This is the lowest level of system identification. The idea is to develop a transfer function that gives frequency response results that are a good approximation to the measured frequency response. Usually, there is little use made of theoretical models in constructing these transfer functions. One simply uses the experimentally measured gains, phases, and break frequencies to formulate a model using the principles outlined in Section 2.4. For example, suppose that the measured system frequency response is as shown in Fig. 6.3. The break frequencies are

Upward breaks (zeros) Downward breaks (poles) to = 0 to = 0.1, to = 10

The zero-frequency gain is zero. Thus we may construct the following model for the system:

G = s/[(s + 0.1 )(s + 10)]

Of course, there are systemmatic computer techniques (generally based on minimizing a squared error) for doing this too.

Models constructed in this way may be used to optimize control systems and to predict the system response to various perturbations. Also, if the poles or zeroes are simply related to physical quantities, this procedure may be used to identify them, t See the literature (3-52).

In nuclear reactor application the objective is often to determine the feedback frequency response, since the uncertainty in the zero-power frequency response is usually much smaller than the uncertainty in the feedback frequency response. The results from a frequency response test (power/reactivity) on a power reactor can be analyzed to yield the feedback frequency response. From Eq. (6.1.2), we see that the feedback transfer

function H may be obtained as follows:

H = (1/G) — (1/Gj) (6.2.1)

This approach has been used for several reactors to determine H, and transfer functions have been fitted to the measured H to use for representing feedback effects in a system dynamic model.