The System Identification Toolbox

The System Identification Toolbox in MATLAB is a very useful toolbox when fitting models for system identification using the prediction error model. It provides a convenient and concise way of storing, accessing, and manipulating different data sets and their associated models. Although most time series analyses can be performed using the System Identification Toolbox, at times it is easier to use the econometric toolbox described below. In order to fully appreciate and use the System Identification Toolbox, it is first useful to examine in detail the special data objects that store and hold the information the Iddata and the idpoly objects. 

The Iddata object, which will be denoted by a generic z, stores the data that is used in determining the models. It consists of 2 main fields  

The inputs to the system are stored in z.u, which is a matrix. Each of the columns contains a different input. 

The outputs from the system are stored in z. y, which is a matrix. Each of the columns contains a different output. Thus, the second output of the system would be accessed as z. y ( , 2), regardless of how the variables may be named on the screen. 

The iddata object can be treated as a vector to access all the relevant data between two end points. For example, to take the data located from the 1st to 100th point in the object, the command would be z(l 100). 

---

The most important functions from the System Identification Toolbox are given in Table 7.9 for creating the data object. Table 7.10 for creating the model. Table 7.11 for validating the model, and Table 7.12 for designing the system identification experiment. 

The compact format of ARX and ARMAX models given by Eqs 5.6 and 5.7 can be easily converted into more intuitive, expanded format exemplified by Eq. 5.9. With input (u and e) and output (y) data, the matrices A, B and C can be readily identified employing the System Identification Toolbox for Use with MATLAB (31). An ARX model for a pan, granulation process was developed by Adetayo et al. (3) with a successful application for effective control of the plant. 

There are several computer software packages that are quite helpful in applying some of the computationally intensive methods. The PC-MATLAB System Identification Toolbox (The Math Works, Inc., Sherborn, Mass.) is an easy-to-use, powerful software package that provides an array of alternative tools,... 

The AR model and the variance of e k) can be estimated from an incontrol data set using software such as Matlab System Identification Toolbox [191]. A standard x-chart is designed using control limits at 3 standard deviations (3(t limits) to monitor the residuals j k) and consequently Jhistit). 

Math Works. Matlah System Identification Toolbox. The MathWork-s, Inc., Natick, MA, 2001. 

Although many techniques have been proposed, we limit our discussion to the methods that are widely used in the chemical and petroleum industries. Only the identification of linear transfer function models is discussed. We illustrate the use of the MATLAB System Identification Toolbox. 

Table 7.9 System Identification Toolbox Functions for creating the data object ...

Ljung L. System Identification Toolbox for Use with MATLAB. The Math Works, Natick, MA, 2000. 

Ljung, L. (1987) System Identification - Theory for the User, Prentice Hall, Englewood Cliffs, N. J. MATLAB System Identification Toolbox, User s Guide, 2005, The Math Works, Inc., John Wiley. 

MATLAB System Identification Toolbox, User s Guide, 2000, The Math Works, Inc. John Wiley. 

The obtained model, which was developed using the Toolbox System Identification from MATLAB software, explained 42% of the total data variation within the observation period ... 

---