Online Identification and Control of pH in a Neutralization System

pH control of a neutralization system for wastewater, where the input waste stream ... are tested and compared mainly for disturbance rejection, set-p...
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Ind. Eng. Chem. Res. 2008, 47, 4394–4404

Online Identification and Control of pH in a Neutralization System ¨ zgen* Salih Obut† and Canan O Department of Chemical Engineering, Middle East Technical UniVersity, Ankara, 06531, Turkey

pH control of a neutralization system for wastewater, where the input waste stream has variable properties in terms of acid concentration and flow rate, is investigated with different control algorithms utilizing an online identification technique. Performances of the designed controllers (model predictive (MPC), fuzzy logic (FLC), and conventional PI controller) are tested and compared mainly for disturbance rejection, set-point tracking, and robustness issues theoretically and experimentally on a laboratory-scale pH neutralization system. Additional experiments are done with original wastewater samples taken from an electronic-circuits manufacturing plant. All controllers’ performances are found to be close, while adaptive MPC can be considered better compared to others due its constraint handling capabilities and FLC can be preferred because it can be used without an identification step. 1. Introduction Typical wastewater effluents of chemical plants may contain several types of strong or weak acids/bases as well as their salts. They must be neutralized to protect the environment. However, wastewater neutralization processes are highly nonlinear due to the static S-shaped titration curve and have time-varying characteristics due to changes in acid content of waste streams of different processing units. Therefore, pH control is a challenging problem where advanced control strategies are often considered in the literature. A general method based on the separation of reaction variant and invariant parts presented by Gustafsson and Waller1 and experimentally tested by Gustafsson2 for feedback control and adaptive feedback control of pH in fast acid-base reactions in continuous stirred tank reactors (CSTR) where off-line experimental identification was utilized in the design of the controllers. Gustafsson and Waller3 discussed relative advantages/disadvantages of linear and nonlinear adaptive control methods for practical pH control and have shown that nonlinear control works well if characteristics of the process are well-known. The strong acid equivalent approach introduced by Wright and Kravaris4 is experimentally demonstrated.5 Wright et al.6 combined an online identification method with the strong acid equivalent method to control systems with unknown species. Industrial application of this pH control algorithm is also reported.7 Sung et al.8 proposed a control strategy in which the strong acid equivalent model4 is combined with a small identification tank to identify titration curve of the process stream. They obtained equivalent titration curve for effluent process stream by using an identification reactor. Lin and Yu9 presented a technique for autotuning and gain scheduling of pH control in which a relay feedback experiment is need to be performed. Self-tuning control of a pH neutralization process is also studied.10 Gala´n et al.11 modeled a pH neutralization process using first-order models for different operating regions according to the process titration curve. Based on these models, closed loop behaviors of a gain scheduled PI, a H∞, and a predictive controller are shown. An adaptive dynamic matrix controller, for which model coefficients were updated online, is described * To whom correspondence should be addressed. Telephone: +90312-2102605. Fax: +90-312-2101264. E-mail: [email protected]. † Currently with Department of Chemical Engineering, Hacettepe University, Ankara, 06532, Turkey. E-mail: [email protected].

by Maiti et al.12 for controlling pH neutralization processes in which nonlinearity of titration curve changes with process stream variations. Qin and Borders13 demonstrated a three-region fuzzy logic controller (FLC), which requires prior knowledge of the titration curve, for controlling a pH process. Adroer et al.14 proposed a FLC for a laboratory scale neutralization system, The output of the FLC designed is scaled by a parameter which is a function of process output error history, in order to increase robustness of the controller to buffering variations of the feed stream. Effective control of the neutralization process is revealed. A computer-based pH measurement and fuzzy logic

Figure 1. pH Neutralization System.

Figure 2. Block diagram of a basic FLC.

Figure 3. Block diagram of the proposed fuzzy logic controller.

10.1021/ie070492p CCC: $40.75  2008 American Chemical Society Published on Web 05/30/2008

Ind. Eng. Chem. Res., Vol. 47, No. 13, 2008 4395

Figure 4. Membership functions for error, e ) pHsp - pH, rate of error, de/dt, and manipulated variable change, ∆u.

Figure 6. Membership functions for error, e ) pHsp - pH, rate of error, de/dt, and gain multiplication factor, R.

Table 1. Fuzzy Logic Controller Rule Table Table 2. Tuner Module Rule Table

rate of error (de/dt) error (e) NVB NB NM NS Z PS PM PB PVB

NB NB NB NB NB NM NM NS Z PB

NM NB NB NB NM NM NS Z PS PB

NS NB NB NM NM NS Z PS PM PB

Z NB NM NM NS Z PS PM PM PB

PS NB NM NS Z PS PM PM PB PB

PM NB NS Z PS PM PM PB PB PB

rate of error (de/dt)

PB NS Z PS PM PM PB PB PB PB

error (e)

NB

NM

NS

Z

PS

PM

PB

NB NM NS Z PS PM PB

B M S S S M B

B B M S M B B

VB B B S B B VB

VB VB VB S VB VB VB

VB B B S B B VB

B B M S M B B

B M S S S M B

pH controller using a simple, low cost, pH measurement unit is utilized by Menzl et al.15 Their pH fuzzy controller is found to be applicable to any fermentation process and pH neutralization plants for chemical wastewater. Kavsek-Biasizzo et al.16

used fuzzy model based predictive control for highly nonlinear pH process and have shown that the control scheme is effective. Regunath and Kadirkamanathan17 applied fuzzy nonuniform scheduling approach to weak acid-strong base pH neutralization process and found that integrated absolute error (IAE) score of

Figure 5. Fuzzy logic controller control surface.

Figure 7. Graphical representation of the rules for tuner module.

4396 Ind. Eng. Chem. Res., Vol. 47, No. 13, 2008

Figure 8. Experimental setup for the pH neutralization system.

Figure 9. Titration curves of type 1 and type 2 test feeds.

the fuzzy controller is 67% less than the standard scheduling PI controller. Babuska et al.18 implemented a fuzzy self-tuning PI controller for a small-scale fermentation system successfully. Venkateswarlu and Anuradha19 formulated a dynamic fuzzy adaptive controller (DFAC) and found that DFAC provides improved performance for the control of highly nonlinear pH processes compared to conventional PI, fuzzy, and adaptive PID controllers. Kumar et al.20 studied neutralization of acetic acid with NaOH in a CSTR and concluded that nonlinear PI controller is superior to local linear PI controller. In the light of the literature survey, it is found that, usually, online identification is necessary to capture the time varying nonlinear characteristics of pH neutralization processes. However, this usually necessitates predetermination of some parameters with extra computational cost. On the other hand, heuristics controllers like FLC need only tuning which can be performed with the help of an expertise using trial-and-error procedures. The objective of this study is to investigate performances of model-based and heuristic control approaches for the control of nonlinear pH neutralization process by utilizing model

predictive, fuzzy logic approaches. Simulations and experiments are carried out for a mixed acid-strong base pH neutralization system. Comparisons of these control approaches with conventional PI algorithm are done in order to find an appropriate approach that can be used effectively for pH control. In addition to tailored ones, samples of wastewater from an electronic plant are also used in the experiments to check the results. A short review of Wright and Kravaris’4 minimal-order realization model developed for pH control with PI controller algorithm, brief reviews of MPC, FLC techniques, and description of the experimental setup will be given in the subsequent sections. 2. Strong Acid Equivalent Model In Figure 1, a schematic drawing of a CSTR where neutralization operation takes place, is shown. Assuming perfect mixing and constant volume, material balances around the system can be written as follows:4 V

dxi ) F(ci - xi) + u(bi - xi) for i ) 1, ... , n dt

(1)

Ind. Eng. Chem. Res., Vol. 47, No. 13, 2008 4397

pH control algorithm can be reformulated by considering Y′ as output. Thus, pH value of the effluent stream reaches pHsp if and only if Y′ f 0. A discrete PI controller in terms of Y′ can be used as4

Table 3. Process and the Controller Parameters for Set-Point Tracking process parameters process stream compositions titrating stream compositions Fmain Vmain Fid Vid time intervals pH value (set point)

controller parameters PI AMPC FLC

0.002 M HCl 0.002 M HNO3 0.005 M H3PO4 0.1 M NaOH

u′k - u′k-1 ) -

0.50 L/min 15.0 L 0.15 L/min 0.45 L 1. 0 - 700 s

pHsp ) 7.0

2. 700-1400 s 3. 1400-1900 s 4. 1900-2400 s

pHsp ) 5.0 pHsp ) 6.5 pHsp ) 8.5

P1 ) P2 ) 0.85 P ) 30, C ) 1, f ) variable, constrained error normalization factor rate-of-error normalization factor error normalization factor

[

dY′ ) -FY ′ - A(pHsp) dt

0 e u (mL/min) e 350 Ne ) 1.354 Nde ) 0.026 Ndu ) 6.171

[

∑

∑

]

ai(pHsp)bi u′

i)1

#species

Y ′ ) A(pHsp) -

]

#species

(2)

ai(pHsp)bi (T(pHsp) - T(pH))

i)1

(3)

where ai(pH) are functions of pH and the dissociation constants of acids and bases and T(pH) represents inverse of titration curve of the effluent stream with formulations4 given below for an acid as

pi + (pi - 1) 1+

[H ] [H ] +···+ Kapi Ka2iKa3i · · · Kapi

[H+] [H+]Pi-1 [H+]Pi +···+ + Kapi Ka2iKa3i · · · Kapi Ka1iKa2i · · · Kapi

∑

(4)

ai(pH)x1i

i)1 #species

T(pH) ) A(pH) +

∑

∑

ai(pHsp)bi

i)1

M

y(k) )

∑ a ∆u(k - i) + a

Mu(k - M - 1) + d(k)

i

(7)

i)1

where u is input, y is output, ai’s are step response coefficients, M is model horizon, and d(k) is unmeasured disturbance. The value of d(k) can be calculated by using input data history of the plant and by measuring the current plant output, y*(k) d(k) ) y * (k) -

[

]

M

∑ a ∆u(k - i) + a

Mu(k - M - 1)

i

i)1

(8)

In industrial MPC implementations, future values of disturbance, d(k + i) for i ) 1, 2, . . . , P, are kept constant over prediction horizon, P. This application can result in sluggish response when a slow disturbance enters to upstream of the dominant lag.22–24 As an alternative, instead of constant unmeasured disturbance, constant slope of the disturbance can be assumed. That is, ∆d(k) ) d(k + i) - d(k + i - 1) ) constant for i ) 1, 2, . . . , P. In MPC, changes in future manipulated variable (∆ui for i ) 1, 2, . . . , C) are calculated by minimizing a quadratic objective function P

∑

M

[r - y(k + i)]2 +

i)1

∑ f[∆u(k + C - j)]

2

(9)

ymin e y(k + i) e ymax

(10)

j)1

subject to following constraints

#species

A(pH) +

A(pHsp) +

(6)

Model predictive control, MPC, is a powerful control technique in which future plant behavior is optimized by using an explicit plant model. It is also possible to include input and/ or output constraints in the optimization problem. Most of MPC implementations use discrete step or impulse response convolution models to represent plant dynamics. A single input-single output process can be modeled with the following discrete convolution model21

∆u

+ Pi-1

+

]

#species

3. Model Predictive Controller

min

+

ai([H ]) ) -

]

∆t Y′ + KcY′k τI k

where ∆t is sampling time of the discrete controller. In the design of PI controller Kc and τI are found as functions of flow rate, F, time constant of the process τp, sampling time, ∆t, poles of the discrete controller (P1 and P2). Values of P1 and P2 have to be found by trial and error to obtain an adequate performance.

where ci, bi, and xi are total ion concentration of ith species in process, titrating and effluent streams, respectively. F and u are volumetric flow rates of the process stream and titrating stream respectively, and V is volume of liquid in the reactor vessel. All state equations are uncoupled and have same time constants. Therefore, as shown by Wright and Kravaris,4 by measuring effluent pH value, it is not possible to determine the value of total ion concentrations, xi. A minimal order model providing same input-output behavior as in eq 1 is also derived by Wright and Kravaris.4 The minimal-order model simplification is done by taking into account that the titrating streams are highly concentrated and that their flow rates are usually very small compared to that of process streams (u , F) (Figure 1) for most of the industrial processes, Thus, minimal-order model can be written with deviation variables Y′ ) Y - A(pHsp) and u′ ) u - FT(pHsp) as V

[

[

Kc 1 +

(5) ai(pH)x2i

i)1

with A(pH) ) 10pH - Kw10pH. The quantity Y′ is defined as strong acid equivalent of the effluent stream in deviation form, F is flow rate of the process stream.4

umin e u(k + i) e umax

where r is the set point and umin, umax, ymin, and ymax are the constraints. After solving the optimization problem to obtain optimal future control moves (∆u(k + C - i) for i ) 1, 2, . . . , C), only the first element of this optimal set, ∆u(k), is applied to process. The entire optimization problem is repeated at the next sampling interval by moving the horizon of MPC one step ahead. Prediction horizon, P, control horizon, C, and move suppression factor, f are the tuning parameters of MPC. In the present study, the linear process model given in eq 2 is used in an MPC algorithm. For the MPC, step response

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Figure 10. Set-point tracking responses for PI controller (a, simulation; b, experiment), AMPC (c, simulation; d, experiment), and FLC (e, simulation, f, experiment).

Ind. Eng. Chem. Res., Vol. 47, No. 13, 2008 4399 Table 4. Normalized Performance Scores for Set-Point Tracking simulation score

experiment score

controller

IAE

IACC

IAE

IACC

PI AMPC FLC

0.911 1.000 0.891

1.000 0.736 0.675

0.996 1.000 0.960

0.945 0.756 1.000

Table 5. Process and the Controller Parameters for Disturbance Rejection process parameters process stream

titrating stream Fmain Vmain Fid Vid disturbances

controller parameters PI AMPC FLC

type 1 f 0.002 M HCl 0.002 M HNO3 0.0050 M H3PO4 type 2 f 0.020 M HCl 0.020 M HNO3 0.0001 M H3PO4 0.1 M NaOH 0.50 L/min 15.0 L 0.15 L/min 0.45 L at time ) 200 s f change from type 1 to type 2 at time ) 1400 s f change from type 2 to type 1 P1 ) P2 ) 0.85 P ) 35, C ) 1, f ) variable, constrained error normalization factor rate-of-error normalization factor error normalization factor

0 e u (mL/min) e 350 Ne ) 1.354 Nde ) 0.026 Ndu ) 6.171

coefficients are obtained by a simulation program using this simplified process model. In simulation studies, performance of the MPC algorithm is found to be not successful, giving steady-state error with sluggish response, when conventionally a constant disturbance assumption is made. Changes in concentration of acids in process effluent stream usually ends as slow disturbances. In the literature,22–24 this drawback is overcome by using constant derivative disturbance assumption. Therefore, the MPC algorithm is redesigned by assuming a constant derivative disturbance which improved the disturbance rejection capability of MPC to an acceptable level. Nevertheless, although the constant derivative assumption is successfully incorporated in this study, use of this assumption must carefully be considered for other applications. In all simulations and experimental runs, control horizon, C, is taken as one and kept constant. Prediction horizon, P, and move suppression factor, f, are tuned by simulations. It is observed that, according to the identification data (identified steady-state titration curve), the values of f have to be changed to achieve an adequate control performance (low integral absolute error, IAE, score) and to obtain smooth changes in control inputs (less integral absolute control change, IACC, score). Therefore, slope of process gain around the set point is used to adapt f value to changes in process gain around the set-point, resulting in an adaptive MPC (AMPC). 4. Fuzzy Logic Controller (FLC) After the introduction of fuzzy logic by Zadeh,25 different FLC designs were developed like Mamdani type and Sugeno type. FLC’s incorporate simple if-then (condition-action) rules to solve control problems without using a process model. They are designed using the operator’s knowledge about the process rather than the mathematical model of the process. Therefore,

FLC’s are suitable to control processes that have complex nature or which are difficult to model and where expertise knowledge is available. Typical structure of a FLC is given in Figure 2. It has four main parts: input signal normalization and fuzzification, fuzzy inference engine, fuzzy rule base, and defuzzification and denormalization to crisp control input.26 FLC’s are tuned by modifying input and output membership functions, MF’s, rule base and also by changing input normalization factors, Ne, Nde, and output denormalization factor, Ndu. Among these, the latter one has a stronger influence on the performance of FLC.27 In this study, a Mamdani-type FLC is proposed with a structure shown in Figure 3. In the proposed FLC, error (e ) pHsp - pH) and rate of error (de/dt) are used as inputs and manipulated variable change (∆u ) uk - uk-1) is selected as output. Nine MF’s (negative very big, NVB; negative big, NB; negative medium, NM; negative small, NS; zero, Z; positive small, PS; positive medium, PM; positive big, PB; positive very big, PVB) for error, seven MF’s (NB, NM, NS, Z, PS, PM, PB) for rate of error, and seven MF’s (NB, NM, NS, Z, PS, PM, PB) for change in manipulated variable are defined in FLC structure. Triangular-type membership functions are used for both inputs and the output and they are tuned for their best values by simulations. The graphical representations of membership functions for inputs and the output are given in Figure 4. The 9-by-7 rule table is prepared for the FLC by considering that, as base is added to the neutralization reactor, pH value in the reactor increases or vice versa. The rule table and the corresponding fuzzy control surface are shown in Table 1 and Figure 5, respectively. In the FLC algorithm, nonlinear pH process is directly controlled by measuring only the effluent pH value without using the identification reactor. However, in order to improve the performance of FLC for high-gain regions of a pH process, a tuning mechanism by means of a tuner (Figure 3) is added to reduce possible oscillations by multiplying the output, ∆u, by the output of tuner which is called gain multiplication factor, R. Seven MF’s for error (e ) pHsp - pH), seven MF’s for rate of error (de/dt), and five MF’s for gain multiplication factor, R, are used in the tuner (Figure 6). The tuning module adjusts tuner output value, R, according to error and rate of error and increases it when output is away from the set point and decreases it when output is close to the set point. The magnitude of this change depends on the second inputs’ value. The rule table and control surface of the tuner are given in Table 2 and Figure 7, respectively. 5. Experimental Section In the experimental setup (Figure 8), two CSTR’s (neutralization and identification reactors) are used. The control objective is to keep effluent pH value of neutralization reactor at a desired set-point value, mostly at pH ) 7.0, by adjusting the flow rate of the titrating stream of the neutralization reactor. Thus, the controlled variable is the pH value of the effluent stream of the neutralization reactor and the manipulated variable is the flow rate of the titrating stream of the neutralization reactor. The major disturbances that can affect the system are variations in acid composition and flow rate of the entering acid stream to the neutralization reactor. Acidic feed solution (process stream) is prepared by selecting different amounts and types of acids from acid feed tanks by a three-way valve. Volume of the neutralization reactor is 15 L. Reactor content is mixed with an axial flow type impeller and

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Figure 11. Disturbance rejection responses for PI controller (a, simulation; b, experiment), AMPC (c, simulation; d, experiment), and FLC (e, simulation; f, experiment).

Ind. Eng. Chem. Res., Vol. 47, No. 13, 2008 4401 Table 6. Normalized Performance Scores for Disturbance Rejection simulation score

experiment score

controller

IAE

IACC

IAE

IACC

PI AMPC FLC

1.000 0.643 0.382

0.799 1.000 0.686

0.419 1.000 0.335

0.745 0.481 1.000

effluent stream is taken out at the impeller level where the highest efficiency of mixing is obtained. Effluent stream tube with sufficiently large diameter is located at a desired liquid level to enable constant volume in neutralization reactor. In addition, baffles are located in the neutralization reactor to prevent vortex formation. Identification reactor, which has a volume of 0.45 L, has similar properties as the neutralization reactor. Effluent stream of the identification reactor is fed to the neutralization reactor which can further be considered as disturbance in flow rate or in composition to neutralization reactor. Acid feed peristaltic pumps are adjusted to constant flow rates of 0.5 and 0.15 L/min for the neutralization and identification reactors, respectively. Thus, the time constant of neutralization reactor is approximately 10 times greater than that of identification reactor. Neutralizations in the reactors are done separately with two input base streams, flow rates of which are adjusted by two peristaltic pumps. Flow rate of the titrating stream of neutralization reactor is estimated by the controller as a function of the pH value for the solution in neutralization reactor. In both reactors, pH values of solutions are measured with two separate pH electrodes located at the exit locations of effluent streams. Both measured values are supplied to the controller through AD/DA converters. Experimental runs are performed nearly at room temperature around 20-25 °C. In experiments, acid solutions are prepared using tap water to reflect real plant conditions. Sampling time of 5 s is used in all experimental runs. Experiments are performed to find the set-point tracking, disturbance rejection, and robustness performances of the designed controllers by using a three-acid mixture (HCl, HNO3, and H3PO4) similar to the acid ingredients of industrial wastewater of the electronic-circuits manufacturing plant located near Ankara, Turkey. Two test feeds, type 1 and type 2, are used in simulations and experiments. In type 2, strong acid concentrations are 10-fold greater and the weak acid concentration is 50 times less than that of type 1. The titration curves for the two feeds are shown in Figure 9. During the experiments, in order to identify the incoming stream, in terms of pH, and to find its time varying characteristics, a portion of the main input stream is fed continuously to the identification reactor and titrated with a base input stream. Sung et al.8 suggest to use time intervals equal to half-time constant of the neutralization reactor (0.5 V/F) for identification of the incoming stream in terms of pH value (titration curve). Thus, for each time interval, rectangular pulses are introduced in the base flow rate entering to identification reactor. The duration of pulse inputs are adjusted long enough by the operator in order to reach the attainable maximum pH value in the identification reactor. Also, magnitude of pulses are adjusted such that system response can cover the entire operating range of the pH value. Here, the operator’s expertise is important. Then, identification is done by solving the model of process to find Y′ and T(pH) for the same pulse input using eq 3. Thus, for every ∆pH g 0.15, calculated T(pH) value is matched with measured pH value and the steady-state titration curve is constructed. In order to reduce possible effects of noise on identification data, raw data is filtered once and cubic spline is

applied. Then, for 0.5 V/F time durations, pH measurements of neutralization reactor are used to find T(pH) and Y′, from identified titration curve, which is further used in the control algorithm for the same time interval until the next identification step. 6. Results and Discussion Simulations and experimental studies are done to find setpoint tracking, disturbance rejection capabilities, and robustness issues of the controllers (PI, AMPC, and FLC). Performances of the controllers are evaluated according to integral of absolute error, IAE, and integral absolute of control change, IACC, scores as IAE )

∫

∞

0

|e(t)|dt

IACC )

∫

∞

0

|∆u(t)|dt

(11)

The scores above are further normalized by dividing them by the largest corresponding value of each set, and comparisons are made based on the normalized scores. In simulation studies, trial runs are performed to find the optimal controller parameters for PI, AMPC, and FLC considering performance scores and these parameters are later used in the experiments. 6.1. Set-Point Tracking. In all runs, input acid mixture (HCl, HNO3, and H3PO4) is titrated by a base solution (NaOH). Setpoint tracking performances of the proposed controllers are found for different set-point changes. Process parameters, controller parameters, and set-point changes for different time intervals are given in Table 3 for both the simulation and experimental runs. In experiments, only the duration in the second set-point interval given in Table 3 is increased by 400 s due to the unknown additional buffering effect introduced by the tap water used which slows down the response and which is not possible to replicate in simulations. PI and AMPC can only be activated after the first identification run due to the need of titration curve data to evaluate the strong acid equivalent (Y′) from the pH measurements. On the other hand, although FLC does not require this, it is also activated at the end of the first identification for comparison purposes. Set-point tracking responses of the pH control system are shown in Figure 10 for the PI controller, AMPC and FLC. It is observed that, in the experiments, response is more sluggish due to the additional buffering effect of tap water. In simulations, considering the normalized IAE scores (Table 4), all the controllers are found to have similar performances while FLC has the least scores, whereas, considering the IACC scores, the least scores are obtained for FLC in simulations and for AMPC in experiments. This result obtained for AMPC can be due to its constraint handling capability. Nevertheless, considering that IAE scores are more important than IACC scores, FLC can be taken as slightly better than the others in set-point tracing performance. 6.2. Disturbance Rejection. The most important problem in wastewater neutralization processes is the changes in the feed compositions. Feed flow rate disturbances may be handled by using storage surge tanks equipped with flow controllers. Therefore, regulatory performance is more important than servo performance for pH neutralization processes. Thus, process stream acid concentrations are changed to find the disturbance rejection performance of the proposed controllers. In Table 5, the process and controller parameters used in these runs are given. Two input acid stream compositions, type 1 and type 2, used in the simulation and experimental runs are buffer dominant and strong acid dominant acid mixtures, respectively (Table 5).

4402 Ind. Eng. Chem. Res., Vol. 47, No. 13, 2008

Figure 12. Robustness test responses for PI controller (a, simulation; b, experiment), AMPC (c, simulation; d, experiment), and FLC (e, simulation; f, experiment).

Ind. Eng. Chem. Res., Vol. 47, No. 13, 2008 4403 Table 7. Normalized Performance Scores for Disturbance Rejection with Modeling Error simulation score

experiment score

controller

IAE

IACC

IAE

IACC

PI AMPC FLC

1.000 0.662 0.397

0.796 1.000 0.682

0.540 1.000 0.275

0.966 0.725 1.000

The responses of each control system to acid composition changes are given both for simulation and experiment runs in Figure 11. The deviation from the set point is found to be more when input stream is changed from type 2 to type 1 than that of from type 1 to type 2. This is due to fact that type 2 is the strong acid dominant mixture in which the process is much more sensitive to disturbances around the set point. In simulation studies, a tuner for FLC is used by introducing a factor R to eliminate the aggressive control action seen due to the presence of noise in trial simulation runs. However, in the experimental runs, use of the same R factor resulted in sluggish response, suggesting the omission of the tuner. Therefore, experiments are repeated without the tuner. Considering the IAE scores given in Table 6, FLC (not necessitating identification) is found to be better both in simulations (with tuner) and in experiments (without the tuner) than the other two controllers. In the experiments of disturbance rejection, the lowest IACC score is obtained for the AMPC similar to set-point tracking studies. 6.3. Robustness. Robustness of the controllers is tested by reducing the volume of the main reactor by 10%. Since disturbance rejection is more important than the set-point tracking for neutralization processes, robustness of the controllers is tested for disturbance rejection case only. The process parameters are the same as those for disturbance rejection given in Table 5. As indicated in Figure 12, all of the controllers are found robust to modeling errors and there is no significant change in the responses with only a 3% increase in the IAE scores in the simulations. In the experiments, however, AMPC is found to be more sensitive to modeling errors (that is less robust) while FLC has better performance than the others considering the IAE scores given in Table 7.

6.4. Test of the FLC Using Actual Plant’s Wastewater. As an example, performance of only FLC, which is found slightly better than others, is tested for disturbance rejection case by using actual plant wastewater samples. Two wastewater samples with comparatively different acid contents (low and high) were taken at different times in a daily operation of the electronic-circuits manufacturing plant. Process and controller parameters are taken as in Table 5 with a difference in the concentrations of the samples. Also, titrating stream concentration is increased to 3.0 M NaOH due to different range of acid concentration of the actual plant effluent. In addition, for disturbance test, the reactor process stream is changed only from type 1 (low acid content wastewater) to type 2 (high acid content wastewater) with pHsp ) 7.0. In Figure 13, experimental response of the FLC is shown. The FLC is able to keep the effluent pH value at pH ) 7.0 with a short settling time (about 15% of time constant of the neutralization reactor). Thus, performance of the designed FLC shown by simulation studies and laboratory experiments is also verified by the experiment performed with actual plant wastewater. 7. Conclusions Two advanced control techniques, model predictive control and fuzzy logic control, are successfully implemented to a laboratory-scale pH neutralization system. An identification reactor is used successfully in identifying the titration curve of the incoming wastewater stream in this wastewater neutralization system. Experimentally obtained responses are found be more sluggish compared to those of simulation responses due to the buffering effect of the tap water used in experiments. In the implementation of PI controller and adaptive MPC, an identification reactor is utilized which is easy to implement and use, whereas FLC does not necessitate an identification reactor. In AMPC design, constant disturbance assumption is replaced by constant derivative of disturbance to obtain faster response without steady-state error. Experimental runs showed that the designed AMPC is better (giving least IACC scores) for adjusting the control moves due to adaptation done by the f factor resulting in its constraint handling capability. The experiment done for disturbance rejection, using actual plant wastewater, revealed that the designed FLC is satisfactory in performance in controlling the pH of the actual plant wastewater with short settling times. Finally, in pH control of the neutralization process, although all designed controllers can effectively be used, FLC is found to be better than the other designed controllers, showing a less normalized IAE score in all tests. In addition to performance score comparison, in the use of FLC an identification reactor with additional equipments such as a pH sensor, a pump, and extra piping, etc. is not required. The design of FLC can be done without complex identification and modeling issues. Thus, although tuning of FLC is time consuming and requires operator expertise, it can be preferentially and effectively be used in controlling the pH neutralization process under changing operating conditions. Acknowledgment

Figure 13. Experimental response of the FLC for disturbance rejection test performed using actual plant waste water samples.

This study is financially supported by State Organization Department (Project No. BAP-03.04.DPT.2002K120540-08). We acknowledge their support.

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Nomenclature b ) total ion concentration in the titrating stream (mol/L) c ) total ion concentration in the process stream (mol/L) C ) control horizon d ) disturbance e ) error between output of the pH process and its target value F ) process stream flow rate (L/min) Kp ) process transfer function gain M ) model horizon P ) prediction horizon r ) set-point vector t ) time (s) u ) titrating stream flow rate (L/min) V ) volume (L) x ) total ion concentration in an acid/base mixture (mol/L) Y ) strong acid equivalent (mol/L) Greek Letters R ) gain multiplication factor λ ) weighting matrix diagonal element τ ) process transfer function time constant Subscripts i ) ith component id ) identification reactor main ) main/neutralization reactor sp ) set point Superscript ′ ) deviation from

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ReceiVed for reView April 5, 2007 ReVised manuscript receiVed February 25, 2008 Accepted March 14, 2008 IE070492P