Transfer function identification by digital filtering and the solution of overdetermined equations
Smith Rh · 1979
A major problem in the design of system compensation networks is determining the system equations. A simple two stage procedure of identification has been developed for this problem. The method does not require special test signals provided that the normal operating signals are of sufficient bandwidth to excite all modes of response. The first stage of the procedure is to use digital filters to reduce the data to linear algebraic equations. In principle there are many suitable filters but it is necessary to consider the effect of noises in the input and output signals. A filter to decrease the effects of noise is described. The linear equations so produced are generally ill-conditioned leading to erroneous result if conventional matrix inversion techniques are employed. Theoretically there is no limit to the number of equations that may be produced. An obvious solution to the problem of ill-conditioning would appear to be to produce more equations than theoretically required and use the 'Generalized Inverse' to produce the solution. Unfortunately this approach does not yield the required solution as the equations have errors on both sides. A new technique for dealing with linear equations where there are errors on both sides has been developed and is described.