Different types of nonlinear sliding mode technique for nonlinear uncertain type 1 diabetes model

Document Type : Research Paper

Authors

Department of Electrical Engineering, Qom University, Qom, Iran

Abstract

In this paper, the robust controller is designed based on different types of sliding mode techniques for the nonlinear model of Bergman insulin-glucose regulation of type 1 diabetes. It is assumed that the nonlinear model includes unknown uncertainties. The convergence of patient person states to the healthy guy ones is the main purpose of the presented designing procedures. The stability of the closed-loop system, the robustness of suggested schemes, and the convergence of tracking error to zero in finite time are the main advantages of the suggested method. The reduction of chattering phenomena is guaranteed in this approach. The proposed methods depict the promising performance of the derived controllers in the injected rate of insulin in diabetes diseases. The simulation results illustrate the promising performance of the planned policy. Also, the sliding mode techniques are compared with the others to show the best-proposed design.

Keywords

[1] A. Abu-Rmileh, W. Garcia-Gabin, and D. Zambrano, Internal model sliding mode control approach for glucose regulation in type 1 diabetes, Biomed. Signal Process. Control 5 (2010), no. 2, 94–102.
[2] E. Ackerman, L.C. Gatewood, J.W. Rosevear and G.D. Molnar, Model studies of blood-glucose regulation, Bull. Math. Biophys. 27 (1965), no. 1, 21–37.
[3] S. Ahmad, N. Ahmed, M. Ilyas and W. Khan, Super twisting sliding mode control algorithm for developing artificial pancreas in type 1 diabetes patients, Biomed. Signal Process. Control. 38 (2017), 200–211.
[4] R.N. Bergman, Y.Z. Ider, C.R. Bowden and C. Cobelli, Quantitative estimation of insulin sensitivity, Amer. J. Physio.-Endocr. Metabol. 236 (1979), no. 6.
[5] V.W. Bolie, Coefficients of normal blood glucose regulation, J. Appl. Physiol. 16 (1961), no. 5, 783–788.
[6] C. Cobelli and A. Mari, Validation of mathematical models of complex endocrine-metabolic systems: a case study on a model of glucose regulation, Medic. Bio. Engin. Comput. 21 (1983), no. 4, 390-–399.
[7] C. Dalla Man, R.A. Rizza and C. Cobelli, Meal simulation model of the glucose-insulin system, IEEE Trans. Biomed. Engin. 54 (2007), no. 10, 1740–1749.
[8] M. Djouima, A. Taher Azar, S. Drid and D. Mehdi, Higher order sliding mode control for blood glucose regulation of type 1 diabetic patients, Int. J. Syst. Dyn. Appl. 7 (2018), no. 1, 65–84.
[9] L. DiMeglio, C. Molina and R. Oram, Type 1 diabetes, Lancet 391 (2018), 2449–2462
[10] W. Garcia-Gabin, J. Veh´ı, J. Bondia, C. Tar´ın and R. Calm, Robust sliding mode closed-loop glucose control with meal compensation in type 1 diabetes mellitus, IFAC Proc. 41 (2008), no. 2, 4240–4245.
[11] R. Hovorka, V. Canonico, L.J. Chassin, U. Haueter, M. Massi-Benedetti, M.O. Federici, T.R. Pieber, H.C. Schaller, L. Schaupp, T. Vering and M.E. Wilinska, Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes, Physiol. Measurement 25 (2004), no. 4, 905.
[12] J. Jaremko and O. Rorstad, Advances toward the implantable artificial pancreas for treatment of diabetes, Diabetes Care 21 (1998), no. 3, 444–450.
[13] E.D. Lehmann, T. Deutsch, A physiological model of glucose–insulin interaction in type 1 diabetes mellitus, J. Biomed. Engin. 14 (1992), no. 3, 235-–242.
[14] P. Kaveh and Y. Shtessel, Blood glucose regulation using higher-order sliding mode control, J. Robust Nonlinear Control. 18 (2008), no. 4-5, 557–569.
[15] C. Li and R. Hu, PID control based on BP neural network for the regulation of blood glucose level in diabetes, Proc. 7th IEEE Int. Conf. Bioinf. Bioengin., 2007, pp. 1168–1172.
[16] G. Marchetti, M. Barolo, L. Jovanovic, H. Zisser and D. Seborg, An improved PID switching control strategy for
type 1 diabetes, IEEE Trans. Biomed. Eng. 55 (2008), no. 3, 857–865.
[17] D.N. Maryam Abadi, A. Alfi and M. Siahi, An improved fuzzy PI controller for type 1 diabetes”, R. J. Appl. Sci. Engin. Technol. 4 (2012), no. 2, 4417–4422.
[18] H. Roman, V. Canonico, L. Chassin, U. Haueter, M. Massi-Benedetti, M. Orsini Federici, T.R. Pieber, H.C. Schaller, L. Schaupp, T. Vering and M.E. Wilinska, Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes, Physiol. Measurement 25 (2004), no. 4.
[19] E. Ruiz-Velazquez, R. Femat and D. Campos-Delgado, Blood glucose control for type 1 diabetes mellitus: A robust tracking H∞ problem, Control Engin. Practice 12 (2004), no. 9, 1179–1195.
[20] J.T. Sorensen, A physiologic model of glucose metabolism in man and its useto design and assess improved insulin therapies for diabetes, Doctoral Dissertation, Massachusetts Institute of Technology, 1985.
[21] N.P. Tadrisi, A.R. Vali and R. Ghasemi, Back stepping sliding mode control of blood glucose for type I diabetes, Int. J. Medic. Health Biomed. Bioengin. Pharm. Engin. 8 (2014), no. 11, 779–783.
[22] B. Topp, K. Promislow and G. De Vries, A model of β-cell mass, insulin and glucose kinetics: Pathways to diabetes, J. Theor. Bio. 206 (2000), no. 4, 605–619.
[23] K. van Heusden, E. Dassau, H.C. Zisser, D.E. Seborg and F.J. Doyle III, Control-relevant models for glucose control using a priori patient characteristics, IEEE Trans. Biomed. Eng. 9 (2012), no. 7, 1839–1849.
[24] S. Yasini, M.B. Naghibi-Sistani and A. Karimpour, Active insulin infusion using fuzzy-based closed loop control, 3rd Int. Conf. Intel. Syst. Knowledge Engin., Mashhad, 2008, pp. 429–434.
[25] J. Wang, Ch. Liu, Y. Wang and G. Zheng, Fixed time integral sliding mode controller and its application to the suppression of chaotic oscillation in power system, Chinese Phys. B 27 (2018), no. 7.
Volume 14, Issue 9
September 2023
Pages 115-126
  • Receive Date: 15 November 2022
  • Accept Date: 12 December 2022