HIL Real-Time Simulation of a Digital Fractional Order PI Controller for Time Delay Processes

Transcription

1 HIL Real-Tme Smulaton of a Dgtal Fractonal Order PI Controller for Tme Delay Processes Crstna I. Muresan, Roxana Both, Eva H. Dulf, Adran Neaga, Clara Ionescu Abstract Fractonal order control has been used extensvely n the last decade for controllng varous types of processes. Several desgn approaches have been proposed so far, the closed loop performance results obtaned beng tested usng dfferent smulaton condtons. The hardware-n-the-loop (HIL real-tme smulaton offers a more relable method for evaluatng the closed loop performance of such controllers pror to ther actual mplementaton on the real processes, such HIL smulaton beng hghly sutable especally for complex, hazardous processes n whch human and equpment errors should be avoded. The present paper proposes a hardware-nthe-loop real-tme smulaton settng for a dgtal fractonal order PI controller n a Smth Predctor structure. The desgned control strategy and fractonal order controller s then tested under nomnal and uncertan condtons, consderng a tme delay process. I. INTRODUCTION ractonal order calculus has been used ntensvely n the Fcontrol of nteger order plants [1-3], beng consdered to enhance the system control performance []. Several approaches regardng the desgn for fractonal order plants have been developed, the great majorty beng tested through smulaton usng varous case scenaros. In order to further mplement such controllers, a more relable real-tme smulaton s necessary. The present paper proposes a hardware-n-the-loop (HIL real-tme smulaton of a Smth Predctor wth a fractonal order PI prmary controller for a tme delay process. The HIL method chosen for the smulaton of the closed loop control dffers from pure real-tme smulaton by the addton of a real component n the loop. Wth ths approach, the accuracy and effcency of the controller can be tested drectly on the real control unt, whle the plant s smulated usng varous smulaton envronments. Very few HIL realtme smulaton of fractonal order controllers have been used so far []. In ths paper, the hardware-n-the-loop settng s done wth the process runnng on a PC, whle the Smth Predctor structure and the dgtal fractonal order PI controller s mplemented on a Natonal Instruments process computer. The case study used n ths paper s the lqud carbon monoxde level n a cryogenc carbon sotopes separaton column. Such plants are very complex unts that separate the Crstna I. Muresan, Roxana Both, Eva H. Dulf, Adran Neaga, Clara Ionescu are wth the Techncal Unversty of Cluj-Napoca, Automaton Department, Gh. Barţu Street, no.-, Cluj-Napoca, Romana (e-mal: crstna.pop@aut.utcluj.ro, roxana.both@aut.utcluj.ro two stable carbon sotopes based on the dstllaton of carbon monoxde at extremely low temperatures ( -19 o C. A hardware-n-the-loop smulaton of the control strategy s therefore hghly sutable for such complex processes due to a number of reasons, such as cost reducton, shorter testng tmes and safety. The paper s structured as follows. In Secton, the case study used n ths paper s presented. Secton 3 offers a descrpton of the HIL mplementaton of the Smth Predctor wth a fractonal order PI controller. Secton offers some real-tme smulaton examples, also consderng varous uncertan stuatons. The last secton of the paper presents the concludng remars. II. CRYOGENIC CARBON ISOTOPE DISTILLATION PLANT The carbon sotope cryogenc dstllaton unt s bult at the Natonal Insttute for Research and Development of Isotopc and Molecular Technologes Cluj-Napoca (NIRDIMT- [], havng the schematc representaton as shown n Fgure 1. The man components are: the dstllaton column (C, the condenser (C1 at the top of the column cooled wth lqud ntrogen, the boler (B at the bottom of the column, and the vacuum jacet (M - used for thermal solaton, snce the column operates at very low temperatures. Thermal solaton s ensured by vacuum pumps (denoted PVP n Fgure 1, whle carbon monoxde s fed as a gas through a feedng system, at an ntermedary pont n the column, ept ntally n a specal reservor (R. Manometers (M1, M, M3 are nstalled at several ponts of the dstllaton column, to measure the pressures [7]. The dstllaton of carbon monoxde s the process that ensures the overall carbon sotopes separaton. At very low temperatures, the carbon monoxde (CO contanng predomnant 1 C has a dfferent bolng pont than the CO contanng am ncreased rato n the 13 C sotope. Thus, the 1 CO and 13 CO wll coexst n the column n an ascendng gaseous phase and a descendng lqud form. Snce the vapor pressure of 1 CO s hgher than that of 13 CO, the 1 C sotope accumulates n the gaseous phase, beng extracted as waste at the top of the column. The carbon monoxde enrched n 13 C accumulates n the lqud phase and s extracted as end product at the bottom of the column [7]. Snce the rato of the vapor pressure s very close to unty, the separaton of the carbon sotopes s very dffcult to acheve. The column must operate at some very strct prescrbed setponts and all secondary processes nvolved must be controlled as well [] /13/$ IEEE

2 Such secondary processes are for example the control of the lqud carbon monoxde level (h b, the control of the top and bottom pressures, the control of the lqud ntrogen level that cools the gaseous ascendng phase. features, enablng the desgn of the controller based solely on the tme delay free model of the process transfer functon. Fgure. Smth Predctor wth fractonal order PI controller The desgn of the fractonal order PI controller s based on two performance specfcatons: the open loop phase margn (φ m and gan crossover frequency (ω [1]: ω =.1 and φ m = o ( The robustness condton that ensures the performance measures n ( may be wrtten as: Fgure 1. Schematc representaton of the carbon sotope separaton plot plant Mantanng a constant lqud carbon monoxde level (h b at the boler of the column s of outmost mportance, snce t s based on the bolng of ths quantty that the gaseous stream flow s produced. The entre separaton process may be compromsed f an excessve bolng of the lqud carbon monoxde s performed, generatng a gaseous stream flow close or over the value of maxmum column capacty. Such phenomenon leads to the column floodng [9], wth serous dsadvantages regardng the effcency of the carbon sotope separaton process and leadng to an end-product of poorer concentraton. The lqud carbon monoxde level depends upon the carbon monoxde feed flow nto the column, the carbon monoxde waste flow from the column and the electrcal power suppled to the boler. To control the lqud carbon monoxde level the manpulated nput s the carbon monoxde feed flow, whle the waste flow and the electrcal power are mantaned constant. Thus the smplfed transfer functon of the process, dentfed usng expermental data [1], s gven as:.1 s G(s = e (1 s +.s +.3 III. HIL STRUCTURE OF THE SMITH PREDICTOR CONTROL STRATEGY WITH FRACTIONAL ORDER PI CONTROLLER The closed loop control scheme s gven n Fgure, where G(s s the ratonal part of the transfer functon n (1, G (s s the nomnal model of G(s, τ s the process tme delay and τ s the nomnal value of the delay and C FO-PI s the fractonal order PI controller. The choce of the Smth Predctor s based on ts nherent tme delay compensaton G G jωτ jϕm ( j e C ( jω = ω (3 FO PI e Equaton ( may be rewrtten as: j ( ( ( ϕm +τω j C jω = ω ( FO PI e Usng the fractonal order PI controller transfer functon: C s the parameters may then be obtaned usng: FO PI (s = p + ( p p + ( jω j( ϕm +τω e = G jω ( Solvng ( for p and, yelds: π ( X ( jω cot Imag( X ( jω ( = Re sp sp (7 ω = Imag sp π sn ( ϕm +τω e sp =. G jω where X ( jω ( X ( jω ( However, p and n (7 and (, respectvely, are gven as a functon of the fractonal order. In order to completely defne the fractonal order PI controller n (, an adequate value of the fractonal order must be found. Classcal desgn methods for FO controllers mply the use of optmzaton technques, such as Matlab s fmncon (

3 functon, wth sgnfcant drawbacs n terms of convergence. Instead, the authors choose an algorthm that automatcally selects the fractonal order whch maxmzes the open loop gan margn [1]. Fgure 3 shows the output of the algorthm, wth the open loop gan margn as a functon of Fgure. Hardware-n-the-loop closed loop confguraton Gan margn - absolute values Lambda Fgure 3. Open loop gan margn as a functon of the fractonal order Fgure. Bloc Dagram of the controller mplementaton usng LabVIEW The result n Fgure 3 shows that the maxmum open loop gan margn s acheved wth =1.1, thus a controller tuned wth such a fractonal order would exhbt a hgher robustness to gan varatons than any other fractonal order PI controller. For =1.1, the remanng fractonal order PI controller parameters n (7 and ( [1]: p =.11 and =. (9 To smulate the closed loop scheme from Fgure n a real tme hardware-n-the-loop settng a NI PXI-13 process computer s used. NI PXI-13 s one of the Natonal Instruments products by ntegratng processng and connectvty technologes on the maret. Among the ntegrated technologes are ncluded: analog to dgtal converter (ADC, dgtal to analog converter (DAC, counters, etc. The embedded system conssts of the followng modules: NI PXI-7, NI PXI-, NI PXI- 1. Module NI PXI-1 was chosen to mplement the controller, due to the fact that t has both analog and dgtal nputs and outputs. The hardware-n-the-loop confguraton of the closed loop scheme wth Smth Predctor and fractonal order PI controller s gven n Fgure, whle the fractonal order PI controller mplementaton scheme usng LabVIEW envronment s gven n Fgure. In order to obtan the desred HIL structure the controller s mplemented and runs on the NI PXI-13 process computer whle the process s mplemented and executed on a personal computer. Both mplementatons are done usng the Natonal Instruments LabVIEW envronment. Fgure. Bloc Dagram of the process mplementaton usng LabVIEW The measured output s receved usng NI PXI-1 module channel AI_Ch, defned n Measurement and Automaton Explorer (MAX. Ths component of LabVIEW s used to manage devces and nterfaces, vrtual channels or tass. In the upper part of the dagram data save operaton s performed. Before the Whle loop s started n the upper rght sde a.txt fle s opened where the data, representng the control sgnal, wll be saved. The Case structure performs the log and the save functonalty. The obtaned control sgnal s sent to the process usng NI PXI-1 module channel AO_Ch. Fgure presents the bloc dagram of the LabVIEW process mplementaton. The control sgnal s acqured, from the NI PXI-13 on to the personal computer usng the data acquston modules ICP/CON I-7. After the control sgnal s appled to the process, the obtaned output sgnal of the process wll be sent to the NI PXI-13 usng the same data acquston modules. Also, le n the controller bloc dagram, data save operaton s performed whch can be observed n the upper part of the dagram. In ths case are saved the control sgnal and the measured output values. The man reasons for LabVIEW mplementaton of the

4 hardware-n-the-loop confguraton are: t s a graphc envronment for fast mplementaton of measurement, testng and control applcatons and t presents several advantages regardng data acquston, processng when nstalled on embedded systems le NI PXI-13 process computer. IV. REAL-TIME HARDWARE-IN-THE-LOOP SIMULATION RESULTS The fractonal order PI controller n Fgure s mplemented n ts dgtal form usng the recursve Tustn dscretzaton method [11]. Fgure 7 shows the closed loop system response to a step change of 1% n the reference sgnal consderng varous samplng tmes for the dscretzaton of the fractonal order ntegrator, usng recursve formulas of order and 9, respectvely. The smulaton was performed usng Matlab programmng envronment, wth a step change n the reference sgnal occurrng at 1 mnutes smulaton tme. The smulatons show that more accurate results are obtaned usng a hgher order recursve dscretzaton formula and a lower samplng tme. For hgher samplng tmes and lower order of dscretzaton, the performance specfcatons are not met. The dgtal fractonal order PI controller mplemented on the PXI was obtaned usng a 9 th order recursve approxmaton formula and a samplng tme of.1 mnutes. Fgure shows that the closed loop smulaton results usng the hardware-n-the-loop settng are smlar to the results obtaned usng Matlab. The step change n the reference sgnal occurs at the begnnng of the smulaton tme. The robustness of the fractonal order PI controller s then tested consderng [-%, +%] varaton of the process tme delay. The real-tme hardware-n-the-loop smulaton results are gven n Fgure 9, consderng a step change n the reference sgnal at 1 mnutes smulaton tme. The results show that the control strategy ensures a robust performance of the closed loop system, wth the settlng tme and the overshoot mantaned below the mposed specfcatons. V. CONCLUSIONS The fractonal order controller has been specfcally desgned to ensure an ncreased robustness even for sgnfcant tme delay varatons. The smulaton results n Matlab show that the closed loop system meets the mposed performance crtera, however pror to the actual mplementaton of the fractonal order PI controller, a more relable testng s requred. The hardware-n-the-loop real-tme smulaton offers sgnfcant advantages over classcal smulaton snce the fractonal order PI controller and the Smth Predctor structure are mplemented on the actual process computer. Usng ths smulaton method, the control strategy s tested drectly on the process computer n a more realstc settng. The hardware-n-the-loop real-tme smulaton results, smlar to those obtaned usng Matlab, show that the desgned control strategy can be further used n a real process control loop. The smulaton results also prove that the desgned controller can meet the mposed performance crtera even for sgnfcant tme delay varatons. ACKNOWLEDGMENT Ths wor was supported by a grant of the Romanan Natonal Authorty for Scentfc Research, CNCS UEFISCDI, project number PN-II-RU-TE REFERENCES [1] Kall, A., Mran, N., Mlha, T. M., Chour, S., Elalam, N.: Low earth-orbt satellte atttude stablzaton wth fractonal regulators, Int. J. Syst. Sc. 3(1,, pp. 9 [] Manabe, S.: A suggeston of fractonal-order controller for flexble spacecraft atttude control, Nonlnear Dynam. 9,, pp. 1 [3] Dulf, E.H., Festla, Cl., Dulf, F.-V., Pop, C.-I., Both, R., Fractonal Order Controller Desgn for 13C Separaton Column, Proceedngs of The 19th Medterranean Conference on Control and Automaton 11, do: 1.119/MED [] Zhao, C., Xue, D., Chen, Y.: A fractonal order PID tunng algorthm for a class of fractonal order plants, Proceedngs of the IEEE Internatonal Conference on Mechatroncs and Automaton, Nagara Falls, Canada,, do: 1.119/ICMA.. [] V. Bhambhan, Y. Han, S. Muhopadhyay, Y. Luo, Y.Q. 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5 Output (% Input (% order, T s =.1mn =.1mn =.1mn =1mn 1 order, T s =.1mn =.1mn =.1mn =1mn Tme (mn Tme (mn a b Fgure 7. Closed loop smulaton results usng dgtal fractonal order PI controller a Output sgnal b Input sgnal Output (% Matlab smulaton HIL real-tme smulaton Ouput (% τ= mn τ= mn τ= mn τ=7 mn τ=9 mn τ=1 mn τ=11 mn τ=1 mn τ= mn Tme (mn Tme (mn a a Input (% 1 Matlab smulaton HIL real-tme smulaton Tme (mn b Fgure. Matlab and HIL real-tme smulaton results a output b nput Input (% 1 τ= mn τ= mn τ= mn τ=7 mn τ=9 mn τ=1 mn τ=11 mn τ=1 mn τ= mn Tme (mn b Fgure 9. HIL real-tme closed loop smulaton results consderng ±% varaton of the process tme delay a output b nput