Dual-Control of Autothermal Thermophilic Aerobic Digestion Using Aeration and Solid Retention Time

Autothermal thermophilic aerobic digestion (ATAD) is an advanced sewage sludge treatment which allows compliance with increasingly demanding regulations. Concerning sludge pasteurization, a certain average temperature must be assured in the digester during batch treatment. Aeration flow is the variable most manipulated to regulate the digester temperature. Additionally, the manipulation of the batch sludge flow—which is related to the solid-retention-time—is considered to improve temperature regulation despite variations in air and sludge temperatures and the variability of raw sludge organic content. Thus, a dual-input control structure was provided where the aeration and solid-retention-time contributed as faster and slower inputs, respectively. Two controllers intervened, and the set-point for the batch average temperature was chosen to meet the minimum effluent quality established by the US regulations or European recommendations, considering that lower set point temperatures save aeration costs. A set-point for the aeration allowed us to achieve an extra goal, which aimed at either reducing operation costs or increasing production rates. The two feedback controllers were designed following the robust control methodology known as quantitative feedback theory (QFT). Improvements were compared with single-input (aeration-flow) control strategy and open-loop control strategy. Simulations were performed on a benchmark non-linear simulation model for ATAD.


Introduction
New regulations in the increasingly stringent wastewater treatment sector promote the use of advanced wastewater and sludge treatments.The sludge that is obtained in wastewater treatments is rich in nutrients and organic matter, which makes it reusable as a soil fertilizer [1] after proper processing.Autothermal thermophilic aerobic digestion (ATAD) is a reference technology for sludge stabilization and pasteurization [2,3].ATAD treatment is based on the aeration of the raw sludge in a closed reactor for a specified retention time.When sludge pasteurization is mandatory, the digester is usually operated in batch-mode (a sequence of feeding-reaction-withdrawal that is repeated batch after batch) to avoid hydraulic shorts and ensure time-temperature conditions.By supplying a suitable amount of air, several biochemical reactions consume the organic matter content in the sludge, which reduces the potential of the sludge to attract disease vectors (insects, rodents, birds, etc.) [4].Exothermic reactions generate heat, which maintains the reactor temperature at around 55 • C without the need to apply external heat energy.The high temperature during the batch time reduces the pathogen concentration in the sludge [5][6][7].
The control of the reaction is vital to achieving proper stabilization (vector attraction reduction) and pasteurization (pathogen reduction) levels as per the regulations and recommendations guidelines.
Water 2017, 9, 426 3 of 15 design the robust controllers.Section 3 evaluates the expected performance of the dual-control where quality, cost, and production indexes are evaluated to show the improvements versus single-control and manual control.In Section 4, the main conclusions are presented.

Steady-State Analysis of the ATAD
Current benchmark simulation models (BSMs) [26] were extended to ATAD technology through the benchmark simulation model AT_BSM [13,25].This was used in this work for the ATAD analysis, and for the simulation and validation of the proposed control strategies.
In AT_BSM, the digester (Figure 1a) was modeled as a tank with two completely-stirred volumes (liquid and gaseous phases).Biological reactions and energy balances were considered [27].The biochemical model (Figure 1b) was based on the standard ASM1 with slight modifications to make it consistent with observations from the ATAD reactors (acid-base reactions and liquid-gas transfers).Temperature evolution was obtained through the system energy balance, which considered several heat fluxes involved in the process: influent and effluent heat energy, heat fluxes through walls and gas-liquid surface, and heat transfer from the mixing equipment.A total number of 24 dynamic variables were included in a state-space model [13].A 24 h (1 day) cycle sequence was established in AT_BSM: 0.5 h for sewage feeding; 23 h for reaction (aerated reaction phase); and 0.5 h for sludge withdrawal.During each cycle (batch), a portion of the total reactor volume (V ATAD = 2350 m 3 ) was drained and filled.Next, the solids retention time (SRT) is given by: where Q raw is the mean influent flow per batch.The mean effluent flow per batch Q out is equal to Q raw minus the evaporation shrinkages.For a stable operation of the digester, SRT can be moved over 10-15 d (day).The ability to change SRT involves the existence of a pre-holding tank [13] to regulate the influent flow and to absorb fluctuations of the outlet flow.The influent definition consists of: (i) a constant composition given by simulations of the benchmark simulation model No.2 (BSM2) evaluated by Vrecko et al. [28]; and (ii) a significant variability of the biodegradable content.Departing from an exhaustive analysis of the raw sludge in the BSM2, 2/3 parts of the mixed raw sludge were due to the slowly biodegradable substrate (X s,in ) [13].For simplicity, X s,in was used as the principal indicator to quantify the biodegradable organic matter content in the raw sludge.The sludge temperature T sludge and the air temperature T air considered long-term and short-term variations [13].
The mean aeration flow per batch Q a was rated up to 65,000 m 3 /d.
Water 2017, 9, 426 3 of 15 The remainder of the paper is organized as follows.Section 2 studies the influence of air-flow and solid-retention-time on the digester temperature, and the control strategies are defined, as is the dual-control structure used to achieve them.Appendix A thoroughly describes the method used to design the robust controllers.Section 3 evaluates the expected performance of the dual-control where quality, cost, and production indexes are evaluated to show the improvements versus single-control and manual control.In Section 4, the main conclusions are presented.

Steady-State Analysis of the ATAD
Current benchmark simulation models (BSMs) [26] were extended to ATAD technology through the benchmark simulation model AT_BSM [13,25].This was used in this work for the ATAD analysis, and for the simulation and validation of the proposed control strategies.
In AT_BSM, the digester (Figure 1a) was modeled as a tank with two completely-stirred volumes (liquid and gaseous phases).Biological reactions and energy balances were considered [27].The biochemical model (Figure 1b) was based on the standard ASM1 with slight modifications to make it consistent with observations from the ATAD reactors (acid-base reactions and liquid-gas transfers).Temperature evolution was obtained through the system energy balance, which considered several heat fluxes involved in the process: influent and effluent heat energy, heat fluxes through walls and gas-liquid surface, and heat transfer from the mixing equipment.A total number of 24 dynamic variables were included in a state-space model [13].A 24 h (1 day) cycle sequence was established in AT_BSM: 0.5 h for sewage feeding; 23 h for reaction (aerated reaction phase); and 0.5 h for sludge withdrawal.During each cycle (batch), a portion of the total reactor volume (VATAD = 2350 m 3 ) was drained and filled.Next, the solids retention time (SRT) is given by: where Qraw is the mean influent flow per batch.The mean effluent flow per batch Qout is equal to Qraw minus the evaporation shrinkages.For a stable operation of the digester, SRT can be moved over 10-15 d (day).The ability to change SRT involves the existence of a pre-holding tank [13] to regulate the influent flow and to absorb fluctuations of the outlet flow.The influent definition consists of: (i) a constant composition given by simulations of the benchmark simulation model No.2 (BSM2) evaluated by Vrecko et al. [28]; and (ii) a significant variability of the biodegradable content.
Departing from an exhaustive analysis of the raw sludge in the BSM2, 2/3 parts of the mixed raw sludge were due to the slowly biodegradable substrate (Xs,in) [13].For simplicity, Xs,in was used as the principal indicator to quantify the biodegradable organic matter content in the raw sludge.The sludge temperature Tsludge and the air temperature Tair considered long-term and short-term variations [13].The mean aeration flow per batch Qa was rated up to 65,000 m 3 /d.
(a) (b)   Regulation tasks on AT_BSM were performed on the batch average temperature T avg .Manipulated variables SRT and Q a remained constant for the 1-day batch time, and were updated by the control law batch after batch.Therefore, constant manipulated inputs were considered for the present steady-steady analysis.T avg was on-line computed as the mean value of N i = 1440 records of instantaneous temperature T i .These were captured during the 1-day treatment evolution (one T i sample was taken every minute).For proper pasteurization, the USEPA [8] establishes a minimum time D (d) as a function of the sludge temperature T i ( • C), which is expressed by: D = 50, 070, 000 10 0.14 In contrast, the European Commission [9] recommends that the temperature inside the reactor should be over 55 • C for at least 20 h without admixture or withdrawal during treatment.Fuchs and Fuchs [29] asserted that sufficient batch-time at a temperature between 50 and 70 • C assured reliable disinfection.After several simulations on AT_BSM, we adopted T avg set-points around 55 • C to meet the pasteurization regulations.
As in Nájera et al. [16], our analysis studied the steady-state temperature T avg reached after 50 days at constant conditions of manipulated inputs, air and sludge temperatures, and influent composition.Figure 2 shows the results around the temperature of interest T avg = 55 • C. A wide range of manipulated inputs, Q a and SRT, were analyzed.A relatively high organic matter content X s,in was fixed to 30 kg/m 3 in the analysis so that the required temperature could be provided by the manipulation of both Q a and SRT over their respective ranges.Considering that Q a is directly proportional to the aeration cost and SRT is inversely proportional to the sludge flow (production-rate), operating points of "minimum cost" and "maximum production" are highlighted in Figure 2 (some curves have been excluded in Figure 2b since their SRT values were out of the range over 10-15 d).
Water 2017, 9, 426 4 of 15 Regulation tasks on AT_BSM were performed on the batch average temperature Tavg.Manipulated variables SRT and Qa remained constant for the 1-day batch time, and were updated by the control law batch after batch.Therefore, constant manipulated inputs were considered for the present steady-steady analysis.Tavg was on-line computed as the mean value of Ni = 1,440 records of instantaneous temperature Ti.These were captured during the 1-day treatment evolution (one Ti sample was taken every minute).For proper pasteurization, the USEPA [8] establishes a minimum time D (d) as a function of the sludge temperature Ti (°C), which is expressed by: In contrast, the European Commission [9] recommends that the temperature inside the reactor should be over 55 °C for at least 20 h without admixture or withdrawal during treatment.Fuchs and Fuchs [29] asserted that sufficient batch-time at a temperature between 50 and 70 °C assured reliable disinfection.After several simulations on AT_BSM, we adopted Tavg set-points around 55 °C to meet the pasteurization regulations.
As in Nájera et al. [16], our analysis studied the steady-state temperature Tavg reached after 50 days at constant conditions of manipulated inputs, air and sludge temperatures, and influent composition.Figure 2 shows the results around the temperature of interest Tavg = 55 °C.A wide range of manipulated inputs, Qa and SRT, were analyzed.A relatively high organic matter content Xs,in was fixed to 30 kg/m 3 in the analysis so that the required temperature could be provided by the manipulation of both Qa and SRT over their respective ranges.Considering that Qa is directly proportional to the aeration cost and SRT is inversely proportional to the sludge flow (production-rate), operating points of "minimum cost" and "maximum production" are highlighted in Figure 2 (some curves have been excluded in Figure 2b since their SRT values were out of the range over 10-15 d).The ratio Qa/Qraw represents the aeration cost in a fairer way for analysis.It indicates the amount of air required per unit of treated sludge.Figure 3 evaluates that ratio for several production rates from 157 m 3 /d to 235 m 3 /d, which corresponded to the SRT from 15 d to 10 d, respectively, as per Equation (1).The bar diagram (Figure 3) shows the trade-off between reducing the aeration cost and increasing the production-rate.Results are shown for several temperatures.They reveal the importance of achieving the strictly required pasteurization temperature to save aeration costs for the same production rate.Temperature Tmax,st means that the maximum achievable temperature (61.4 °C, 61.1 °C, 60.6 °C, 60.45 °C, 60.1 °C, 59.7 °C) for each SRT (from 15 d to 10 d, respectively) and for Xs,in = 20 kg/m 3 ; thus, Tmax,st involved the best attainable stabilization level, which was different for each SRT and Qa (see Nájera et al. [16] for further details).The aeration-cost savings were around 30% if pasteurization was solely achieved, and was out of scope for this work if this decision compensated a post-treatment for the required sludge stabilization.Tavg = 55 °C and Tavg = 56.8°C distinguished the minimum required temperature to meet the USEPA and EU pasteurization criteria, respectively.The ratio Q a /Q raw represents the aeration cost in a fairer way for analysis.It indicates the amount of air required per unit of treated sludge.Figure 3 evaluates that ratio for several production rates from 157 m 3 /d to 235 m 3 /d, which corresponded to the SRT from 15 d to 10 d, respectively, as per Equation (1).The bar diagram (Figure 3) shows the trade-off between reducing the aeration cost and increasing the production-rate.Results are shown for several temperatures.They reveal the importance of achieving the strictly required pasteurization temperature to save aeration costs for the same production rate.Temperature T max,st means that the maximum achievable temperature (61.4 • C, 61.1 • C, 60.6 • C, 60.45 • C, 60.1 • C, 59.7 • C) for each SRT (from 15 d to 10 d, respectively) and for X s,in = 20 kg/m 3 ; thus, T max,st involved the best attainable stabilization level, which was different for each SRT and Q a (see Nájera et al. [16] for further details).The aeration-cost savings were around 30% if pasteurization was solely achieved, and was out of scope for this work if this decision compensated a post-treatment for the required sludge stabilization.T avg = 55 • C and T avg = 56.8• C distinguished the minimum required temperature to meet the USEPA and EU pasteurization criteria, respectively.

Dual-Control System of the ATAD
Two control strategies were attempted to achieve pasteurization temperatures (Table 1): MISO COST, which yielded the lowest aeration cost; and MISO PROD, which yielded the highest production rate.The feedback control structure to accomplish them is shown in Figure 4.One strategy or the other was selected by changing the aeration set-point Qa,ref.
Overall, smaller values of Qa,ref save aeration costs, but indirectly lead to higher SRT values, which involves lower production rates.On the other hand, higher values of Qa,ref increase the aeration levels to eventually treat more sludge (SRT decreases).Furthermore, Qa,ref can be rated to adapt the effluent flow to a second treatment stage, which, for example, would consist of an anaerobic digestion for full stabilization.For the same digester temperature, shrinkages by evaporation are larger when solid-retention-times are larger.Thus, the strategy that minimizes aeration costs (less Qa) also minimizes transport costs (less Qout).The feedback control structure assured that the batch average temperature Tavg was regulated to a specified set-point Tavg,ref despite changes in temperatures Tair, Tsludge, and variability of the biodegradable organic matter content in the raw sludge Xs,in.Whenever the pasteurization requirement was met, as small as possible values for Tavg,ref were selected, since smaller temperatures reduce aeration costs for the same production rate.Accordingly, the Tavg,ref was chosen as 55 °C or 56.8 °C for USEPA or EU recommendations, respectively (Table 1).
If the input energy that Xs,in carried in was not sufficient to maintain the Tavg,ref, this set-point was reduced for stable operation [14].This situation was observed through a sharp decrease in the slope of the batch Ti-temperature profile.An algorithm for its detection is described in Zambrano [13] and

Dual-Control System of the ATAD
Two control strategies were attempted to achieve pasteurization temperatures (Table 1): MISO COST, which yielded the lowest aeration cost; and MISO PROD, which yielded the highest production rate.The feedback control structure to accomplish them is shown in Figure 4.One strategy or the other was selected by changing the aeration set-point Q a,ref .Overall, smaller values of Q a,ref save aeration costs, but indirectly lead to higher SRT values, which involves lower production rates.On the other hand, higher values of Q a,ref increase the aeration levels to eventually treat more sludge (SRT decreases).Furthermore, Q a,ref can be rated to adapt the effluent flow to a second treatment stage, which, for example, would consist of an anaerobic digestion for full stabilization.For the same digester temperature, shrinkages by evaporation are larger when solid-retention-times are larger.Thus, the strategy that minimizes aeration costs (less Q a ) also minimizes transport costs (less Q out ).

Dual-Control System of the ATAD
Two control strategies were attempted to achieve pasteurization temperatures (Table 1): MISO COST, which yielded the lowest aeration cost; and MISO PROD, which yielded the highest production rate.The feedback control structure to accomplish them is shown in Figure 4.One strategy or the other was selected by changing the aeration set-point Qa,ref.
Overall, smaller values of Qa,ref save aeration costs, but indirectly lead to higher SRT values, which involves lower production rates.On the other hand, higher values of Qa,ref increase the aeration levels to eventually treat more sludge (SRT decreases).Furthermore, Qa,ref can be rated to adapt the effluent flow to a second treatment stage, which, for example, would consist of an anaerobic digestion for full stabilization.For the same digester temperature, shrinkages by evaporation are larger when solid-retention-times are larger.Thus, the strategy that minimizes aeration costs (less Qa) also minimizes transport costs (less Qout).The feedback control structure assured that the batch average temperature Tavg was regulated to a specified set-point Tavg,ref despite changes in temperatures Tair, Tsludge, and variability of the biodegradable organic matter content in the raw sludge Xs,in.Whenever the pasteurization requirement was met, as small as possible values for Tavg,ref were selected, since smaller temperatures reduce aeration costs for the same production rate.Accordingly, the Tavg,ref was chosen as 55 °C or 56.8 °C for USEPA or EU recommendations, respectively (Table 1).
If the input energy that Xs,in carried in was not sufficient to maintain the Tavg,ref, this set-point was reduced for stable operation [14].This situation was observed through a sharp decrease in the slope of the batch Ti-temperature profile.An algorithm for its detection is described in Zambrano [13] and The feedback control structure assured that the batch average temperature T avg was regulated to a specified set-point T avg,ref despite changes in temperatures T air , T sludge , and variability of the biodegradable organic matter content in the raw sludge X s,in .Whenever the pasteurization requirement was met, as small as possible values for T avg,ref were selected, since smaller temperatures reduce aeration costs for the same production rate.Accordingly, the T avg,ref was chosen as 55  If the input energy that X s,in carried in was not sufficient to maintain the T avg,ref , this set-point was reduced for stable operation [14].This situation was observed through a sharp decrease in the slope of the batch T i -temperature profile.An algorithm for its detection is described in Zambrano [13] and Zambrano et al. [25].Here, it was implemented under the block "bending-point detector" of Figure 4. Consequently, Nájera et al. [14] presented a fuzzy logic algorithm to provide the corrections ∆T avg,ref .
This task was included in the block "set-point corrector" of Figure 4.
The main novelty in feedback control was the use of two manipulated inputs-Q a and SRT-to regulate the digester temperature.The fastest input Q a quickly reacted to any T avg temperature deviation, and progressively gave way to the participation of the slowest input SRT.In this way, Q a recovered its steady state Q a,ref to meet steady-state control strategies.SRT deviated from its bias point whenever any disturbance persisted.The dynamic collaboration between the two inputs was tailored by a proper design of controllers C Qa and C SRT based on a robust methodology in Rico-Azagra et al. [24] in the framework of quantitative feedback theory (QFT) with the following main characteristics summarized.Appendix A provides details on the design of the controllers from a more technical point of view for robust control practitioners.The dual-control design first required dynamic modeling of the process.Thus, dynamical models were identified from the two manipulated inputs (SRT, Q a ) to the output (T avg ), and from the disturbance inputs (T air , T sludge ) to the output (T avg ).Several operating points were considered, as summarized in Table 2.This yielded dynamical models with known parameter uncertainty (see Appendix A).A thorough study of the dynamic properties of the process models helped to allocate the frequency band between the two manipulated inputs: Q a was planned to work at higher frequencies than SRT to achieve a better transient performance.The frequency of 20 rad/s was the frontier between input contributions.The control specifications were guaranteed for the whole set of models.Hence, the terminology of robust control is used.For robust stability, a phase margin of 45 • was selected.As performance specifications, it was decided that sharp variations in T air and T sludge up to ±5 • C between two consecutive batches should not deviate T avg more than ±0.6 • C from its set-point T avg,ref .Furthermore, this set-point should be recovered at no longer than seven days.Thus, the robust controllers were designed based on the process models and the control specifications (see Appendix A).The controllers were: where the variable z is introduced by the Z-transform, which is a method for the design of sampled-data control systems [30].Here, the sample-time equaled the batch time (i.e., 1 day).In Figure 4, each sample was distinguished by the index n.The "zoh" block performed a zero-order-hold of the computed control actuations during the 1-day treatment.The "mean-value-function" computed T avg each day as the mean value of 1440 records of instantaneous temperature T i .A T i sample was taken every minute (t s1 = 1 min).Additionally, the sampler of the output to update the control law was labelled t s2 = 1 d.A step-change in the Q a set-point would deviate T avg from its set-point, which would be properly corrected by Equations ( 3) and ( 4) in a similar way, as T avg deviations due to step-changes in T air and T sludge were compensated.However, that step-change in Q a set-point was driven straight away to the actuation Q a at the step time.A pre-filter (F Qa in Figure 4) could conveniently smooth the peak at the beginning of the transient response of Q a .In our case, a suitable pre-filter was: To point out the benefits of using two control inputs, MISO (Multiple Input Single Output) control strategies in Table 1 were compared with SISO (Single Input Single Output) control, which uses a single control input.In this last case, only the aeration flow (Q a ) could provide the T avg regulation capacity required by the control specifications for robust disturbance rejection.Accordingly, the designed controller was: In the SISO strategy, SRT takes a fixed value (i.e., this input does not participate in the closed-loop dynamic regulation).Equation ( 6) provided the expected closed-loop control specifications for any SRT value in Table 2.An even simpler control method would manually fix both the Q a and SRT; thus, they would not participate in the dynamic T avg regulation.We denote this mode as OL (open-loop).

Results and Discussion
This section shows several time-domain simulations that were run on the AT_BSM inside the control scheme of Figure 4.
Figure 5 shows the time evolution of the main variables in a first experiment.X s,in remained constant at 30 kg/m 3 , and sudden changes of ∆T sludge = −3 • C and ∆T air = −5 • C took place at t = 50 d and t = 70 d, respectively.Maximum deviations of T avg (0.39 • C and 0.27 • C) were below the maximum permitted of 0.6 • C for a 5 • C disturbance step, and the settling-time to recover the 55 • C set-point was around seven days as expected.In the first moments after any disturbance, Q a quickly assumed the regulation task, and progressively SRT became more relevant.The steady state of those manipulated inputs was reached before 20 days as prescribed.In steady-state, the SRT necessarily reached different equilibria to compensate the disturbances.However, Q a always recovered the set-point Q a,ref .In this way, Q a,ref was conveniently selected based on the desired strategy: minimum aeration cost (MISO COST) for t < 90 d, or maximum production rate (MISO PROD) for t > 90 d.Focusing on the Q a,ref change that took place at t = 90 d, it could check the expected performance in the T avg set-point recovery and the smooth transition of manipulated inputs SRT and Q a .To point out the benefits of using two control inputs, MISO (Multiple Input Single Output) control strategies in Table 1 were compared with SISO (Single Input Single Output) control, which uses a single control input.In this last case, only the aeration flow (Qa) could provide the Tavg regulation capacity required by the control specifications for robust disturbance rejection.Accordingly, the designed controller was: In the SISO strategy, SRT takes a fixed value (i.e., this input does not participate in the closed-loop dynamic regulation).Equation ( 6) provided the expected closed-loop control specifications for any SRT value in Table 2.An even simpler control method would manually fix both the Qa and SRT; thus, they would not participate in the dynamic Tavg regulation.We denote this mode as OL (open-loop).

Results and Discussion
This section shows several time-domain simulations that were run on the AT_BSM inside the control scheme of Figure 4.
Figure 5 shows the time evolution of the main variables in a first experiment.Xs,in remained constant at 30 kg/m 3 , and sudden changes of ΔTsludge = −3 °C and ΔTair = −5 °C took place at t = 50 d and t = 70 d, respectively.Maximum deviations of Tavg (0.39 °C and 0.27 °C) were below the maximum permitted of 0.6 °C for a 5 °C disturbance step, and the settling-time to recover the 55 °C set-point was around seven days as expected.In the first moments after any disturbance, Qa quickly assumed the regulation task, and progressively SRT became more relevant.The steady state of those manipulated inputs was reached before 20 days as prescribed.In steady-state, the SRT necessarily reached different equilibria to compensate the disturbances.However, Qa always recovered the set-point Qa,ref.In this way, Qa,ref was conveniently selected based on the desired strategy: minimum aeration cost (MISO COST) for t < 90 d, or maximum production rate (MISO PROD) for t > 90 d.Focusing on the Qa,ref change that took place at t = 90 d, it could check the expected performance in the Tavg set-point recovery and the smooth transition of manipulated inputs SRT and Qa.A second experiment considered variability in Xs,in, Tair, and Tsludge (see Figure 6a).Figure 6b depicts the evolution of the main variables involved in a MISO COST feedback control strategy.The digester temperature Tavg was conveniently regulated to 55 ± 0.2 °C thanks to a fast actuation Qa (around Qa,ref of minimum cost), which compensated the fastest disturbance dynamics, and to a slow actuation SRT, which mainly compensated the midterm variability of air and sludge temperatures.A second experiment considered variability in X s,in , T air , and T sludge (see Figure 6a).Figure 6b depicts the evolution of the main variables involved in a MISO COST feedback control strategy.The digester temperature T avg was conveniently regulated to 55 ± 0.2 • C thanks to a fast actuation Q a (around Q a,ref of minimum cost), which compensated the fastest disturbance dynamics, and to a slow actuation SRT, which mainly compensated the midterm variability of air and sludge temperatures.On the other hand, Figure 7a depicts the evolution of the digester temperature T avg for manual control, where Q a = 18,750 m 3 /d and SRT = 12.5 d.The absence of feedback information impeded a suitable regulation of the temperature, which deviated from the desired value due to the variability of input conditions (Figure 6a). Figure 7b shows the variables for a SISO feedback control strategy where SRT = 12.5 d.The digester temperature T avg was conveniently regulated to 55 ± 0. On the other hand, Figure 7a depicts the evolution of the digester temperature Tavg for manual control, where Qa = 18,750 m 3 /d and SRT = 12.5 d.The absence of feedback information impeded a suitable regulation of the temperature, which deviated from the desired value due to the variability of input conditions (Figure 6a).Finally, considering Xs,in, Tair, and Tsludge in Figure 6a, the AT_BSM simulations were separately performed for the comparison of several control strategies.The following evaluation indexes were computed using the data for the same period of 100 d (N = 100 batches).
(i) Pasteurization USEPA Index − IQP USEPA (%) quantifies the quality of pasteurization as per USEPA guidelines [4,8]:  On the other hand, Figure 7a depicts the evolution of the digester temperature Tavg for manual control, where Qa = 18,750 m 3 /d and SRT = 12.5 d.The absence of feedback information impeded a suitable regulation of the temperature, which deviated from the desired value due to the variability of input conditions (Figure 6a).Finally, considering Xs,in, Tair, and Tsludge in Figure 6a, the AT_BSM simulations were separately performed for the comparison of several control strategies.The following evaluation indexes were computed using the data for the same period of 100 d (N = 100 batches).
(i) Pasteurization USEPA Index − IQP USEPA (%) quantifies the quality of pasteurization as per USEPA guidelines [4,8]:  Finally, considering X s,in , T air , and T sludge in Figure 6a, the AT_BSM simulations were separately performed for the comparison of several control strategies.The following evaluation indexes were computed using the data for the same period of 100 d (N = 100 batches).
Water 2017, 9, 426 9 of 15 (i) Pasteurization USEPA Index-emphI QPUSEPA (%) quantifies the quality of pasteurization as per USEPA guidelines [4,8]: 100, where where t s1 = 6.94 × 10 −4 d is the sampling time of intra-batch T i -temperature records, N i = 1440 is the number of T i -samples in a batch, and D (i) (Equation ( 2)) is the minimum time required at T i -temperature.An I QPUSEPA index value equal to 100% meant strict agreement with the regulation.I QPUSEPA greater than 100% was safer, but revealed worthless expenses.(ii) Pasteurization EU Index-I QPEU (%) computed the percentage of treated-sludge that met the EU recommendation (55 • C for at least 20 h) [9]: 100, where k where PTime (j) (h) represents the total time in which the sludge has been at a temperature greater than 55 • C during the aerated reaction phase of the j-th batch.One hundred percent corresponds to the maximum I QPEU value that was attainable.I QPEU values smaller than 100% indicated that some batch violated the EU regulation.(iii) Cost Index-I C (%) considers the aeration and pumping energies employed per unit of treated sludge volume.The index is normalized as a percentage of an average energy requirement (E ref = 12 kWh/m 3 sludge) extracted from USEPA [8]: 100, where where E Qa is the aeration energy; E pump is the pumping energy; and t batch is the batch-time (1 day).(iv) Production Index − I P (%) is expressed as a ratio between the treated sludge flow and the maximum flow that could be treated: I P is a reliable index only if the ATAD is properly operated (i.e., the pasteurization index should also reach suitable values).For example, an over-flow event in the pre-holding tank or the desire of maximizing the production rate would involve the digester being operated at full-capacity, giving a maximum I P .However, part of the raw sludge could not be properly treated.
The strategies compared are summarized in Table 3.The desired digester temperature was chosen to meet the minimum level of pasteurization required by the regulation.Thus, either 55 • C or 56.8 • C were chosen to meet the USEPA or EU criteria, respectively.Accordingly, the feedback control strategies adapted their T avg,ref .The OL strategy lacked feedback control loops.It used fixed Q a and SRT, which were estimated off-line.First, a mean SRT = 12.5 d was adopted.Then, Q a = 18,750 Water 2017, 9, 426 10 of 15 m 3 /d was estimated to achieve T avg = 55 • C, considering a theoretical behavior (mean temperatures T air = T sludge = 15 • C and ideal constant composition of the influent, with X s,in = 30 kg/m 3 ).Another Q a = 21,500 m 3 /d was similarly estimated to achieve T avg = 56.8• C. The SISO strategy used a feedback control structure, which regulated T avg to T avg,ref by moving Q a as the feedback controller (Equation ( 6)) dictates; SRT was manually fixed to 12.5 d.All MISO strategies used the same control structure (Figure 4) and control elements (Equations ( 3)-( 5)).MISO COST and MISO PROD set-points are detailed in Table 1.A standard MISO strategy (MISO STD) selected Q a,ref values in between those of MISO COST and MISO PROD strategies and avoided extreme behaviors since the minimization of aeration costs involves minimum production rates, and the maximization of production rates involves maximum aeration costs.The evaluation indexes are presented in Table 4. Since the set-point temperature was chosen to strictly meet either the USEPA or EU regulations, the yielded quality indexes fully agreed with it.They revealed how a less-detailed criterion (EU regulation) led to safer quality levels, but involved higher cost indexes.For the following comparisons, let us take as the meaningful quality index I QPUSEPA for T avg,ref = 55 • C and I QPEU for T avg,ref = 56.8• C. Comparing the OL and SISO strategies, both yielded the same I P since both used the same SRT.A smaller expense I C for OL involved insufficient aeration, which was in consonance with a poorer quality index.Therefore, closed-loop control was compulsory for continuous supervision and correction of the digester temperature in such a way that the required quality was achieved, and the SISO and MISO control strategies proved this.The added value of MISO vs. SISO strategies is the possibility of attending to a second objective in MISO control.Thus, the MISO COST strategy reduced the aeration expenses (smaller I C ) in comparison with the SISO control to achieve a similar quality.In the same way, the MISO PROD strategy improved the production-rate in comparison with the SISO control (see their I P ). Figure 3 pointed out the trade-off between minimizing the aeration-cost and maximizing the production-rate.Consequently, a smaller I P in the MISO COST than in the SISO was the price paid for a smaller I C in the former.A larger I C in the MISO PROD than in the SISO was the price paid for a larger I P in the former.Nevertheless, the flexibility of the MISO control ensures that the plant operator has full control of those objectives thanks to a closed-loop that can regulate them.As evidence of this, the MISO STD yielded similar indexes to the SISO control.

Conclusions
This paper has shown a novel feedback control structure for ATAD reactors, which takes advantage of the use of air-flow and the solid-retention-time to regulate the digester temperature to a desired set-point.The air-flow supplies a fast reaction against temperature deviations, meanwhile the solid-retention-time dominates the steady-state temperature regulation.Two feedback controllers compute these actuations.This dual control also affords the regulation of the air-flow (the fastest input) to a desired set-point, thanks to which different strategies can be attempted for the same pair of controllers.Obviously, the air-flow set-point has a direct influence on the aeration cost, which can therefore be conveniently handled.Furthermore, the air-flow set-point indirectly conditions the solid-retention-time to achieve the digester temperature.Thus, the air-flow set-point confers a great flexibility to obtain a maximum production-rate, or to conveniently adapt the production-rate to upstream or downstream plant operations.The digester temperature has been regulated to the minimum value that assures USEPA (or EU) recommendations for pasteurization.Similarly, the temperature set-point could be raised, promoting larger stabilization levels, but higher aeration-costs.
Dual-input control strategies were compared with a single-input (aeration) control strategy and a manually controlled reaction.Certain indexes showed the benefits of the novel structure.These indexes evaluated the pasteurization quality (as per USEPA and EU recommendations), the operation cost (aeration, sludge feeding, and sludge withdrawal), and the production-rate.
The feedback controllers were designed in the frequency domain based on the principles of quantitative feedback theory (QFT).The robust controllers assured the temperature regulation based on prescribed closed-loop performance and stability, despite variations of air and sludge temperatures and variations of the raw sludge organic content.
A benchmark simulation model for ATAD technology was used for the preliminary studies, the identification of simple models for control design, the validation experiments, the computation of the evaluation indexes, and for the comparison of control strategies.Thanks to the contribution of the fast input (Q a ), the steady state was reached more quickly at the output (T avg ) than at the slowest input (SRT).A maximum period of 20 days was chosen for SRT to reach its steady-state.Thus, ω = 0.2 rad/d was chosen as the switching frequency for each branch participation.
The following frequency response model, W d (s = jω), expresses an upper limit for the desired frequency response T avg when input step disturbances appear at T air or T sludge .
As stated in Section 2.2, T avg (t) must not deviate more than ±0.6 • C from its set-point T avg,ref (t) whenever step changes of ±5 • C take place at T air (t) or T sludge (t).Additionally, the set-point must be recovered no longer than seven days after the disturbance occurs (a temperature deviation inside a band of ±0.05 • C around the set-point was assumed as recovered equilibrium).This dynamic performance was relatively ambitious for the sampling time t s2 = 1 d.Thus, the controllers were designed in the discrete domain using the z-transform [30], which makes the most of the available frequency band ω = [0, π/ts2] rad/d.Note that the sampling time t s2 was in consonance with the discrete nature of the reactor operation: manipulated inputs Q a and SRT held during a 1-day batch, and then a mean temperature T avg was computed for the batch.Consequently, the equivalent of continuous plants (Equations (A1)-(A4)) into discrete plants yielded P zoh Qa (z), P zoh SRT (z), P zoh Tair (z), P zoh Tsludge (z).To achieve robust controllers, the required performance was an upper limit that must be observed by the whole set of plants [31].This was formulated as: T avg (z) The controllers were designed via loop-shaping in the frequency domain to achieve the robust specifications (Equations (A6)-(A9)) with the participation of two control branches (Equation (A10)).Figure A2 shows how the shaping of the open-loop functions meet the bounds that represent the robust control specifications.A thorough description of the general methodology can be found in Rico-Azagra et al. [24].The yielded controllers are Equations ( 3) and (4).Figure A3 proves the fulfilment of the robust control specifications (Equations (A6)-(A9)) and Figure A4 shows the frequency band allocation between branches (Equation (A10)).The controllers were designed via loop-shaping in the frequency domain to achieve the robust specifications (Equations (A6)-(A9)) with the participation of two control branches (Equation (A10)).Figure A2 shows how the shaping of the open-loop functions meet the bounds that represent the robust control specifications.A thorough description of the general methodology can be found in Rico-Azagra et al. [24].The yielded controllers are Equations ( 3) and (4).Figure A3 proves the fulfilment of the robust control specifications (Equations (A6)-(A9)) and Figure A4 shows the frequency band allocation between branches (Equation (A10)).

Figure 3 .
Figure 3. Aeration cost ratio vs. production-rate for several temperatures and Xs,in = 20 kg/m 3 .

Figure 3 .
Figure 3. Aeration cost ratio vs. production-rate for several temperatures and X s,in = 20 kg/m 3 .

2 •
C thanks to the single actuation of Q a .The absence of a second controller to handle SRT impeded the achievement of a second goal by means of an extra set-point.Water 2017, 9, 426 8 of 15

Figure 6 .Figure 7 .
Figure 6.Validation experiment: (a) disturbance inputs; and (b) control variables and controlled variable for MISO COST strategy.

Figure 6 .
Figure 6.Validation experiment: (a) disturbance inputs; and (b) control variables and controlled variable for MISO COST strategy.

Figure 6 .Figure 7 .
Figure 6.Validation experiment: (a) disturbance inputs; and (b) control variables and controlled variable for MISO COST strategy.
margin of 45° was stated for robust stability despite uncorrelated variations of Equations (A6)-(A9)) must be met for all discrete-equivalent plants and over the frequencies ω = [0, π] rad/d.Furthermore, the desired frequency band allocation was

Table 1 .
Control strategies.MISO: multiple input single output.

Table 1 .
Control strategies.MISO: multiple input single output.

Table 2 .
Set of equilibrium points.T air = T sludge = 15 • C.
Note: X s,in was considered above 30 kg/m 3 during the experiments.

Table 3 .
Strategies for comparisons.

Table 4 .
Evaluation of strategies.In brackets the indexes are expressed as a percentage of the OL indexes.