PARAMETER ESTIMATION FOR THE FSF MODEL

This section deals with the problem of estimating the parameters of a reduced order FSF model from process input-output data using the least squares algorithm. 

We assume that the process being identified is stable, linear and time invariant and can be accurately represented by a reduced nth order FSF model. For an arbitrary process input u k) and the measured process output y k), the frequency sampling filter model can be written as 

In order to formulate the least squares solution, Equation (4.24) is written in a matrix form for M pairs of input-output data 

The least squares estimates of the FSF model parameters are given by 

Although we could extend the least squares estimation results for SISO systems directly to the p-input, g-output multivariable case, we prefer to treat these systems as q multi-input, single-output (MISO) systems. This way, we can take full advantage of the orthogonal decomposition algorithm developed in Chapter 3 for parameter estimation and structure selection of the p subsystems associated with each of the q outputs. This will be illustrated using an industrial data set in Chapter 5. 

---