毕业设计MATLAB_使用System Identification Toolbox对非线性动态系统进行基于数据的建模.zip

DATA-BASED MODELING OF ENGINE THROTTLE VALVE DYNAMICS

TABLE OF CONTENTS

Data-BASED Modeling of Engine Throttle Valve Dynamics ................................................................................... 1

Introduction To Problem ................................................................................................................................................. 2

Data Based Modeling Approach .................................................................................................................................... 2

Process of Data Based Model Creation .................................................................................................................. 4

Black Box Modeling Approach ...................................................................................................................................... 4

Understanding Nonlinear Model Structures ...................................................................................................... 5

Parameters of A Nonlinear Grey Box Model ..................................................................................................... 36

Using Models for Simulation and Analysis ............................................................................................................. 36

Code Generation ........................................................................................................................................................... 39

References ........................................................................................................................................................................... 41

known, but the values of various physical constants in the equations are unknown; the data

The emphasis is on the black box modeling approach. It will be shown that even though no a priori

knowledge of model structure is required, it is often helpful to have some intuition about the nature

The following example were created using R2010a release. Some of the "Best Fit" value might be

slightly different depending on the version of MATLAB® you are using.

The throttle controls the air mass flow into the intake manifold of an engine. The throttle body

The task here is to create a mathematical representation of the dynamics of the DC motor, throttle

driving motor (normalized voltage) and the resulting angle of the throttle valve (degrees).

FIGURE 1: A THROTTLE VALVE

We set up an experiment to measure the input and output signals of this system. The data was

For our analysis, we divided the data into estimation and validation sets. Thus, the data sets 1, 2 and

3 were used for creation of models, while the data sets 4 and 5 were used for validating the

performance of the model. The data sets were also down-sampled to a frequency of 100 Hz.

A data-centric approach to modeling is summarized by the flowchart in Figure 7. More detailed

descriptions can be found in product documentations and textbooks; for example, see:

-

- System Identification – Theory for the User, Lennart Ljung, Prentice Hall, 2

nd

ed., Section 1.4

good results are obtained. A “good result” mainly means you

fidelity/performance are usually performed on a different data

set than the one(s) used for estimation.

parameter values), but also lowers the implementation costs,

were you to deploy this model on actual hardware.

BLACK BOX MODELING APPROACH

using data (step 4) and then comparing/contrasting them. The

task ends with choosing one of these models that appears to

emulate the observed behavior (output data values) reasonably

extent, a trial and error approach. Hence some patience and

time is required to try out various forms and estimating their parameters. In the following we show

some of the nonlinear model structures that are commonly employed for such tasks.

discrete-time case, a difference equation. For example, the equation of motion of a mass-spring-

damper system is a second order differential equation:

2

y/dt

2

+ c dy/dt + k y(t) = F(t) ………… (1)

(1), you get the familiar transfer function form:

If you discretize the differential equation above using backward Euler formula: dx/dt = (x(t)-x(t-

Ts))/Ts, you get a difference equation that shows the relationship between the uniformly sampled

values of input F(kTs) and output y(kTs), k = 0, 1, 2, …; Ts = sampling interval:

F(kTs)

Using Ts = 1 for notational simplicity and moving the delayed terms to RHS, we have the following

difference equation:

In the difference equation (3) above, the output y(k) is a weighted sum of variables y(k-1), y(k-2)

and F(k). In Statistics and System Identification literature, these variables are called regressors.

Thus, the above equation is en example of a linear-in-regressors model: the output is a linear

will use to model the throttle dynamics. Nonlinear ARX models use a nonlinear combination of