Study of pH Control for Brine Dechlorination
The MIT Faculty has made this article openly available.
Please share
how this access benefits you. Your story matters.
Citation
Sha’aban, Yusuf A. et al. "Control Improvement Using MPC: A Case
Study of pH Control for Brine Dechlorination." IEEE Access 6 (March
2018): 13418 - 13428 © 2018 IEEE
As Published
http://dx.doi.org/10.1109/access.2018.2810813
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Version
Final published version
Citable link
https://hdl.handle.net/1721.1/124435
Terms of Use
Creative Commons Attribution 4.0 International license
Control Improvement Using MPC: A Case Study
of pH Control for Brine Dechlorination
YUSUF A. SHA’ABAN 1,2, (Member, IEEE), FURQAN TAHIR3, PHILIP W. MASDING4, JOHN MACK3, AND BARRY LENNOX5, (Fellow, IEEE)
1Department of Electrical and Computer Engineering, Ahmadu Bello University, Zaria 810001, Nigeria 2Center for International Studies, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 3Perceptive Engineering Ltd, Vanguard House, Sci Tech Daresbury, Cheshire WA4 4AB, U.K. 4Inovyn ChlorVinyls, Runcorn WA7 4JE, U.K.
5School of Electrical and Electronic Engineering, The University of Manchester, Manchester M13 9PL, U.K. Corresponding author: Yusuf A. Sha’aban (yusuf.shaaban08@alumni.imperial.ac.uk )
This work was supported in part by the Petroleum Technology Development Fund and in part by the Massachusetts Institute of Technology Library.
ABSTRACT This paper describes a case study carried out to quantify the benefits achieved from the applica-tion of model predictive control (MPC) to regulate the pH in a brine dechlorinaapplica-tion process. A mechanistic model of the process was developed and used to design a PI controller with feedforward compensation. The model was also used to quantify the potential benefits of commissioning an MPC controller on the process. Following the analysis with the mechanistic model, the designed MPC scheme was applied to the actual process. Through real-time results, it is shown that the deployment of this controller led to substantial improvements in disturbance rejection capabilities when compared to the existing PI controller with lead– lag feedforward compensator. The improved disturbance rejection led to a reduction in pH variation which resulted in reduced operational costs, more reliable production, and improvement in the efficiency of the dechlorination process.
INDEX TERMS Brine dechlorination, control system synthesis, mechanistic model, model-based control, pH control, predictive control, real-time process control, simulation.
I. INTRODUCTION
Over the years, sustainable process operations have become a social responsibility. In addition, new legislation is being brought in to curb emissions. Consequently, there has been general efforts by individuals, corporations, and industries to reduce their respective carbon footprints. In the process industries, a major way of ensuring sustainability is by reduc-ing energy consumption. This can be achieved in a number of ways such as changes in process design, energy reuse and the use of process control. PID control, often referred to as the backbone of regulatory control, accounts for over 90 % of all industrial control schemes [1], [2]. When properly applied and tuned, it can often achieve the performance obtainable by more advanced control schemes [3]. However, high per-formance and other practical requirements associated with some industrial applications, e.g. explicit constraint handling, necessitate the consideration of more advanced controllers such as model predictive control (MPC). In addition, MPC can contribute to sustainable process operations if its inherent optimization capabilities are properly explored.
Over the past four decades, MPC has had a notable impact in the process industry. This can be credited to the eco-nomic benefits associated with MPC mainly due to its abil-ity to address certain practical issues (such as constraints and multivariable interactions) efficiently, availability of sup-porting theory, optimization in the loop and improved per-formance [4], [5]. Industrial application of MPC is often reserved for large-scale multi-input-multi-output (MIMO) systems. Small-Scale and single-input-single-output (SISO) systems, such as the one studied in this work are mostly controlled using PI controllers. However, there have been suggestions that significant benefits can be achieved from the implementation of SISO MPC even in the unconstrained case [4].
A number of factors have contributed to the relatively limited presence of small-scale MPC in industrial applica-tions. Notable amongst these are the costs associated with its implementation such as software licensing and model-ing. Disruptions associated with plant tests and trials also contribute to these costs. Consequently, there has been a
13418
2169-3536 2018 IEEE. Translations and content mining are permitted for academic research only.
renewed interest by control systems suppliers to reduce the cost and effort associated with modeling [6], [7]. Control improvement projects are justifiable only if the benefits (envi-ronmental, economic etc) outweigh the associated costs. It is therefore important to have a reasonable estimate of such benefits prior to developing an advanced control strategy.
Process mechanistic models can often be used to estimate benefits achievable via control improvements by comparing the existing control strategy with its proposed replacement. Improved mechanistic models are developed by fitting pro-cess data to models [8], which are derived from first prin-ciples using the mass balances as well as physical/chemical phenomenon describing process operations. The mechanis-tic models can then be used for plant test planning and other preliminary studies before final controller design and implementation.
In this paper, a small-scale MPC was used to improve the performance of a loop originally controlled using PI control with lead-lag feedforward compensation. Before the implementation of MPC on the actual plant, a mechanistic model of the process was developed and used to study plant behavior. This was to gain an understanding as to whether the benefits of implementing a new controller outweighed the cost of implementation. The developed mechanistic model can also be used to train plant operators while minimizing disruptions to process operations. The main contributions of this paper can be summarized as follows: A mechanis-tic model is developed (and parameterized) for the Brine dechlorination process. This model is then used to quantify the potential benefits of commissioning a predictive control scheme. Motivated by these findings, an MPC scheme is then designed and implemented on the process to improve the pH set-point tracking, disturbance rejection as well as to overcome valve stiction. Through real-time results, it is shown that the MPC scheme achieves an improvement of around 57% in mean absolute tracking error during periods with significant load current disturbances (as compared to the existing PI controller).
The paper is structured as follows; a background of the process and the motivation for improved control are pre-sented in Section II. The benefits of implementing MPC in the context of performance improvement and robustness to measured disturbance is presented in SectionIII. Information on the development and control of the mechanistic model is presented in SectionIV. The results when the controller was applied to the real plant are presented in SectionV, and the paper is concluded in SectionVI.
II. THE CONTROL PROBLEM
A. PROCESS BACKGROUND
The system studied in this paper is a chloro-alkali plant. It uses the membrane technology [9] for the electrolysis of brine to produce chlorine gas, Cl2and hydrogen gas, H2. A
block diagram of the chloro-alkali production stages is shown in Fig.1.
FIGURE 1. Block diagram showing the chloro-alkali production stages.
FIGURE 2. Membrane cell [10].
Brine (at a PH of around 2) and caustic soda, NaOH (30 %) flow into the anode and cathode sections of the electrolytic cell respectively. The anolyte (depleted brine, at a higher pH) and NaOH (30 %) flow out of the anode and cathode chambers respectively. A diagram of the membrane cell is shown in Fig.2and the overall process equation is described by:
2NaCl(aq)+2H2O(l)→ Cl2(g)+2NaOH(aq)+H2(g) (1)
The rate of electrolysis is proportional to the magnitude of electric current. Therefore, the magnitude of electric current is correlated with brine flow rate.
A change in electric current and brine flow affects the pH of depleted brine flowing out of the cell. Chlorine bubbles make up part of the brine volume causing it to expand when the electric current is increased. This expansion produces higher order dynamics in the pH response. The anolyte exit-ing the anode chamber is saturated with dissolved chlorine. Therefore, it is sent for dechlorination before being recy-cled or purged out as waste water.
The dechlorination process is in two stages: first physical dechlorination is applied to extract chlorine which can be
sold, and subsequently, chemical dechlorination is employed to remove all traces of chlorine from the anolyte. Before proceeding with physical dechlorination, the pH of depleted brine is regulated to the desired set-point (typically around 2) through the PI control scheme. This decreases the solubility of Cl2 in depleted brine. It is important to regulate the pH
of the anolyte at this point as it affects the final pH of the purge; any fluctuation in pH is amplified further downstream resulting in increased processing cost. The goal is for the purge to be of neutral pH i.e. pH of 7, and whenever the pH is specification, the waste brine needs to be diverted to off-specification tanks for further processing. This highlights the importance (and serving as a motivation in this work) of good set-point control as otherwise, the off-specification tanks can fill up necessitating a production slow-down.
Physical dechlorination involves spraying the acidified brine into a vacuum of over 50 kPa. The extracted chlorine at this point is fed to the chlorine stream. The evaporated water from the dechlorinated brine is condensed and the condensate now at a much higher pH passes through two stages of chemical dechlorination before disposal or further treatment if pH is off-specification.
B. VARIABILITY ASSESSMENT
Variability assessment, using metrics such as product stan-dard deviation (sprod), is often used to quantify control system
improvements during steady-state operations. In this section, the metrics used for variability analysis during steady-state operation are discussed. The discussion of variability due to plant disturbance is given in section IV-A. During normal plant operations, when control is poor, plants are charac-terized by long-term drifts, cycles from special causes and inherent random variabilities [11]. In such cases, control improvement can often lead to a reduction in product variabil-ity. An ideal condition is when all variances are eliminated except for the natural variability of the process. The capability standard deviation, scap, is the minimum standard deviation
that is believed to be attainable in the product quality mea-sure. Data collected under normal operating conditions can be used to estimate scap using the mean square successive
difference (MSSD) [11]: scapk= s Pn i=2+k(y(i) − y(i − 1 − k))2 2(n − 1 − k) , (2)
where k is the discrete dead-time in samples and y is the product quality measure of interest. Minimum variability is achievable using an ideal feedback such as minimum variance control [12]. An estimated standard deviation for minimum variance control Sapc can be computed using Fellner’s
for-mula [13]: sapc=scap s 2 − scap stot 2 . (3)
Due to its aggressiveness, minimum variance control can result in undesirable process upsets. Hence, sapc gives a
TABLE 1.Variability metrics at different set-points from historical plant data.
variability limit against which the controller performance can be judged. The resulting percentage reduction in standard deviation is given as:
sred= 1 −sapc stot ×100. (4)
where stot is the standard deviation of the product quality
measure (including the effect of noise), so that when noise is neglected sprod≈stot.
C. CONTROL STRUCTURE AND OBJECTIVES
Due to the correlation between the load current and brine flow, only change in load current was used as a measured disturbance (as opposed to both brine flow and load cur-rent) in modeling and controller development. A model with SISO structure and a measured feedforward disturbance was used. This structure was selected to capture the dynamics between HCl valve position which serves as the Manipulated Variable (MV) and pH of anolyte which is the Controlled Variable (CV). The magnitude of load current was used as the measured disturbance i.e. the feedforward Variable (FFV).
To define the control objectives, the variability metrics introduced in sectionII-B were used to estimate the capa-bility of the process. To achieve this, historical closed-loop plant data were collected and analyzed. It was observed that different set-points for pH ranging between 1.7 and 2.1 were used in the plant. The data was preprocessed to discard regions with significant electric load current disturbance. The variability metrics computed for the different set-points are shown in Table1. The values show that total variability stan-dard deviation stot varied between 0.01 and 0.02, while the
estimated plant capability scapvaried between 0 and 0.01. The
estimated achievable improved variability sapcwas also in the
range of 0.01. The resulting predicted achievable reduction in variability sredis between 67 and 87 %. Therefore, a properly
tuned controller was expected to reduce variability by approx-imately 70 %. Bearing in mind that measurement noise was neglected in obtaining these results, not much improvement is expected in terms of variability during steady-state plant operations i.e. when there are no significant changes in load current.
STATEMENT OF CONTROL PROBLEM
Considering the results of variability analysis, the control problem can be stated as follows: to regulate the pH of brine
flowing into the anolyte tank such that variability during steady-state operation is at least maintained and to improve the rejection of load current (and brine flow) disturbance.
This will, in turn, ensure efficient dechlorination of brine, so that the final pH is within allowable specification for discharge. Effective disturbance rejection will reduce the fre-quency of diverting depleted brine to the off-specification tanks for treatment thereby reducing the costs associated with this task. It will also minimize the production disruptions due to filling up of the off-specification tanks.
III. MODEL PREDICTIVE CONTROL ALGORITHM
MPC is an optimal control scheme in which the current control action is obtained by solving on-line, at each sam-pling instance, a finite horizon optimal control problem. The optimization yields an optimal control sequence and the first move in this sequence is applied to the plant [4].
MPC offers several advantages over traditional control schemes, including the ability to explicitly take account of process constraints, as well as to handle multivariable, non-minimum phase and unstable processes. For these rea-sons, MPC has been widely implemented for advanced pro-cess control within various industries [14]. Furthermore, various MPC schemes to improve robustness whilst reduc-ing computational load and conservatism have also been proposed in the literature over the past few decades (see e.g. [15], [17], [18] and the references therein).
In this paper, a ‘feedforward’ MPC scheme which includes the effect of measured disturbance (load current) in the pre-dictions for the future output was considered [15]. In this way, the impact of load current changes on set-point tracking can be preempted and mitigated through predictive control.
Let us consider an empirical, first-order incremental Output-Error (OE) model of the form:
yk+1−yk = A1(yk− yk−1) + su X i=0 Bi1uk−i+ sd X j=0 Dj1dk−j (5) where yk is an n-dimensional vector of CVs, uk is an nu
-dimensional vector of MVs and dk is an nd-dimensional
vector of FFVs, all at sample time k. The symbols suand sd
denote the delay spreads for the MVs and FFVs respectively, and A1, Bi, ∀i and Dj, ∀j are appropriately-dimensioned
matrices of coefficients within the model. Finally, the1 in equation (5) denotes incremental signals such that:
1uk = uk− uk−1, 1dk = dk− dk−1
Let us define ysp ∈ Rn as the user-specified vector of
set-points (target pH) for the CVs. Then, manipulation of equa-tion (5) shows that the set-point error ek+1∈ Rnis given by:
ek+1= yk+1− ysp =(I − A1)ek+ A1ek−1+ su X i=0 Bi1uk−i+ sd X j=0 Dj1dk−j (6) where I is an n × n identity matrix.
Given the dynamics in (5), the MPC algorithm computes at sampling instance k, the control move which minimizes a cost function of the form:
J = N
X
i=1
(yk+i− ysp)TQ(yk+i− ysp) +1uTk+i−1R1uk+i−1
(7) subject to the control and move constraints:
u ≤ u ≤ u, (8a)
1u ≤ 1u ≤ 1u (8b)
where N is the prediction horizon, ysp is the CV set-point,
and Q, R are the set-point- and move-weights, respectively. Furthermore, 1u := 1uk 1uk+1 ... 1uk+N −1 , 1u := 1uk 1uk+1 ... 1uk+N −1 , and 1u := 1uk 1uk+1 ... 1uk+N −1 ,
with analogous definitions applying to the control vectors u,
u and u, respectively.
It follows that the overall system can now be written in the form: sk+1=Gsk+m1uk (9) where sk := 1uk−1 1dk−1 1uk−2 1dk−2 ... 1uk−q 1dk−q ek ek−1 , m := I 0 0 0 ... 0 B0 0 , G := 0 0 · · · 0 0 0 0 0 0 0 · · · 0 0 0 0 0 I 0 · · · 0 0 0 0 0 0 I · · · 0 0 0 0 0 ... ... ... ... ... ... ... ... 0 0 · · · I 0 0 0 0 B1 D1 · · · Dq−1 Bq Dq I − A1 A1 0 0 · · · 0 0 0 I 0
with q being the larger of the two delay spread values (suand sd).
Let us introduce a matrix C which extracts - from (9) -rows corresponding to the prediction error (i.e. ek+1). Then,
by iterating equation (9) we obtain:
pk=fsk+H1u (10) where pk = ek+N ek+N −1 ... ek+1 , f = CGN CGN −1 ... CG , H = CGN −1m CGN −2m · · · CGm Cm CGN −2m CGN −3m · · · Cm 0 ... ... · · · ... ... Cm 0 · · · 0 0
By inserting (10) into (7) and re-arranging, the constrained MPC problem - at each sampling instance k - can be summa-rized as: J? = minimize 1u 1u T(HTQH + ˆˆ R)1u +2SkTFTQHˆ 1u + SkTFTQFSˆ k (11) subject to : f ≤ E1u ≤ f , 1u ≤ 1u ≤ 1u
where ˆQis a diagonal matrix of Q, ˆRis a diagonal matrix of
R, and E := I 0 0 · · · 0 I I 0 · · · 0 ... ... ... ... ... I I I · · · I , f :=u − uk−1, f :=u − uk−1
As mentioned above, the first move (1uk) of the optimal
computed sequence 1u is applied to the process and the optimization problem (7) is solved again at the next time step.
IV. DEVELOPMENT AND CONTROL OF MECHANISTIC MODEL
Testing a control scheme on a running plant brings with it the risk of disturbing production and so it is desirable to avoid it. Alternatively, if a dynamic model of the plant is available then the proposed control scheme can be tested and tuned on that with no risk at all. If the model is reasonably accurate, only minor adjustment will be needed when the control scheme is finally commissioned.
In this case, a simplified model of the plant was derived and programmed using VisSim software. Fig. 3 shows a schematic of the resulting model.
In the model, the electrolyzer is represented as a CSTR. The extremely turbulent flow and gas production inside the cell mean that it is well-mixed which makes the CSTR a good approximation to the real situation. Inlet flows to the cell are dominated by the brine but there is a small flow of concentrated 32 % NaOH which diffuses through the mem-brane and significantly alters its pH at exit. This exit flow is mixed with HCl reagent in downstream pipework. The
pipework is modeled as a partly mixed volume which means it is somewhere between plug flow and a CSTR.
The effective volume of liquid in the cell depends on the actual brine and the gas. There is a known relationship between electrical load on the cell and gas fraction so the liquid volume can be adjusted accordingly. Brine simply overflows out of the cell and a weir equation is used to model that process. The concentration of the brine was converted to a measured pH using an experimentally determined titration curve measured in the lab.
The system discussed here has two inlet flows Qr and Qe
and an exit flow Qout. The aim is to calculate the
concen-tration at the exit. For the electrolyzer, the inlet flows are the acidified brine and a diffusion of caustic through the membrane. For the partially mixed volume, the inlet flows are the flow from the electrolyzer and the HCl reagent. We can assume good mixing (CSTR) or a combination of well-mixed and plug flow by introducing the concept of the fractional dead-time,θf [16]. The dead-time associated with a system
with a given fractional dead-time is: θ = V
Fθf, (12)
where V is the liquid volume in the tank. In particularθf =0
represents a CSTR andθf = 1 represents a pure plug flow.
The step response of such a system is first order plus dead-time. The rate of change of mols in the tank is given by:
dN
dt = QrCr+ QeCe− QoutCt. (13)
The concentrations of the inlet streams (Ceand Cr) are all
known. For example, the HCl reagent is 18% wt/wt. We base the exit concentration on the effective well-mixed volume:
Ct = N Vm
, (14)
where Vmis the well-mixed volume such that Vm= V(1−θf).
The concentration at the exit is given by Ct delayed by the
dead-time i.e. Cd = Cte−sθ. In the case of the electrolyzer,
we assume θf = 0 so that it is well-mixed. The partially
mixed volume is mostly a pipe hence it is close to plug flow withθf =0.9.
For the overflow calculation, the objective is to calculate the exit flow from the electrolyzer based on simple weir model and the effective liquid volume which is the true liquid volume plus the space occupied by the entrained gas bubbles. The true liquid volume is given by:
V =
Z
(Qe+ Qr− Qout)dt. (15)
(16) The overflow, Qoutis computed as:
Qout = Gk(GV− GV0), (17)
GV = V
1 − gf
FIGURE 3. Schematic of the mechanistic Model.
where GV is the effective volume. The parameter gf is the
fractional volume occupied by gas bubbles which follows a linear relationship with the electrical load and is typically around 25 %. The empirical parameter Gk is adjusted to
match the model to plant data, thereby allowing for improve-ment of the model to capture real plant performance, and
GV0 is the nominal volume of the electrolyzer.
A. OFFLINE CONTROL SCHEME EVALUATION
Assuming a discrete time linear transfer function structure, the plant model can be described as:
y(t) = Gm(q)um(t) (19)
where the matrix Gm(q) = G H , um(t) =
u(t − k)
ud(t − kd)
,
u is the MV with discrete dead-time k and ud is the FFV
with a discrete dead-time kd. In this section, the mechanistic
model serves as the plant. This model was used to tune the PI controller with lead-lag feedforward compensation.
Step responses were used to obtain estimates of the process dead-time and settling time. Using the mechanistic model, the estimated dead-time and settling time from HCl valve to pH were 18 seconds and 67 seconds respectively. The corresponding values for load current to pH were 77 seconds and 240 seconds. Linear incremental OE models were devel-oped from identification data collected by exciting the plant. Step tests were used for the input/output response (i.e. HCl valve to pH). However, in the real process, step tests are not allowed on the electric load current as there is a limit to the
FIGURE 4. Mechanistic model step response from HCl valve to pH.
allowable rate of change in load current. This limit is more stringent during load current ramp downs because brine flow is correlated with the magnitude of load current and starving the cells of brine could damage them. Therefore, a series of ramps were used for the disturbance/output response (load current to pH). The step response from HCl valve to pH is shown in Fig.4while the response from load current to pH is shown Fig.5. An empirical, OE model (5) is developed using this input/output data. The MPC scheme, based on this model, is then compared with the PI scheme (based on the mechanis-tic model) to quantify the performance improvement. It can be seen that the process (i.e. disturbance/output response) has directionally dependent dynamics, which is due to the
FIGURE 5. Mechanistic model step response from load current to pH.
FIGURE 6. Mechanistic model output versus OE model output using validation data - HCl valve to pH.
FIGURE 7. Mechanistic model output versus OE model output using validation data - load current to pH.
non-linear nature of the pH scale. Plots comparing model outputs with test validation data are shown in Fig.6and Fig.7
for u − y and ud− yrespectively.
The flow of brine out of the electrolyzer, as modeled in the mechanistic model, is affected by a number of parameters as shown in the simple overflow equation (17). This flow is
TABLE 2.Controller performance (on the mechanistic model).
FIGURE 8. Plot of load current disturbance applied to mechanistic model.
limited to positive values (i.e. no back-flow) and is delayed by a dead-time, Gθ, which represents how long it takes to reach the pH control system. Since the dynamics of the pro-cess (mechanistic model) depend on these parameters. The parameters GV0, GK and Gθ were used in the mechanistic
model to capture disturbances such as inconsistencies in raw material and other modeled plant disturbances. Varying these parameters ensured that the controllers were tuned in a robust manner to accommodate uncertainties in process dynamics and other variations in process parameters.
A model predictive controller was tuned and Mean Absolute Error (MAE) was used as a performance mea-sure. To test controller robustness, the parameters GV0, GK
and Gθ were varied within ±20% of their nominal values. Simulations were then carried out with load current ramp dis-turbances. The performance improvements obtained, in per-centage MAE, are summarized in Table 2. There was an improvement in MAE of up to 94% while the lowest improve-ment was approximately 65%. Plots of the load current profile and resulting pH response with nominal parameter values are shown in Fig.8and Fig.9respectively.
While the variability assessment carried out in Section 2 gave an estimate of control improvements during steady-state operation, the study carried out in this section gives an estimate of improvements in the rejection of load current disturbances.
These results, presented in Table 2, show that if a rea-sonable model of the plant is available for MPC design, significant improvements in load current disturbance rejec-tion are achievable. Therefore, based on the results presented in Table2, it is clearly worth designing and commission-ing MPC on the actual process. However, the restriction
FIGURE 9. Response of mechanistic model with nominal parameter values.
on the use of only ramp test signals can affect the quality of the resulting test data. This restriction does not allow for the use of test signals, such as pseudo-random binary sequence (PRBS) and generalized binary noise (GBN), that would enable the rich process excitation over a wider range of frequencies. A ramp input allows for the excitation of lower (but not higher) frequencies and this can affect the accuracy of the estimates of the process time constant [19]. The next section discusses real-time MPC development and implementation on the actual plant.
V. REAL-TIME PROCESS CONTROL
As stated in the variability analysis presented in SectionII-B, emphasis was on improvement in the rejection of load current disturbance. The distributed control system (DCS) in use on the Inovyn chlorine plant was a DeltaVTM DCS from Emerson Process Management. Therefore, an OPC link was set up between DeltaV and ControlMV software package (Perceptive Engineering Limited, UK).
Using knowledge gained from the control of the mech-anistic model, identification data was collected using a series of step and ramp tests. Plant test data was col-lected over a period of 6 hours. The estimated dead-time and process settling dead-time for HCl valve to pH were 24 seconds and 60 seconds respectively. The correspond-ing values for electric current to pH were 48 seconds and 228 seconds.
Incremental OE models (5) were developed by applying the upper diagonal recursive least squares (UD-RLS) identifi-cation algorithm on the plant step test data [20]. The UD-RLS algorithm has the advantages of being relatively simple to compute, good convergence properties and industrial appli-cations have shown its benefit over alternative identification algorithms [20], [21]. Though model adaptation was not used. Based on estimates of the settling time obtained using the simulation as described in SectionIV, a sampling time of 12 seconds was used for the initial controller design. For these models to capture the dynamics of the slower response, a constrained horizon of 26 was used. A compressed
FIGURE 10. Plot showing effect of stiction on PID.
FIGURE 11. Plot showing effect of stiction on MPC.
FIGURE 12. Plot showing effect of stiction on MPC with read-back.
horizon of 15 and compression width of 5 were used to reduce computational load. After controller tuning, set-point and move rate weightings of 1.5 and 3.1 were selected respec-tively. These values allowed for effective disturbance rejec-tion and damped the response to set-point changes to prevent overshoot.
FIGURE 13. Sample of response to load disturbance with different controllers.
Following implementation of the controller on the real plant, some improvements were observed in the rejection of load current disturbance. However, initial analysis of con-troller performance showed that stiction in the HCl valve had an effect on controller performance. The effect was more pronounced in MPC as shown in Figs. 10 and11 for PID and MPC respectively. Spikes with overshoots of around 2 % were observed in valve position read-back for both PID (which is same used in section IV) and MPC. The more pronounced effect in MPC was due to a control interval of 12 seconds while PID was sampling every second, which meant that the valve was in continuous motion, thus reducing the effect of stiction. MPC valve movement, on the other hand, was less frequent, at 12 seconds interval, and was, therefore, more prone to performance deterioration due to stiction.
Two steps were taken to minimize the effect of stiction. First, the read-back of valve position, i.e. the actual measure-ment of the valve position, was used for prediction within the MPC control scheme in (10). Secondly, an MPC with a faster control interval was designed. The effect of stiction on MPC with read-back is shown in Fig. 12. A sampling time of 2 seconds, which gave more accurate estimates of dead-time and time to steady-state, was used for the faster model. The estimates of dead-time and time to steady-state for HCl valve to pH were 32 seconds and 66 seconds
respectively. The corresponding values for the load current to pH were 54 seconds and 276 seconds. The improvements to the control scheme resulted in 45.83 % reduction in stan-dard deviation of the CV, in comparison to the PI controller, from 0.024 to 0.013.
The MPC controller was tuned using set-point and move rate weights of 1.2 and 17 respectively. As with the initial tuning, these values gave a good compromise between speed of response and disturbance rejection. In achieving this, pri-ority was given to the disturbance rejection capabilities of the controller which was the main objective of the control improvement case study. A constrained horizon of 120 (pre-diction horizon), compressed horizon of 100 and compression width of 10 were used to speed-up the online calculations. For these settings, the control horizon was set equal to the prediction horizon. The controller was then tested for load current ramp disturbance. The real-time process responses obtained for PID and MPC are shown in Fig.13. The top graph in Fig.13indicates the controller switching between PID and MPC. The improvement in set-point tracking by MPC is apparent in the pH response plot. The improved per-formance due to additional tuning is captured in the response (shown in Fig.13after 250 minutes). As shown on the graph, MPC was able to maintain the pH closer to the set-point even with a larger load current ramp disturbance than the one used with the PI controller. The ramp sizes are shown in Table3.
FIGURE 14. pH response and HCl valve position showing periodic oscillations.
TABLE 3. MAE for controllers.
A. PERFORMANCE EVALUATION
The controller was tested for load current ramp disturbances and MPC was able to maintain the pH to within ±0.1 of set-point. The values of MAE for the respective controllers are given in Table3. These were computed for regions with significant load current disturbance. Using MAE as a per-formance measure, an improvement of about 57 % over PI was achieved. The estimated improvements in MAE using the mechanistic model ranged between 65 to 94 %, as shown in SectionIV. Therefore, the estimates using the mechanistic model were reasonable considering the effects of uncertain-ties and other unmeasured events affecting dynamics of the actual plant, which provides some validation for completing the simulated exercise first. Due to plant operations and other factors such as plant safety limitations, it was not possible to test controller performance at low loads.
As done for PID, data was collected and portions of data with variability due to change in load current removed. The total variability with MPC control, Smpc, for a
set-point of 2.1 was computed as 0.0101 giving an improvement of 42.29 % over PID, hence satisfying the first objective of the controller as stated in the control problem statement of Section II. As expected, these improvements were not as good as the estimates for minimum variance control that were presented in Table1. However, observing the plots in Fig.13
show that for the PID controller, there was a periodic long-term variability with a period of about 50 minutes between time points 70 mins and 180 mins on Fig.13. A zoomed-in plot of the pH and HCl valve position are shown in Fig. 14
for clarity. This periodic variability was eliminated by the MPC controller. MPC demonstrated substantial benefits in load current disturbance rejection over the initially well-tuned PI controller. This controller coped adequately with the
complex dynamics of the process. Note that the plant had to be maintained at a set-point of 2.1 during controller trial periods. Therefore, it was not possible to compute variability for other set-points.
VI. CONCLUSIONS
In this paper, two pH control schemes for the dechlorination of depleted brine in a Chloro-alkali plant were discussed and compared. The considered industrial process had dynamics that could benefit from the application of small-scale MPC. Variability assessment was carried out to estimate achievable benefits. A mechanistic model was developed and used to improve the existing PI controller and also to estimate the potential benefits achievable by replacing existing controller with MPC and also to effectively plan for the replacement of this controller. The PI controller was based on the mechanistic model whilst the MPC scheme incorporated an empirical model based on plant step test data. Both control schemes achieved good performance. However, as demonstrated by the real-time results, improved disturbance rejection was obtained through MPC. The improvements were similar to estimates obtained using the mechanistic model. Benefits of initial MPC scheme were limited due to practical problems such as noise and valve stiction. However, further improve-ments were obtained by taking practical steps to address the encountered problems (including faster control interval, and the use of valve position read-back within the control scheme). Final controller implementation demonstrated an improvement of about 46 % in standard deviation during steady-state plant operations (when plant disturbances are mild) and 57 % improvement in mean absolute error during periods with significant load current disturbances. Effective regulation of pH prevented the frequent diversion of waste brine for pretreatment before being discharged as waste water. This resulted in a reduction in energy usage (carbon footprint) and cost of operations associated with treatment leading to a more reliable production and sustainable operation. Further improvements are expected if the control problem is formu-lated as a multivariate considering other process variables further downstream. This forms part of the future work.
REFERENCES
[1] D. Ender, ‘‘Process control performance: not as good as you think,’’
Control Eng., vol. 40, no. 10, pp. 180–190, 1993.
[2] L. Desborough and R. Miller, ‘‘Increasing customer value of industrial con-trol performance monitoring—Honeywell’s experience,’’ in Proc. AIChE
Symp. Ser., 2002, pp. 169–189.
[3] K. J. Åström and T. Hägglund. ‘‘The future of PID control,’’ Control
Eng. Pract., vol. 9, no. 11, pp. 1163–1175, 2001, accessed: Oct. 29, 2017, doi:10.1016/S0967-0661(01)00062-4.
[4] M. Maciejowski, Predictive Control With Constraints. Upper Saddle River, NJ, USA: Prentice-Hall, 2002.
[5] D. S. Carrasco and G. C. Goodwin, ‘‘Feedforward model predictive con-trol,’’ Annu. Rev. Control, vol. 35, no. 2, pp. 199–206, 2011, accessed: Oct. 29, 2017, doi:10.1016/j.arcontrol.2011.10.007.
[6] A. J. Isaksson, ‘‘Some aspects of industrial system identification,’’ IFAC
Proc. Vol., vol. 46, no. 32, pp. 153–159, 2013, accessed: Oct. 29, 2017, doi:10.3182/20131218-3-IN-2045.00192.
[7] A. C. Bittencourt, A. J. Isaksson, D. Peretzki, and K. Forsman, ‘‘An algo-rithm for finding process identification intervals from normal operating data,’’ Processes, vol. 3, no. 2, pp. 357–383, 2015, accessed: Oct. 29, 2017, doi:10.3390/pr3020357.
[8] P. Masding and B. Lennox, ‘‘Use of dynamic modelling and plant historian data for improved control design,’’ Control Eng. Pract., vol. 18, no. 1, pp. 77–83, 2010, accessed: Oct. 29, 2017, doi:10.1016/j.conengprac. 2009.09.005.
[9] P. Schmittinger et al., Chlorine. Hoboken, NJ, USA: Wiley, 2000. [10] Eurochlor. How is Chlorine Produced. Accessed: Oct. 1, 2016.
[Online]. Available: http://www.eurochlor. org/the-chlorine-universe/how-is-chlorine-produced.aspx
[11] J. P. Shunta,Achieving World Class Manufacturing Through Process
Con-trol. Upper Saddle River, NJ, USA: Prentice-Hall, 1997.
[12] M. J. Grimble, ‘‘Controller performance benchmarking and tuning using generalised minimum variance control,’’ Automatica, vol. 38, no. 12, pp. 2111–2119, 2002, accessed: Oct. 29, 2017, doi: 10.1016/S0005-1098(02)00141-3.
[13] S. P. Bailey and W. H. Fellner, ‘‘Some useful aids for understanding and quantifying process control and improvement opportunities or how to deal with process capability catch 22,’’ in Proc. ASQC/ASA Fall Tech. Conf., Rochester, NY, USA, 1993.
[14] S. J. Qin and T. A. Badgwell, ‘‘A survey of industrial model predictive control technology,’’ Control Eng. Pract., vol. 11, no. 7, pp. 733–764, 2003, accessed: Oct. 29, 2017, doi:10.1016/S0967-0661(02)00186-7.
[15] D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, ‘‘Constrained model predictive control: Stability and optimality,’’
Auto-matica, vol. 36, no. 6, pp. 789–814, 2000. accessed: Oct. 29, 2017, doi:10.1016/S0005-1098(99)00214-9.
[16] F. G. Shinskey, pH and pION Control in Process and Waste Streams, New York, NY, USA: Wiley, 1973.
[17] F. Tahir and I. M. Jaimoukha, ‘‘Causal state-feedback parameteriza-tions in robust model predictive control,’’ Automatica, vol. 49, no. 9, pp. 2675–2682, 2013, accessed: Oct. 29, 2017, doi:10.1016/j.automatica. 2013.06.015.
[18] F. Tahir and I. M. Jaimoukha, ‘‘Robust feedback model predictive control of constrained uncertain systems,’’ J. Process Control, vol. 23, no. 2, pp. 189–200, 2013, accessed: Oct. 29, 2017, doi:10.1016/j.jprocont. 2012.08.003.
[19] C. Brosilow and B. Joseph, Techniques of Model-Based Control, Upper Saddle River, NJ, USA: Prentice-Hall, 2002.
[20] D. J. Sandoz, M. J. Desforges, B. Lennox, and P. R. Goulding, ‘‘Algo-rithms for industrial model predictive control,’’ Computing Control
Eng. J., vol. 11, no. 3, pp. 125–134, 2000. accessed: Oct. 29, 2017, doi:10.1049/cce:20000306.
[21] M. O’Brien, J. Mack, B. Lennox, D. Lovett, and A. Wall, ‘‘Model pre-dictive control of an activated sludge process: A case study,’’ Control
Eng. Pract., vol. 19, no. 1, pp. 54–61, 2011, accessed: Oct. 29, 2017, doi:10.1016/j.conengprac.2010.09.001.
[22] Y. A. Sha’aban, B. Lennox, and D. Laurí, ‘‘PID versus MPC performance for SISO dead-time dominant processes,’’ IFAC Proc. Vol., vol. 46, no. 32, pp. 241–246, 2013, accessed: Oct. 29, 2017, doi: 10.3182/20131218-3-IN-2045.00054.
YUSUF A. SHA’ABAN (M’09) received the B.Eng. degree in electrical engineering from Ahmadu Bello University, Zaria, Nigeria, in 2007, the M.Sc. degree in control systems from the Imperial College, London, U.K., in 2010, and the Ph.D. degree in electrical engineering (control engineering) from The University of Manchester, Manchester, U.K., in 2015.
Between 2015 and 2017, he was a Ph.D. Plus (Post. Doc.) Intern and a Tutor with The Univer-sity of Manchester and Manchester Metropolitan UniverUniver-sity, respectively. He is currently a Senior Lecturer with Ahmadu Bello University and a Visiting Faculty/Research Fellow at the Centre for International Studies, Massachusetts Institute of Technology, Cambridge, MA, USA. His research interests include model predictive control applications, machine learning, distributed energy systems optimization, and smart grid.
Dr Sha’aban is a member of the IET and the Council for the Regulation of Engineering in Nigeria. He was a recipient of the Petroleum Technology Development Fund Award in 2009 and 2012, and the Total/MIT ETT Fellowship in 2017.
FURQAN TAHIR received the B.S. degree in electronic engineering from the GIK Institute, Pakistan, in 2006, and the M.Sc. and Ph.D. degrees in control engineering from the Imperial College London, U.K., in 2008 and 2014, respectively. He is currently an Engineering Consultant with Per-ceptive Engineering Limited, U.K.
His research interests include the development and real-time application of robust model predic-tive control scheme, process monitoring and opti-mization solutions. He has authored several publications in these research areas.
Dr. Tahir is a member of the IET. He has also been the recipient of the Rector’s Award and Hertha Ayrton Centenary Prize from Imperial College London.
PHILIP W. MASDING was born in Reading, U.K., in 1963. He received the B.Sc. degree in engineering science and the Ph.D. degree based on research into control systems for hybrid vehicles from the University of Durham in 1985 and 1988, respectively.
Since 1989, he has been with the Chlor -Alkali Industry, first with ICI and then with Inovyn since 2000. He is currently involved in control system design and mathematical modeling. He focused on models of the electrolysis process and is currently developing a model of the polyvinyl chloride reaction process. He is a Chartered Engineer and a member of the Institute of Engineering Technology.
JOHN MACK received the B.Eng. degree (NZCE) from Auckland University. He is a Founding Mem-ber and the Engineering Director with Perceptive Engineering. He is a Chartered Engineer. He has 12 years’ experience in advanced process control (APC) systems.
He has successfully managed, developed, and commissioned several APC and optimization schemes within the chemical, pulp and paper, nutritional powders, water treatment, and pharma-ceutical industry sectors. He is also involved in the software development, system integration, and the business development.
BARRY LENNOX trained as a Chemical Engi-neer. He joined the School of Electrical and Elec-tronic Engineering, The University of Manchester, in 1997. He co-founded the applied control com-pany, Perceptive Engineering in 2003. He is also a Co-Inventor of Acoustek, which is a patented, acoustic technique for surveying heat exchanger tubes and locating blockages in long lengths of gas-filled pipelines. He is currently a Professor of applied control, the Director of the Robotics and Artificial Intelligence for Nuclear Robotics Hub, and the Research Director with the Dalton Cumbrian Facility, The University of Manchester. He has authored or co-authored over 200 articles related to the application of control systems and instrumentation to process systems and robotics.
