Control of pressure and temperature of chemical reactor

Transcription

1 Journal of Middle East Applied Science and echnology (JMEAS Control of pressure and temperature of chemical reactor M. AZZOUZI Ziane Achour University of Djelfa, Faculty of Sciences and echnology, Djelfa, Algeria ( Abstract-- he paper presents a study on the robustness of two automatic controllers that control the operation of a pyrolysis reactor. his reactor is one of the devices used in the oil refinery of Pitesti in Romania, which is known as the greatest center of the separation and extraction of oil in the Eastern Europe. he pyrolysis that we analyzed is a unit conversion of oil and the production of other synthetic compounds including ethylene; this last is much used in everyday life as it is a petroleum product that can generate very significant after several reactions of several components. he study is a comprehensive analysis that can identify and control the temperature and then the pressure of pyrolysis, to study their robustness and then to robustify them. Index erms--pyrolysis reator, robustness, temperature control, Systems identification, WinPim, WinReg. 1. NOMENCLAURE WinPim: software of identification and model validation WinReg: software of digital control Ft: flow of the thermal agent a: temperature of the thermal agent F p : the product flow p : the product temperature e : the alloy temperature e0 : prescribed value of the temperature R: gas constant Fa: feed rate Fe: extraction rate p: pressure p0: given value for the pressure ARX: Autoregressive model with external input W0: natural frequency Xi: damping factor s: sampling period : period n: order RC: emperature Recording Controller PRC: Pressure Recording Controller PRBS: pseudorandom binary sequence w cr : crossover frequency = phase margin G: gain margin : delay margin M: modulus margin HR(q -1 : polynomial of specification of performances of the polynomial R HS(q -1 : polynomial of specification of performances of the polynomial S H: transfer function A(q -1, B(q -1 : model polynomials A m (q -1, B m (q -1 : reference model polynomials R(q -1, S(q -1, (q -1 : RS controller polynomials D: delay P: divider 2. INRODUCION he pyrolysis reactor in our case is intended to obtain the ethylene, one of its products after its several reactions. Oil and steam are introduced into the plant by two access routes at a constant debit; the quantity of heat required is obtained from a fire system that uses the right fuel methane gas [5], [6]. 3. EMPERAURE CONROL emperature is a parameter representative for the chemical and petrochemical processes with the transfer of heat. In temperature control systems RC, we will calculate the mathematical model for heat transfer of the thermal agent of the product which will be heated or cooled. he structure of temperature controller is given in figure (1 [3] [7]. F t hermal agent - e 0 RC + e F P, P (Product Fig.1. emperature control 3.1. IDENIFICAION AND CONROL One generates a PRBS signal that has an amplitude of +/-1%, with a recorder of 8, a divider of 2, and a sampling period s = 5s, which implies that the duration of the test is equal to: 2 (N-1 *p*s = 21.33min. hen this signal must be filtered around bullets [1] [11]. According to the estimation of polynomial degrees, we could deduce that 44

2 Journal of Middle East Applied Science and echnology (JMEAS the polynomial A is of second-degree polynomial and B is the first degree, the results of the identification and regulation by WinPIM and respectively WinReg are: he model Model structure identification system: ARX Identification method: recursive least squares parametric adaptation algorithm: gain decreasing Pole placement method for regulation s = 5s D = 0 B q q H q Aq 1.683q 0.707q Method of pole placement R q q q q S 3 q 1 q q q q he reference model Am q q 0.05q q q he Nyquist diagram with the locations of closed loop poles of the figure (2 are taken in two different cases, they show the difference between a controller without prespecification of performance thereof given above, and a robust controller to be given later by adding some performances [4] [8]. N r ABLE I Specification of the performances racking Regulation HR HS Double Double Simple Double Simple w0 xi w0 xi n w0 xi n he robustness margins corresponding to the previously specified performance are reported in table (2, the goal here is to change on performance so that we can bring and maintain the margins obtained in the range of known robustness margins [2] [12]. ABLE 2 Successive improvement of the robustness margins Nr G ( o (s (6.22dB (4.37dB (6.22dB (6.71dB (5.5dB (7.99dB 2.200(6.85dB 2.004(6.04dB M (-5.83dB (-8.06dB (-7.50dB (-7.76dB (-7.30dB (-4.80dB (-5.45dB (-6.13dB Fig.2. Nyquist diagram and closed loop poles 3.2. ROBUSIFICAION OF HE CONROLLER he specification of the performance in tracking and regulation to clarify the dominant auxiliary poles of the closed loop are successively represented in table (1 [14]. 45 Indeed, one can determine if this control system will perform adequately over the entire operating range, and what source of uncertainty is most likely to compromise the performance. he robustness margins above can be confirmed by traces of the sensitivity function shown in figure (3 [10] [13].

3 Journal of Middle East Applied Science and echnology (JMEAS 4. PRESSURE CONROL In case of pressure control, we determine for example, a mathematical model for a capacity of pneumatic food with a fluid (gas phase, see Figure (5. he idea is to send a pseudo-random binary sequence SBPA; on the open-loop pressure control, acting on the process without support, having an amplitude of + / -1%. Number of registers N = 8. Frequency of divider p = 2. And a sampling period e = 3s, which imply that the test duration is equal to: 2(N-1*p*e=12.8min. Fa Steam ank Fig.3. uning of the sensitivity function he new controller polynomials with the reference model are given as follows: 3 4 Rq q q 30.06q 87.18q q 78.80q 1629q S q 0.34 q q q q 0.35 q q q q he reference model 1 Am q q q 1 1 q q o simulate the behavior of the controller, one uses the step response of the reference model given earlier by considering the existence of a step-type disturbance with amplitude of 2.5 * 10-3 %, applied at time 40s, a graphical representation of the step response under and without disturbance is shown in figure (4, the insurance of the performance in tracking and regulation can be shown [6] [9]. Fig.4. Step response under and without disturbance Fig. 5. Pressure control After filtering the data recorded previously and estimating of polynomials degrees by using WinPim. It was found that A is a polynomial of second degree, while B is a polynomial of first degree, the validation test has confirmed the quality of the chosen model, the results of the identification and control by WinPim and are WinReg, respectively are: he model Structure: ARX Algorithm: decreasing gain Method: Recursive least squares Sampling period: e=3s Delay: D=0 B q q H q 2 Aq q q Méthode de placement des pôles R q q 3.87q S 2 q 1 q q q 2.76q q q 0.151q q q Model of reference Am P PRC Pressure sensor Fe 46

4 Journal of Middle East Applied Science and echnology (JMEAS 4.1. ROBUSNESS ANALYSIS he robustness test is important to identify the operating factors which are not necessarily considered in the development phase of the method, but that could affect the results, and therefore to anticipate problems that may occur during the application of the chosen method [5]. Figure. 7. Closed loop poles without and with performances o perform the robustness of system pressure control, performance tuning was done in 16 cases, starting from the state farther down the interval of robustness, it is in the first case, without any performance, to arrive at the perfect robustness, we note in each case the four margins of robustness in table (3. Fig. 6. Nyquist diagram without and with performances he distance between the desired poles and the actual poles is weighted to penalize more the errors associated with poles which have the stability and performance, and minimized with the method of least squares [7, 15]. hen the diagram of the poles from the beginning until the end of regulation is illustrated by Figure (7. Nr G ( o C (s M (4.23dB (-8.72dB (4.75dB (-7.85dB (4.42dB (-8.41dB (4.86dB (-7.76dB (4.64dB (-8.08dB (5.10dB (-7.46dB (4.85dB (-7.80dB (4.68dB (-8.07dB (5.19dB (-7.36dB (5.42dB (-7.06dB (5.02dB (-7.57dB (5.52dB (-6.97dB (5.96dB (-6.75dB (6.16dB (-6.27dB (6.39dB (-6.07dB (6.80dB (-5.80dB able.3. Successive Amelioration of the controller robustness First, we must know that finding different results for each set of parameters does not mean that we move away from the base solution. Obviously, with operating values significantly different, the calculation procedure does rarely results completely identical yield. Polynomials of the controller after the addition of performance are given in able (3., Am (q -1 R(q -1 S(q -1 (q -1 P(q -1 (0=0.115 (1= Am(1=1 Am(2= Am(3=0.663 Am(4= R(0= R(1= R(2=0.486 R(3=0.003 R(4=0.014 R(5=0.086 S(0=1.000 S(1= S(2=0.517 S(3= S(4= (0= (1=3.124 (2= (3=0.221 P(1=1.000 P(2= P(3=0.606 P(4= able. 3. Controller polynomials with performances he new polynomials of the controller and the reference model are : 47

5 Journal of Middle East Applied Science and echnology (JMEAS R q 77.22q S q 0.14q q q 1.16q q 6 629q 0.39q q 0.35q q 0.34q q q q he reference model Am q 1.06q 0.35q q q 4 4 Fig.8. Sensitivity function of 16 analysis case RESULS he adjustment is considered in the frequency domain, because the stability and robustness, and performance time of the closed loop system, can be represented [8]. WinReg software facilitates the handling and the study of evolution of a series of results obtained with a series chaged performance, and the sensitivity function for these 16 cases is shown in figure (8. 4. CONCLUSIONS he application in this article was a data processing taking a pyrolysis reactor installed at the oil refinery of Pitesti, this application has allowed us to conclude: Adjustment of performance parameters often involves more moderate than those that can potentially be obtained using a high order controller. he model uncertainties are directly taken into account to ensure robust performance and stability in closed-loop system. Measurements are sensitive to changes in analytical conditions, it is essential to maintain these constant conditions or introduce precaution in the description of the method. One assesses the robustness of the temperature Based on the qualitative and quantitative responses. REFERENCES [1] D. Popescu, D. Stefanoiu, C. Lupu, C. Petrescu, B. Ciubotaru & C. Dimon, Industrial Automation, Edition AGIR, pp , [2] K. Melloul, A. El Kamel, P. Borne, Linear Programming and applications; tutorial and exercises, Edition echnip, pp , [3] M. Azzouzi, Systèmes numériques pour la commande avancée des installations pétrolières et pétrochimique, PhD hesis, Politehnica University of Bucharest, Bucharest, Romania, [4] D. Popescu, C. Lupu, C. Petrescu and M. Matescu, Sisteme de Conducere a proceselor industriale, Edition Printech, pp , [5] A. Oustaloup, La robustesse: Analyse et synthèse des commandes robustes, Edition Hermes, pp , [6] Y. D. Landau and G. Zito, Digital Control Systems: Design, Identification and Implementation, pp , First Edition of Springer, [7] P. Harriott, Chemical reactor design,, CRC First Edition, pp , [8] M. Azzouzi, D. Popescu, Optimisation d un réacteur de pyrolyse par SiSCon, Conférence Internationale Francophone d Automatique; CIFA 2008,

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