ROBOTICA & MANAGEMENT - Vol. 23, No. 2, December 2018, pp. 9-12
 

Optimal Sliding Mode Control for Tracking Trajectory Problem of Triple Pendubot


Xuan Dung Huynh *, Thanh Nguyen Nguyen **, Gia Bao Hong *, Dinh Dat Vu *, Minh Tam Nguyen *

* Ho Chi Minh City University of Technology and Education (HCMUTE)
Faculty of Electrical and Electronics Engineering (FEEE-HCMUTE)
01- Vo Van Ngan, Thu Duc District, Ho Chi Minh city, Vietnam
E-mail: 1627001@student.hcmute.edu.vn; 16151113@student.hcmute.edu.vn 14151025@student.hcmute.edu.vn; tamnm@hcmute.edu.vn;
** Ton Duc Thang University (TDTU)
Faculty of Electrical and Automation Engineering
19- Nguyen Huu Tho, District 7, Ho Chi Minh city, Vietnam
E-mail: 41403135@student.tdtu.edu.vn


Abstract:
 Triple pendubot – which is advanced model of classical pendubot, is constructed by single input that applied to first link and three link continuous connected. This is a typical nonlinear, unstable and fast-reacting system. With its structure as a SIMO system, it is hard to be controlled by traditional sliding mode controller, especially in the case that set-point changes constantly. This paper proposes a solution mathematical improvement of Lyapunov inequality based on Sliding Mode Algorithm which was inferred in former research. After that, authors use genetic algorithm to find parameters control which are satisfied Lyapunov inequality above. Finally, we use Matlab/Simulink software to simulate system and algorithm. And obtained results are also presented to prove effective proposal.

Keywords: Triple Pendubot; sliding controller; genetic algorithm; SIMO system; Lyapunov Inequality; nonlinear; Matlab/Simulink.

Full Text

References

[1] Eom M., Chwa D.: “Robust swing-up and balancing Control using a nonlinear disturbance observer for the pendubot system with dynamic friction”, IEEE Transaction On Robotics, Vol. 31, No. 2, Apr. 2015.

[2] Gulan M., Salaj M., Rohal-Ilkiv B.: “Achieving an equilibrium position of pendubot via swing-up and stabilizing model predictive control”, J. of Electrical Engineering, Vol. 65, No. 6, pp. 356-363, 2014.

[3] Kourtikakis E., Kapellakis E., Fasoulas J., Sfakiotakis M.: “An embedded controller for the pendubot”, 15th International Symposium on Ambient Intelligence and Embedded System, Sept. 2016.

[4] Hoo D.S.: “Balancing Control for the pendubot using sliding mode”, 44th International Symposium on Robotics (ISR), 2013.

[5] Rudra S., Barai R.K.: “Design of block back-stepping based nonlinear state feedback controller for pendubot”, IEEE First International Conference On Control, Measurement and Instrumentation, 2016.

[6] Zhang M., Tarn T.: “Hybrid control of the pendubot”, IEEE/ASME Transactions on Mechanics, Vol. 7, No. 1, March 2002.

[7] Xin X.,  Juuri K.: “Existence and design of a strongly stabilizing controller for the pendubot”, SICE Annual Conference 2012, at Akita University, Akita, Japan.

[8] Lai L., Fu Y., Ko C.: “MQPSO algorithm based Fuzzy PID Control for a pendubot system”, The 2017 International Conference on Artificial Life and Robotics, pp. 19-22, Seagaia Convention Center, Miyazaki, Japan.

[9] Fantoni I., Lozano R., Spong M.W., , “Passivity based control of the pendubot”, Proceedings of the American Control Conference, June 1999.

[10] Gulan M., Salaj M., Abdollahpouri M., Rohal-Ilkiv B.: “Real-time MHE-based nonlinear MPC of a pendubot system”, International Federation of Automatic Control, pp. 422-427, 2015.

[11] Saif A.-W.A.: “Strong Stabilization of the Non-linear pendubot system”, 12th International Multi-Conference on Systems, Signal and Devices, 2015.

[12] Jianfeng X., Huzhen S.: “The study on pendubot control linear quadratic regulator and Particle Swarm Optimization”, Journal of Digital Information Management, Vol. 15, Num. 1, Feb. 2013.

[13] Wang W., Zhao D., Liu D.: “Design of a stable sliding mode controller for a class of second-order underactuated system”, IEEE Proceedings Control Theory and Applications, Vol. 151, No. 6, 2004.

[14] Qian D., Yi J., Zhao D.: “Hierarchical sliding mode control for a class of SIMO under-actuated systems”, Control and Cybernetics, Vol. 37, No. 1, 2008.

[15] Hao Y., Yi J., Zhao D., Qian D.: “Design of a new incremental sliding mode controller”, IEEE 7th World Congress on Intelligent Control and Automatic, pp. 3407-3412, 2008.

[16] Kien C.V., Son N.N., Anh H.P.H.: “Swing up and balancing implementation for the pendubot using Advanced Sliding Mode Control”, International Conference of Electrical, Automation and Mechanical Engineering, 2015.

[17] Zeharm D., Benmahammed K.: “Optimal sliding mode control of the pendubot”, International Research Journal of Computer Science and Information System, Vol. 2, Num. 3, pp. 45-51, April 2013.