Optimal State-Feedback Design for Inverted Pendulum System by Flower Pollination Algorithm

Deacha Puangdownreong

doi:10.15866/ireaco.v9i5.10142

Optimal State-Feedback Design for Inverted Pendulum System by Flower Pollination Algorithm

Deacha Puangdownreong^(1*)

^(*) Corresponding author

Authors' affiliations

DOI: https://doi.org/10.15866/ireaco.v9i5.10142

Abstract

The inverted pendulum system is one of the classical-unstable plants commonly used as a case study in control system design and simulation. To stabilize such system, the state-feedback design is performed by calculating the appropriate feedback gains. The state-feedback design can be considered as the optimization framework. In this paper, optimal state-feedback design for the inverted pendulum system using the flower pollination algorithm (FPA), one of the most efficient metaheuristic optimization techniques, is proposed. Results obtained by the FPA will be compared with those obtained by the conventional design method named the Ackermann’s formula. As simulation results, it was found that the FPA can provide optimal feedback gains for the inverted pendulum system superior to Ackermann’s formula. System responses with state-feedback gains optimized by the FPA yield shorter rise time, smaller overshoot, shorter settling time and zero steady-state error.
Copyright © 2016 Praise Worthy Prize - All rights reserved.

Keywords

State-Feedback Design; Inverted Pendulum; Flower Pollination Algorithm; Metaheuristic Optimization

Full Text:

PDF

References

K. Ogata, Modern Control Engineering (Prentice-Hall, 2010).

R.C. Dorf, R.H. Bishop, Modern Control Systems (Prentice-Hall, 2005).
http://dx.doi.org/10.1002/rnc.1054

B.C. Kuo,Automatic control systems (John Wiley & Sons, 2003).

C.L. Phillips, R.D. Harbor, Feedback Control Systems (Prentice-Hall, 1991).
http://dx.doi.org/10.1016/0005-1098(90)90061-l

W. Younis, M. Abdelati, Design and Implementation of an Experimental Segway Model, API Conference Proceeding, Vol. 1107, pp. 350–350, 2009.
http://dx.doi.org/10.1063/1.3106501

T. Takei, R. Imamura, S. Yuta, Baggage Transportation and Navigation by a Wheeled Inverted Pendulum Mobile Robot, IEEE Transactions on Industrial Electronics, Vol. 56: 3985–3994, 2009.
http://dx.doi.org/10.1109/tie.2009.2027252

S. Kajita, F. Kanehiro, K. Kaneko, K. Fujiwara, K. Yokoi, H. Hirukawa, Biped Walking Pattern Generation by a Simple Three-Dimensional Inverted Pendulum Model, Advanced Robotics, Vol. 17, pp. 131–147, 2003.
http://dx.doi.org/10.1163/156855303321165097

N. Motoi, T. Suzuki, K. Ohnishi, A Bipedal Locomotion Planning Based on Virtual Linear Inverted Pendulum Mode, IEEE Transactions on Industrial Electronics, Vol. 56, pp. 54–61, 2009.
http://dx.doi.org/10.1109/tie.2008.2004663

S. Kajita, M. Morisawa, K. Miura, S. Nakaoka, K. Harada, K. Kaneko, Biped Walking Stabilization Based on Linear Inverted Pendulum Tracking, IEEE/RSJ 2010 International Conference on Intelligent Robots and Systems, Taipei, pp. 4489–449, 2010.
http://dx.doi.org/10.1109/iros.2010.5651082

V. Zakian, Control Systems Design: A New Framework (Springer-Verlag, 2005)
http://dx.doi.org/10.1007/1-84628-215-2

V. Zakian, U. Al-Naib, Design of Dynamical and Control Systems by the Method of Inequalities, IEEInternational Conference, Vol. 120, pp.1421–1427, 1973.
http://dx.doi.org/10.1049/piee.1973.0289

A.I. Abdulla, J.M. Ahmed, S.M. Attya, Genetic Algorithm (GA) Based Optimal Feedback Control Weighting Matrices Computation, Al-Rafidain Engineering, Vol.21, pp. 25–33, 2013.
http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.7546

P.S. Oliveira, L.S. Barros, L.G.Q. Silveira Júnior, Genetic Algorithm Applied to State Feedback Control Design, IEEE/PES Transmission and Distribution Conference and Exposition, 2010.
http://dx.doi.org/10.1109/tdc-la.2010.5762925

S. Jalilzadeh, P. Farhang, M.R.S. Tirtashi, PSO Based State Feedback Controller Design for SVC to Enhance the Stability of Power System, International Journal of Engineering and Technology, Vol. 2, pp. 1426–1432, 2012.
http://dx.doi.org/10.4236/epe.2011.32012

J. Wang, B.T. Brackett, R.G. Harley, Particle Swarm-Assisted State Feedback Control: from Pole Selection to State Estimation, American Control Conference, pp. 1493–1498, 2009.
http://dx.doi.org/10.1109/acc.2009.5160514

X.S. Yang, Flower Pollination Algorithm for Global Optimization, Unconventional Computation and Natural Computation, Lecture Notes in Computer Science, Vol. 7445, pp. 240–249, 2012.
http://dx.doi.org/10.1007/978-3-642-32894-7_27

K. Balasubramani, K. Marcus, A Study on Flower Pollination Algorithm and Its Applications, International Journal of Application or Innovation in Engineering & Management (IJAIEM), Vol. 3, pp. 320–325, 2014.
http://dx.doi.org/10.1080/17509653.2015.1059298

N. Sakib, Md.W. Kabir, Md.S. Rahman, M.S. Alam, A Comparative Study of Flower Pollination Algorithm and Bat Algorithm on Continuous Optimization Problems, International Journal of Applied Information Systems (IJAIS), Vol. 7, pp. 13–19, 2014.
http://dx.doi.org/10.5120/ijais14-451231

X.S. Yang, M. Karamanoglua, X. He, Multi-Objective Flower Algorithm for Optimization, International Conference on Computational Science (ICCS 2013), Procedia Computer Science, Vol. 18, pp. 861 – 868, 2013.
http://dx.doi.org/10.1016/j.procs.2013.05.251

D. Lastomo, M.R. Djalal, D. Wido, I. Robandi, Optimization of PID Controller Design for DC Motor Based on Flower Pollination Algorithm, The International Conference on Electrical, Telecommunication and Computer Engineering (ELTICOM 2015), 2015.
http://dx.doi.org/10.1109/ic4.2015.7375578

S.M. Nigdeli, G. Bekdaş, X.S. Yang, Application of the Flower Pollination Algorithm in Structural Engineering, Metaheuristics and Optimization in Civil Engineering, Modeling and Optimization in Science and Technologies, Springer International Publishing Switzerland, Vol. 7, pp. 25–42, 2016.
http://dx.doi.org/10.1007/978-3-319-26245-1_2

R.H. Cannon, Dynamic of Physical Systems (McGraw-Hill, 1967).

A.M. Bloch, N.E. Leonard, J.E. Marsden, Controlled Lagragians and the Stabilization of Mechanical Systems I: the First Matching Theorem, IEEE Transactions on Automatic Control, Vol. 45, pp. 2253–2270, 2000.
http://dx.doi.org/10.1109/9.895562

B. J. Glover, Understanding Flowers and Flowering: An Integrated Approach(Oxford University Press, 2007).
http://dx.doi.org/10.1093/acprof:oso/9780198565970.001.0001

P. Willmer, Pollination and Floral Ecology(Princeton UniversityPress, 2011).
http://dx.doi.org/10.1515/9781400838943

N.M. Waser, Flower Constancy: Definition, Cause and Measurement,The American Naturalist, Vol. 127, pp. 596 – 603, 1986.
http://dx.doi.org/10.1086/284507

L. Chittka, J.D. Thomson, N.M. Waser, Flower Constancy, Insect Psychology,and Plant Evolution, Naturwissenschaften, Vol. 86, pp. 361–177, 1999.
http://dx.doi.org/10.1007/s001140050636

I. Pavlyukevich, Lévy flights, Non-Local Search and Simulated Annealing, Journal of Computational Physics, Vol. 226, pp. 1830–1844, 2007.
http://dx.doi.org/10.1016/j.jcp.2007.06.008

Hannane, A., Fizazi, H., Metaheuristics and Neural Network for Satellite Images Classification, (2016) International Review of Aerospace Engineering (IREASE), 9 (4), Article in press.

Otsmani, Z., Khiat, M., Chaker, A., Metaheuristic Method for Minimizing the Periodic Preventive Maintenance Cost in an Electrical System, (2013) International Review of Electrical Engineering (IREE), 8 (1), pp. 379-387.

Shyamala, V., Christopher, T., Managing Privacy of Sensitive Attributes Using MFSARNN Clustering with Optimization Technique, (2015) International Review on Computers and Software (IRECOS), 10 (9), pp. 907-911.
http://dx.doi.org/10.15866/irecos.v10i9.7219

Al-Khafaji, A., Shaharuddin, N., Mat Darus, I., Modelling of a Flexible Single-Link Manipulator Using Metaheuristic Algorithms, (2014) International Review of Mechanical Engineering (IREME), 8 (6), pp. 1075-1092.
http://dx.doi.org/10.15866/ireme.v8i6.3012

Punlabpho, S., Jearsiripongkul, T., Control System for Double Inverted Pendulum on a Cart by H-Infinity Controller, (2015) International Review of Automatic Control (IREACO), 8 (4), pp. 300-306.
http://dx.doi.org/10.15866/ireaco.v8i4.6968

Yusuf, L., Magaji, N., Comparison of Fuzzy Logic and GA-PID Controller for Position Control of Inverted Pendulum, (2014) International Review of Automatic Control (IREACO), 7 (4), pp. 380-385.

Manzoor, M., Maqsood, A., Hasan, A., Quadratic Optimal Control of Aerodynamic Vectored UAV at High Angle of Attack, (2016) International Review of Aerospace Engineering (IREASE), 9 (3), pp. 70-79.
http://dx.doi.org/10.15866/irease.v9i3.8119

El Majdoub, K., Ouadi, H., Touati, A., LQR Control for Semi-Active Quarter Vehicle Suspension with Magnetorhehological Damper and Bouc-Wen Model, (2014) International Review on Modelling and Simulations (IREMOS), 7 (4), pp. 703-711.
http://dx.doi.org/10.15866/iremos.v7i4.2305

Win, T., Hesketh, T., Eaton, R., Construction Tower Crane SimMechanics-Visualized Modelling, Tower Vibration Impact on Payload Swing Analysis and LQR Swing Control, (2014) International Review on Modelling and Simulations (IREMOS), 7 (6), pp. 979-993.
http://dx.doi.org/10.15866/iremos.v7i6.4851

Refbacks

There are currently no refbacks.

Username
Password
Remember me