Skip to main content

2017 | OriginalPaper | Buchkapitel

Fractional Order Back Stepping Sliding Mode Control for Blood Glucose Regulation in Type I Diabetes Patients

verfasst von : Hamid Heydarinejad, Hadi Delavari

Erschienen in: Theory and Applications of Non-integer Order Systems

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper a fractional order backstepping sliding mode controller is proposed for Blood Glucose regulation using Bergman minimal model. A feedback control law is designed based on backstepping algorithm and a fractional order sliding surface is introduced. The backstepping algorithm makes the controller immune to matched and mismatched uncertainties and the fractional order sliding mode control provides robustness. Simulation results show that the proposed fractional order backstepping sliding mode controller are able to reject both matched and mismatched uncertainties and disturbance with a chattering free control law and the simulation results of the proposed controller are compared with the Backstepping sliding mode controller.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Bergman, R.N., Philips, L.S., Cobelli, C.: Physiologic evaluation of factors controlling glucose tolerance in man. J. Clin. Investig. 68(6), 1456–1467 (1981)CrossRef Bergman, R.N., Philips, L.S., Cobelli, C.: Physiologic evaluation of factors controlling glucose tolerance in man. J. Clin. Investig. 68(6), 1456–1467 (1981)CrossRef
2.
Zurück zum Zitat Marchetti, G., Barolo, M., Jovanovic, L., Zisser, H., Seborg, D.E.: An improved PID switching control strategy for type 1 diabetes. IEEE Trans. BioMed. Eng. 55(3), 857–865 (2008)CrossRef Marchetti, G., Barolo, M., Jovanovic, L., Zisser, H., Seborg, D.E.: An improved PID switching control strategy for type 1 diabetes. IEEE Trans. BioMed. Eng. 55(3), 857–865 (2008)CrossRef
3.
Zurück zum Zitat Parker, R.S., Doyle, F.J., Peppas, N.A.: A model-based algorithm for blood glucose control in type I diabetic patients. IEEE Trans. BioMed. Eng. 46(2), 148–157 (1999)CrossRef Parker, R.S., Doyle, F.J., Peppas, N.A.: A model-based algorithm for blood glucose control in type I diabetic patients. IEEE Trans. BioMed. Eng. 46(2), 148–157 (1999)CrossRef
4.
Zurück zum Zitat Wai Ting, C., Quek, C.: A novel blood glucose regulation using TSK-FCMAC: a fuzzy CMAC based on the zero-ordered TSK fuzzy Inference scheme. IEEE Trans. Neural Netw. 20(5), 856–871 (2009) Wai Ting, C., Quek, C.: A novel blood glucose regulation using TSK-FCMAC: a fuzzy CMAC based on the zero-ordered TSK fuzzy Inference scheme. IEEE Trans. Neural Netw. 20(5), 856–871 (2009)
5.
Zurück zum Zitat Grant, P.: A new approach to diabetic control: fuzzy logic and insulin pump technology. Med. Eng. Phys. 29(7), 824–827 (2007)CrossRef Grant, P.: A new approach to diabetic control: fuzzy logic and insulin pump technology. Med. Eng. Phys. 29(7), 824–827 (2007)CrossRef
6.
Zurück zum Zitat Allam, F., Nossair, Z., Gomma, H., Ibrahim, I., Abdelsalam, M.: Evaluation of using a recurrent neural network (RNN) and a fuzzy logic controller (FLC) in closed loop system to regulate blood glucose for type-1 diabetic patients. Int. J. Intell. Syst. Appl. 4(10), 58–71 (2012) Allam, F., Nossair, Z., Gomma, H., Ibrahim, I., Abdelsalam, M.: Evaluation of using a recurrent neural network (RNN) and a fuzzy logic controller (FLC) in closed loop system to regulate blood glucose for type-1 diabetic patients. Int. J. Intell. Syst. Appl. 4(10), 58–71 (2012)
7.
Zurück zum Zitat Kaveh, P., Shtessel, Y.B.: Blood glucose regulation using higher-order sliding mode control. Int. J. Robust Nonlinear Control 25(18), 557–569 (2008)MathSciNetCrossRefMATH Kaveh, P., Shtessel, Y.B.: Blood glucose regulation using higher-order sliding mode control. Int. J. Robust Nonlinear Control 25(18), 557–569 (2008)MathSciNetCrossRefMATH
8.
Zurück zum Zitat Hernandez, A.G.G., Fridman, L., Levant, A., Shtessel, Y.B., Leder, R., Monsalve, C.R., Andrade, S.I.: High-order sliding-mode control for blood glucose: practical relative. Control Eng. Pract. 21(5), 747–758 (2013)CrossRef Hernandez, A.G.G., Fridman, L., Levant, A., Shtessel, Y.B., Leder, R., Monsalve, C.R., Andrade, S.I.: High-order sliding-mode control for blood glucose: practical relative. Control Eng. Pract. 21(5), 747–758 (2013)CrossRef
9.
Zurück zum Zitat Tadrisi Parsa, N., Vali, A.R., Ghasemi, R.: Back stepping sliding mode control of blood glucose for type I diabetes. Int. J. Med. Health Biomed. Pharm. Eng. 8(11), 749–753 (2014) Tadrisi Parsa, N., Vali, A.R., Ghasemi, R.: Back stepping sliding mode control of blood glucose for type I diabetes. Int. J. Med. Health Biomed. Pharm. Eng. 8(11), 749–753 (2014)
10.
Zurück zum Zitat Ali, S., Padhi, R.: Optimal blood glucose regulation of diabetic patients using single network adaptive critics. Optim. Control Appl. Methods 32(2), 196–214 (2009)MathSciNetCrossRefMATH Ali, S., Padhi, R.: Optimal blood glucose regulation of diabetic patients using single network adaptive critics. Optim. Control Appl. Methods 32(2), 196–214 (2009)MathSciNetCrossRefMATH
11.
Zurück zum Zitat N’Doye, I., Voos, H., Darouach, M., Schneider, J.G.: Static output feedback H\(\infty \) control for a fractional-order glucose-insulin system. Int. J. Control Autom. 13(4), 798–807 (2015)CrossRef N’Doye, I., Voos, H., Darouach, M., Schneider, J.G.: Static output feedback H\(\infty \) control for a fractional-order glucose-insulin system. Int. J. Control Autom. 13(4), 798–807 (2015)CrossRef
12.
Zurück zum Zitat Leon-Vargasa, F., Garellib, F., De Battistab, H., Vehia, J.: Postprandial blood glucose control using a hybrid adaptive PD controller with insulin-on-board limitation. Biomed. Signal Process. Control 8(6), 724–732 (2013)CrossRef Leon-Vargasa, F., Garellib, F., De Battistab, H., Vehia, J.: Postprandial blood glucose control using a hybrid adaptive PD controller with insulin-on-board limitation. Biomed. Signal Process. Control 8(6), 724–732 (2013)CrossRef
13.
Zurück zum Zitat Ghorbani, M., Bogdan, P.: Reducing risk of closed loop control of blood glucose in artificial pancreas using fractional calculus. In: 36th Annual International Conference of the Engineering in Medicine and Biology Society, pp. 4839–4842 (2014) Ghorbani, M., Bogdan, P.: Reducing risk of closed loop control of blood glucose in artificial pancreas using fractional calculus. In: 36th Annual International Conference of the Engineering in Medicine and Biology Society, pp. 4839–4842 (2014)
14.
Zurück zum Zitat Goharimanesh, M., Lashkaripour, A., Abouei Mehrizi, A.: Fractional order PID controller for diabetes patients. J. Comput. Appl. Mech. 46(1), 69–76 (2015) Goharimanesh, M., Lashkaripour, A., Abouei Mehrizi, A.: Fractional order PID controller for diabetes patients. J. Comput. Appl. Mech. 46(1), 69–76 (2015)
15.
Zurück zum Zitat Adhikary, N., Mahanta, C.: Integral backstepping sliding mode control for underactuated systems: swing-up and stabilization of the cart-pendulum system. ISA Trans. 51(6), 870–880 (2013)CrossRef Adhikary, N., Mahanta, C.: Integral backstepping sliding mode control for underactuated systems: swing-up and stabilization of the cart-pendulum system. ISA Trans. 51(6), 870–880 (2013)CrossRef
16.
Zurück zum Zitat Tenreiro Machado, J., Kiryakova, V., Mainardi, F.: Recent history of fractional calculus. Commun. Nonlinear Sci. Numer. Simulat. 16(3), 1140–1153 (2011) Tenreiro Machado, J., Kiryakova, V., Mainardi, F.: Recent history of fractional calculus. Commun. Nonlinear Sci. Numer. Simulat. 16(3), 1140–1153 (2011)
17.
Zurück zum Zitat Monje, C.A., Chen, Y., Vinagre, B.M., Xue, D., Feliu-Batlle, V.: Fractional-Order Systems and Controls. Springer, London (2010)CrossRefMATH Monje, C.A., Chen, Y., Vinagre, B.M., Xue, D., Feliu-Batlle, V.: Fractional-Order Systems and Controls. Springer, London (2010)CrossRefMATH
18.
Zurück zum Zitat Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego, California (1999)MATH Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego, California (1999)MATH
19.
Zurück zum Zitat Li, Y., Chen, Y.Q., Podlubny, I.: Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Comput. Math. Application. 59(5), 1810–1821 (2010)MathSciNetCrossRefMATH Li, Y., Chen, Y.Q., Podlubny, I.: Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Comput. Math. Application. 59(5), 1810–1821 (2010)MathSciNetCrossRefMATH
20.
Zurück zum Zitat Li, Y., Chen, Y.Q., Podlubny, I.: Mittag-Leffler stability of fractional order nonlinear dynamic systems. Automatica 45(8), 1965–1969 (2009)MathSciNetCrossRefMATH Li, Y., Chen, Y.Q., Podlubny, I.: Mittag-Leffler stability of fractional order nonlinear dynamic systems. Automatica 45(8), 1965–1969 (2009)MathSciNetCrossRefMATH
21.
Zurück zum Zitat Li, C., Deng, W.: Remarks on fractional derivatives. Appl. Math. Comput. 187(2), 777–784 (2007)MathSciNetMATH Li, C., Deng, W.: Remarks on fractional derivatives. Appl. Math. Comput. 187(2), 777–784 (2007)MathSciNetMATH
22.
Zurück zum Zitat Aguila-Camacho, N., Duarte-Mermoud, M.A., Gallegos, J.A.: Lyapunov functions for fractional order systems. Commun. Nonlinear Sci. Numer. Simul. 19(9), 2951–2957 (2014)MathSciNetCrossRef Aguila-Camacho, N., Duarte-Mermoud, M.A., Gallegos, J.A.: Lyapunov functions for fractional order systems. Commun. Nonlinear Sci. Numer. Simul. 19(9), 2951–2957 (2014)MathSciNetCrossRef
23.
Zurück zum Zitat Palumbo, P., Ditlevsen, S., Bertuzzi, A., De Gaetano, A.: Mathematical modeling of the glucose-insulin system: a review. J. Math. Biosci. 244(2), 69–81 (2013)MathSciNetCrossRefMATH Palumbo, P., Ditlevsen, S., Bertuzzi, A., De Gaetano, A.: Mathematical modeling of the glucose-insulin system: a review. J. Math. Biosci. 244(2), 69–81 (2013)MathSciNetCrossRefMATH
24.
Zurück zum Zitat Balakrishnan, N.P., Rangaiah, G.P., Samavedham, L.: Review and analysis of blood glucose (BG) models for type 1 diabetic patients. Ind. Eng. Chem. Res. 50(21), 12041–12066 (2011)CrossRef Balakrishnan, N.P., Rangaiah, G.P., Samavedham, L.: Review and analysis of blood glucose (BG) models for type 1 diabetic patients. Ind. Eng. Chem. Res. 50(21), 12041–12066 (2011)CrossRef
25.
Zurück zum Zitat Fisher, M.E.: A semi closed-loop algorithm for the control of blood glucose levels in diabetics. IEEE Trans. BioMed. Eng. 38(1), 57–61 (1991)CrossRef Fisher, M.E.: A semi closed-loop algorithm for the control of blood glucose levels in diabetics. IEEE Trans. BioMed. Eng. 38(1), 57–61 (1991)CrossRef
26.
Zurück zum Zitat N’Doye, I., Voos, H., Darouach, M., Schneider, J.G., Knauf, N.: Static output feedback stabilization of nonlinear fractional-order glucose-insulin system. In: IEEE EMBS 19th International Conference on Biomedical Engineering and Sciences, pp. 589–594 (2012) N’Doye, I., Voos, H., Darouach, M., Schneider, J.G., Knauf, N.: Static output feedback stabilization of nonlinear fractional-order glucose-insulin system. In: IEEE EMBS 19th International Conference on Biomedical Engineering and Sciences, pp. 589–594 (2012)
27.
28.
Zurück zum Zitat Komurcugil, H.: Adaptive terminal sliding-mode control strategy for DC-DC buck converters. ISA Trans. 51(6), 673–681 (2012)CrossRef Komurcugil, H.: Adaptive terminal sliding-mode control strategy for DC-DC buck converters. ISA Trans. 51(6), 673–681 (2012)CrossRef
29.
Zurück zum Zitat Liang, C., Li, Y.: Attitude analysis and robust adaptive backstepping sliding mode control of spacecrafts orbiting irregular asteroids. Math. Probl. Eng. 15–30 (2014) Liang, C., Li, Y.: Attitude analysis and robust adaptive backstepping sliding mode control of spacecrafts orbiting irregular asteroids. Math. Probl. Eng. 15–30 (2014)
30.
Zurück zum Zitat Delavari, H., Lanusse, P., Sabatier, J.: Fractional order controller design for a flexible manipulator robot. Asian J. Control. 15(3), 783–795 (2013)MathSciNetCrossRefMATH Delavari, H., Lanusse, P., Sabatier, J.: Fractional order controller design for a flexible manipulator robot. Asian J. Control. 15(3), 783–795 (2013)MathSciNetCrossRefMATH
31.
Zurück zum Zitat Yin, C., Dadras, S., Zhong, S.M., Chen, Y.Q.: Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach. Appl. Math. Model. 37(4), 2469–2483 (2013)MathSciNetCrossRef Yin, C., Dadras, S., Zhong, S.M., Chen, Y.Q.: Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach. Appl. Math. Model. 37(4), 2469–2483 (2013)MathSciNetCrossRef
32.
Zurück zum Zitat Trigeassou, J.C., Maamri, N., Sabatier, J., Oustaloup, A.: A Lyapunov approach to the stability of fractional differential equations. Signal Process. 91(3), 437–445 (2011)CrossRefMATH Trigeassou, J.C., Maamri, N., Sabatier, J., Oustaloup, A.: A Lyapunov approach to the stability of fractional differential equations. Signal Process. 91(3), 437–445 (2011)CrossRefMATH
33.
Zurück zum Zitat Weia, Y., Chena, Y., Lianga, S., Wanga, Y.: A novel algorithm on adaptive backstepping control of fractional order systems. Neurocomputing 165, 395–402 (2015)CrossRef Weia, Y., Chena, Y., Lianga, S., Wanga, Y.: A novel algorithm on adaptive backstepping control of fractional order systems. Neurocomputing 165, 395–402 (2015)CrossRef
34.
Zurück zum Zitat Wang, Z.: Synchronization of an uncertain fractional-order chaotic system via backstepping sliding mode control. Discrete Dyn. Nat. Soc. (2013) Wang, Z.: Synchronization of an uncertain fractional-order chaotic system via backstepping sliding mode control. Discrete Dyn. Nat. Soc. (2013)
35.
Zurück zum Zitat Delavari, H.: A novel fractional adaptive active sliding mode controller for synchronization of non-identical chaotic systems with disturbance and uncertainty. Int. J. Dyn. Control. 67, 2433–2439 (2011)MathSciNet Delavari, H.: A novel fractional adaptive active sliding mode controller for synchronization of non-identical chaotic systems with disturbance and uncertainty. Int. J. Dyn. Control. 67, 2433–2439 (2011)MathSciNet
36.
Zurück zum Zitat Delavari, H., Ranjbar, A.N., Ghaderi, R., Momani, S.: Fractional order control of a coupled tank. Nonlinear Dyn. 61(3), 383–397 (2010)MathSciNetCrossRefMATH Delavari, H., Ranjbar, A.N., Ghaderi, R., Momani, S.: Fractional order control of a coupled tank. Nonlinear Dyn. 61(3), 383–397 (2010)MathSciNetCrossRefMATH
Metadaten
Titel
Fractional Order Back Stepping Sliding Mode Control for Blood Glucose Regulation in Type I Diabetes Patients
verfasst von
Hamid Heydarinejad
Hadi Delavari
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-45474-0_18

Neuer Inhalt