Comparison of Two Nonlinear Predictive Control Algorithms for Dissolved Oxygen Tracking Problem at WWTP

Journal of Automation, Mobile Robotics & Intelligent Systems VOLUME, N 6 Comarison of Two Nonlinear Predictive Control Algorithms for Dissolved Oxygen Tracking Problem at WWTP Submitted: 8 th June 5; acceted: 5 th Setember 6 Robert Piotrowski DOI:.433/JAMRIS_-6/ Abstract: The wastewater treatment lant is classified as a comlex system due to its nonlinear dynamics, large uncertainty in the disturbance inuts, multile time scales in the internal rocess dynamics and multivariable structure. Aeration is an imortant and exensive activity that is carried out during wastewater treatment lant oeration. A recise aeration control in biological rocesses for all the oerating conditions is necessary in order to guarantee adequate biological conditions for microorganisms. Theore, the most imortant is to oerate the biological rocesses so that a minimal energy was consumed and minimal DO concentration demand was alied. The aer rooses a two advanced control systems to track the dissolved oxygen erence trajectory. A decentralized and multivariable nonlinear redictive control algorithms are designed and comared. Simulation tests for the case study wastewater treatment lant are resented. Keywords: aeration, dissolved oxygen, wastewater treatment, mathematical modelling, nonlinear system, redictive control. Introduction.. General information Progressive develoment of technology and human oulation growth caused the amount of roduced sewage to increase. Years of exerience and scientific research, gave rise to the idea about wastewater treatment lant (WWTP). It is a comlex, nonlinear biological-chemical-hysical system with strong interactions between rocesses. Processes are difficult to control due to large disturbances such as inflow and load, nonlinearity, time-varying and comlexity with strong couling of the rocess variables. The oular treatment technology used in the field of WWTPs is the biological. Most of the municial WWTPs use activated sludge rocesses. Activated sludge ers to a mass of microorganisms where hel clean u wastewater. This is a rocess in which air or oxygen is forced into sewage liquor to develo a biological floc which reduces the organic content of the sewage. Activated sludge is used where high removal of organic ollution is required. For effective wastewater treatment, an activated sludge requires a continuous suly of oxygen/air. Aeration is used in different arts of a WWTP, esecially is alied to biological rocesses (e.g. nitrification, denitrification and hoshorus removal). Additionally, energy consumtion of aeration rocesses has the major share in energy bill at a WWTP. Dissolved oxygen (DO) concentration is the most imortant control arameter in the biological WWTP. Unfortunately, in industrial ractice, the control of DO is usually carried out using a simle feedback loo (e.g. linear PI algorithm with constant arameters) that does not aim at all at combining the tracking functions with the energy cost otimization. Good control erformance for all the oerating conditions cannot be achieved. Furthermore, the lack of on-line measurements at the WWTP, may result in limited use of advanced control systems... Survey of related works As mentioned earlier, control of DO is very imortant and difficult activity in the activated sludge rocesses. As the DO dynamics is nonlinear and tyically WWTP oerates under high variability of the influent quality and ollutant arameters. Works related to control of DO have a long history. Different control technologies have been researched over the last years, e.g. adative controller [], on/off controller with genetic algorithms [], multivariable PID controller [], nonlinear multiregional PI controller [3], fuzzy controller []. The second grou of DO control strategies are algorithms, where beside DO measurement, additionally ammonia nitrogen (NH 4 ), nitrate (NO 3 ) and hoshate (PO 4 ) measurements are included for control system design [,7]. An interesting and comrehensive review of DO control can be found in []. The model redictive control (MPC) technology is an attractive method for dynamic otimizing control. The MPC otimizer enables for direct incororation of the constraints in the control roblem into the otimization task at each time ste, what is a great advantage of this technology. During the last years, many industrial alications of control systems have utilized the MPC technology []. The MPC algorithm was also alied for DO control at the WWTP. The linear MPC algorithm was roosed in [] and its alication to benchmark simulation WWTP. In [5] the hybrid nonlinear redictive controller was alied. The binary control signals were ormulated to nonlinear rogramming task at every samling time. Interesting control results were obtained. In [7] the MPC system of DO control based on self-organizing radial basis function neural 8

Journal of Automation, Mobile Robotics & Intelligent Systems VOLUME, N 6 Air Blowers station Influent from mechanical art Anaerobic section Internal recycle Anoxic section Aerated section Internal recycle External recycle Secondary settler Effluent Waste sludge Fig.. Scheme of biological WWTP at Kartuzy network model was designed and examined for the benchmark simulation WWTP. In [6] a decentralized nonlinear hierarchical redictive control system was roosed. Biological reactor to be couled with an aeration system and in order to track rescribed DO trajectories. The uer level controller (UCL) rescribes trajectories for airflows desired to be delivered into the aerobic biological reactor zones. The lower level controller (LLC) forces the aeration system to follow those set oint trajectories. This controller was synthesized as a hybrid (discrete and continuous maniulated variables) nonlinear MPC. Authors of the aer [6] derived a nonlinear hybrid redictive control algorithm for the LLC. Dedicated oerators were used to derive genetic algorithms, thus allowing for efficient handling of the switching constraints and nonlinear hybrid system dynamics. In [5] a nonlinear multivariable hierarchical MPC was alied to design the ULC. This controller extends to lants with several aerobic zones sulied by an aeration system of limited caacity. This controller handles the airflow distribution between the zones. The constraint on the airflow that can be delivered by the aeration system is then active. The ULC roduces the airflow demands as set oints for the LLC. In summary, the aim of the aer is the design of the hybrid nonlinear control system to erform an efficient control quality of DO concentration for different oerating conditions. This aer further develos the results resented in [6,5]. Two advanced hierarchical nonlinear redictive control systems are designed and comared. Only DO and airflow measurements are alied for control systems design. In this aer, as oosite for revious research works [6,5] dynamic of aeration system is omitted and treated as a static system, which rovides the amount of air required by the control system. Simulation tests for case study lant are resented.. Descrition of the WWTP Kartuzy WWTP is tyical system with a continuous flow throughout the lant. This system consists of two arts. One is the mechanical where solids, mineral and insoluble organic ollutants are removed. The second is the biological art that is comosed of the activated sludge rocess. The activated sludge method is alied for biological wastewater treatment rocesses. Only a biological art is considered in the aer. The structure of biological art for the case study lant is shown in Fig.. The advanced biological treatment with nutrient removal is accomlished in the activated sludge reactor designed and oerated according the University of Cae Town (UCT) rocess. The first zone where the hoshorus is released is anaerobic. The second zone where the denitrification rocess is conducted is anoxic. The internal recirculation of mixed liquor originates from the anoxic zone. The returned activated sludge from the bottom of the clarifiers and the internal recirculation from the end of the aerobic zone (containing nitrates) are directed to the anoxic zone. The last art of the reactor (aerobic) is aerated by a diffused aeration system. This zone is divided into four comartments of various intensity of aeration. The anaerobic, anoxic, and four aerobic tanks have volumes of 8, 8, 7, 76, 86, and 5 m 3, resectively. Oxygen is sulied to aerated tanks by the aeration system (blowers, ies, throttling valves and diffusers). Wastewater is mixed with activated sludge, which hels during the rocess of wastewater treatment. Different aeration methods are alied: high-urity oxygen aeration, mechanical aeration, and diffused aeration [3]. The last technique is used at the Kartuzy WWTP. The aeration system delivers air to each of the aeration tanks. The wastewater and activated sludge are searated into two arallel secondary settlers. The volume of each secondary settler is aroximately 6 m 3. The activated sludge is internally recirculated from the anoxic tank to the anaerobic zone and from the last aerobic zone to the anoxic tank. These recirculations are tyically set to 45 to % and % of influent waste. Additionally, the wastewater is recirculated from the secondary settlers to the anoxic tank (45 to % of influent waste). The excess waste sludge is removed, chemically stabilized, and stored. 3. Control structures It is industry ractice that simle technology is used to control of DO: manual control, rule-based control and PI controller with fixed arameters. High quality of Articles 9

Journal of Automation, Mobile Robotics & Intelligent Systems VOLUME, N 6 control cannot be obtained by conventional and linear control methods. MPC technology is an attractive otimizing method for advanced control of dynamic nonlinear systems. The nonlinear MPC algorithm uses the DO model for rediction. The redictive control adjusts its oeration in advance, before there are changes in the outut of the control system. The two structures of the new control systems are illustrated in Figs. 3. The controller s objective is to force the S o,j (controlled variable) into zones indicated by rescribed erences S o,j and, at the same time, to minimize the associated electricity cost by blowing air. The controller s objective is to force the S o,j (controlled variable) into zones indicated by rescribed erences S o,j and, at the same time, to minimize the associated electricity cost by blowing air. The maniulated variables in the control systems are airflows to the each of the aerobic tanks. Decentralized control system (Fig., control system ), based on information about DO concentration calculates control trajectories of the airflows, taking into account its constraints on minimum and imum value as well as the rate of change in one ste rediction. Resiration R is the disturbing variable that affects DO concentration. All aeration tanks are connected to a single aeration system. Hence, four indeendently oerating controllers may have a roblem with distributing required amounts of air correctly (e.g., for large inflow to the WWTP and/ or a sudden increase in concentration of ollutants in wastewater flow). Theore, a multivariable, nonlinear MPC is also designed (Fig. 3, control system ). 4. Mathematical models 4.. Model of biological WWTP The most oular mathematical descrition of biological rocesses at WWTP is a series defined by Activated Sludge Models (ASMs) roosed by International Water Association (IWA). The models (ASM, ASM, ASMd, ASM3) were resented and summarized in []. A critical reviews of activated sludge modelling for seven most commonly used models were resented in [8]. In the aer the biological rocesses are modelled by ASMd model. ASMd consists of state variables and kinetic and stoichiometric arameters. Values of those arameters are equal to their default values at C [9]. ASMd model was calibrated based on real data sets from the Kartuzy WWTP. Additionally, data from the lant ermitted to define the quality of load: chemical oxygen demand (COD), total nitrogen concentration (TN) and total hoshorous concentration (TP). Verification of the modelling results was satisfactory and so they were used for control uroses. 4.. Model of DO concentration A dynamics of dissolved oxygen for the j-th aeration tank is described by the following nonlinear differential equation: () S o, S o, 4 DO concentration erence trajectory Airflow trajectory Q air DO concentration trajectory S o Fig.. Structure of the control system Nonlinear MPC Q air, Q air, 4 Nonlinear MPC4 MODEL OF BIOLOGICAL WWTP Airflow erence trajectory Inflow Dynamic model of DO concentration S o S o, S o, 4 DO concentration erence trajectory Airflow trajectory Q air DO concentration trajectory S o Q air, Fig. 3. Structure of the control system Nonlinear Multivariable MPC Q air, 4 MODEL OF BIOLOGICAL WWTP Dynamic model of DO concentration S o Airflow erence trajectory Inflow Articles

Journal of Automation, Mobile Robotics & Intelligent Systems VOLUME, N 6 where S o dissolved oxygen concentration, k La oxygen transfer function, Q air airflow, R - resiration, S o,sat = 8.637 g O /m3 dissolved oxygen saturation concentration, K o =. g/m 3 Monod s constant. The function, k La (Q air ), describes the oxygen transfer and deends on the aeration actuating system and sludge conditions. Different aroaches to modelling this function are resented in literature. In this aer, the linear model is alied: () where α =.8 /m3 [8]. The resiration R is an imortant arameter to biological rocesses taking lace in aerobic zones. The resiration varies with time, deends on the biomass concentration, and describes oxygen consumtion by the microorganism. This variable can be calculated using the ASMd model [9]; however, to determine R, another 8 nonlinear differential equations in the ASMd model are required. Because of the comlexity of the ASMd model, resiration R is treated as an external disturbance signal. Resiration can be measured by a resirometer. In some research, resiration was assumed to measure and be used for monitoring and control of biological rocesses. However, dedicated measuring equiment is very exensive; hence, this variable is rarely being measured. Theore, resiration has to be estimated to be used for control. Different aroaches based on the augmented Kalman filter were taken for joint estimation of resiration and oxygen transfer functions [4]. Another aroach was resented in literature [9]. A sequential algorithm with the Kalman filter was roosed and investigated. The aroach resented in [4] is used in this aer. It is based on oint estimation of resiration at the aroriate time instant valid for a articular rediction horizon sufficient to be taken as constant. 5. Predictive controllers design A model of DO concentration is needed to design an MPC (see ()). For the j-th aeration tank, the following discrete model can be formulated: where. (4) In (4), it is imortant to note that there is a oneste delay. This has no ractical significance because of the variability of the aforementioned slow resiration in relation to the rate dissolved oxygen concentration changes. Moreover, it is ossible to treat the temorary estimate as a constant rediction of resiration over a suitably selected length of rediction horizon. Because (4) contains measurements, resiration (i.e., differentiation of the measurement noise resent in the measurement of dissolved oxygen) occurs during estimation. Results of revious studies [4] indicate that, rovided a tyical signal is within accetable noise levels, its effect on the quality of estimates can be omitted (see Figs. 4 7). In Figs. 4 7 the examles trajectories of the DO concentration and resiration R are resented, with (Fig. 4 and 6) and without (Fig. 5 and 7) measuring noise. Knowing the measurement errors characteristic of devices for measuring the DO concentration, the standard deviation of measurement equal. g O /m 3 was assumed. Results confirm the assumtion of low imact of measurement noise in the measurement of DO concentration on the quality of estimate of resiration R. In addition, simlification of the model and the resulting inaccuracies are eliminated by feedback mechanism which is an integral art of the control system. 5.. Control system The nonlinear MPC erformance function for j-th aeration tank is defined as: (3) (5) where k and T are the discrete time instant and dissolved oxygen samling interval. At the time instant ( k+ ) T, the estimate Rˆ j ( k ) of R j ( kt ) can be obtained by discretizing (3), solving the resulting discrete time equation for the unknown resiration value Rj( k) = Rj( kt), and substituting the exression Soj, ( k), Soj, ( k + ) with the measurements m m, + S k = S kt. Hence: S ( k ) S ( k ) where ( ) ( ) oj, oj, oj, oj, The first term in (5) reresents the tracking error. The second and third terms describe rates of changes of the control inut over H (rediction horizon) while the fourth term reresents the control cost. The weights α, β and χ are tuning knobs used to achieve a desired comromise between the tracking error, the intensity of switching the blowers, and the cost of the energy used for uming air. min Let Q and Q be the minimum and imum value of the airflow, resectively. The constraints Articles

Journal of Automation, Mobile Robotics & Intelligent Systems VOLUME, N 6.8 3.6 DO concentration So [g O / m 3 ].4..8.6.4. DO concentration So [g O / m 3 ].5.5..4..4.6.8 Fig. 4. DO concentration in aeration tank without measurement noise Resiration R [mg / m 3 h].9.7.5.4.3....4..4.6.8 Fig. 6. Resiration in aeration tank without measurement noise.5..4..4.6.8 Fig. 5. DO concentration in aeration tank with measurement noise Resiration R [mg / m 3 h].9.7.5.4.3....4..4.6.8 Fig. 7. Resiration in aeration tank with measurement noise on minimum and imum values of control action at each rediction ste are defined as follows: (6) are taken from the measurements. This results in the otimised Q ( k k),..., Q ( k+ H = k ) DO trajectories over the rediction horizon. 5.. Control system The MPC erformance function is written as: where and. Moreover, Q is the imum value of the rate of change. The constraints are given by: (7) where. At the time instants kt the nonlinear MPC solves its otimisation task by minimising the erformance function (5) with resect to the aeration flows subject to the constraints (6) and (7). The DO concentrations So, j( k+ ik ) at the aerobic zones redicted over H are calculated by using the discretized models (3). The resirations Rj ( k+ i ) in these models are relaced by their redictions that are calculated according to (4) based on the DO measurements at the aerobic zones. The initial conditions (8) The first term in (8) reresents the tracking error. The second and the third term describe the rate of change of the control inut over H, while the fourth term reresents the control cost. The weights δ, ϕ, and γ were calculated based on simulation tests. min The constraints on Q and Q are given by: ( ) min Q Q k+ i k Q ; i =,, H (9) j {,,3,4} Articles

Journal of Automation, Mobile Robotics & Intelligent Systems VOLUME, N 6 Resiration R [mg/m 3 h].8.6.4..4...4..4.6.8 Fig. 8. Resiration in aeration tank Resiration R [mg/m 3 h].4..4...4..4.6.8 Fig. 9. Resiration in aeration tank Resiration R3 [mg/m 3 h].4..4...4..4.6.8 Fig.. Resiration in aeration tank 3 Resiration R4 [mg/m 3 h].9.7.5.4.3....4..4.6.8 Fig.. Resiration in aeration tank 4 where min 3 3 Q = m h and Q = 5m h. The constraints on Q are defined as follows: Q ( k+ i k) Q ( k+ i k) Q j {,,3,4} ; Q ( ) ( ) =,, k k Q i H k k Q () 3 where Q = 5m h. The nonlinear MPC generates at time instant k, the 4 control sequence, { Q ( k),..., Q( k+ H }, j = based on a discretised nonlinear model (3) with the redicted trajectory of R j ( k ) over k [ kk, + H ] (4) by minimizing the erformance function (8) with 4 resect to { Q( k),..., Q( k+ H )} j= subject to the constraints (9)-(). 6. Simulation tests and comarative analysis In this section the roosed two novel control systems (see section 5) were tested by simulation, based on real data records from the case study Kartuzy WWTP. The commercial simulation ackage Simba [8] was alied to modelling biological rocesses at a WWTP (ASMd model). Matlab environment was alied to imlementing two advanced control strategies. The Sequential Quadratic Programming (SQP) solver was alied to solve the nonlinear MPC otimisation task. The amount and comosition of the influent wastewater to WWTP is varied during the day. Their variability is modelled by four arameters (disturbances): inflow Q in, COD, TN and TP. The inut disturbances were as follows: Q in (between -35 m 3 /h) and COD (between 7- mg/dm 3 ) were time-varying; TN (equal 9 mg/dm 3 ) and TP (equal mg/dm 3 ) were constants over time. Their values and variability corresond to the real values of the influent wastewater for case study WWTP. First, it examined the effect of the length of the rediction horizon H and the length of the rediction ste T, on control quality and comutation time. Control errors were increase by shortening H and lengthening T. As a result of numerical analysis, simulation arameters of redictive controllers were as follows: H = stes and T=5 min. Simulation results are shown for four aeration tanks. Most imortant arameter disturbing the rocess of aeration is the resiration R (Figs. 8-). It ers to the rate of oxygen consumtion by bacteria as a result of biochemical reactions. These results show that the resiration disturbance is time-varying, lecting the varying load of the WWTP (inflow and load). Control results for DO tracking at Kartuzy WWTP are illustrated. The different range of DO changes are set, which corresonds to the otimal conditions of aeration wastewater. In Figs., 4, 6 and 8 the set Articles 3

Journal of Automation, Mobile Robotics & Intelligent Systems VOLUME, N 6 DO concentration So, [g O / m 3 ].8.6.4..4. S o, S o, 3.4.5.7.9 Fig.. DO concentration in aeration tank control system DO concentration So, [g O / m 3 ].8.6.4..4. S o, S o, 3.4.5.7.9 Fig. 4. DO concentration in aeration tank control system DO concentration So, [g O / m3 ].8.6.4..4. S o, S o, 3.4.5.7.9 Fig. 3. DO concentration in aeration tank control system DO concentration So, [g O / m3 ].8.6.4..4. S o, S o, 3.4.5.7.9 Fig. 5. DO concentration in aeration tank control system oint S o and DO tracking S o for control system are resented. In Figs. 3, 5, 7 and 9 the results for control system are illustrated. For both control algorithms was calculated Root Mean Square (RMS) error, given by: RMS = ( So So ) n () where n denotes the number of samles. The control results of RMS error are summarized in Table. Table. DO tracking error Control system RMS error aeration tank 3 4 Control system.43..8.34 Control system.44.4.8.49 The control results, for two control systems, show on a good tracking erformance by using nonlinear advanced control strategies. It can be seen to follow the DO trajectory with good accuracy. The control system demonstrates better quality control, but takes longer to comlete required calculations. The control system is characterized by a larger RMS error. For this system, RMS error does not exceed.5 in value (see Table ). Control results could be even better, but not for constraints included in the redictive control systems (see [6] [7] and [9] []). The average time to solve one redictive otimization task for control system is longer (much larger number of decision variables). However, this time is small enough to carry out the calculation on-line with aroriate rediction horizon, required by the dynamics of the lant and the disturbances rate of change. The main advantage of control system is less comutations effort. In addition, in case of failure of one of the controllers the other three controllers can still control the suly of oxygen the individual aerated tanks. In some cases, for examle increased inflows of sewage with a high concentration of ollutants, set oints trajectories of DO concentration can vary significantly and control system may have a roblem with the roer distribution of the required amount of air (it is connected with the fulfillment of constraints, see [6] [7]). This situation can cause a deviation of the control trajectories. Better quality control for control system takes into account the needs of all aerobic tanks and the ossibility of aeration system and theore is able to find a comromise in the air the division. 4 Articles

Journal of Automation, Mobile Robotics & Intelligent Systems VOLUME, N 6 DO concentration So, [g O / m 3 ].8.6.4..4. S o, S o, 3.4.5.7.9 Fig.. DO concentration in aeration tank control system DO concentration So, [g O / m 3 ].8.6.4..4. S o, S o, 3.4.5.7.9 Fig. 4. DO concentration in aeration tank control system DO concentration So, [g O / m3 ].8.6.4..4. S o, S o, 3.4.5.7.9 Fig. 3. DO concentration in aeration tank control system DO concentration So, [g O / m3 ].8.6.4..4. S o, S o, 3.4.5.7.9 Fig. 5. DO concentration in aeration tank control system 7. Conclusions Control of dissolved oxygen at a WWTP is imortant for economic and rocess reasons. The aer has addressed an imortant and difficult control roblem. A novel aroach to the dissolved oxygen concentration tracking has been resented. Two nonlinear redictive control systems have been designed and comared. Its roerties and tracking erformance have been investigated by simulation based on real data sets from Kartuzy case study lant. Promising results have been observed. AUTHOR Robert Piotrowski Gdansk University of Technology, Faculty of Electrical and Control Engineering, Narutowicza /, 8-33 Gdansk. E-mail: robert.iotrowski@g.gda.l. REFERENCES [] Åmand L., Olsson G., Carlsson B., Aeration control a review, Water Science & Technology, vol. 67, no., 3, 374 398. DOI:.66/ wst.3.39. [] Belchior C.A.C., Araújo R.A.M., Landeck J.A.C., Dissolved oxygen control of the activated sludge wastewater treatment rocess using stable adative fuzzy control, Comuters and Chemical Engineering, vol. 37, no.,, 5 6. DOI:.6/j.comchemeng..9.. [3] Błaszkiewicz K., Piotrowski R., Duzinkiewicz K., A Model-Based Imroved Control of Dissolved Oxygen Concentration in Sequencing Wastewater Batch Reactor, Studies in Informatics and Control, vol. 3, no 4, 4, 33 33. [4] Chotkowski W., Brdys M.A., Konarczak K., Dissolved oxygen control for activated sludge rocesses, International Journal of Systems Science, vol. 36, no., 5, 77 736. DOI:.8/7758866. [5] Cristea S., de Prada C., Sarabia D., Gutiérrez G., Aeration control of a wastewater treatment lant using hybrid NMPC, Comuters and Chemical Engineering, vol. 35, no. 4,, 638 65. DOI:.6/j.comchemeng..7.. [6] Duzinkiewicz K., Brdys M.A., Kurek W., Piotrowski R., Genetic hybrid redictive controller for otimised dissolved oxygen tracking at lower control level, IEEE Transactions on Control Systems Technology, vol. 7, no. 5, 9, 83-9. DOI:.9/TCST.8.4499. [7] Han H.-G., Qiao J.-F., Chen Q.-L., Model redictive control of dissolved oxygen concentration based on a self-organizing RBF neural network, Control Engineering Practice, vol., no. 4,, 465 476. DOI:.6/j.conengrac... Articles 5

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