MME2151: The Lumped-Parameter Model (Also Called Lumped-Element Model, or Lumped-Component Model) Simplifies: Electro-Mechanical Systems Technology Assignment, SIT, Singapore

Background

Modeling and system identification of the electromechanical system is an important tool for design and performance optimization. In practice, there is a need to optimize the power transfer from system inputs to the load. This requires a good knowledge of the system parameters to design and specify system parameters.

Lumped Parameter Model

The lumped-parameter model (also called lumped-element model, or lumped-component model) simplifies the description of the behaviour of spatially distributed physical systems into a topology consisting of discrete entities that approximate the behaviour of the distributed system under certain assumptions. It is useful in electrical systems (including electronics), mechanical multibody systems, heat transfer, acoustics, etc.

This is much like the idea of a rigid body in elementary mechanics. In physical reality, no solid object is truly rigid under all circumstances, if for no other reason than that the speed of light limits the ability for information about forces at one end of the object to update the motion at the other end of the object instantaneously. While it’s fictional, a rigid body is still an extremely useful abstraction for doing statics & dynamics as long as we understand its limitations.

Matlab/Octave Primer

Introduction

MATLAB and GNU Octave are computational tools we will use for this mini-project. In this section, we introduce some of the basic commands and tools available. Once you’ve figured out how to fire MATLAB up, you can try simple things at the command prompt such as:

a = 2;
b = 3;
a + b

Try to fool around with the semicolons, and with other operations such as a^b, etc, and convince yourself that MATLAB is at least as good as your calculator. MATLAB likes arrays (vectors) and array operations – something that we will exploit time and again. Try the following and see if it makes any sense to you. If it does not, try again, or try harder!

v=[0 1 2]
u=[3; 4; 5]
w=[1 2 3; 4 5 6; 7 8 9]
transpose(u)
inverse(w)
v + u’
u(2)
v(1)
w(:,2)
w(2,:)
x=[5 6 7]
x * v % invalid, why?
x .* v % valid. what does this operation do? This is IMPORTANT!

You can always get help on a command (say inverse) by typing help inverse. And of course, there’s also Google. The percent sign denotes the start of a comment, and MATLAB ignores it. So far, we’ve been talking about using MATLAB in an interactive mode. But it is far more powerful and liberating to use it in a “batch” mode, by writing function and script files.

Project Deliverables

Your project report must address the following requirements:

1. Select a suitable lump-parameter model for the system under test. Explain the reason for selecting either a 1^st order model or a 2^nd order system model for the unknown system.
2. Design the process needed for you to estimation the parameters of the DC drive. Show the steps taken in your report.
3. Compare the step response between your model and the system under test. What are the mean error and standard deviation between the step response of your model and the collected data?
4. How do you propose to improve the accuracy of your parameter estimates?
5. Explain two possible use cases for parameter estimation.

You may use block diagrams to describe the process you adopted for performing the system identification. Use charts and plots to explain how you derive the mean error and 1 error between your model response and the unknown system.