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A real-time optimization control method for coagulation process during drinking water treatment

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Abstract

Coagulation process is a key link of drinking water treatment. For the large lag characteristic of coagulation process, conventional PID control could not achieve a satisfactory effect for the frequent changes of raw water quality. Thus, a composite control scheme based on random forest algorithm and second-order sliding mode controller is proposed in this paper. Within the proposed composite control scheme, RF model provides timely feedforward control for coagulant dosage according to the changing raw water quality, and SOSM controller adjusts the coagulant dosage to adapt the nonlinearity and uncertainty of coagulation process as a feedback controller. The combination of feedforward control and feedback control constitutes the real-time optimization control of coagulation process. The experimental results show that the proposed composite control scheme has better adaptability to the changes of raw water quality and higher control accuracy for stable effluent turbidity compared with the exponential reaching law sliding mode control and conventional PID control.

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References

  1. Peleato, N.M., Legge, R.L., Andrews, R.C.: Characterization of UF foulants and fouling mechanisms when applying low in-line coagulant pre-treatment. Water Res. 126, 1–11 (2017). https://doi.org/10.1016/j.watres.2017.08.064

    Article  Google Scholar 

  2. Salehin, S., Kulandaivelu, J., Rebosura, M., Jr., Khan, W., Wong, R., Jiang, G., Smith, P., McPhee, P., Howard, C., Sharma, K., Keller, J., Donose, B.C., Yuan, Z., Pikaar, I.: Opportunities for reducing coagulants usage in urban water management: The Oxley Creek Sewage Collection and Treatment System as an example. Water Res. (2019). https://doi.org/10.1016/j.watres.2019.114996

    Article  Google Scholar 

  3. Munoz-Vazquez, A.-J., Sanchez-Orta, A., Parra-Vega, V.: A novel PID control with fractional nonlinear integral. Nonlinear Dyn. 94(4), 3041–3052 (2018). https://doi.org/10.1007/s11071-018-4543-0

    Article  MATH  Google Scholar 

  4. Cao, L., Xiao, B., Golestani, M.: Robust fixed-time attitude stabilization control of flexible spacecraft with actuator uncertainty. Nonlinear Dyn. 100(3), 2505–2519 (2020). https://doi.org/10.1007/s11071-020-05596-5

    Article  Google Scholar 

  5. Cho, H., Kerschen, G., Oliveira, T.R.: Adaptive smooth control for nonlinear uncertain systems. Nonlinear Dyn. 99(4), 2819–2833 (2020). https://doi.org/10.1007/s11071-019-05446-z

    Article  MATH  Google Scholar 

  6. Hu, X., Song, Q., Ge, M., Li, R.: Fractional-order adaptive fault-tolerant control for a class of general nonlinear systems. Nonlinear Dyn. 101(1), 379–392 (2020). https://doi.org/10.1007/s11071-020-05768-3

    Article  Google Scholar 

  7. Ma, J., Park, J.H., Xu, S.: Global adaptive finite-time control for uncertain nonlinear systems with actuator faults and unknown control directions. Nonlinear Dyn. 97(4), 2533–2545 (2019). https://doi.org/10.1007/s11071-019-05146-8

    Article  MATH  Google Scholar 

  8. Zhang, J., Ding, F., Zhang, B., Jiang, C., Du, H., Li, B.: An effective projection-based nonlinear adaptive control strategy for heavy vehicle suspension with hysteretic leaf spring. Nonlinear Dyn. 100(1), 451–473 (2020). https://doi.org/10.1007/s11071-020-05527-4

    Article  Google Scholar 

  9. Zhao, R., Xie, W., Wong, P.K., Cabecinhas, D., Silvestre, C.: Adaptive vehicle posture and height synchronization control of active air suspension systems with multiple uncertainties. Nonlinear Dyn. 99(3), 2109–2127 (2020). https://doi.org/10.1007/s11071-019-05412-9

    Article  Google Scholar 

  10. Zhou, Y.S., Wang, Z.H.: Robust motion control of a two-wheeled inverted pendulum with an input delay based on optimal integral sliding mode manifold (vol 85, pg 2065, 2016). Nonlinear Dyn. 85(3), 2075–2075 (2016). https://doi.org/10.1007/s11071-016-2860-8

    Article  MathSciNet  Google Scholar 

  11. Mobayen, S., Tchier, F.: An LMI approach to adaptive robust tracker design for uncertain nonlinear systems with time-delays and input nonlinearities. Nonlinear Dyn. 85(3), 1965–1978 (2016). https://doi.org/10.1007/s11071-016-2809-y

    Article  MathSciNet  MATH  Google Scholar 

  12. Suryawanshi, P.V., Shendge, P.D., Phadke, S.B.: Robust sliding mode control for a class of nonlinear systems using inertial delay control. Nonlinear Dyn. 78(3), 1921–1932 (2014). https://doi.org/10.1007/s11071-014-1569-9

    Article  Google Scholar 

  13. Liu, H.T., Chen, G.J.: Robust trajectory tracking control of marine suRFce vessels with uncertain disturbances and input saturations. Nonlinear Dyn. 100(4), 3513–3528 (2020). https://doi.org/10.1007/s11071-020-05701-8

    Article  Google Scholar 

  14. Liu, Z.G., Xue, L.R., Sun, W., Sun, Z.Y.: Robust output feedback tracking control for a class of high-order time-delay nonlinear systems with input dead-zone and disturbances. Nonlinear Dyn. 97(2), 921–935 (2019). https://doi.org/10.1007/s11071-019-05018-1

    Article  MATH  Google Scholar 

  15. Zhang, S., Kong, L.H., Qi, S.W., Jing, P., He, W., Xu, B.: Adaptive neural control of unknown non-affine nonlinear systems with input deadzone and unknown disturbance. Nonlinear Dyn. 95(2), 1283–1299 (2019). https://doi.org/10.1007/s11071-018-4629-8

    Article  MATH  Google Scholar 

  16. Hu, X., Wei, X.J., Zhang, H.F., Han, J., Liu, X.H.: Global asymptotic regulation control for MIMO mechanical systems with unknown model parameters and disturbances. Nonlinear Dyn. 95(3), 2293–2305 (2019). https://doi.org/10.1007/s11071-018-4692-1

    Article  MATH  Google Scholar 

  17. Pai, M.C.: Dynamic output feedback RBF neural network sliding mode control for robust tracking and model following. Nonlinear Dyn. 79(2), 1023–1033 (2015). https://doi.org/10.1007/s11071-014-1720-7

    Article  MathSciNet  MATH  Google Scholar 

  18. Li, H.Y., Shi, P., Yao, D.Y., Wu, L.G.: Observer-based adaptive sliding mode control for nonlinear Markovian jump systems. Automatica 64, 133–142 (2016). https://doi.org/10.1016/j.automatica.2015.11.007

    Article  MathSciNet  MATH  Google Scholar 

  19. Ma, L., Wang, C.Q., Ding, S.H., Dong, L.L.: Integral sliding mode control for stochastic Markovian jump system with time-varying delay. Neurocomputing 179, 118–125 (2016). https://doi.org/10.1016/j.neucom.2015.11.071

    Article  Google Scholar 

  20. Mobayen, S.: Finite-time robust-tracking and model-following controller for uncertain dynamical systems. J. Vib. Control 22(4), 1117–1127 (2016). https://doi.org/10.1177/1077546314538991

    Article  MathSciNet  MATH  Google Scholar 

  21. Liu, J.X., Vazquez, S., Wu, L.G., Marquez, A., Gao, H.J., Franquelo, L.G.: Extended State Observer-Based Sliding-Mode Control for Three-Phase Power Converters. IEEE Trans. Industr. Electron. 64(1), 22–31 (2017). https://doi.org/10.1109/Tie.2016.2610400

    Article  Google Scholar 

  22. Wang, Y.Y., Xia, Y.Q., Li, H.Y., Zhou, P.F.: A new integral sliding mode design method for nonlinear stochastic systems. Automatica 90, 304–309 (2018). https://doi.org/10.1016/j.automatica.2017.11.029

    Article  MathSciNet  MATH  Google Scholar 

  23. Wang, Y.Y., Xia, Y.Q., Shen, H., Zhou, P.F.: SMC Design for Robust Stabilization of Nonlinear Markovian Jump Singular Systems. IEEE Trans. Autom. Control 63(1), 219–224 (2018). https://doi.org/10.1109/Tac.2017.2720970

    Article  MathSciNet  MATH  Google Scholar 

  24. Park, I.S., Kwon, N.K., Park, P.: Dynamic output-feedback control for singular Markovian jump systems with partly unknown transition rates. Nonlinear Dyn. 95(4), 3149–3160 (2019). https://doi.org/10.1007/s11071-018-04746-0

    Article  MATH  Google Scholar 

  25. Li, Z.J., Huang, Z.C., He, W., Su, C.Y.: Adaptive impedance control for an upper limb robotic exoskeleton using biological signals. IEEE Trans. Industr. Electron. 64(2), 1664–1674 (2017). https://doi.org/10.1109/Tie.2016.2538741

    Article  Google Scholar 

  26. Xu, B., Sun, F.C.: Composite intelligent learning control of strict-feedback systems with disturbance. IEEE T Cybern. 48(2), 730–741 (2018). https://doi.org/10.1109/Tcyb.2017.2655053

    Article  Google Scholar 

  27. Ning, X.L., Yang, Y.Q., Li, Z., Gui, M.Z., Fang, J.C.: Ephemeris corrections in celestial/pulsar navigation using time differential and ephemeris estimation. J. Guid. Control Dyn. 41(1), 268–275 (2018). https://doi.org/10.2514/1.G002711

    Article  Google Scholar 

  28. Li, Z.J., Su, C.Y., Li, G.L., Su, H.: Fuzzy approximation-based adaptive backstepping control of an exoskeleton for human upper Limbs. IEEE T Fuzzy Syst. 23(3), 555–566 (2015). https://doi.org/10.1109/Tfuzz.2014.2317511

    Article  Google Scholar 

  29. Li, Z.J., Su, C.Y., Wang, L.Y., Chen, Z.T., Chai, T.Y.: Nonlinear disturbance observer-based control design for a robotic exoskeleton incorporating fuzzy approximation. IEEE Trans. Industr. Electron. 62(9), 5763–5775 (2015). https://doi.org/10.1109/Tie.2015.2447498

    Article  Google Scholar 

  30. Hamdy, M., Ramadan, A., Abozalam, B.: A novel inverted fuzzy decoupling scheme for MIMO systems with disturbance: a case study of binary distillation column. J Intell. Manuf. 29(8), 1859–1871 (2018). https://doi.org/10.1007/s10845-016-1218-x

    Article  Google Scholar 

  31. Peng, K.X., Zhang, K., You, B., Dong, J., Wang, Z.D.: A quality-based nonlinear fault diagnosis framework focusing on industrial multimode batch processes. IEEE Trans. Industr. Electron. 63(4), 2615–2624 (2016). https://doi.org/10.1109/Tie.2016.2520906

    Article  Google Scholar 

  32. Peng, K.X., Zhang, K., Dong, J., You, B.: Quality-relevant fault detection and diagnosis for hot strip mill process with multi-specification and multi-batch measurements. J. Franklin I 352(3), 987–1006 (2015). https://doi.org/10.1016/j.jfranklin.2014.12.002

    Article  MATH  Google Scholar 

  33. Wang, H.S., Zhang, R.X., Chen, W.D., Liang, X.W., Pfeifer, R.: Shape detection algorithm for soft manipulator based on fiber bragg gratings. IEEE-Asme T Mech. 21(6), 2977–2982 (2016). https://doi.org/10.1109/Tmech.2016.2606491

    Article  Google Scholar 

  34. Wang, H.S., Wang, C., Chen, W.D., Liang, X.W., Liu, Y.T.: Three-dimensional dynamics for cable-driven soft manipulator. IEEE-Asme T Mech. 22(1), 18–28 (2017). https://doi.org/10.1109/Tmech.2016.2606547

    Article  Google Scholar 

  35. Ding, S., Li, S.: Second-order sliding mode controller design subject to mismatched term. Automatica 77, 388–392 (2017). https://doi.org/10.1016/j.automatica.2016.07.038

    Article  MathSciNet  MATH  Google Scholar 

  36. Ding, S., Li, S., Zheng, W.X.: Nonsmooth stabilization of a class of nonlinear cascaded systems. Automatica 48(10), 2597–2606 (2012). https://doi.org/10.1016/j.automatica.2012.06.060

    Article  MathSciNet  MATH  Google Scholar 

  37. Qian, C.J., Lin, W.: A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Trans. Autom. Control 46(7), 1061–1079 (2001). https://doi.org/10.1109/9.935058

    Article  MathSciNet  MATH  Google Scholar 

  38. Bhat, S.P., Bernstein, D.S.: Finite-time stability of continuous autonomous systems. Siam J. Control Optim. 38(3), 751–766 (2000). https://doi.org/10.1137/S0363012997321358

    Article  MathSciNet  MATH  Google Scholar 

  39. Zhang, J.F., Han, Z.Z., Zhu, F.B.: Finite-time control andL1-gain analysis for positive switched systems. Optim. Control Appl. Methods (2014). https://doi.org/10.1002/oca.2129

    Article  Google Scholar 

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (51708299), Science and Technology Project of Water Conservancy of Jiangsu Province (2020056), Major Science and Technology Program for Water Pollution Control and Treatment (2012ZX07403-001).

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Authors and Affiliations

  1. College of Automation and College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China

    Dongsheng Wang, Junfei Wu, Lianqing Deng, Zhixuan Li & Yan Wang

  2. Jiangsu Engineering Laboratory for Internet of Things and Intelligent Robots, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China

    Dongsheng Wang, Junfei Wu, Lianqing Deng, Zhixuan Li & Yan Wang

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  1. Dongsheng Wang
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Correspondence to Dongsheng Wang.

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Wang, D., Wu, J., Deng, L. et al. A real-time optimization control method for coagulation process during drinking water treatment. Nonlinear Dyn 105, 3271–3283 (2021). https://doi.org/10.1007/s11071-021-06794-5

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