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Optimal novel super-twisting PID sliding mode control of a MEMS gyroscope based on multi-objective bat algorithm

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Abstract

This paper proposes a novel super-twisting PID sliding mode controller (STPIDSMC) using a multi-objective optimization bat algorithm (MOBA-STPIDSMC) for the control of a MEMS gyroscope. In order to enhance the robustness of the control system, a sliding surface based on PID controller is designed. The chattering phenomenon in PID sliding mode control (PIDSMC) which is usually caused by the excitation of fast unmodelled dynamic is the main problem. The chattering phenomenon will be removed by using super-twisting control. A metaheuristic method, the multi-objective bat algorithm (MOBA) is applied for optimal design of the MEMS gyroscope in order to tune the parameter of the proposed controller. The performance of the MOBA-STPIDSMC is compared with four other controllers such as sliding mode control (SMC), PIDSMC, STPIDSMC and a single objective bat algorithm super-twisting PID sliding mode controller (BA-STPIDSMC). Numerical simulations clearly confirmed the effectiveness of the proposed controller.

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References

  • Almutairi NB, Zribi Mohamed (2009) Sliding mode control of a three-dimensional overhead crane. J Vib Control 15(11):1679–1730

    Article  MathSciNet  MATH  Google Scholar 

  • Alonso JB, Henríquez A, Henríquez P, Rodríguez-Herrera B, Bolaños F, Alpízar P, Cabrera J (2015) Advance in the bat acoustic identification systems based on the audible spectrum using nonlinear dynamics characterization. Expert Syst Appl 42(24):9528–9538

    Article  Google Scholar 

  • Bettayeb M, Djennoune S (2016) Design of sliding mode controllers for nonlinear fractional-order systems via diffusive representation. Nonlinear Dyn 84(2):593–605

    Article  MathSciNet  MATH  Google Scholar 

  • Coello CC, Lechuga MS (2002) MOPSO a proposal for multiple objective particle swarm optimization. In: IEEE Proceedings of the 2002 congress on evolutionary computation, 2002. CEC’02, vol 2, pp 1051–1056

  • Coello CAC, Pulido GT, Lechuga MS (2015) Handling multiple objectives with particle swarm optimization. IEEE Trans Evol Comput 8(3):256–279

    Article  Google Scholar 

  • Eker I (2006) Sliding mode control with PID sliding surface and experimental application to an electromechanical plant. ISA Trans 45(1):109–118

    Article  Google Scholar 

  • Elmokadem T, Zribi M, Youcef-Toumi K (2016) Trajectory tracking sliding mode control of underactuated AUVs. Nonlinear Dyn 84(2):1079–1091

    Article  MathSciNet  MATH  Google Scholar 

  • Fei J, Ding H (2012) Adaptive sliding mode control of dynamic system using RBF neural network. Nonlinear Dyn 70(2):1563–1573

    Article  MathSciNet  Google Scholar 

  • Fei J, Lu C (2017) Adaptive sliding mode control of dynamic systems using double loop recurrent neural network structure. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2017.2672998

  • Fei J, Xin M (2012) An adaptive fuzzy sliding mode controller for MEMS triaxial gyroscope with angular velocity estimation. Nonlinear Dyn 70(1):97–109

    Article  MathSciNet  Google Scholar 

  • Fei J, Zhou J (2012) Robust adaptive control of MEMS triaxial gyroscope using fuzzy compensator. IEEE Trans Syst Man Cybern Part B (Cybernetics) 42(6):1599–1607

    Article  Google Scholar 

  • Gautam R, Patil AT (2015) Modeling and control of joint angles of a biped robot leg using PID controllers. In: 2015 IEEE international conference on engineering and technology (ICETECH), pp 1–5

  • Guzmán E, Moreno JA (2015) Super-twisting observer for second-order systems with time-varying coefficient. IET Control Theory Appl 9(4):553–562

    Article  MathSciNet  Google Scholar 

  • Jaddi NS, Abdullah S, Hamdan AR (2015) Multi-population cooperative bat algorithm-based optimization of artificial neural network model. Inf Sci 294:628–644

    Article  MathSciNet  Google Scholar 

  • Jha AK, Inman DJ (2004) Sliding mode control of a gossamer structure using smart materials. J Vib Control 10(8):1199–1220

    MATH  Google Scholar 

  • Karagiannis D, Radisavljevic-Gajic V (2016) Sliding mode boundary control for vibration suppression in a pinned-pinned Euler–Bernoulli beam with disturbances. J Vib Control. https://doi.org/10.1177/1077546316658578

  • Knowles J, Corne D (2003) Properties of an adaptive archiving algorithm for storing nondominated vectors. IEEE Trans Evol Comput 7(2):100–116

    Article  Google Scholar 

  • Ko C-N, Wu C-J (2008) A PSO-tuning method for design of fuzzy PID controllers. J Vib Control 14(3):375–395

    Article  MATH  Google Scholar 

  • Kuntanapreeda S (2015) Super-twisting sliding-mode traction control of vehicles with tractive force observer. Control Eng Pract 38:26–36

    Article  Google Scholar 

  • Li Y, Xu Q (2010) Adaptive sliding mode control with perturbation estimation and PID sliding surface for motion tracking of a piezo-driven micromanipulator. IEEE Trans Control Syst Technol 18(4):798–810

    Article  Google Scholar 

  • Moghanni-Bavil-Olyaei MR, Ghanbari A (2014) Design of an adaptive fuzzy sliding mode control using supervisory fuzzy control for micro-electro-mechanical systems (MEMS) z-axis gyroscope. J Low Freq Noise Vib Act Control 33(2):163–187

    Article  Google Scholar 

  • Moreno JA, Osorio M (2012) Strict Lyapunov functions for the super-twisting algorithm. IEEE Trans Autom Control 57(4):1035–1040

    Article  MathSciNet  MATH  Google Scholar 

  • Pati A, Singh S, Negi R (2014) Sliding mode controller design using PID sliding surface for half car suspension system. In: 2014 students conference on engineering and systems (SCES), pp 1–6

  • Premkumar K, Manikandan BV (2016) Bat algorithm optimized fuzzy PD based speed controller for brushless direct current motor. Eng Sci Technol Int J 19(2):818–840

    Article  Google Scholar 

  • Rahmani M (2017) MEMS gyroscope control using a novel compound robust control. ISA Trans. https://doi.org/10.1016/j.isatra.2017.11.009i

    Google Scholar 

  • Rahmani M, Ghanbari A, Ettefagh MM (2016a) Robust adaptive control of a bio-inspired robot manipulator using bat algorithm. Expert Syst Appl 56:164–176

    Article  Google Scholar 

  • Rahmani M, Ghanbari A, Ettefagh MM (2016b) Hybrid neural network fraction integral terminal sliding mode control of an Inchworm robot manipulator. Mech Syst Signal Process 80:117–136

    Article  Google Scholar 

  • Rahmani M, Ghanbari A, Ettefagh MM (2016c) A novel adaptive neural network integral sliding-mode control of a biped robot using bat algorithm. J Vib Control. https://doi.org/10.1177/1077546316676734

  • Rodrigues D, Pereira LA, Nakamura RY, Costa KA, Yang XS, Souza AN, Papa JP (2014) A wrapper approach for feature selection based on bat algorithm and optimum-path forest. Expert Syst Appl 41(5):2250–2258

    Article  Google Scholar 

  • Serhan H, Henaff P, Nasr C, Ouezdou F (2008) Dynamic control strategy of a biped inspired from human walking. In: 2008 2nd IEEE RAS & EMBS international conference on biomedical robotics and biomechatronics, pp 342–347

  • Vázquez C, Collado J, Fridman L (2014) Super twisting control of a parametrically excited overhead crane. J Frankl Inst 351(4):2283–2298

    Article  MathSciNet  MATH  Google Scholar 

  • Vinagre BM, Monje CA, Calderón AJ, Suárez JI (2007) Fractional PID controllers for industry application. A brief introduction. J Vib Control 13(9–10):1419–1429

    Article  MATH  Google Scholar 

  • Xiao L, Zhu Y (2015) Sliding-mode output feedback control for active suspension with nonlinear actuator dynamics. J Vib Control 21(14):2721–2738

    Article  MATH  Google Scholar 

  • Xin M, Fei J (2015) Adaptive vibration control for MEMS vibratory gyroscope using backstepping sliding mode control. J Vib Control 21(4):808–817

    Article  MathSciNet  Google Scholar 

  • Yammani C, Maheswarapu S, Matam SK (2016) A multi-objective shuffled bat algorithm for optimal placement and sizing of multi distributed generations with different load models. Int J Electr Power Energy Syst 79:120–131

    Article  Google Scholar 

  • Yan W, Hou S, Fang Y, Fei J (2017) Robust adaptive nonsingular terminal sliding mode control of MEMS gyroscope using fuzzy-neural-network compensator. Int J Mach Learn Cybern 8(4):1287–1299

    Article  Google Scholar 

  • Yang XS (2010) A new metaheuristic bat-inspired algorithm. In: González JR, Pelta DA, Cruz C, Terrazas G, Krasnogor N (eds) Nature inspired cooperative strategies for optimization (NICSO 2010). Studies in computational intelligence, vol 284. Springer, Berlin, Heidelberg, pp 65–74. https://doi.org/10.1007/978-3-642-12538-6_6

  • Yang NC, Le MD (2015) Optimal design of passive power filters based on multi-objective bat algorithm and Pareto front. Appl Soft Comput 35:257–266

    Article  Google Scholar 

  • Yılmaz S, Küçüksille EU (2015) A new modification approach on bat algorithm for solving optimization problems. Appl Soft Comput 28:259–275

    Article  Google Scholar 

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Correspondence to Mehran Rahmani.

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Rahmani, M., Komijani, H., Ghanbari, A. et al. Optimal novel super-twisting PID sliding mode control of a MEMS gyroscope based on multi-objective bat algorithm. Microsyst Technol 24, 2835–2846 (2018). https://doi.org/10.1007/s00542-017-3700-6

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