6- 4.1 Excitation Signal

In experiments using external excitation, a plant con­trol device, often a reactor control rod, is moved in accordance with a prescribed signal while the prescribed signal and one or more output variables are recorded The signal is usually either sinusoidal or pseudorandom (such as Fig. 6.6) With the former the transfer function expressed in complex form is simply

G(co)=^-e10 (6 27)

A.

for an output variable В sin (cot + ф) With a pseudorandom signal the input and output must be cross correlated and a Fourier transform carried out on the result (see Set 6-3) As a signal generator in these experiments, one of the following may be used a function generator (of sine waves usually), a stored function on tape (usually pseudorandom), or a random or pseudorandom electronic noise generator It is important that the function-generator output not deviate significantly from a constant frequency and that it contain no significant harmonics The function generator might take any of the following forms a constant-speed motor driving a control actuator, an electronic oscillator driving a control-positioning circuit, or a square wave (“up” or “down”) or ternary signal (“up,” “hold,” or “down”) driving a control switch. Regarding pseudorandom noise generation, a stored tape has been used41 as well as an on-line generator107 Some experiments use commercial random-noise generators 84

An important characteristic of the excitation variable is its amplitude The amplitude must be large enough to overcome unwanted noise without requiring excessively long experimental times It will be shown in Sec 6-7 that the amplitude, unwanted noise, and test duration all combine to determine the accuracy of the result

The amplitude cannot be made arbitrarily large, how­ever, since nonlinear aspects of the system can complicate data analysis It can be shown91 that, because of non­linearities in the neutron kinetics equations, Eqs 6 11 and 6 12, one type of nonlinearity resulting from a sinusoidal reactivity excitation is a power function

N(t) = N0 + N, sin (2nft) + N2 sin (47rft + в) + (6 28)

where the harmonic to-fundamental ratio is

N2 _ 1 N, lG0(2f)l /А^Л

N, 2 N0 lG0(f)l ‘

This usually means that the harmonic content is of the same order of magnitude as the modulation fraction, N,/N„

Another important characteristic of the excitation signal is its frequency band The frequency content desired depends on the information to be obtained It is sufficient that frequencies cover the band

Ji_<2fff<_i — (6.30)

Unax Lmin

if rmax and rmin are the largest and smallest system time constants of interest In practice the amplitudes and frequencies attainable may not be those desired because of equipment limitations, so compromises may be required. Although there is little difficulty in attaining the lowest frequency desired, either the available power or the

limitations of materials are likely to place a limit on the highest frequency attainable. Also, the inverse relation between amplitude and frequency, if constant-speed motors are used (e. g., to drive a control rod in and out in a periodic triangular wave shape), places limits on the maximum frequency

linear rod speed 2 X frequency