one-can system,
what type of experiments and what
measurements would be made to study
the orifice flow characteristics?
Introduction
Labs
Meas Systems
Experimentation
Modeling
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Summary
There is no experiment without theory–and there is no
theory without experiment.
Because of the insight it builds, system modeling is essential for guiding
engineering experimentation.
Depending on the objective of an experiment, you might be able to walk
into the lab and run the right tests, collect the right data, and collect the
right amount of data. But this is not easy to do.
We will examine ways to use models to help guide laboratory experience.
A key objective is to develop confidence in specifying and making valid
measurements on purpose.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
We will build experience in system modeling
System modeling is the process of studying a physical or engineering
system and using fundamental physical laws to better understand the
system and guide formulation of quantifiable representations, typically in
the form of mathematical equations.
As engineers, we rely on models to help design and control systems we are
building and evaluating.
A key objective of laboratory study is to provide practice that builds
insight and the ability to recognize how to use physical laws for modeling,
how to make simplifying assumptions, and how to judge validity of models.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
Example: a simple pendulum model
Even a system as simple as a rock on a string requires assumptions and
abstraction to help formulate a useful model.
For example, in (a) below the mass of the rock is modeled as a point mass, m,
located a distance L from the pivot.
The ‘simple’ pendulum should be distinguished from a ‘compound’ pendulum to
be studied in the lab which has both a concentrated total mass at a center of
gravity and distributed mass quantified by the moment of inertia.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
Identifying key variables and parameters is an important
first step in system modeling
The familiar mass-spring-damper system shown below, is commonly used to
model many practical physical and engineering systems.
It is important to recognize key quantities: inputs, system variables, parameters.
In this case, the force is an input, specified by the environment. Quantities such
as the mass velocity, Vm , and spring displacement, xk , are system variables. The
system parameters are the mass, m, spring stiffness, k, and damping, b.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
System component characterization requires background
knowledge
A large part of formulating system models is understanding the constitutive
relations for system elements or components, which may come from past
engineering studies.
Constitutive relations relate two or more system variables, and these relationships
should be formulated so it is possible to describe practical devices and processes.
Example: The purely translational spring in the mass-spring-damper model relates the force on the spring to how much it
deflects, x. If this relation, based on Hooke’s law, is linear, Fk = k · x, which identifies the stiffness, k. Determining k
requires we know the spring material and geometric properties, as shown below. Alternatively, we might run experiments in the
lab to find the constant relating Fk and x.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
Mathematical models of systems
A mathematical model of a system may take many forms and should allow
you to answer relevant questions about design, performance, etc.
It is important to remember that all models are formed after making
simplifying assumptions, and these should be understood and tested, as
will be demonstrated in this course.
The form of the mathematical models that can be useful in practice should
be familiar. The use of the following will be introduced in this course as
well as in a related lecture course:
1
Basic algebraic relations: y = g(x)
2
First and second order differential equations
3
‘State space’ equations (systems of 1st order ODEs)
4
Transfer functions
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
Dynamic systems imply change with respect to one or
more independent variables
In general, models of engineering systems may take the form of partial differential
equations (PDEs):
f (x1 , · · · , xn , y,
∂2y
∂2y
∂y
,··· ,
,··· ,
, u1 , · · · , ur ) = 0
∂x1
∂x1 ∂x1
∂x1 ∂xn
were the u variables are external inputs to the system, xn are dependent
variables, and y and higher order derivatives are the minimum physical system
variables of interest required to describe the system, or states.
In DSC, system-level models typically are ODEs, with time, t, as a single
independent variable of interest,
f (t, y,
dy
d2 y
dn y
, · · · , 2 , · · · , n , u1 , · · · , ur ) = 0
dt
dt
dt
the y and derivatives of y represent the system states.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
The simplest dynamic system is modeled by 1st order
linear ODEs
A linear 1st order system model can be expressed in the standard form,
τ
dx
+ x = u(t)
dt
where x is the state, u(t) is the input, and τ is the system time constant.
The system modeled by this equation requires only one ‘state’ variable to explain
all dynamic behavior. Both systems shown below would be modeled by this type
of ODE.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
When is a system not linear? Why do we care?
The distinction between linear and nonlinear systems is important in dynamic
systems and controls.
Linear and nonlinear relationships arise in the constitutive relationships for the
system elements.
Example: A coil spring’s force, Fk , might be well represented by the linear relation, Fk = kx, where x is the
extension/compression, and k is a constant stiffness. However, a bungee cord might only be linear over a small range of x
values. As x becomes long, bungee cords generate nonlinear force-displacement curves.
This is important because when derived in final form the overall system ODEs will
be linear or nonlinear, depending on the basic constitutive relations used.
As will be shown in this lab, solving linear equations is much easier than solving
nonlinear equations. Also, nonlinear systems may respond differently depending
on initial conditions and on magnitude of the input(s).
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
Example: deriving compound pendulum model
Refer to the compound pendulum that
will be studied in lab, and define the
angular momentum about the CG,
T = −mglC sin θ,
h = Jω = J θ˙
if there are no other applied torques.
This equation can be written in terms
of the angular displacement, θ,
and relate this to the value about the
axis of rotation (or pivot), O,
h˙ = J0 θ¨ = −mglC sin θ
2
J0 = J + mlC
.
Then, apply Newton’s law about the
axis of rotation,
dh/dt = h˙ = T,
where the net torque, T , is,
ME 144L Dynamic Systems and Controls Lab (Longoria)
so the final equation,
J0 θ¨ + mglC sin θ = 0.
is a 2nd order ODE, which is nonlinear
because of the sin θ term.
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
Verifying and validating system models
The modeling process requires decisions and this lab will be used to test
those decisions.
If a model you’ve built behaves the way you expect it to, adheres to the
laws of physics as you understand them, then you have verified the model.
If the model you’ve built provides results that compare to within some
acceptable margin to actual physical test results, then you have validated
the model.
This lab will provide practice in verifying and validating models.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
Using computer-based methods for instrumentation,
analysis, and control
Finally, this lab will make extensive use of computer-based methods for:
developing systems that manage data acquisition hardware which is
used to measure signals from sensors
processing data and displaying results
solving systems of differential equations that model our laboratory
experiments
comparing model and experiment results
implementing feedback control systems
The ME 144L laboratory course uses the LabVIEW software environment
for these purposes.
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
Summary of course objectives
1
To learn about and apply tools that support modeling, design, and
control of engineering systems through hands-on laboratory studies
2
To learn how to design and use physical experiments by using system
models and to assess system models
3
To gain familiarity with methods from measurement science and
engineering
4
To gain experience modeling, experimentation, and simulation,
especially to understand how to make good decisions when using
these methods in engineering practice
ME 144L Dynamic Systems and Controls Lab (Longoria)
Introduction
Labs
Meas Systems
Experimentation
Modeling
Computing
Summary
Summary
1
This laboratory course is independent but related to a DSC lecture
course, however, all subject matter needed will be introduced.
2
We will focus on relatively simple laboratory experiments that allow
us to apply DSC concepts.
3
We will introduce sensing and instrumentation concepts that support
experimentation.
4
We will emphasize using modeling to guide our laboratory experience.
5
We will use LabVIEW to model and analyze systems, but also to
control collection of signals and to implement feedback controls
systems.
6
The first few weeks of lab will build familiarization with LabVIEW
usage.
ME 144L Dynamic Systems and Controls Lab (Longoria)

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