EmEQUENCY DOMGW JDENTIFICATION OF DlIiTERENTIAZ, PRESSURE CELLS.

Phtllip McGlone Joseph McGhee’ Ian A. Henderson

ABSTRACT

This paper outlines the identification of a pneumatic differential pressure cell using a multifiequency binary sequence, 01 MBS, test signals. The rVp cell consists of a diaphragm, I pilot relay flapper/nozzle and a feedback bellows The reported experimental results show that the cell has a first order linear response.

INTRODUCTION

Differential pressure cells ( d p cells), which measure pressure differences, are. commonly used to measure fluid flow along pipes, or liquid level in open or closed tanks. For example, when considering Iaminar fluid flow through a pipe nerwork, fluid particles will posses three components of energy. These three elements are the parbcle’s kinetic energy, the body force energy (gravky) and a component of potential energy, by merit of the fluid pressure. Jointly, these energies appem in the conservation of energy relation hown as Bernoulli’s equation. When a constriction, such as an orifice plate, is encountered in the pipe, a fluid particle must speed up tbrough this pinching of the pipe in order to maintain a constant volume flow rate through the pipe. Assumhg that the pipe is horizontal, this increase in the kinetic energy is cantered by a decrease in the fluid pressure in order to Atah an energy balance. The difcerential pressure cell exploits this change in pressure in order to evaluate the volume flow rate.

In the classical approach to frequency d y s i s , a system is excited with a sinusoidal signal. The resulting forced steady- state output response is then measured. The effect of the system upon the magnitude and phase of the input signal i s recorded, aIong with the corresponding input signal parameters. This process is then repeate4 over and over again until enough data has been colIected over a representative bandwidth for the system under examination. The mapitude and phase of the steady state response is then plotted using an appropriate gapbical representation such as a Bode diagram, a Nyqyist graph or a Nicbolls chart. However. this method is t ime consuming, since the experiment has to be repeated for at Ieast as m y times as there are harmonic frequencies of interest in order to build up enough data for a wide band system. Consequently ifthe system is subject to dnff due to any ambient thermal, mocbaaical, electrical or other temporal infiuences the experimental results may be corrupted. CruciaIly this method of interrogation means that the system is off line for the duration ofthe analysis.

Notably briefer experimental times can be achievad using multifrequency test signals [ 11. This is because the system is forced simuitaneously with all of the harmonic frequencies of interest. Vay low amplitude mulfiequency signals superimposed in tandem with &e set point signal permits hterrogation. At the same time the system may continue to operate normally about its set-point. The benefit of using mdtifcequency test signals is immediately apparent. The instnment can sustain routine procedures, results are swift and consequently drift problems need not provoke any concern.

SYSTEM IDENTIFICATION

The response of a d p cell has been identified multifrequency binary test signals, ( M B S ) [2,3]. Because the method uses multifrequency binary test signah, this effectively means that dl frequencies are analysed during the same experiment. Thus temperature variations or any other temporal deviations have minimal influence on experimental results. The procedure uses a discrete Fourier transfom kchruque. Both the target system and the associated soffware have been developed in house. AU of the input forcing and output response data, which are collected using computer based digih1 s i g d processing @SP) boards, are subssquentIy d y s e d either as on-line or off-line si& processing tasks.

Because the differential pressure ceIl is pneumatically powered, the elecuonic muItEequency binary test si@, W S ) , input to the cell, and the pneumatic output are both converted to tbe required pneumatic / electronic form by the we of some electronic interface C ~ G U ~ Q 121. Sensitive piezoraktive pressure -duces form the point of contact between the celI and the system identification instrument.

1 l i e authors a e at the Indwtriai control Centre, University of Strathclyde, 50, George Street, Glasgow GI IQE, Scotland ( e-mail: phd@icu.strath.ac.uk, http://www,icc.strath.ac,uk).

One of the most powafuI system identification methods makes use of hdBS sequences, which have been amlied to a number of different processes as quoted in the bibliography and references in [ll. Application to temperature seas or^ is reported in [4]. There are several valuable benefits to the we of this method; interrogation is carried out exirmely quickly and is achieved without disturbance of the set point. Obviously this facilitates system identification without the need to take the system off line, of primary sigmficance to industrial users. As a rem14 potential questions commonly experienced with drift can be safely put to one side. This M B S procedure is also used in the internally developed ins-ent h o r n as System Detection or SYD. Tbis package was developed within the depmmt of EIectronic and Etectrical engineerins at StrathcIyde University. The SYD package comprises a target system that carries out the interrogation, and a software package, which governs the M33S and also analyses the output of the system under investigation [4]. The most eficient and interesting of the MBS interrogation forcing signals have been investigated and tabulated by the authors and their collaborators over several years, and are now well established as a sound and flourishing interrogation method [1,5,6]. The technique has been applied successfully to variaus forms of system and instrumentation [7,8]. Simulation echoed by real experiment has underlined the usefulness and veracity of the MBS system identification techniques.

An example of the MBS signal used in the experiment is shown in Figure l(a). This particular signal is the Ociave Extended binary si@ descnied in [5]. The first thirty harmonics of this sequence are shown in Figure I@). Most of the signal power is held within the dominant h o n k s . Tbe canonical disposition of ihe dominant terms is resolved by the value of de percentage power in each irtdividual t e r n For the octave extended signal the interrogation metbod uses the seven dominant harmonics corresponding to f& Z&, 4fb 8% lSf,, 16% and 30&, where fD is the fundamentaI harmonic. These seven harmonics, which contain 58.6% of the signal power, with 8.4* 3% power pet component, cover approximately 5 octaves. Because the ovenvhelming majonQ of the signal power is concentrated within such a limited number of harmonics, the salient features of the system response are quickly arrived at. Conversely the low power harmonics can be ignored BS they contribute so little information to the -fer function. Even in the case of the classical analysis technique the same low power harmonics would not reveal much infomtio~, because in both methods system noise tends to swamp low amplitude harmonics. The sampled function can be reconshcted provided the sampling theorem constraints are met. The user, by judicious choice of the M B S amiutes, ensures these mmtraints are satisfied. From this information the system response i s evaluated by a mdt i f rqency hierrOgation. The use of MBS interrogation methods, which belong to the non- paramebic group of identification methods, ensures that very few a priori assumptions about system parameters is required. As the interrogation process is performed within a very short time, it is possible to appIy several basic periods ofthe MBS to reduce the effects of any noise. The frequency o f the particUlar harmonics can be tailored to investigate interesting areas of the instrument's specmi response. For illusbation, the cut off point in a h t order system could be investigated in detail, or the harmonics may be chosen to straddle the resonance peak in a second order system

DIFFERENTIAL PRESSURE CXLL

The cell under examination was the Foxboro 13a. This pneumatic ce11,has the ability to measure pressure differences up to a maximum of 6 . 2 ~ 1 0 ~ Pa. The cell was calibrated for a fnaximum input pressure difference of 3 . 1 ~ 1 0 ~ Pa. This value was chosen as it bisects the specified range. Under typical conditions a l l measurement and cone01 signals for pneumatic instruments operate within the range [ O . ~ - ~ ] X I O ~ Pa Gauge pressure. his is the span of the ~QI cell instrument With standard operating conditions, therefore the dp should report 6x104Pa of Gauge pressure, when the volume flaw rate is at the value demanded by the process.

With the standard span as delheated above, a small amplitude computer generated M B S interrogation signal was applied to the d!p cell high-pressure port A minor electronic shiffing circuit connects the computer to and from the differential pressure cell. This interface enabres conversion of the eiectronically generated signal between the computer and the pneumatic signal form required by the system For the measured signals this circuitry also performs the reverse operatioa The interface connects to a three-ported solenoid valve [2]. This cirmit acts as a transducer to interface between the electronic digital conirolhg signal and the pneUmaticaUy powered d / p cell. The shifting circuit is employed to ensure that the p a e m t i c signal's mark to space ratio faithfully fOUows that of the applied M B S si@.

T h e solenoid valve output was connected to the high pressure port of the cell and the low pressure port was held at 5x103 Pa. This was to give a raised zero so tbat the system was not susceptible to changes in atmospheric pressure. The signal born the shifting circuit is applied to a relay order to fire the solenoid valves. The inputs to the solenoid are set at 1 . 9 5 ~ 1 0 ~ Pa and 2.1Sx104 Pa. The sip1 therefore was of amplitude 2x103 Pa about a mean value o f 2 .05~10~ Pa. This amounts to ody 3% of the span, a very low value of the order of system noise that would be expected not to disturb the ongoing process. The mean value corresponds to an output pressure of 6x104 Pa, the nominal operating condition.

Sensitive piaoresistive bridge pressure transducers form the point of communication between the cell and the system identification k-ent. Both of the input and Output MBS signals were measured and recorded using these transducers. T h i s permits the DSP board to implement a build up of a data set for discrete Fourier transform @FT) anaIysis in real time. The DFT analysis is perfomed automaticaUy by the computer and once calculated is displayed. The software offers the phase and amplitude results for each harmonic in tabular format. The transfer functlon is therefore elementary to calculate

and plot. A typical result is shown in Figure 2. It was then proposed to examine the feasibility to use the frequency domain identikation process to identify defective

systems. A series o f experiments was launched to test this hypothesis [g]. This investigation also targeted an instnunent with a collection of induced defects in several of the differential pressure cell ~bsystems. Dk!mct components have had various defects temporarily introduced. For example, an input leak of WOW diameter was engiueered for the input port. Interesting faults intraduced into the feedback block were loosening of the flapper and blocking of the nozzle restriction. The latter is quite a commonty occurring fault in industrial process plants. One at a h e , the system was set up with these defects, and the MBS identification method vas applied to the fault induced cell. The results show quite notable signatures for the feedback block. Whilst the flapper is distinct fiom the nozzle, it shows skdarhy in the context of comparison with the input btock,

CONCLUSIONS

The experimental results, which are illustrated in Figure2 show the differential pressure cell to be a fmt order system. The &U, which has been designed to measure slowly changing bdk processes, performs well to that specitlcation. However, h m the frequency domain identitication process there are indications of degradation in performance at relatively high fiequmcies for the d/p cell system, Nevertheless, this degenerative behaviour should cause no embarrassment as the ” p r o b l ~ ” d e & itself well beyond the opemtio~l envelope of the insimnent. Further work has been carried out to assess the possibility that multifrequency signal examination could also be engaged to identify probable individual defects in m y subsystem element. The results have been very encouraging. From the compiled library of defect: signatures, it is now possible to iden* miScellaneous faults io various subsystem components. It seems reasonable to extend this procedure ta the examination of other systems and instruments.

Godfrey K. (Ed), Perhdrbatiion Signah for System JdentiJmtion, Prentice MI v), London, 1993. McGlone, P., McGhee, S. anaenderson, LA., “Mdwequency stochastic methods for identitication of differential pressure cells andlor their defects,”Froc. of 9th IMaKO TC-4 h t m t i o n a l Symposium, pp. 25-28, September 1997. McGlone, P., McGhee, J. and Henderson, I. A., ’Performance evaluation of a differential pressure cell’ Trans IEEE Ins* Me@., 47(S), 1271-1276. McGhee, J., Henderson, 1. A. and Jackowska-StmdUo, E. M. ‘Temperature sensor identification Wrth multifrequency binary sequences’, in [l]. 277-295. Henderson, LA., McGhee, J. and El-Fan&, M., ’Data Measurement’, 1997, ISBN 09531409 0 3, Universities Design and Print, Indusbal Control Cenfq University of Strathclyde. Henderson LA., Jackowska-Strumillo L., McGhee J., McGlone, P. and Sankowski D., ‘Sysrem Identification Using Identification Patterns’, 1999, Cod. Rec IMTC 99, lEEE Cat No 99CH36309, ISBN 0-7803-5276-9, Vol2, pp. 911- 916. Jackowska-Skunillo L., Sadowski, D,, McGhee J. and Henderson I.A., ‘Modelling and MBS experimentation for temperature sensors’, 1997, Measurement, 20, 1, pp. 49-60. JackowskaSirumilla L., ‘Temperature sensors monitoring and diagnosing by the use of MBS data patterns’, 1998, Proc. of the 9th Int. Symp. on System Modelling Control, SMC’98 (CD-ROM), Ed. by P.S. Szczepaniak, Zakopane, Poland. McGlone, P., McGhee, 5. and Henderson, I.A., “Identification Of Defects In Differential Pressure Cells”, Proc. of htemationar Symposium on System Science, September 1998, Wroclaw, PoIand, 230-236

Figure. 1. Experimental polar plot of results for the identification of a d/p cell using an MBS signal

I I I I +V 0.4

MBS 0.2

0 0

-0.2 -V

1 I 1 I J 5 IO 15 20 25 30

Bits Harmonic number

Figure 2. The octave extended MBS sigual in the t ime domain is given in (a) and the first 30 harmonics are shown in @)

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