Băieşu Alina, Cărbureanu Mădălina

Transcription

1 ECAI International Conference 8th Edition Electronics, Computers and Artificial Intelligence 30 June -02 July, 206, Ploiesti, ROMÂNIA Internal Model Control for Wastewater ph Neutralization Process Department of Control Engineering, Computers and Electronics Petroleum-Gas University Ploiesti, Romania agutu@upg-ploiesti.ro, mcarbureanu@upg-ploiesti.ro Abstract This paper presents the results of testing an advanced control method, Internal Model Control (IMC) on wastewater ph neutralization process. Because the process has a strong nonlinearity it was modeled using different linear models for different operating ranges so that the IMC controller can use the adequate model parameter values according to the current operating range. The results obtained using the multi-model standard IMC algorithm are compared with the ones obtained using the conventional PID (Proportional-Integral-Derivative) algorithm tuned using the same model parameter values used for designing the IMC controller. The simulations showed that using the proposed multi-model standard IMC algorithm is a feasible alternative for controlling this kind of process with a high nonlinear behavior, obtaining good static and dynamic performance. Keywords IMC algorithm, PID algorithm, wastewater ph neutralization, controller, control, automatic system I. INTRODUCTION From all the plant chemical processes, the most important, from the point of view of the influence on the rest of the chemical processes, is the process of wastewater ph neutralization. This process is known for its dynamic and high nonlinear behavior, being very sensitive around its neutral point (ph=7 units) ([-5]). According [6] and [7], the process high nonlinearity around the equivalence point it is due to the nature and concentration of the chemical reagent, being enphasised the fact that the reduction of the reagent concentration leads to a reduction of the ph leap around the equivalence point. The ph value has a high variation even when it is used a small amount of strong acid type reagent (H2SO4) or a strong alkaline type reagent (NaOH, Ca(OH)2). Also, the neutralization process of a strong acid with a strong base is bigger than the neutralization of a weak acid with a strong base ([8]). The titration curves from literature associated to the wastewater ph neutralization process emphasize the process high nonlinear behavior and complexity ([-4] and [9]). The wastewater ph control can be made by means of conventional control (PID or Gain-Scheduling PID), advanced control (IMC or Model Predictive Control-MPC) or intelligent control (fuzzy logic, adaptive neuro-fuzzy inference systems (ANFIS), artificial neural networks (ANNs)). The solution of using PID, fuzzy logic, ANFIS and ANNs were tested in [0], [] and [2]. The advantage of IMC algorithm is represented by its simple form and the fact that the tuning parameters can be easily tuned ([3] and [4]). Garcia and Morari introduced for the first time the Internal Model Control concept [5] which was later developed by other researchers like Francis and Wonham [6], Zames [7], Arkun et al. [8]. This algorithm was studied and used in practical applications because it is simple and effective [9]. Internal Model Control (IMC) is a method that offers good control performance even when disturbances appear, but its efficiency depends on the process model accuracy. If the model is very well approximated the system will also work very well [4]. The IMC design implies two steps: finding/ identifying the process model; designing the controller - obtaining the controller model using the identified process model. There are two types of IMC controllers that can be used depending on the desired control performance, namely standard and advanced. In the standard variant, designing the IMC controller involves the use only of the process proportional gain reverse, as model for the primary controller (Fig. 2). In the advanced variant, designing the IMC controller implies using as model for the primary controller, the reverse of the whole dynamic model of the process. The paper contains three main parts: A short description of the wastewater ph neutralization process from a Romanian refinery and of the process mathematical model; The IMC controller design based on the process model parameters obtained studying the process dynamics; The presentation of the results of the simulations made with the proposed standard

2 2 IMC control structure and a comparison of these results with the ones obtained using PID (PI) algorithm. II. The proposed system from Fig. has the following components: The wastewater ph neutralization process. This process takes place at the mixing-reaction basin as follows: the wastewater it is pumped in the first compartment of the mixingreaction basin (the mixing chamber); in this compartment are dosed the chemical reagents (H2SO4 (F) for an alkaline ph control or Ca(OH)2 (F2) for an acid ph control), the mixture being stirred by an paddle stirrer; then the obtained mixture it is pumped in the reaction chamber (the second compartment) of the same basin where are taking place the specific chemical reactions (in this case the neutralization reaction); The ph controller block, composed from an comparison element and the controller itself, having the following operating principle: THE WASTERWATER PH NEUTRALIZATION PROCESS In literature, for the wastewater ph neutralization process it is presented a set of mathematical models, models that are based on the researches developed by McAvoy, Hsu and Lowenthals [20] that lead to the main equation of these models. The models developed by Gustafsson and Waller [2], Mwembeshi, Kent and Salhi [22], Henson and Seborg [23], are models that completed the researches made by McAvoy. Another mathematical model for this process is the one used by Ibrahim R. in his Ph.D. thesis [24]. For the wastewater ph neutralization process, it was used the mathematical model presented in [24]. The main equation of this model are two diffrential equations that emphasise the dymanic behaviour of the process: Vd dt FC ( F F2 ) Vd F2 C 2 ( F F2 ) dt In () and (2), F represents the acid stream flowrate [liters/hr] with concentration C [mol/liter], F2 is the alkaline stream flowrate [liters/hr] with concentration C2 [mol/liter], V is the ph neutralization compartment volume [liters], while α and β represents the concentrations of acid and alkaline components in neutralization basin [mol/liter]. After the study of the wastewater ph neutralization process from a Romanian refinery, the authors proposed a control system for wastewater ph that has the block diagram presented in Fig.. Figure. Generalized block diagram Wastewater ph neutralization control system. through the comparison element it is determined the error value (as difference between the ph set point (phi) value and ph measured value at the process output; the error value it is send to the controller which establishes (according to the error value) the chemical reagents (H2SO4 (F) or Ca(OH)2 (F2)) flowrates necessary for controlling an alkaline or an acid ph; according to the simplified models of the process the IMC controller computes the control variable C (for F flowrate) or C2 (for F2 flowrate), depending on the nature of the measured ph (acid, respectively alkaline); The ph transducer that measures the ph value at the process output; Two actuators (EE and EE2) - dosing pumps; The chemical reagents tanks placed inside and outside the chemical reagents hall. According to the neutralization plant operating manual, the neutralization of an acid type ph it is performed using a solution of 0% hydrated lime (Ca(OH)2), while for neutralizing an alkaline type ph it is used an acid type chemical reagent, such as H2SO4 with a concentration of 95%. Both neutralizers are injected through dedicated pumps [25]. In Table are presented the following parameters: F representing the H2SO4 flowrate with concentration C (95%), F2 representing Ca(OH)2 flowrate with concentration C2 (0%) and V the volume of admixture-reaction tank [25].

3 Internal Model Control for Wastewater ph Neutralization Process TABLE I. ([24], [25]). CHEMICAL C F [liters /hr] [25 300] III. [%] [mol/ liter] STEP REACTANTS PARAMETERS C2 F2 [liters /hr] [ ] [%] [mol/ liter] 0.5 V [liters] Figure 3. Internal Model Control structure with tunable controller: K the controller gain, Gp(s) the process transfer function, Gm(s) the process model transfer function, Gm(0) the model static gain, Gc(s) the internal model controller transfer function, r setpoint, e error, c control variable, d disturbance, y process output [27] r e - The general structure of an Internal Model Control system it is presented in Fig. 2 [26]. d r K INTERNAL MODEL CONTROLLER DESIGN Figure 2. Internal Model Control system structure: Q(s) primary controller transfer function, Gp(s) process transfer function, Gm(s) process model transfer function, r setpoint, e error, c control variable, d disturbance, ym model output, y process output. - e Q(s) c d Gm(s) ym In case of a set point or disturbance step change, the steady-state error is zero if the controller static gain is equal to the reverse of the model static gain [27]: (3) In the standard variant of the IMC algorithm, the primary controller transfer function Q(s) is chosen as a zero order transfer function, equal to the reverse of the model gain:. Gm (0) (4) In this case, the IMC controller transfer function, which consists of the primary controller Q and the model transfer function Gm, is: G C (s) Q(s) Q(s) G m (s) G m (0) G m (s) (5) In order to have a tunable controller a gain K, having the standard value equal to, was introduced in the structure, as in Fig. 3. If the value of K is increased, we will obtain an increase in the control variable power. In this case, the IMC controller has the transfer function [27]: G C (s) K G m (0) G m (s). c d GP(s) y Gm(s) The process dynamics were investigated using step changes in F and F2 flows around the equivalence point (ph=7 units), depending on the nature of the ph (acid or alkaline); Q(s) Gm(0) G(s) c - Q(0). Gm (0) According to process graphical step response (Fig. 4-6 and 8-0) the simplified process model can be represented as a first order transfer function y Gp(s) 3 (6) G m (s) Km, Tm s where Km is the process model gain computed as Km F [%] or F2 [%], ph [%] and Tm is the process model time constant computed as T Tm t, 4 where Tt is the process transient time defined as the time in which the process output reaches 98% from its final value. Using (4) and (7), (6) becomes: G C (s) K (Tms ). K mtms A conclusion of the first dynamic tests was that the process has a strongly nonlinear behavior around the investigated point. Due to this aspect the simulations were further conducted over three operating ranges around this equivalence point (ph=7 units). The numerical results (the process model parameters values) are presented in Table II where it can be observed that the process is strongly nonlinear, characterized by different gains (Km) and time constants (Tm).

4 4 TABLE II. PROCESS MODEL PARAMETER VALUES Process input variables F [liters/ hr] F2 [liters/ hr] Process output variable ph [units] IV. Process model parameters Tm [hrs] Km SIMULATION RESULTS c( t ) c 0 ( t ) k R ( e( t ) The PI algorithm was tuned using the model parameter values (Km and Tm) from Table II, using formulas k R 0.9, Km and Figure 6. The process response (blue), the IMC control system setpoint step change from 6.9 to 7.8 units having F2 flow as t edt ), Ti 0 where c0(t) is the initial control value, e(t) - error value, kr - controller gain and Ti - integral time constant. Figure 5. The process response (blue), the IMC control system setpoint step change from 5.4 to 6.9 units having F2 flow as. The simulation results of the proposed standard IMC control structure are presented in this section, where it is also made a comparison between the results of the simulations obtained using the PID (PI) algorithm: Figure 4. The process response (blue), the IMC control system setpoint step change from 4.2 to 5.4 units having F2 flow as Ti Tm. As we can observe from the figures above, the best response is obtained using the proposed IMC structure because we obtain the smallest transient time. Also, in both cases, using IMC and PI controllers, the control system steady-state error is zero. An even better control system dynamic response (smaller transient time) is obtained if the IMC controller gain K is increased, as in Fig. 7. Figure 7. The IMC control system response, with K= (red), the IMC control system response, with K=2 (magenta) and the IMC control system response, with K=3 (blue) for a ph set point step change from 6.9 to 7.8 units having F2 flow as Using data from Table II the designed control system performance was tested for step changes in set point (desired) ph value. The results are presented in Fig. 4-. In each figure is presented the process response (with blue), the IMC control system response (with red) and PI control system response (with green). The same tests were made also in case of decreasing the ph value. The results are showed in Fig. 8.

5 Internal Model Control for Wastewater ph Neutralization Process Figure 8. The process response (blue), the IMC control system setpoint step change from 0.8 to 9.77 units having F flow as 5 Also, in both cases, using IMC and PI controllers, the control system steady-state error is zero. In order to obtain a reduction of the control system transient time, the IMC controller gain K can be increased, as in Fig.. Figure.. The IMC control system response, with K= (red), the IMC control system response, with K=2 (magenta) and the IMC control system response, with K=3 (blue) for a PH set point step change from 8.07 to 7.0 units having F flow as Figure 9. The process response (blue), the IMC control system setpoint step change from 9.77 to 8.07 units having F flow as V. CONCLUSIONS Controlling the ph neutralization process it is a difficult task because of the highly nonlinear behavior around the equivalence point (ph=7 units). Figure 0. The process response (blue), the IMC control system setpoint step change from 8.07 to 7.0 units having F flow as This aspect makes very difficult to use the same controller that can be available on the entire ph domain. This paper presents the results that can be obtained when a multi-model standard IMC controller it is used. The main contributions are: Also in this case, as we can observe from Fig. 8-0 that the best dynamic response of the control system is obtained using the proposed IMC structure because we obtain the smallest transient times as it is showed in Table III, where are presented the transient time values for all tested operating ranges, using the designed IMC and PI control algorithms. TABLE III. ph[units] TRANSIENT TIME VALUES Transient time IMC [hrs] Transient time PI [hrs] Different process models for different operating ranges around the equivalence point (ph=7 units), were identified. These models have the same structure (first order transfer function) but different parameter values (gain and time constant). According to the current process operating range the IMC controller will consider the adequate model. - The proposed multi-model IMC controller was designed and implemented using the previously found models; - A PI controller was also designed and implemented. The same model parameter values according to the operating point as in case of IMC control algorithm were used for tuning; - The results obtained using the proposed IMC controller were compared with the ones obtained using the designed PI controller. The results showed that the proposed standard multi-model IMC structure leads to better dynamic performance than using a PI controller, characterized by smaller transient time values. The simulations results emphasize the idea that using the proposed multi-model standard IMC algorithm alternative for controlling this kind of process, with a high nonlinear behavior, it is a feasible one. Also, in case of using the proposed IMC controller dynamic performance can be improved by increasing the value of the controller gain (K), without having stability issues. The only problem is the power

6 6 consumption. Increasing the controller gain, increases the control variable power, increasing in this way the consumption. REFERENCES [] [2] [3] [4] [5] [6] [7] [8] [9] [0] [] [2] [3] Ş., Agachi, Chemical Processes Automation, ClujNapoca:Science Book House, 994, pp C., Luca, Al., Duca, and I. Crişan, Analytical Chemistry and Instrumental Analysis, Bucharest: Didactic and Pedagogical Press, 983, pp V. Marinoiu and N. Paraschiv, Chemical Process Automation, Vol. III, Bucharest: Technical Press, 992, pp D. J. Pietrzyk and C.W. Frank, Analitical Chemistry, Bucharest: Technical Press, 989, pp M., Pishvaie and M. Shahrokhi, Control of ph processes using fuzzy modeling of titration curve, Fuzzy Sets and Systems, Vol. 57, No. 22, 2006, pp D.A. Skoog and D.M. West, Fundamentals of Analytical Chemistry, Second Edition, Holt London Edition, Clarke, Doble & Brendon Ltd., Plymounth, 969, pp D.A. Skoog, D.M. West and F.J. Holler, Fundamentals of Analytical Chemistry, Fifth Edition, Saunders College Publishing, 988, pp J. Kang, M. Wang, and Z. Xiao, Modeling and control of ph in pulp and paper wastewater treatment process, J. Water Resource and Protection, Vol. 2, 2009, pp M. Cărbureanu and C. Gheorghe, ph variation in the presence of the coagulants used in oil-well industry wastewater treatment, Rev. Chim., Vol. 65, No. 2, 204, pp M. Cărbureanu, The development of a neuro-fuzzy expert system for wastewater ph control, Control Engineering and Applied Informatics Journal, Vol. 6, No. 4, 204, pp M. Cărbureanu, Automatic systems for wastewater ph control- a comparative study, Journal of Electrical Engineering, Electronics, Control and Computer Science JEEECCS, Vol., No., 205, pp M. Cărbureanu, Neuro-Fuzzy Expert System for Wastewater Treatment Processes Control, Ph. D. Thesis, Department of Control Engineering, Computers and Electronics, PetroleumGas University from Ploiesti, 204. D. Ene and A. Băieşu, Internal model controller design for proportional-type processes, Petroleum-Gas University Bulletin, Technical Series, Vol LXVII, No. 3, 205, pp [4] A. Băieşu, N. Paraschiv, and D. Mihaescu, Using an internal model control method for a distillation column, IEEE International Conference on Mechatronics and Automation Beijing, China, pp , ISBN: , 20. [5] C. E. Garcia and M. Morari, Internal model control.. A unifying review and some new results, Ind. Eng. Chem. Proc. Des. Dev., vol. 2, no. 2, pp , 982. [6] B. A. Francis and W. M. Wonham, The internal model principle of control theory, Automatica 2, 5, pp , 976. [7] G.Zames, Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses, IEEE Trans. Automatic Control 26 (2): pp , 98 [8] Y. Arkun, W. M. Canney, J. Hollett and M. Morari, Experimental study of internal model control, Industrial&Engineering Chemistry Process Design and Development, pp , DOI: 0.02/i200032a06, 986. [9] Saxena S. and Hote Y.V., Advances in Internal Model Control Technique: A Review and Future Prospects, IETE Technical Review, 29(6):46. DOI: 0.403/ , 202. [20] T. J. McAvoy, E. Hsu, and S. Lowenthals, Dynamics of ph in controlled stirred tank reactor, Ind. Eng. Chem. Process Des Develop, Vol., No., 972, pp [2] T. K. Gustafsson and K. V. Waller, Dynamic modeling and reaction invariant control of ph, Chemical Engineering Science, Vol. 38, No. 3, 983, pp [22] M. M. Mwembeshi, C. A Kent, and S. Salhi, An approach to robust and flexible modelling and control of ph in reactors, Chemical Engineering Research and Design, Vol. 79, No. 3, 200, pp [23] M. A. Henson and D.E. Seborg, Adaptive nonlinear control of a ph neutralization process, Control Systems Technology, IEEE Transactions, Vol. 2, No. 3, 994, pp [24] R. Ibrahim, Practical Modelling and Control Implememtation Studies on a ph Neutralization Process Pilot Plant, Ph.D. Thesis, Department of Electronics and Electrical Engineering, Faculty of Engineering, University of Glasgow, [25] Operating Manual of the ECBTAR Wastewater Treatment from the Romanian Refinery, 200. [26] T. Marlin, Process Control, New York, McGraw Hill, Inc., 995. [27] V.Cîrtoaje, S. Frâncu and A. Guţu, Valenţe noi ale reglării cu model intern, Buletinul Universităţii Petrol-Gaze din Ploieşti, Vol. LIV, nr. 2, Seria Tehnică, 2003.