Setting up a Modelin in Simulink

1. Introduction
Always start simple. As a first stage develop a very simple model and get some results from it, see if these are remotely reasonable. Then improve the model, get more results, refine the model further, etc. Trying to start straight away on a complex model is almost guaranteed to cause huge difficulties, which you may not be able to resolve in the time available.
Work in SI units. Although it may superficially appear to give easier numbers if you work in mm, it immediately becomes very easy to get things wrong by a factor of 1000.
The first stage of the process is vital and needs careful thought. This is because it involves considering the system and finding out about all the elements within it, what functions they perform and the relationship between the input(s) and output(s). The process is rather similar to reverse engineering a product. Errors made at this stage mean all future work will contain the consequences of these errors and the results will be incorrect.

2. Determining System Characteristics
For purely mechanical systems it is usually reasonably straightforward to carry out the necessary measurements to determine dimensions, weights, moments of inertias, stiffnesses, etc.
An exception to this is when analysing hydrodynamic bearings which normally operate with small clearances and determining these with sufficient accuracy will demand accurate measurement facilities. Other exceptions are gears, which require specialist measuring machines and for automotive gear boxes, where low levels of noise are required, very close tolerances are specified. Splines are also difficult to measure accurately.
It is difficult to estimate the moments of inertias of irregular bodies unless a digital solid model is available, in which case most CAD/CAE systems will provide these. Where a digital solid model is not available, compound pendulum theory can be applied to results from simple experiments.

Where a system is a combination of electrical and mechanical components, the problem becomes more difficult. Twenty years ago it was normal to use discrete electronic components, which would often have values marked on them, or else they could be cut out and their properties measured with appropriate instrumentation. Current practice is to put a large number of functions on a single chip and specialised sophisticated test equipment is needed to stand any chance of establishing the properties and performance of such sub systems. Indeed it may be almost impossible to determine the characteristics of such a sub system without access to appropriate documentation.
The investigation carried out in this module will use a combination of information supplied by manufacturers, measurements taken and quite a lot of assumptions.

Once all the characteristics of all the elements have been determined, it should then be possible to write an equation for every element (similar to the process of writing system equations for the free body diagrams of every element in a mechanical system). However, even with manufacturers documentation, there are still likely to be difficulties with electro-mechanical components, such as fuel injectors. To determine the characteristics of fuel injectors specialist equipment is needed. As this is not available, we will have to get around this lack of data by making assumptions and estimates. For some electro-mechanical components, such as solenoids and some electric motors, performance characteristics are often available.

3. Developing the Model
Once all the element characteristics are available - or it has been decided which will not be available and about which some assumptions must be made, a start can be made on building the model.
One important starting point and assumption for modelling the fuel injection system might be that as the primary control of the system is the air mass flow, the characteristics of the fuel injectors will be ignored and it will be assumed that they are delivering the appropiate quantity of fuel. The fuel flow rate for maximum power can be determined from the manufacturers specification by assuming an overall efficiency at maximum power (probably about 30% for a petrol engine) and if stoichiometric combustion is assumed, then the required air mass flow rate can be determined.
Sorting out how even a simple model should be put together requires a lot of thought and you will have to make a lot of carefully labeled sketches. Start on a large piece of paper, spacing everything out, as inevitably there will be elements and links to add in later as the model develops.

4. Errors and Unexpected Behavior
Once you start building the model in Simulink, run a simulation after each element and link is added. Use a 'scope from the 'Sinks' group of blocks to see the output. This will ensure that you can identify when any unexpected behavior starts and investigate the problem immediately.
Where unexpected behavior does occur, check the block characteristics and also check the calculations you have done to determine the characteristics. Also check the simulation parameters, as inappropriate time steps can give completely incorrect results. The use of 'Auto' settings in the simulation parameters may also give incorrect results in many cases. Normally an incorrect value or simulation parameter will send the output very rapidly to + or to - infinity.
It is more difficult to detect and correct errors where the output only slowly diverges, this could be due to a poor estimate of some element characteristic.

Return to Part B Introduction

David J Grieve, 8th September 2006.