7 s e Aol » * cluded measurvements using the \» EXPERIENCES WITH DYNAMIC TESTING S‘/D filfin, L METHODS AT THE MOLTEN-SALT REACTOR EXPERIMENT reachufy, fre~ quency, power, testing, per~ formance, signals, MSRE KEYWORDS: . W. KERLIN, S. J. BALL R. C. STEFFY, *andM R. BUCKNER** Oak Ridge National Labowatm'y, Oak dede, Tennessee 37830 Keceived May 23, 1970 | Revised September 14, 1970 - A series of veactivity-to-power frequency re- sponse measuremenis was made on the Molten- Salt Reactor Experviment. This was done for P30 and #°U fuels, for a range of operating power levels, at several points in the sysiem opervaling history, and for several different test procedures. A comparison of expevimental resulis with prior theoretical predictions confirmed ithe validity of the theoretical predictions. The test program in- pseudorandom binary sequence, pseudorandom ternary sequence, n-sequence, and the multifrequency binary se- I. INTRODUCTION An extensive dynamics testing prograra was carried out at the Molten-Salt Reactor Experiment (MSRE)." The tests consisted of reactivity to power f{rcquency response measurements. The purpose of the test program was: T 1. to demonstrate the safety and operability of the system 2. to check the validity of the theoretical anal- ysis so that the safety of the plant could be *Present address: tanocga, Tennessee, **University of Tennessee, Knoxville, Tennessee. Pres- ent address: Savannah River Laboratory, Aiken, South Carolina, Tennessee Valley Authority, Chat- NUCLEAR TECHNOLOGY =~ VOL. 10 FEBRUARY 1971 reassessed if necessary and so that con- firmed methods could be established for analyzing future, high- performance molten- salt reactors 3. to evaluate techniques for performing dy- namics experiments and methods of data analysis. Tests were performed at several different power levels, al several different times in the system’s operating history, and for the reactor fueled with U and with ***U. Items 1 and 2 were the main objectives of the test program, but this paper em- phasizes item 3 since it should be of general in- terest to those planning dynamics tests in other systems. Those interested only in the perfor- mance of the MSRE could skip Secs. II and III and proceed directly to the results in Sec. IV. Il. PLANNING THE TESTS A. Objective The primary test objective was to measure the reactivity-to-power frequency response over the range of frequencies where important system dy - namic effects occurred. Inspection of the fre- quency response predictions (see Figs. 8 and 14 of Ref. 1) indicated that measurements down to ~0.005 rad/sec at the low frequency end were needed. It would have been desirable to carry the -high frequency end of the measurements out to about. 50 rad/sec if the zero-power reactor kinet- ics effects were to be observed. If the interest were in feedback effects, the upper frequency need not have been greater than ~0.5 rad/sec. The ap- proach used here was to determine the high fre- quency (1.0 to 100.00 rad/sec) response by noise 103 Kerlin et al. measurements during zero-powar operation. Sub- sequent at-power measurements concentrated on the 0.005- to 0.5-rad/sec range where feedback effects were important. B. Equipment Used in Experimenta! Measurements The selection of the experimental methods for the MSRE dynamics tests was based on the infor- mation required and on the capabilities of the available equipment. Fortunately, the emphasis on low frequency results (0.005 to 0.5 rad/sec) made it possible to obtain the important part of the system frequency respouse using the standard MSRE control rods to introduce the input reacti- vity perturbations. The MSRE has three identical control rods, each with an active length of 59.4 in. One rod is normally designated as the regulating rod and is used for fine control. The other two rods are used as shim rods for coarse adjustments. The rods are actually flexible, stainless-steel hoses on which are strung gadolinium oxide poison cylin- ders. The rods are mounted in thimbles which have two 30-deg offsetting bends so that the rods can be centrally located even though there is no room for the control-rod drive assemblies above the central axis of the core. The maximum rod speed is ~0.5 in./sec. Typical rod travel in the experiments was ~0.5 in. for most of the 2%y tests and 0.3 in. for most of the 2**U tests. This gave a reactivity change of ~0.025% (7¢) in the **U tests and ~0.02% (12¢) in the 2%V tests, Figure 1 shows the control-rod and drive as - sembly. The position indication for each rod was obtained from a synchro geared to the rod drive mechanism. A coarse synchro (5-deg rotation per inch of rod travel) was used in early tests and a fine synchro (60-deg rotation per inch of rod travel) was used in later tests. The signal from the position synchro was amplified and low-pass filtered (1-sec time constant) to eliminate high frequency noise and the accompanying aliasing ef- fect prior to input into the Bunker Ramo computer, BR-340, where the signal was digitized every 0.25 sec and recorded on magnetic tape. The nuclear power level signal was furnished by the output of a compensated ion chamber loca- ted adjacent to the core. This signal was also amplified, Jow-pass filtered (1-sec time constant), digitized at 0.25-sec intervals, and recorded on magnetic tape. | ' The BR-340 computer was also used in con- junction with a portable analog computer for generation of the input signal for the test. A com- puter program was prepared for on-line genera- tion of each test signal used in the tests (the signals are described in Sec. II.C.2). 104 EXPERIENCES WITi{ DYNAMIC TESTING C. Test Signals 1. Introduction. Test signal selection was influ- enced by considerations of accuracy requirements, frequency range over which information was needed, and hardware capabilities. The following input signals were used during the testing pro- gram: a. pulse c . step . pseudorandom binary sequence QL o . pseudorandom ternary sequence @ . n-sequence bty . multifrequency binary sequence (flat input spectrum) | g. multifrequency binary sequence (prewhit- ened output spectrum). Pulse and step tests are easy to implement, but these signals give results with limited accuracy. This is because the signals are nonperiodic, and therefore have a continuous frequency spectrum and resulting low signal energy in the neighbor- hood of a frequency of interest. The other five signals are more trouble to im- plement, but they permit more accurate results, This is because they are periodic, and therefore concentrate the signal energy in discrete harmon- ic frequencies. In all of the tests using periodic signals, the period is determined by the lowest desired frequency: ro2 where T ='period w1 = lowest desired frequency. For example, the required period for a test in which the lowest required frequency is 0.01 rad/sec in 628 séc. All other harmonics would be at integer multiples of 0.01 rad/sec. The accura- cy of the results is improved by using input sig- nals consisting of more than 1 cycle. In the MSRE measurements 2 to 10 cycles were used, 2. Properties of mput Signals. a. Pulse. The energy density e of a pulse of duration T and amplitude A at frequency w is given by: ‘e _A*T? [sin(wT/Z)] 2 2r L wT/2 | FEBRUARY 1971 NUCLEAR TECHNOLOGY VOL. 10 'NUCLEAR TECHNOLOGY Kerlin et al. FXPERIENCES WITH DYNAMIC TESTING REVERSIBLE DRIVE MCTOR SOLENOID ACTUATED RELEASE GEAR AND ARM ' \, . / 4 A l SWITCH i ] DRIVE UNIT —// ‘ SPACER lg { LOWER LIMIT L? SWITCH '-3 3~in. x 2~in. ECCENTRIC REDUCER GUIDE BARS, ——_] 4 AT 90° BEADED POISON ELEMENTS—< | 2~in. CONTAINMENT THIMBLE —- y | | ‘1 ("' COOLANT TO DRIVE ASSEMBLY /'—“COOUNG \O/ GAS INLET L \ //’ " o~ COOLING GAS CONTAINER -~ ——POSITION INDICATOR SYNCHRO TRANSMITTER FIXED DRIVE SUPPORT AND 3~ in. CONTAINMENT TUBE COOLANT TO POISON ELEMENTS %in.0.D0.-304 S.S.- FLEXIBLE HOSE CABLE a0 ~—— SPRING LOADED ANTIBACKLASH HEAD AND IDLER GEAR oi™ I6-in. RADIUS x 30° BEND Fig. 1. Control-rod drive assembly, This spectrum appears in Fig. 2. Note that the amplitude is expressed as energy spectral density (energy per unit frequency). | ' | b. Step. A step input may be thought of as a pulse whose duration has gone to infinity. The step test is suitable only for systems whose re- sponse settles to some constant value after the VOL. 10 FEBRUARY 1971 step input. This requires that the system’s zero- frequency gain be a finite constant (including zero). In principle, the step input contains an infinite amount of energy, but this energy is concentrated in the low frequencies where it is of little use. ¢. Pseudorandom Binary Sequence. The pseu~ dorandom binary sequence (PRBS) is often used 105 Lot o Naatag Kerlin et al. 0.1 w = FREQUENCY (rad/sec) T = PULSE DURATION (sec 0.01 ENERGY PER UNIT FREQUENCY AZ T2 0.00! Q.4 | 10 100 DIMENSIONLESS FREQUENCY (w T) Fig. 2. Energy spectrum of a square pulse. for frequency response measurements and for ap- proximate impulse response measurements. The methods for generating the PRBS are well known.”? These methods give periodic sequences of +1’s and -1’s (each member of the sequence is called a bit). The total number of bits in the se- quence N must be 22 - 1 for any integer value of Z. The period of the signal is given by the prod- uct of the number of bits N and the bit time in- terval At The spectrum of the PRBS with pulse amplitude A and total test duration T is given by: 2 . 2 py =2 WADET (G (g 2 | A0=;1VzT for k=0, (1) where A; = amplitude of the energy spectrum at the A’th harmonic frequency. The spectra for several sequences are shown in Fig. 3. Note that the short sequences concentrate most of the signal energy in the first few harmonics and the longer sequences spread the signal power among more harmonics. | In planning a test, one must select the period to give the required lowest frequency. The required upper frequency fixes the sequence length N or equivalently (since the period is fixed) the bit dur- ation. The following relation specifies the har- monic number at which the signal power is half as large as the amplitude of the harmonic with the 106 EXPERIENCES WITH DYNAMIC TESTING A Py Y A e L gratuam. e, oet ) - A T Ay s R T R AT 'y 2 Y . e LUl S R SN s M. e o T O v Tl O o iy R R R B AR Ref T B NI TR e e s ST | PO L IO LR ] L R S A F o T T e A E N - greatest amplitude’ (thereby furnishing a measure of the bandwidth of the signal): kr =0.44N , (2) where 2, =harmonic number of the harmonic with half the power as the harmonic with the greatest power, Thus, if the lowest frequency is ; rad/sec, and the required highest frequency is wy, rad/sec, then the number of bits is given by: N =227 %L (3) w1 The bit duration A is fixed by the highest fre- quency of interest. The relation is At = — | (4) Of course, these are just rules of thumb. If the total signal energy is too small, the signal energy per harmonic may be too small even for the har- monic with the largest amplitude. . - d. Pseudovandom Tevnary Sequence. The pseu- dorandom ternary sequence* (PRTS) is similar to the PRBS, but three levels of the input signal are 1.0 DENOTES HARMONIC FREQUENCY BASIS ~ SAME TOTAL DURATION 0.5 FOR ALL SIGNALS 0.2 0.1 . w O 2 005 4 o s g Wi 9% 002 D a x . — LS 0.0t o ac. 2 w 0.005 - -t T 4 | ' 1 ° 0.002 . o i L] i ' o @ ! y 0.001% 1 2 5 10 20 50 100 HARMONIC NUMBER Fig. 3. Energy spectrum for several PRBS signals. NUCLEAR TECHNOLOGY VOL. 10 FEBRUARY 1971 AMPLITUDE (NORMALIZED TO PRBS) used (-1, 0, +1). The number of shifts in these- quence is given by N = (37‘ - 1) for integer values of 7. The spectrum of the PRTS with pulse amplitude A and total test duration I'is given by: 8 (N +1)A°%T [sin(kfr/N)]2 . A = & : for % odd 3 2 kRu/N A’ / (5) Ay =0 for k& even. This shows that the shape of the PRTS spectrum is the same as for the PRBS. However, only the odd harmonics are non-zero and they have an am- plitude which is one-third larger than the corres- ponding amplitude of a PRBS harmonic for a sequence with the same value of N. Figure 4 shows a comparison of these signals. The proper- ties given in-Egs. (2) through (4) for the PRBS also apply for the PRTS. - The PRTS is of interest because it has the ad- vantage that it discriminates against nonlinear effects. This may be advantageous because it allows one to use large amplitude signals in fre- quency response measurements. The PRTS has the disadvantage that in the MSRE (and in many other reactor systems) a three-level input is harder to implement with system hardware than a two-level signal. e. n-Sequence. The n-sequence’ is obtained by a simple modilication of the PRBS. The modifica- tion consists of inverting every other bit in a PRBS. Since the number of bits Nin a PRBS is o o 0.01 0.0t O.1 | 10 NORMALIZED HARMONIC NUMBER (k/N) Fig. 4. Envelope of amplitude spectra for PRBS, PRTS, and n-sequence, ' NUCLEAR TECHNOLOGY VOL. 10 FEBRUARY 1971 Kerlin et al. EXPERIENCES WITH DYNAMIC TESTING always odd, the number of bits in an n-sequence obtained by nicdification of an N-bit PRBS is 2N. The spectrum of the n-sequence with N bits, pulse amplitude A, and total test duration T is given by: | | A2 e (T \K: 4, = AN+ DA% [sm(k/r/N)J for b odd N? kw/N 1 ©) A =0 for & even. Figure 4 shows a comparison of the spectrum for the n-sequence and the PRBS and PRTS. Since the shape of the amplitude spectrum is the same as for the PRBS, the bandwidth relations [Egs. (2) through (4)] still apply. The n-sequence discriminates against nonlin- ear effects as in the case of the PRTS signal. f. Multifrequency Binary Sequence (MIFBS)— Flat Spectrum. In all frequency response mea- surements, a major objective is to select input signals with a large fraction of the total available signal energy concentrated in the frequencies selected for measurement. Generally, it is de- sirable to space the harmonics evenly on a loga- rithmic scale except in regions where more resolution is needed. Since the harmonics of the PRBS, PRTS, and n-sequence are evenly spaced on a linear scale, the spacing of the harmonics is too dense at the higher frequencies (see Fig. 3). This constitutes a waste of signal energy in identifying nearby harmonics which are only slightly different from one another. An alternate procedure is to design a test sig- nal which maximizes the {raction of the total signal energy in harmonics selected by the ex- perimenter. A signal of this type can be obtained by a computer optimization of the polarities of the pulses 'in a pulse chain of fixed length. The ob- jective function, which is minimized in the opti- mization, is the difference between the desired spectrum and the spectrum obtained for a given pulse chain. Experience shows that as much as 65 to 75% of the total signal power can be concen- trated in selected harmonics.®”’ Furthermore, the signal can be designed so as to discriminate against nonlinear effects. A typical signal used in the MSRE experiments appears in Fig. 5. g. Multifrequency Binary Sequence (MFBS)— Prewhitened Spectrum. One of the main reasons for interest in the PRBS, PRTS, and ii-sequence is that the amplitude spectrum can be made quite flat over a wide frequency range. This is important in measurements with large noise contamination of the input signal. The procedure for such a system would be to use as much input signal energy as possible (within limits set by system operating 107 T R AR it it 45N S TR AT NSNS R TR W TN e FRACTION OF TOTAL SIGNAL ENERGY - : 5' nN - At o, — _ - ‘ B#gfl?maw&ys LR N e SRR O I PR 2 a7 o 3 AR e PPNy L T G N R L s e N el R SR R ¥ S ;- T P G B LG S Ao L A N T A R R Er : T N e O By i e e R Rogee ¥y B TS e T e S G IR AT i g ) e Rl M g Y g ¥, £ ] U TR ;;1;"?5“, Y ST ¥ I T 4: ..; P Y L 3 ?;:}‘;;,‘, i P u :‘ " > 5 e Kerlin et al. M e M0k L U0 UUJHU”U”UU e “l Ate3 sec 7 (o) THE INPUT SIGNAL io~! NOTE. THE TWELVE DESIRED CONTAIN 753 %, OF THE TOTAL SIGNAL ENERGY O DESIRED HARMONICS D OTHER HARMONICS BELOW SCALE 1073 10 0~} 10° 10! FREQUENCY (rad/sec) (b) ENERGY SPECTRUM | Fig. 5. MFBS flat spectrum signal and its spectrum, - conditions and nonlinear effects) and to divide this energy evenly among the desired harmonics so that the signal-to-noise ratio would be as high as possible at each measurement frequency. In systems in which the predominant noise contamination is in the output signal, the same observations apply as were mentioned above in connection with an input-noise problem. That is, each output harmonic should contain the maximum possible signal energy. Thus, for systems with output noise problems (a common case) the output amplitude spectrum should be flat. This can be accomplished by using an input signal whose am- plitude spectrum has a shape which is the recip- rocal of the amplitude spectrum of the system frequency response. | A method has been developed’ for obtaining a flat output spectrum if preliminary estimates of the amplitude of the system frequency response are available from theoretical calculations or from preliminary measurements. The procedure is the same as described in the previous section, except that the desired amplitude spectrum used in the optimization has the shape of the recipro- cal of the expected shape of the amplitude of the - system {requency response. The amplitude spec- trum of a typical input signal for a prewhitened MFBS test is shown in Fig. 6. 3. Signal Input Procedures. Three different pro- cedures were used in the tests. The changes were required to overcome problems with the control rods and with the system background flux noise. 108 EXPERIENCES WITH DYNAMIC TESTING a. Open-Locp Rod Positioning. This procedure was used in the early tests. The desired input signal generated by the BR-340 computer was used to actuate withdraw and insert signals to the control-rod drive motor. The withdraw and insert times were different because the coasting characteristics of the rod were different for withdrawals and insertions. The withdraw and insert times were adjusted manually during the beginning of the test to give the desired pulse shapes. This procedure . worked well when the control rods were new, but the wear associated with long-term operation caused difficulty in later tests. b. Flux Demand. The flux demand procedure was used to overcome the problems associated with open-loop tests. The procedure was to feed the test sequence in as a flux demand signal for the flux-servo system. This caused the control rods to move to satisfy the flux demand. In this test, the spectrum of the flux signal had the ap- proximate shape of the spectrum of the test se- .quence. The amplitude of the spectrum of the input was approximately the amplitude of the flux signal divided by the amplitude of the system fre- quency response at that frequency. This procedure worked satisfactorily for the final tests with the ?**U loading. The only condi- tion was that the flux servo system had to be ad- A : T 0N AT Ooon "‘"* Ot = 3 sec (@) THE INPUT SIGNAL NOTE: THE SIX DESIRED HARMONICS CONTAIN 72 7% OF THE TOTAL SIGNAL ENERGY FRACTION OF TOTAL SIGNAL ENERGY O DESIRED HARMONICS 0 OTHER HARMONICS BELOW SCALE 03" _ 1002 2 5 107! 2 5 10°® 2 5 10! FREQUENCY (rod/sec) (6) ENERGY SPECTRUM Fig. 6. MFBS prewhitened signal and its spectrum, NUCLEAR TECHNOLOGY VOL. 10 FEBRUARY 1971 o= justed to avoid hunting by the control rod. This was necessary because of loose coupling in the rod drive mechanism (see Fig 1), which caused an error in every indicated rod position change. If each rod position change was preceded by a change in the opposite direction, then each read- ing was in error by a multiplicative factor. When rod position changes in arbitrary directions were made, the indicated position error was not a simple factor and it was impossible to obtain re- liable rod position indications. When the reactor operated with °°U fuel, a change in system characteristics made the flux demand procedure unacceptable. Shortly after operation began with ***U fuel, the void fraction in the fuel salt increased significantly with an ac- companying increase in flux noise. This noise component in the error signal in the servo caused excessive rod motion. This was unacceptable be- cause of the problem with erroneous rod position signals. - ¢. Closed-Loop Rod Positioning. The prob- lems with the flux demand test led to the closed- loop rod positioning procedure. In this procedure, the flux signal from the ion chamber was discon- nected from the servo system and was replaced by the rod position signal. Then, the error signal which actuated the control-rod drive was the dif- ference between actual and desired rod position signal. This procedure was satisfactory in all tests. Hi. DATA ANALYSIS METHODS Three different digital computer codes were used in the data analysis. These are described briefly below: 1. FOURCO.? This code computes the Fourier transform of the output signal and the input sig- nal, and computes their ratio to give the frequen- cy response. 2. CPSD.? This code is based on a digital simulation of bandpass filters. The filters have adjustable bandwidths, as opposed to the other two analysis methods in which the effective band- widths are determined by the duration of the data record analyzed. 3. CABS.'® This code computes the autocorre- lation function of the input, the autocorrelation function of the output, and the cross-correlation function for input and output. These are then Fourier transformed (using FOURCO) to give the input power spectrum, the output power spectrum, and the cross power spectrum. The frequency response is given by the ratio of the cross power spectrum to the input power spectrum. NUCLEAR TECHNOLOGY VOL. 10 FEBRUARY 1971 Kerlin et al. EXPERIENCES WITH DYNAMIC TESTING IV. RESULTS The large number of different tests (over 50) makes it impossible to show all the results in this paper. Instead, some typical results will be shown, and 2 comparison with theoretical results will be made. (The reader may consult Refs. 7, 9, and 11 for more details on test results.) Frequency Response Results a. 250U Fuel, litial Operation. For these early tests, the input consisted of a reactivity pulse, a reactivity step, or a pseudorandom binary reac- tivity input. The input procedure was the open- loop rod positioning procedure, and all three data analysis methods were used. Figure 7 shows the zero-power frequency response for the **°U-fueled reactor with fuel salt stationary. This figure also shows the noise analysis results'? at high fre- quency. The comparison of the magnitude with calculations is quite good. The phase results are less satisfactory. | | . Figure 8 shows the frequency response at 2.5 MW. The agreement between the shape of the measured frequency response and the shape of the predicted frequency response is good for magni- tude and phase. The differences between the theoretical and experimental results for the absc- lute value of this magnitude are not compietely understood, but it is suspected that the problems with accurate rod position indications and with establishing the true power level by heat balances are largely responsible for the differences. (The frequency response is a strong function of power level. See Figs. 8 and 14 of Ref. 1.) The autocor- relation function of the rod position signal and the cross-correlation function for the 2.5 MW test ap- pear in Figs. 9 and 10. The blips near each end are due to asymmetry in the pulses (the positive pulses do not have exactly the same shape as the negative pulses). These blips are predictable " from the theoretical properties of pseudorandom binary signals with asymmetrical pulses.'® These blips were not observed during the first tests (be- fore the power was increased to 2.5 MW), but they have been observed intermittently in subsequent: tests. They cause no problems in obtaining fre- quency response results. They are included here to illustrate an unexpected feature in the test re- sults which were bothersome until the cause was understood. : : Figure 11 shows the results at 7.5 MW. From this figure, it appears that the dip in the amplitude at ~0.24 rad/sec in the predicted frequency re- sponse is too large in the theoretical predictions. Since this calculated dip was due to fuel recircu- lation effects,’ it appears that more mixing of the 109 Kerlin et al. EXPERIENCES WITH DYNAMIC TESTING 104 0.0t 01 ZERO FOWER T-sec PULSE, TEST NC 1 7-sec PULSE, TEST NO 2 3.5-sec PULSE, TES™ NO 3 3 5-sec PULSE, TEST NO 4 NOISE ANALYSIS 10 w, FREQUENCY (rod /sec) 20 ' N o -40 PHASE (deg) =100 0.001 0.0t ZERO POWER 7-sec PULSE , TEST NO. | 7-sec PULSE , TEST NO. 2 A 3.5-sec PULSE ,TEST NO. 3 & 3.5-sec PULSE ,TEST KO. 4 © 0.1 w, FREQUENCY (rad/sec) Fig, 7. fuel salt in the external loop should be included in the theoretical model. A measure of the adequacy of the theoretical model is its ability to predict the natural period of oscillation of the power response following a re- activity perturbation. The comparison of the experimental results with theoretical predictions (see Fig. 9 of Ref. 1) appears in Fig. 12. b. ¥°U Fuel, Intermediate Tests. Measure- ments were made again after 1 year of power operation (2100 equivalent full-power hours). Pseudorandom binary sequence inputs were used at power levels of 1, 5, and 7 MW. The open-loop rod positioning procedure was used. These tests showed no significant changes in the dynamic characteristics due to aging. c. ¥5U Fuel, Final Tests. A final set of mea- surements for the ***U-fueled system were made after more than 9000 equivalent full-power hours of operation. Input steps, pseudorandom binary 110 Frequency response at zero power; fuel static, sequences, and pseudorandom ternary sequences were used. The last attempts at open-loop rod positioning were made in some of the PRBS tests. This procedure worked occasionally, but it was not reliable. The flux demand method was used for most of these tests to overcome problems encountered with the open-loop rod positioning method. Figure 13 shows results from flux de- mand tests using one of the few satisfactory PRTS signals. These results show that there were no aging effects which caused significant changes in the power hours of operation. d. 23U Fuel, Mitial Operation. Plans were made to use the flux demand technique in the dy- namics tests for the ?**U loading, but this proce- dure proved unacceptable because of the problems mentioned in Sec. II.C.3. This led to the use of the closed-loop rod positioning method, which proved to be satisfactory, and which was used in all subsequent tests. Pseudorandom binary se- quences and pseudorandom ternary sequences NUCLEAR TECHNOLOGY VOL. 10 FEBRUARY 1971 Kerlin et al. EXFERIENCES WITH DYNAMIC TESTING \ | T T 3 RN . c/ofv iE\a f ; — i,. ‘| T o) b AR E e N ®| o PPl e o c 1&g togO® Tv .2 S o 4 = .4,,.0/ - X T 5 O o /s v . ° / ) g ,éwy..,.,POWER LEVEL -~ 2.5 MY o STEP TEST o g ; , I 127-BIT PRBS-CPSD ANALYSIS ®© LY i . 127-BIT PRBS—CABS ANALYSIS & PRy X 511-BIT PRBS-CPSD ANALYS!S A 1 511-BIT PRBS-CABS ANALYSIS © 0.001 0.002 0.005 0.01 0.02 0.05 0.1 0.2 0.5 1.0 FREQUENCY (rod/sec) ' 90 ) POWER LEVEL — 2.5 mW s STEP TEST o 70 127-BIT PRBS-CPSD ANALYSIS @ 50 127-8IT PRBS-CABS ANALYSIS A 511-BIT PRBS-CPSD ANALYSIS A 50 511-8IT PRBS-CABS ANALYSIS V 40 S 30 LY X 20 § 10 r o — . Q -10 -THEORETICAL -20 ' -30 -40 -50 -60 -70 0.001 0.002 0.005 0.01 0.02 005 01 2.2 0.5 1.0 FREQUENCY (rod/sec) Fig. 8. Frequency response, power = 2,5 MW, - i s = D > . e £ | = [ z . Z O - U Z 5 | % x .'w o o O O O 3 = » D < | X . . o actouet e I R o RIS PR SRR - WP 0 400 Fig. 9. Input NUCLEAR TECHNOLOGY VOL. 10 800 1200 1600 CORRELATION TIME (sec) autocorrelation function for a 511-bit PRBS test at 2.5 MW, FEBRUARY 1971 ' » 111 NN RS PR R N T e ST S R T A A T Ci s e A o m& E l » Kerlin et al. EXPERIENCES WITH DYNAMIC TESTING ! » x X x X xy X X " CROSS~-CORRELATION FUNCTION (Arbitrary Units) 0 400 800 ’ 1200 1600 CORRELATION TIME (sec) Fig. 10. Cross-correlation function for a 511-bit PRBS test at 2.5 MW, — T Q C o - w| o vo % = sy L - 7.5 MW TRL z STEP TEST o o 127-BIT PRBS-CPSD ANALYSIS e 127-BIT PRBS-CABS ANALYSIS A S11-BIT PRBS-CPSD ANALYSIS A , S511-BIT PRBS-CABS ANALYSIS ¥ 0002 0005 Q.01 002 005 o1 0.2 05 10 FREQUENCY (rad/sec) 80 70 60 40 PHASE (deg) .30 |JPOWER LEVEL - 7.5 MW STEP TEST | -40 1427-BIT PRBS-CPSD ANALYSIS _so | 127-BIT PRBS-CABS ANALYSIS 511-BIY PRBS-CPSD ANALYSIS -60 } 511-BIT PRBS-CABS ANALYS!S 0.001 0.002 0.005 0.01 0.02 0.05 0.1 0.2 0.5 1.0 FREQUENCY (rod/sec) Fig. 11, Frequency response, power = 7.5 MW, 112 A NUCLEAR TECHNOLOGY VOL. 10 FEBRUARY 1971 Kerlin et al. FXPERIENCES WITH DYNAMIC TESTING ~were used. Typical results are shown in Figs. 14 soermenta| and 15 for PRBS and PRTS tests. The PRBS re- sults shown in Fig. 14 arc in good agreement with theory and the scatter is small. The theory still shows too large a dip at 0.24 rad/sec, indicating too little mixing in the theoretical model. The PRTS results shown in Fig. 15 have the same general form as the PRBS results, but the scatter is excessive. This is apparently due to the prob- lems in determining the rod position accurately for the three-level signal (see Sec. II.C.3). PERIOD OF OSCILLATION (min) e. ¥ Fuel, Final Tests. A final series of 2).02 005 Ot 02 05 1.0 20 50 100 : POWER LEVEL (MW) | tests was run ~9 months later. For the final tests, the PRBS, the n-sequence, the MFBS-flat Fig. 12, MSRE natural periods of oscillation. spectrum, and the MFBS-prewhitened spectrum 10° POWER LEVEL - 8 Mw ANALYSIS METHOD o CABS 5 ——THEORY 2 S c Q «i o < < 102 < < o 5 2 10! 140 / Py ° - 60 - 2 o 3 ~d °l P w . N v .\ o q O X \\\% o * -20 e N\ oood’o % q\ OWM;O%°EM -100 1073 2 5 1072 2 5 107! 2 5 100 FREQUENCY (rad/sec) Fig. 13. Frequency-response results from a flux-demand test performed on the ?**U-fueled reactor using a PRTS test pattern., ’ | - VNUCLEAR TECHNOLOGY VOL. 16 FEBRUARY 1971 113 Kerlin et al. EXPERIENCES WITH DYNAMIC TESTING il -1 m AT = ' ANA — » /4« LYSIS METHODS £ 2 ./ o FOURCO, CABS,CPSD — S P (EACH GAVE SAME RESULTS) 45 o ' 1 - —HEQY = POWER LEVEL - 8MW 90 > < ANALYSIS METHOD A - © « CABS | - THEORY 60 n\i‘“‘ 111 . ch . ’ T \é 13 :30 1 3 w @\ < s R il Rogrin N D \N B -30 }— . - H 3 L 1073 2 5 102 2 5 107t 2 5 100 9 I a FREQUENCY (rad/sec) Fig. 14. Results from a 127-bit PRBS with the reactor at 8 MW, 103 THEORETICAL ) 3n nogp 0% 2 5 102 2 5 10' 2 5 10° FREQUENCY (rad/sec) Fig. 15. Frequency-response results from a rod- demand test using a 242-bit PRTS test pattern. — 102 Z o 5 2 10! 10°3 2 5 1072 2 5 10t 2 5 100 FREQUENCY (rad/sec) 90 .\ 60 \\\ 30 \\ ~ ° o\, THEORETICAL g "N » L O \>\ O O OQ‘\\ 7] VO ;:I \\cl‘}é OO(ZDO\\\ a Ox]:b%%\\\ -30 \\ ) - \\\ -60 ™S N -90 1072 2 5 10! 2 5 109 2 5 10! - FREQUENCY (rad/sec) Fig. 16. MSRE frequency response—PRBS signal, 114 NUCLEAR TECHNOLOGY VOL. 10 FEBRUARY 1971 N X Kerlin et al. EXPERIENCES WITH DYNAMIC TESTING ‘ ’ { 90 \\ B 60 , \\ , » \\\ = N : THEORETICAL 8 ON ( = N |/ O 0 2 \od!o ococc\r\\ I %%NN Q. '\ -30 * \,\ '\\ \'\ -60 ’ '\\ -90 1072 2 5 107! 2 5 109 2 5 10! FREQUENCY (rod/sec) f 103 ° | ! 2 % t:f&)Q~ . § S1°% THEORETICAL , C 2 L — 10 : z 3 S 0 @ S POWER LEVEL - 7 MW 5 2 10 —_— 2 10 2 5 102 2 5 10!t 2 5 100 | £l® THEORETICAL c FREQUENCY (rod/sec) - 107 Z Fig, 17. MSRE frequency response—n-sequence. s 5 2 10! 103 -2 5 102 2 5 o' 2 5 10° FREQUENCY (rad/sec) %0 N\ O 30 \\ S ' N “THEORETICAL @ o N = SN 1/ w O o5 % K/ 0 oo:\NN o ] - N~ ~ ..60 \\ -90 1 10-2 2 5 107! 2 5 100 2 5 10 NUCLEAR TECHNOLOGY VOL. 10 FEBRUARY 1971 . FREQUENCY (rod/sec) o . Fig. 18. MSRE frequency response—MJFBS with flat input spectrum. 115 Pt Tt T o L SR b 2L i AENIE R - g L Kerlin et al. EXPERIENCES WITH DYNAMIC TESTING were used. Results are shown ir Figs. 16 through 19. These results again demonstrate that there was no significant change in system dynamics due to aging. In these tests, compariscns were made of the different test signals. In general, the advantage of the MFBS was demonstrated. it is not possible to present the details of the comparison here (see Ref. T), but some typical results are shown in Table I. This table shows results for a PRBS test and an MFBS test. Each test censisted of 8 cycles and each cycle was analyzed separately to give an independent estimate of the frequency response. The lower percent deviations for the MFBS tests are due to the higher signal-to-noise ratio at each measurement frequency, which occur because the input signals concentrate the available energy in these frequencies. The prewhitening technique was of little benefit because the amplitude of the MSRE frequency re- sponse did not change very much over the fre- quency range of interest. ’ 0% 102 THEORETICAL GAIN ([;;L'gfl) 10! 103 2 5 102 2 5 10V 2 5 10° FREQUENCY (rod/sec) TABLE I Percent Deviations in Measured Magnitude Ratios Percent Deviation? Frequency (rad/sec) MFBS PRBS 0.016 16.0 34.0 0.049 7.3 16.4 0.082 4.1 7.3 0.12 ‘ 4.6 9.2 0.15 7.0 6.6 0.21 4.4 17.8 0.28 ° 3.9 16.6 0.35 4.0 9.5 0.41 3.9 9.8 0.48 3.6 5.1 0.54 1.8 7.9 0.61 3.3 5.8 “Based on 8 cycles of data. Both signals had same'am- plitude and bit duration. The MFBS had 128 bits and the PRBS had 127 bits. V. CONCLUSIONS The main conclusion as far as the MSRE pro-~ gram is concerned is that the dynamic character- istics of the MSRE were found to be satisfactory and essentially as predicted, for both the ?**U and the ***U fuel loadings. Conclusions having to do with experiences in performing dynamics tests on a system with no special provision for test equipment are: 1. By proper matching of the testing method to the system characteristics and to the characteris- tics of normal system hardware, it was possible S0 T oI\ 60 N \ /THEORETICAL N 30 N AN /N PHASE (deg) o G o / ~ Y NN o -90 . ' 1072 2 5 10! 2 5 10° 2 5 10} FREQUENCY (rod/sec) .Fig. 19. MSRE {requency response—MFBS with prewhitened output spectrum. 116 NUCLEAR TECHNOLOGY VOL. 10 FEBRUARY 1971 to measure the system frequency response without the expense of installing an oscillator rod. 2. A thorough understanding of the properties of test signals is a great help in selecting the optimum test signal for a particular application. Our experience suggests that the MI'BS signal may have the widest general utility of the methods used in the MSRE tests. ACKNOVLEDGMENTS This research was sponsored by the U.S, Atomic Energy Commission under contract with the Union Carbide Corporation, REFERENCES 1. T. W, KERLIN, S. J. BALL, and R, C. STEFFY, ‘““Theoretical Dynamics Analysis of the Molten-Salt Reactor Experiment,’”’ Nucl. Technol., 10, 118 (1971). 2. P. A. N. BRIGGS, K. R. GODFREY, and. P. H. HAMMOND, ‘‘Estimation of Process Dynamic Charac- teristics by Correlation Methods Using Pseudo-Random Signals,”” IFAC Symp. on Identification in Automatic Control Systems, June 12-17, 1967, Prague, Czechoslo- vakia, Part II, pp. 3.1-3.12, Academic, Prague (June 1967). 3. T. W. KERLIN, ‘““The Pseudorandom Binary Signal for Frequency Response Testing,”’ USAEC Report ORNL- TM-1662, Oak Ridge National Laboratory (1966). 4, R. J. HOOPER and E., P. GYFTOPOULQS, ‘On the Measurement of Characteristic Kernels of a Class of Nonlinear Systems,’”’ Proc. Symp. on Neutron Noise, Waves and Pulse Propagation, Conf, 660206, U.S. Atomic Energy Commission (1967). NUCLEAR TECHNOLOGY VOL. 10 FEBRUARY 1971 Kerlin et al. EXPERIENCES WITH DYNAMIC TESTING 5. H. R. SIMPSON, Proc. IEE, 113, 12, 2075 (December 1966). 6. A. Van Den BOS, ‘“Construction of Binary Multi- frequency Test Signals,”’ IFAC Symp. on Identification in Automatic Control Systems, June 12-17, 1967, Prague, Czechoslovakia, Part II, pp. 3.1-3.12, Academic, Prague (June 1967), 7. M. R. BUCKNER, ‘‘Optimum Binary Signals for Frequency Response Testing,”” Doctoral Dissertation, University of Tennessee, Knoxville (1370), 8. S. J. BALL, ‘‘A Digital Filtering Technique for Efficient Fourier Transform Calculations,”” USAEC Re- port ORNL-TM-1662, Oak Ridge National Laboratory (1967). 9. T. W. KERLIN and S. J. BALL, ‘‘Experimental Dy- namic Analysis of the Molten-Salt Reactor Experiment,”’ USAEC Report ORNL-TM-1647, Oak Ridge National Laboratory (1966). 10. T. W. KERLIN and J. L. LUCIUS, ‘““CABS—A For- tran Computer Program for Calculating Correlation Functions, Power Spectra, and the Frequency Response from Experimental Data,”” USAEC Report ORNL-TM- 1663, Oak Ridge National Laboratory (1966). 11. R. C. STEFFY, ‘“Frequency Response Testing of the Molten-Salt Reactor Experiment,”’ Thesis, University of Tennessee, Nuclear Engineering Department (November 1969); and USAEC Report ORNL-TM-2823, Oak Ridge National Laboratory (1970). 12, D. P. ROUX and D. N, FRY, Oak Ridge National Laboratory, Personal Communication, 13. K. R. GODFREY and W. MURGATROYD, Proc. IEE, 112, 3, 565 (March 1965). | 117