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Backstepping Controller Design for a 5 DOF Spherical Inverted Pendulum

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Abstract:

This paper presents a Backstepping controller for five degrees of freedom Spherical Inverted Pendulum. Since the system is nonlinear, unstable, underactuated and MIMO and has a nonsquare form, the classic control design cannot be applied to control it. In order to remedy this problem, we propose in this paper a new method based on hierarchical steps of the Backstepping controller taking into a count the nonlinearities that cannot be neglected. Furthermore, a Linear Quadratic Regulator controller and LQR + PID based on the linearized system model are also designed for performance comparison. Finally, a simulation study is carried out to prove the effectiveness of proposed control scheme and is validated using the virtual reality environment that proves the performance of the Backstepping controller over the linear ones where it brings the pendulum from any initial condition in the upper hemisphere while the base is brought to the origin of the coordinates.

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International Journal of Engineering Research in Africa Vol. 41

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Periodical:

International Journal of Engineering Research in Africa (Volume 41)

Pages:

37-50

DOI:

https://doi.org/10.4028/www.scientific.net/JERA.41.37

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Online since:

February 2019

Authors:

Soukaina Krafes*, Zakaria Chalh, Abdelmjid Saka

Keywords:

Backstepping Controller, Lyapunov, MIMO, Nonlinear Model, Spherical Inverted Pendulum, Stability

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[1] T. H. Deng, M. Deng, A. I. Inoue, Nonlinear control of the underactuated two-link manipulator using the sliding-mode type partial linearisation method, International Journal of Computer Applications in Technology 41 (2011) 230-235.

DOI: 10.1504/IJCAT.2011.042697

[2] Huang An-Chyau and Chen Yung-Feng and Kai Chen-Yu, Adaptive Control of Underactuated Mechanical Systems: Pendubot. (2015) 189-200.

DOI: 10.1142/9789814663557_0010

[3] C. Aguilar-Avelar, J. Moreno-Valenzuela, A composite controller for trajectory tracking applied to the furuta pendulum, ISA Transactions 57 (2015) 286294. doi:http://dx.doi.org/10.1016/j.isatra.2015.02.009.

DOI: 10.1016/j.isatra.2015.02.009

[4] M. Ramrez-Neriaa, H. Sira-Ramreza, R. Garrido-Moctezumaa, A. Luviano-Jurezb, Linear active disturbance rejection control of underactuated systems: The case of the furuta pendulum, ISA Transactions 53 (4) (2014) 920 - 928, disturbance Estimation and Mitigation. doi:http://dx.doi.org/10.1016/j.isatra.2013.09.023.

DOI: 10.1016/j.isatra.2013.09.023

[5] {Olfa Boubaker, The Inverted Pendulum Benchmark in Nonlinear Control Theory : A Survey Regular Paper, 2013[6] N. Sun, Y. Fang, New energy analytical results for the regulation of underactuated overhead cranes: An end-effector motion-based approach, IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 59 (12) (2012) 4723-4734.

DOI: 10.1109/TIE.2012.2183837

[7] C. Aguilar-Avelar, R. Rodriguez-Calderon, S. Puga-Guzman, J. Moreno-Valenzuela, Effects of nonlinear friction compensation in the inertia wheel pendulum, Journal of Mechanical Science and Technology 31 (9) (2017) 4425-4433.

DOI: 10.1007/s12206-017-0843-4

[8] M. Keshmiri, A. F. Jahromi, A. Mohebbi, M. H. Amoozgar, W.-F. Xie, Modeling and control of the ball and beam system using model based and non-model based control approaches, International Journal on Smart Sensing and Intelligent Systems 5 (1).

[9] D. Liu, W. Guo, Nonlinear backstepping design for the underactuated tora system, Journal of Vibroengineering 16 (2014) 552-559.

[10] E. Aranda-Escolstico, M. Guinaldo, F. Gordillo, S. Dormido, A novel approach to periodic eventtriggered control: Design and application to the inverted pendulum, ISA Transactions (2016) - doi:http://dx.doi.org/10.1016/j.isatra.2016.08.019.

DOI: 10.1016/j.isatra.2016.08.019

[11] V. Casanova, J. Alcana, J. Salt, R. Piz, ngel Cuenca, Control of the rotary inverted pendulum through thresholdbased communication, ISA Transactions 62 (2016) 357366. doi:http://dx.doi.org/10.1016/j.isatra.2016.01.009.

DOI: 10.1016/j.isatra.2016.01.009

[12] J. Ghommam, A. Chemori, F. Mnif, The Inverted Pendulum in Control Theory and Robotics: From theory to new innovations, IET Digital Library, 2017, Ch. Finite-time stabilization of underactuated mechanical systems in the presence of uncertainties: application to the cart-pole system.

DOI: 10.1049/pbce111e_ch8

[13] S. Krafes, Z. Chalh, A. Saka, Review: Linear, nonlinear and intelligent controllers for the inverted pendulum problem, in: 2016 IEEE International Conference on Electrical and Information Technologies (ICEIT), 2016, pp.136-141.

DOI: 10.1109/EITech.2016.7519577

[14] Chen Xianmin and Yu Rongrong and Huang Kang and Zhen Shengchao and Sun Hao and Shao Ke. Linear motor driven double inverted pendulum: A novel mechanical design as a testbed for control algorithms. Simulation Modelling Practice and Theory. (2018).

DOI: 10.1016/j.simpat.2017.11.009

[15] Fatima Aliyu Darma and Ado Dan Ado Dan Isa and Auwalu Muhammad Abdullahi and Ismail Abubakar Umar and Lubabatu B. Ila. Fuzzy Logic Control of a Rotary Double Inverted Pendulum System.Applications of Modelling and Simulation. Vol 2, 1 (2018).

[16] Sanchez R.Bonifacio and Ordaz O.Patricio and Poznyak G.Alexander. Robust Stabilizing Control for the Electromechanical Triple-Link Inverted Pendulum System. IFAC-PapersOnLine Volume 51, (13,) 2018, 314-319.

DOI: 10.1016/j.ifacol.2018.07.297

[17] Liu, G. (2006). Modelling, stabilising control and trajectory tracking of a spherical inverted pendulum. Ph.D Thesis. The University of Melbourne.

[18] Pham, D. B., and Lee, S.-G. (2018). Hierarchical sliding mode control for a two-dimensional ball segway that is a class of a second-order underactuated system. Journal of Vibration and Control.

DOI: 10.1177/1077546318770089

[19] L. Sentis, J. P. O. Khatib, Compliant control of multicontact and centerof-mass behaviors in humanoid robots, IEEE TRANSACTIONS ON ROBOTICS 26 (3).

[21] C.-C. Tsai, C.-C. Yu, C.-S. Chang, Aggregated hierarchical sliding-mode control for spherical inverted pendulum, in: Proceedings of 2011 8th Asian Control Conference (ASCC), (2011).

[22] M.-G. Yoon, Dynamics and stabilization of a spherical inverted pendulum on a wheeled cart, International Journal of Control, Automation and Systems 8 (2010) 1271-1279.

DOI: 10.1007/s12555-010-0612-y

[23] M. Fajar, S. Douglas, J. Gomm, Modelling and simulation of spherical inverted pendulum based on lqr control with simmechanics, Applied Mechanics and Materials 391 (2013) 163-167.

DOI: 10.4028/www.scientific.net/AMM.391.163

[24] S.-T. Kao, W.-J. Chiou, M.-T. Ho, Balancing of a spherical inverted pendulum with an omnidirectional mobile robot, in: 2013 IEEE International Conference on Control Applications (CCA), 2013.

DOI: 10.1109/CCA.2013.6662841

[25] C. Raimndez, J. L. Camao, A. Barreiro, Stabilizing an inverted spherical pendulum using a scale quad-rotor, in: The 4th Annual IEEE International Conference on Cyber Technology in Automation, Control and Intelligent Systems.

DOI: 10.1109/CYBER.2014.6917445

[26] G. Liu, D. Nei, I. Mareels, Non-linear stable inversionbased output tracking control for a spherical inverted pendulum, International Journal of Control 81 (1) (2008) 116-133. doi:http://dx.doi.org/10.1080/00207170701383798.

DOI: 10.1080/00207170701383798

[27] A. M. Bloch, N. E. Leonard, J. E. Marsden, Controlled lagrangians and the stabilization of mechanical systems i: The first matching theorem, IEEE TRANSACTIONS ON AUTOMATIC CONTROL 45 (12) (2000) 2253-2270.

DOI: 10.1109/9.895562

[28] R. Olfati-Saber, Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles, Thesis (Ph.D.)Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science.

[29] S. Rudra, R. kumar Barai, M. Maitra, D. Mandal, S. Ghosh, S. Dam, P. Bhattacharya, A. Dutta, Global stabilization of a flat underactuated inertia wheel: A block backstepping approach, International Conference on Computer Communication and Informatics (ICCCI).

DOI: 10.1109/ICCCI.2013.6466318

[30] S. Rudra, R. K. Barai, M. Maitra, D. Mandai, S. Dam, S. Ghosh, P. Bhattacharyya, A. Dutta, Design of nonlinear state feedback control law for underactuated tora system: A block backstepping approach, 7th International Conference on Intelligent Systems and Control (ISCO).

DOI: 10.1109/ISCO.2013.6481129

[31] S. Rudra, R. K. Barai, Design of block backstepping based nonlinear state feedback controller for pendubot, First International Conference on Control, Measurement and Instrumentation (CMI).

DOI: 10.1109/CMI.2016.7413794

[32] A. Ebrahim, G. Murphy, Adaptive backstepping controller design of an inverted pendulum, Proceedings of the Thirty-Seventh Southeastern Symposium on System Theory.

DOI: 10.1109/SSST.2005.1460900

[33] S. Rudra, R. K. Barai, M. Maitra, Block backstepping design of nonlinear state feedback control law for underactuated mechanical systemsdoi:10.1007/978-981-10-1956-2.[34] S. Rudra, R. K. Barai, M. Maitra, Nonlinear state feedback controller design for underactuated mechanical system: A modified block backstepping approach, ISA Transactions.

[35] D. Zhai, A.-Y. Lu, J.-H. Li, Q.-L. Zhang, State and dynamic output feedback control of switched linear systems via a mixed time and statedependent switching law.

DOI: 10.1016/j.nahs.2016.04.007

[36] C. Duan, F. Wu, Analysis and control of switched linear systems via dwell-time min-switching.

[37] C. Duan, F. Wu, Output-feedback control for switched linear systems subject to actuator saturation.

[38] N. Khaled, Virtual Reality and Animation for MATLAB and Simulink Users, Springer-Verlag London, 2012.

DOI: 10.1007/978-1-4471-2330-9