This research represents the second phase of an R&D project whose
goal was to develop an auto-tuner (AT) for decentralized Dead Time Compensator
(DTC) for Multiple Inputs Multiple Outputs (MIMO) open loop stable systems.
An automatic identification algorithm for a transfer matrix each element
of which can be modeled as a first or second order transfer function with dead
times (DTs) has been developed. Such models are suitable for describing the
majority of the systems in the process industries. The proposed algorithm consists
of three stages. In the first stage the system is stimulated around the
operating-point. The novel method, developed here, contains two feedback loops.
The inner loop consists of the process and a known existing conventional
controller and is kept close throughout the identification procedure. The outer
loop contains a decentralized relay controller that forces sequentially a
single cycle in each loop at its most significant frequency for identification.
The outputs and the inputs of the inner loop are sampled during the excitation
procedure. In the second stage these signals are converted using a Fast Fourier
Transform (FFT) and the close loop frequency response matrix of the inner loop
is obtained. As the transfer matrix of the inner loop controller is known the
frequency response matrix of the process is calculated. The algorithm is
equipped with means to avoid computational singularities. In the third and
final stage of the identification process the algorithm fits four parameters of
a second order model with a DT to each element of the frequency response matrix
(a total of 4n2
parameters where n represents the number of
inputs/outputs of the system). A nonlinear Least Squares (LS) problem is solved
in order to determine the parameters. Since this latter problem is not a convex
one a direct search method was combined with the least squares method. This
combination enhances dramatically the convergence to the global minimum. The
combination of LS and the search method reduces complexity by reducing the
number of parameters to two only. Another advantage of the method is that a
feasible range for each parameter can be prespecified.
The identification algorithm was realized and tested both in simulations
(using the Matlab software) and on a laboratory setup. These tests demonstrated
that the algorithm performs in a satisfactory manner and is robust.