Adaptive Fuzzy Feedforward-Feedback Controller Applied to Level Control in an Experimental Prototype

12th 12th IFAC IFAC Symposium Symposium on on Dynamics Dynamics and and Control Control of of Process including Biosystems 12th IFACSystems, Symposium on Dynamics and Controlonline of Available at www.sciencedirect.com Process Systems, including Biosystems 12th IFACSystems, Symposium on Dynamics Control of Florianópolis - SC,including Brazil, April 23-26,and 2019 Process Biosystems Florianópolis SC, Brazil, April 23-26, 2019 Process Systems, including Biosystems Florianópolis - SC, Brazil, April 23-26, 2019 Florianópolis - SC, Brazil, April 23-26, 2019

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IFAC PapersOnLine 52-1 (2019) 219–224

Adaptive Fuzzy Feedforward-Feedback Adaptive Adaptive Fuzzy Fuzzy Feedforward-Feedback Feedforward-Feedback Controller Applied to Level Control in an Adaptive Fuzzy Feedforward-Feedback Controller Applied Controller Applied to to Level Level Control Control in in an an Experimental Prototype Controller Applied to Level Control in an Experimental Prototype Experimental Prototype Experimental Prototype

Felipe Felipe Matheus Matheus Mota Mota Sousa Sousa Felipe Matheus MotaAmarante Sousa Vit´ o ria Matos Barbosa Vit´ o ria Matos Barbosa Amarante Felipe Matheus Mota Sousa Vit´ oria Matos Barbosa Fonseca* Amarante Rodolpho Rodrigues Rodolpho Rodrigues Fonseca* Vit´ o ria Matos Barbosa Amarante Rodolpho Rodrigues Fonseca* Rodolpho Rodrigues Fonseca* Federal University a o a Federal University of of Sergipe, Sergipe, S˜ S˜ ao o Crist´ Crist´ ov˜ v˜ ao, o, SE, SE, Brazil Brazil (*e-mail: (*e-mail: Federal University of Sergipe, S˜ a o Crist´ o v˜ a o, SE, Brazil (*e-mail: [email protected]) [email protected]) Federal University of Sergipe, S˜ a o Crist´ o v˜ a o, SE, Brazil (*e-mail: [email protected]) [email protected]) Abstract: Loads Loads are are one one of of the the most most common common disturbances disturbances sources sources experienced experienced in in chemical chemical Abstract: Abstract: Loads are one of theof common disturbances sources experienced chemical processes, causing causing deterioration ofmost control performance and even even affecting productinquality. quality. If processes, deterioration control performance and affecting product If Abstract: Loads are one of implementing theofmost common disturbances sources experienced inquality. chemical processes, causing deterioration control performance and even affecting product If such inputs are measurable, a feedforward controller can improve significantly such inputscausing are measurable, implementing a feedforward controller can improve significantly processes, deterioration of control performance even variable affecting product quality. If such inputs performance, are measurable, implementing a feedforward controller can improve significantly the control control performance, reducing the deviation deviation of the theand process (PV). Nevertheless the reducing the of process variable (PV). Nevertheless such inputs are measurable, implementing a feedforward controller can improve significantly the control performance, reducing the deviation of the process variable (PV). Nevertheless its effectiveness effectiveness is is highly highly dependent dependent on on satisfactory satisfactory identification identification of of process process and and disturbance disturbance its the control reducing the of identification the process when variable Nevertheless its effectiveness dependent on deviation satisfactory of process and disturbance models, taskperformance, thatisis ishighly time consuming consuming and quite difficult difficult especially they(PV). are non-linear. To models, task that time and quite especially when they are non-linear. To its effectiveness isishighly dependent ondeploy satisfactory identification of capable process and disturbance models, task that time consuming and quite difficult especially when they are non-linear. To cope with such situation, it is usual to of adaptive techniques of handling noncope with such situation, it is usual to deploy of adaptive techniques capable of non-linear. handling nonmodels, task that is time consuming and quite For difficult especially when they are To cope with such situation, it is usual to deploy of adaptive techniques capable of handling nonlinearity and enhance the control control performance. such matter, matter, it was was implemented an adaptive adaptive linearity and enhance the performance. For such it implemented an cope with such situation, it is usual to deploy of adaptive techniques capable of handling nonlinearity and enhance the control performance. For such matter, it was implemented an adaptive fuzzy strategy strategy able able to to correlate correlate process process and and disturbance disturbance parameters parameters according according to to PV PV value value in in aa fuzzy linearity and enhance the control performance. Foransuch matter, it prototype. wasaccording implemented anvalue adaptive fuzzy strategy able tolevel correlate process and disturbance parameters to fuzzy PV in a feedforward-feedback level control loop applied applied to experimental The fuzzy strategy feedforward-feedback control loop to an experimental prototype. The strategy fuzzy strategy ablethe to correlate process and disturbance parameters according to fuzzy PV value in a feedforward-feedback control loop applied to an experimental prototype. strategy was used used to adapt adapt lead-lag compensator parameters and it required required fewerThe experiments than was to thelevel lead-lag compensator parameters and it fewer experiments than feedforward-feedback level control loop applied to an experimental prototype. The fuzzy strategy was used to adapt to theadjust lead-lag and it required fewer experiments than others techniques to adjust thecompensator parameters, parameters showing aa considerable considerable performance improvement. others techniques the parameters, showing performance improvement. was to adapt to the lead-lag compensator parameters and it required fewer experiments than others techniques adjust the parameters, showing a considerable performance improvement. The used performances of classical feedback (FB) and and feedforward-feedback (FFFB) control strategies The performances of classical feedback (FB) feedforward-feedback (FFFB) control strategies others techniques to adjust the parameters, showing a considerable performance improvement. The classical feedback (FB) and feedforward-feedback (FFFB) control strategies wereperformances compared to toofthe the proposed adaptive fuzzy feedforward-feedback (A4FB) control loop were compared proposed adaptive fuzzy feedforward-feedback (A4FB) control loop The performances ofthe classical feedback (FB) and feedforward-feedback (FFFB) control strategies were compared to proposed adaptive fuzzy feedforward-feedback (A4FB) control loop under different servo and regulatory control situations. It was showed that A4FB increased under different servo regulatory controlfuzzy situations. It was showed (A4FB) that A4FB increased were compared to theand proposed adaptive feedforward-feedback control loop under different servo and control situations. Itloops was evaluated showed that increased the disturbance disturbance rejection inregulatory comparison to others others control loops evaluated and,A4FB combined with the rejection in comparison to control and, combined with under different servo and regulatory control situations. It was showed that A4FB increased the disturbance rejection in comparison to others control loops evaluated and, combined with its relatively simple implementation, it is an advantageous control loop for practical purposes. its relatively simple implementation, it istoanothers advantageous control loop for and, practical purposes. the disturbance rejection in comparison control loops evaluated combined with its relatively simple implementation, it is an advantageous control loop for practical purposes. its relatively implementation, is an advantageous control loop for practical purposes. © 2019, IFAC simple (International Federation ofitAutomatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Adaptive Adaptive control; control; Feedforward Feedforward compensation; compensation; Fuzzy; Fuzzy; Level Level control; control; Non-linear Non-linear Keywords: Keywords: Adaptive control; Feedforward compensation; Fuzzy; Level control; Non-linear process control. control. process Keywords: Adaptive control; Feedforward compensation; Fuzzy; Level control; Non-linear process control. process control. 1. INTRODUCTION INTRODUCTION 1. 1. INTRODUCTION 1. INTRODUCTION The most usual control strategy is is feedback feedback (FB) (FB) using using The most usual control strategy The most usual control strategy is feedback (FB) using the classical classical control algorithm PID. Some advantages advantages of the control algorithm PID. Some of The most usual control strategy isrelative feedback (FB) using the classical control algorithm PID. Some advantages of using these controllers include: a fast corrective usingclassical these controllers include: PID. a relative fast corrective the control algorithm Some fast advantages of using controllers include: a relative corrective action,these regardless of the the source of of disturbance, simplicity action, regardless of source disturbance, simplicity using these controllers include: a relative fast corrective action, regardless of the source of disturbance, simplicity and versatility. versatility. However, However, this this control control strategy strategy may may not not and action, regardless of the in source of disturbance, simplicity and versatility. However, this control strategy may not be satisfactory satisfactory by itself processes that need corrective corrective be by itself in processes that need and versatility. However, control strategy may not be satisfactory itself in this processes that need corrective actions before aaby deviation in the the controlled variable, an actions before deviation in controlled variable, an be satisfactory by itself in processes that need corrective actions before a deviation in the controlled variable, an anticipative control action. In these cases, the addition of anticipative control action. In cases, thevariable, addition an of actions before a deviation in these the significantly controlled anticipative control action. In these cases, the addition of feedforward (FF) increases the perforperforfeedforward control (FF) increases significantly the anticipative control action. In these cases, of feedforward (FF) increases significantly the performance of of the thecontrol controller according to Seborgthe et addition al. (2004). (2004). mance controller according to Seborg et al. feedforward control (FF) increases significantly the performance of the controller according to Seborg et al. (2004). mance of the controller according to Seborg et al. (2004). Fig. 1. 1. Block Block diagram diagram of of aa feedforward-feedback feedforward-feedback control control The basic basic idea idea of of the the FF FF control control is is predicting predicting deviations deviations Fig. The Fig. scheme. 1. Block diagram of a feedforward-feedback control scheme. The basic idea disturbances of the FF control is predictingtheir deviations of measurable measurable disturbances and compensate compensate their effects Fig. scheme. 1. Block diagram of a feedforward-feedback control of and effects The basic ideaoutput. of the FF control is predicting deviations of measurable disturbances and compensate their effects in the process In Fig. 1 the feedforward-feedback scheme. Such as described described by by Porru Porru et et al. al. (2014), (2014), one one of of the the in the process output. In Fig. 1 the feedforward-feedback of measurable disturbances and compensate their effects Such as in the process In Fig. 1 the feedforward-feedback (FFFB) schemeoutput. is showed. showed. Such as described by Porru et al. (2014), one of the most effective ways to control a process subject to load (FFFB) scheme is effective ways by to control a process subject in the process In Fig. 1 the feedforward-feedback most to Such as described Porru et al. FF (2014), one control, of load the (FFFB) schemeoutput. is showed. most effective ways to control a process subject to load disturbances is the combination of and FB disturbances isways the combination of FF and FB control, (FFFB) scheme is showed. most effective to control a process subject to load disturbances is the combination of FF and FB control, due to to FF FF accomplish accomplish most most of of the the disturbance disturbance rejection rejection -There are are four four structures structures of of feedforward feedforward compensator compensator due disturbances is the model combination FF andFB FB control,There due toon FFaa accomplish mostof ofprocess theofdisturbance rejection based on reversed of process -, and regulates There are four structures of feedforward compensator (G (s)), namely: static, static with delay, lead-lag and based reversed model -, and FB regulates f f (s)), namely: static, static with delay, lead-lag and due to FF accomplish most of the disturbance rejection (G f f based on a reversed model ofthe process -, and FBofregulates There are four structures of feedforward the process process by compensating compensating the modeling error the (Gf f (s)), namely: static, static withtransfer delay, compensator lead-lag and lead-lag with delay. The feedforward function for the by modeling error ofregulates the FF. FF. based on a reversed model of process -, and FB lead-lag with delay. The feedforward transfer function for process by compensating the modeling error of the FF. namely: static inwith delay, lead-lag (G f f (s)),with lead-lag delay.static, The feedforward transfer functionand for the is However, forbynon-linear non-linear systems, when there there areofsetpoint setpoint the processfor compensating the modeling error the FF. lead-lag compensator compensator is showed showed in 1. 1. systems, when are lead-lag with delay. The feedforward lead-lag compensator is showed in 1. transfer function for However, However, for non-linear systems, when there are setpoint (SP) changes in the process, it is common that process (SP) changes in the process, it is common that process lead-lag compensator is showed in 1. However, for non-linear systems, when there that are setpoint (SP) changes in the process, it is common process G (s) = G (s)/G (s) = (K /K )(τ s + 1)/(τ s + 1) (1) behavior changes significantly and therefore, resulting in f f d p d p p d changes significantly resulting in Gf f (s) = Gd (s)/Gp (s) = (Kd /Kp )(τp s + 1)/(τd s + 1) (1) behavior changes in the process, itand is therefore, common that process Gf f (s) = Gd (s)/Gp (s) = (Kd /Kp )(τp s + 1)/(τd s + 1) (1) (SP) behavior changes significantly and therefore, resulting in Gf f (s) = = (Kd /KFederation 1)/(τ (1) Hosting behavior changes significantly and therefore, resulting in d (s)/G p (s) p )(τp s + of d s + 1) 2405-8963 ©G 2019, IFAC (International Automatic Control) by Elsevier Ltd. All rights reserved.

Copyright © 2019 IFAC 219 Copyright 2019 responsibility IFAC 219Control. Peer review©under of International Federation of Automatic Copyright © 2019 IFAC 219 10.1016/j.ifacol.2019.06.065 Copyright © 2019 IFAC 219

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model parameters modification. As a consequence, the control performance is affected, requiring retuning of the controller to each change, situation that demands time and effort. In these cases, a further improvement is needed because the controllers with fixed gains are not robust enough. For such matters, fuzzy logic can be used to adjust the parameters due to SP changes using error, e(t), or the error change rate, de/dt, as fuzzy inputs for instance. Dettori et al. (2018) tested an adaptive fuzzy strategy to overcome process non-linearities adapting the PID control parameters. The results demonstrated that this control strategy was advantageous, allowing an optimally tuned PID on steam turbine control. The fuzzy inputs are related to the outputs by fuzzy rules defined by the fuzzy structure, which characterize the control objectives and the control strategy used. Schaum et al. (2017) showed an application for the use of a FFFB adaptive control strategy for processes with SP changes, in this case, changes on the biomass concentration in microalgae growth process. It was concluded that the controller effectively yields resilience of initial errors and perturbations, which was desired. Fuzzy logic is widely used on chemical and biochemical systems to deal with non-linearities due to its inherent non-linearity, such as described by Ou et al. (2015). Another example of the application of artificial intelligence in processes with non-linearities is the Lee et al. (1999) work, in which was applied a fuzzy-PID controller for fed-batch fermentation processes. In this case, an adaptive control mechanism was used, since the specific growth rate and substrate concentration vary over time of fermentation. The Fig. 2 shows a set of equidistant triangular membership functions that allows non-linearity characteristics for fuzzy systems. The labels of the mathematical sets L, M and H mean, respectively, low, medium and high. Each membership function indicated in Fig. 2 represents one mathematical set used for fuzzy inference of the input in a fuzzy system, and based on the defined fuzzy set of rules, a non-linear output can be obtained as indicated by Fileti et al. (2007).

According to Lu and Tran (2003), trends in the changes of the gain and time constants of the process and disturbance models can be estimated through experiments and previous knowledge, data that is also required to fuzzy control design. Thus, fuzzy systems could be used to adapt controller parameters considering process nonlinearity, improving the control performance. Considering what was discussed, this paper has as object of study the application of an adaptive fuzzy feedforwardfeedback control strategy (A4FB) to overcome nonlinearities on level control in an experimental prototype. In attempt to prove its effectiveness, classical feedback and feedforward-feedback control strategies were also tested on the prototype to compare the results. For analysis, the control performance was considered using the criteria integral squared error (ISE), integral of absolute error (IAE), control effort (ISU) and the feedforward performance index IF F/F B proposed by Guzm´an et al. (2015). 2. MATERIALS AND METHODS In this paper, it was used a prototype equipped with two water tanks, two pumps, differential pressure sensor, a Pulse Width Modulation (PWM) module and a microR UNO). Water level was decontroller board (Arduino fined as the process variable (PV) and was controlled by manipulating the inflow of the upper bomb, and the lower pump was configured to represent a leakage source in the prototype, a load disturbance on level control. An schematic figure of the level control prototype employed is shown in Fig. 3. All tests were performed using a command script on the R MatLab platform. For reasons of brevity, the script is not shown in the paper. Five step inputs in the manipulated variable (MV) were generated by changing the control signal (u), set as the voltage applied on PWM module, to determine the transfer function for process using the curve reaction method described at Seborg et al. (2004). The control signal was limited in the range of 1 to 5 V due to inactivity of the pump for values below 1 V. The curves were adjusted, R using the Curve Fitting function of the MatLab , for a First Order Process (FOP) model as represented in 2. As expected, the correlation between PV and the voltage applied to PWM board is non-linear, varying considerably in all operational range studied. Gp (s) = Kp (s)/(τp s + 1)

(2)

Thus, for the disturbance variable, three tests were performed, starting the leakage from three different steady states. The disturbance model identification is equal to that described for process models. A wide set of operational points was chosen so the Fuzzy system could be better designed and adjust the parameters more efficiently, once the membership functions were designed based on specialist knowledge acquired from this data.

Fig. 2. Fuzzy membership functions. 220

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system is summarized in Table 1. Table 1. Load disturbances induced on level prototype. disturbance 1 2 3 4

Status 1 0 1 0

Time (s) 450 750 1200 1500

The control performances of the strategies adopted were evaluated by indexes ISE, IAE, ISU and IFF/FB , indicated from 3 to 6.

ISE =

t

e(t)2 dt

(3)

IAE =

t

|e(t)|dt

(4)

t

∆u2 dt

(5)

0

0

ISU =

0

I FF/FB = 1 − IAE FF /IAE FB

Fig. 3. Level prototype. After determining the process and disturbance transfer functions, the PI controller was tuned for each operating condition using the Signal Constraint toolbox available in R MatLab . For the FB tests, the controller gain (Kc ) and the integral time (τI ) used were calculated by the average values obtained from all the tunings performed. To avoid a possible saturation, an anti-reset windup action with back calculation method was used. The tracking time constant τT value of 6 s was chosen based in experimental tests.

(6)

The calculation of the IFF/FB was taken as proposed by Guzm´an et al. (2015) as a comparative index between IAE of feedforward-feedback control loop and IAE of feedback control loop.

3. RESULTS AND DISCUSSION The reaction curves for the process and disturbance are shown in Fig. 4 and 5, respectively.

For FFFB, it was employed the average values calculated for the means of the gains (Kp , Kd ) and time constants (τp , τd ) of both process and disturbance models to determine the parameters of lead-lag controller. The procedure adopted to design the adaptive fuzzy feedforward controller was similar to that proposed by Fonseca et al. (2018). The trends of change in process and disturbance parameters observed in previous tests were adjusted and reproduced in fuzzy sets. The base rule was set with five rules for adjustment of Gp and three rules for Gd , once results shown significantly non-linear behavior of Gp parameters. For both, the instant PV value was used as input of Fuzzy sets. The tests were performed to evaluate FB, FFFB and A4FB control strategies under regulatory control. For the level regulatory control strategy, load changes (LC) created by the activation (1) and deactivation (0) of the lower pump were analyzed. The pattern of disturbances induced on the 221

Fig. 4. Reaction curves for h process. The final results for the controllers parameters are summarized in Table 2. Table 2. Parameters for the PI controller and FF compensator FEEDFORWARD Kf f (cm/V) 1.02 Tz (s) 229.50 Tp (s) 181.30

PI Kc (V/cm) τI (s) τB (s)

0.15 54.90 6.00

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performance in A4FB strategy, aspect resulting from the noise attenuation of fuzzy logic controllers described by Fonseca et al. (2013).

Fig. 5. Reaction curves for the disturbance. The fuzzy rules used are shown in the Table 3 while Fig. 6 shows the designed membership functions for the output variable of the fuzzy system in order to represent the variation of Gff (s) parameters along process operation. Table 3. Fuzzy rule base for parameters adaptation. IF h L M H IF h LL L M H HH

Fig. 7. Level (h) regulatory control using FB, FFFB and A4FB control loops. The ISE criterion was calculated and it is summarized in Table 4. As can be seen, the values of ISE for FFFB and A4FB are lower than that for FB, a reflex of their smaller deviation peaks, corresponding to reductions of 50.9% and 79.3%, respectively. Comparing the feedforward-feedback loops, it was observed a sensitive improvement on level regulatory control after using the fuzzy adaptive scheme, represented by the smaller deviation peak and a reduction on the settling time. Such aspect is due to the non-linearity of both system and disturbance, highly influenced by the fluid level, and the fact that fuzzy adaptation according to the measured PV allows a better adjustment of leadlag parameters for a specific operating point.

Disturbance THEN τd THEN Kd L H M M H L Process THEN τp THEN Kp L L LL LL H M M H HH HH

Table 4. ISE values for FB, FFFB and A4FB Control loop FB FFFB A4FB

Fig. 6. Membership functions for A4FB controller. The dynamic response of the controlled variable is shown in Fig. 7 and for all four load changes induced on the system, the feedback control loop presented higher deviation from the SP in comparison to the feedforward strategies. This behavior is resulting from its control algorithm that requires the existence of error on which the control action is calculated from. Differently from its counterpart, feedforward loop anticipates load deviation, calculating the control action based on the existence and magnitude of measurable disturbances, reducing their effects on process variable and the deviation as consequence. The oscillatory behavior of PV during the tests, observed mainly during LC 3 and LC 4, has two different influences, one caused by actuator dynamics and second by noisy level measurement. As observed in Fig. 7, the noisy level data employed as input for the fuzzy inference did not undermine the control 222

ISE (cm2 ·s) 705.9 346.8 146.5

After implementing lead-lag compensator, it was observed a sensitive reduction of the settling time on regulatory control, as can be seen in Fig. 8. The settling time is defined as the time required to reach and keep the PV within a band of ±5% of its setpoint, and it is noticed that both FB and A4FB needed approximately 170 s to achieve this control requirement. The unexpected fast response of FB is explained by the integral action (I) of PI controller. The tuning prioritized a more aggressive response in which the integral action was enhanced by the considerably small value of τI . The higher error at the beginning of LC 1 rapidly increased the integral control action, leading to the aspect mentioned previously. For a better comprehension of the benefits that come from implementing the adaptive fuzzy feedforward-feedback control, it was calculated the performance indexes IAE and IFF/FB values, summarized in Table 5. The results showed that classical lead-lag feedforward compensator with fixed parameters was able to reject part of the load disturbances, although this was far from ideal. Implementing an adaptive fuzzy feedforward-feedback control proved to be a good strategy enhancement, raising the disturbance rejection from 20.6% to 50.2%, a considerable improvement on PV regulatory control. This advantage was also

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not destabilize the control loop. This effect is better seen in the zoom approximation for LC 1 displayed in Fig. 10.

Fig. 8. Zoom approximation on process variable response. observed by Fonseca et al. (2018) that achieved higher load rejection using A4FB control against feedforwardfeedback control. In the same way, Fonseca et al. (2016) obtained almost 60% more load rejection using another fuzzy feedforward-feedback control in comparison to a classic feedback control. Allied to the fact that fuzzy sets only require knowledge about system dynamic behavior on a linguistic level, these outcomes suggest that fuzzy is an acceptable adaptive technique for correlating disturbance and process parameters even in non-linear systems, requiring fewer experiments and less effort on process control design. Table 5. Performance indexes values for FB, FFFB and A4FB. Control loop FB FFFB A4FB

IAE (cm·s) 621.8 493.6 309.4

Fig. 9. Control outputs for A4FB control loop.

Fig. 10. Zoom approximation on uff response during LC 1.

IFF/FB —– 0.206 0.502

The ISU criterion calculated for all three control loops is shown in Table 6. As noticed by the values, lead-lag implementation increased the control effort over an order of magnitude due to the sudden change in manipulated variable value at the moment of appearance of the load disturbances. It is also noticeable that the ISU value for A4FB increased 28.1% in comparison to that calculated for FFFB, consequence of the continuous variations of leadlag parameters throughout the experiment.

The dependency of process and manipulated variables is illustrated in Fig. 11 for the regulatory process using A4FB control loop. As can be seen, it was used a reverse-acting control and the MV immediately respond to deviations of setpoint value.

Table 6. Control effort values for FB, FFFB and A4FB. Control loop FB FFFB A4FB

Fig. 11. Manipulated variable for A4FB control loop.

ISU (V2 ·s) 0.043 0.899 1.152

4. CONCLUSION

The Fig. 9 displays the control outputs (CO) that composes the control action u for A4FB, corresponding to proportional and integral actions (P and I, respectively) in addition to feedforward signal (uff ). As stated before, uff is responsible for rapidly change the u value as soon as the disturbance is measured, as shown by the high slope of the curves at 450, 750, 1200 e 1500 s. As designed, during regulatory control, the uff value changed slightly as consequence of non-linearity of the process, being capable to incorporate the non-linear dynamic behavior on process control. It was also observed that these modifications did 223

This paper proposed the application of three different control strategies for level control in a prototype. Classical feedback and feedforward-feedback control strategies were compared to an adaptive fuzzy feedforward-feedback control in which the fuzzy system was used to adapt the FF compensator parameters along the operating range. The performance criteria used were ISE, IF F/F B and control effort, and allowed to concluded that the feedforwardfeedback controller performs better than the classic feedback because it considerably minimizes the effects of disturbance at the controlled variable due to its anticipative

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effect. The addition of the adaptive fuzzy strategy considerably improves the results, by considering non-linear characteristics when adjusting the parameters. These results are confirmed by the performance index IFF/FB , which was 2.44 times higher for A4FB comparing to FFFB. The easy implementation of adaptive fuzzy feedforwardfeedback control, combined to its noise attenuation, and the results obtained in this paper, it is possible to conclude that A4FB control is capable to improve process control performance and can be extended to industrial processes. ACKNOWLEDGEMENTS The authors appreciate the financial support provided by FAPITEC. REFERENCES Dettori, S., Iannino, V., Colla, V., and Signorini, A. (2018). An adaptive fuzzy logic-based approach to PID control of steam turbines in solar applications. Applied Energy, 227, 655–664. Fileti, A., Antunes, A., Silva, F., Silveira, V., and Pereira, J. (2007). Experimental investigations on fuzzy logic for process control. Control Engineering Practice, 15(9), 1149–1160. Fonseca, R.R., Franco, I.C., and da Silva, F.V. (2016). 15th IASTED International Conference. In Bioreactor temperature control using a generic fuzzy feedforward control system, 275–280. Campinas-Brazil. Fonseca, R.R., Schmitz, J.E., Fileti, A.M.F., and da Silva, F.V. (2013). A fuzzy–split range control system applied to a fermentation process. Bioresource Technology, 142, 475–482. Fonseca, R.R., Sencio, R.R., Franco, I.C., and Silva, F.V.D. (2018). An adaptive fuzzy feedforward-feedback control system applied to a saccharification process. Chemical Product and Process Modeling, 13(4). Guzm´ an, J., H¨ agglund, T., Veronesi, M., and Visioli, A. (2015). Performance indices for feedforward control. Journal of Process Control, 26, 26–34. Lee, J., Lee, S.Y., Park, S., and Middelberg, A.P. (1999). Control of fed-batch fermentations. Biotechnology Advances, 17(1), 29 – 48. Lu, X. and Tran, H.D. (2003). A fuzzy logic based adaptive feedforward pi controller for nanometer positioning. In Proc. ASPE 18th Annu. Meet., 1358–1361. Ou, K., Wang, Y.X., Li, Z.Z., Shen, Y.D., and Xuan, D.J. (2015). Feedforward fuzzy-pid control for air flow regulation of pem fuel cell system. 40, 11686–11695. Porru, M., Baratti, R., and Alvarez, J. (2014). Feedforward-feedback control of an industrial multicomponent distillation column. IFAC Proceedings Volumes, 47(3), 1266–1271. Schaum, A., Weisbarth, H., and Meurer, T. (2017). Robust adaptive feedforward output-feedback tracking control for microalgae cultures. IFAC-PapersOnLine, 50(1), 12667 – 12672. 20th IFAC World Congress. Seborg, D.E., Edgar, T.F., and Mellichamp, D.A. (2004). Process dynamics and control. Wiley, New York.

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APPENDIX A. LIST OF ACRONYMS AND SYMBOLS A4FB FB FF FFFB Gd Gff Gp IFF/FB IAE ISE ISU LC MV PV u

Adaptive Fuzzy Feedforward-Feedback Feedback control loop Feedforward control loop Feedforward-Feedback control loop Disturbance transfer function Feedforward compensator transfer function Process transfer function Feedforward control performance index Integral of absolute error Integral of squared error Control effort Load change Manipulated variable Process variable Control signal