Adaptive Type-2 Fuzzy Logic Control Applied to the Inverted Pendulum on a Cart Problem

Francisco Ruvalcaba; Miguel Llama; Francisco Jurado

doi:10.15866/ireaco.v11i4.14487

Adaptive Type-2 Fuzzy Logic Control Applied to the Inverted Pendulum on a Cart Problem

Francisco Ruvalcaba^(1*), Miguel Llama⁽²⁾, Francisco Jurado⁽³⁾

^(*) Corresponding author

Authors' affiliations

DOI: https://doi.org/10.15866/ireaco.v11i4.14487

Abstract

This paper introduces the design of an adaptive interval type-2 fuzzy logic controller and its implementation on a pendulum-cart system. It includes the theoretical foundations of: type-2 fuzzy logic system, input-output linearization control, fuzzy systems for functions approximation and adaptive systems. Type-2 fuzzy controllers provide an approach for using wide variety of opinions in control design. The above allows minimizing the effect of uncertainties in the rule base of fuzzy logic systems. These types of controllers provide greater flexibility in the application of human knowledge during the design of control systems in contrast to traditional controllers employing type-1 fuzzy logic. We propose to compare an adaptive interval type-2 fuzzy logic controller with its corresponding adaptive type-1 fuzzy logic controller. These controllers are tested in real-time on an inverted pendulum on a cart experimental prototype under the presence of parametric uncertainties in the mass of the pendulum. Five performance indexes are computed to compare both controllers, showing that type-2 fuzzy systems can help to improve the response of type-1 fuzzy systems.
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Keywords

Type-2 Fuzzy Logic; Interval Type-2 Fuzzy Controller; Adaptive Fuzzy Control

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References

J. M. Mendel, Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions (Prentice-Hall, 2001).

Jerry M. Mendel, Type-2 fuzzy sets and systems: an overview, IEEE Computational Intelligence Magazine, vol. 2 (Issue 1):20-29, February 2007.
http://dx.doi.org/10.1109/mci.2007.357235

L. A. Zadeh, Fuzzy sets, Information and Control, vol. 8 (Issue 3):338-353, 1965.
http://dx.doi.org/10.1016/s0019-9958(65)90241-x

L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-i, Information Sciences, vol. 8 (Issue 3):199-249, 1975.
http://dx.doi.org/10.1016/0020-0255(75)90036-5

Masaharu Mizumoto and Kokichi Tanaka, Some properties of fuzzy sets of type 2, Information and Control, vol. 31 (Issue 4):312-340, 1976.
http://dx.doi.org/10.1016/s0019-9958(76)80011-3

H. A. Hagras, A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots, IEEE Transactions on Fuzzy Systems, vol. 12 (Issue 4):524-539, Aug 2004.
http://dx.doi.org/10.1109/tfuzz.2004.832538

J. R. Castro, O. Castillo, and P. Melin, An interval type-2 fuzzy logic toolbox for control applications, 2007 IEEE International Fuzzy Systems Conference, pp. 1-6, July 2007.
http://dx.doi.org/10.1109/fuzzy.2007.4295341

Li-Xin Wang, A Course in Fuzzy Systems and Control, (Prentice Hall, 1991).

M. C. Kao, C. J. Lin, C. L. Feng, T. H. S. Li, and H. M. Yen. Adaptive type-2 fuzzy tracking control of wheeled mobile robots, 2013 International Conference on Fuzzy Theory and Its Applications (iFUZZY), pp. 1-6, December 2013.
http://dx.doi.org/10.1109/ifuzzy.2013.6825400

H. Chaoui, M. Khayamy, and A. A. Aljarboua. Adaptive interval type-2 fuzzy logic control for pmsm drives with a modified reference frame. IEEE Transactions on Industrial Electronics, 64(5):3786–3797, May 2017.
http://dx.doi.org/10.1109/tie.2017.2650858

X. Tao, J. Yi, R. Yuan, and Z. Liu. Adaptive interval type-2 fuzzy output feedback control based on nonlinear high gain observer for flexible air-breathing hypersonic vehicles, in 2017 32nd Youth Academic Annual Conference of Chinese Association of Automation (YAC), pages 943–948, May 2017.
http://dx.doi.org/10.1109/yac.2017.7967545

Junlong Gao, R. Yuan, J. Yi, and C. Li. Adaptive interval type-2 fuzzy sliding mode controller design for flexible airbreathing hypersonic vehicles, in 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pages 1–6, Aug 2015.
http://dx.doi.org/10.1109/fuzz-ieee.2015.7337828

X. Tao, J. Yi, R. Yuan, and Z. Liu. Control of a flexible airbreathing hypersonic vehicle with measurement noises using adaptive interval type-2 fuzzy logic system, in 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pages 1–6, July 2017.
http://dx.doi.org/10.1109/fuzz-ieee.2017.8015530

F. Yang, J. Yi, X. Tan, and R. Yuan, Robust adaptive type- 2 fuzzy logic controller design for a flexible air-breathing hypersonic vehicle, 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 106-112, July 2014.
http://dx.doi.org/10.1109/fuzz-ieee.2014.6891852

E. Kayacan, O. Kaynak, R. Abiyev, J. Torresen, M. Hovin, and K. Glette, Design of an adaptive interval type-2 fuzzy logic controller for the position control of a servo system with an intelligent sensor, Fuzzy Systems (FUZZ), 2010 IEEE International Conference on, pp 1-8, July 2010.
http://dx.doi.org/10.1109/fuzzy.2010.5584629

K. Chafaa, Y. Laamari, S. Barkati, and S. Chaouch, Adaptive type-2 fuzzy control for induction motor, 5th International Multi-Conference on Systems, Signals and Devices, pp. 1-6, July 2008.
http://dx.doi.org/10.1109/ssd.2008.4632866

Y. Li, Y. Sun, J. Hua, and L. Li, Indirect adaptive type-2 fuzzy impulsive control of nonlinear systems, IEEE Transactions on Fuzzy Systems, vol. 23(Issue 4):1084-1099, Aug 2015.
http://dx.doi.org/10.1109/tfuzz.2014.2346235

M. E. Abdelaal, H. M. Emara, and A. Bahgat. Interval type 2 fuzzy sliding mode control with application to inverted pendulum on a cart, in 2013 IEEE International Conference on Industrial Technology (ICIT), pages 100–105, Feb 2013.
http://dx.doi.org/10.1109/icit.2013.6505655

Jerry M. Mendel, Hani Hagras, Woei-Wan Tan, William W. Melek, and Hao Ying, Introduction To Type-2 Fuzzy Logic Control: Theory and Applications, (Wiley, 2014).
http://dx.doi.org/10.1002/9781118886540

K. J. Astrom and B. Wittenmark, Adaptive control, (Addison Wesley, 1994).
http://dx.doi.org/10.2307/1269433

H. Centeno, M. A. Llama, and V. Santibáñez, Control difuso adaptable: Aplicación experimental a un carro péndulo, Congreso Mexicano de Robótica, 2008. (in Spanish).

I. Fantoni, R. Lozano, Non-linear Control for Underactuated Mechanical Systems, (Springer-Verlag London, 2002).
http://dx.doi.org/10.1007/978-1-4471-0177-2_15

Ramadhani, A., Dharma, A., Robandi, I., Optimization FOU of Interval Type-2 Fuzzy Inference System Using Big Bang – Big Crunch Algorithm for Short Term Load Forecasting on National Holiday Case Study: South and Central Kalimantan-Indonesia, (2015) International Review of Electrical Engineering (IREE), 10 (1), pp. 123-130.
http://dx.doi.org/10.15866/iree.v10i1.4871

Yuhendri, M., Ashari, M., Purnomo, M., A Novel Sensorless MPPT for Wind Turbine Generators Using Very Sparse Matrix Converter Based on Hybrid Intelligent Control, (2015) International Review of Electrical Engineering (IREE), 10 (2), pp. 233-243.
http://dx.doi.org/10.15866/iree.v10i2.2980

Kouadria, M., Allaoui, T., Denaï, M., High Performance Shunt Active Power Filter Design Based on Fuzzy Interval Type-2 Control Strategies, (2015) International Review of Automatic Control (IREACO), 8 (5), pp. 322-330.
http://dx.doi.org/10.15866/ireaco.v8i5.6096

Abadi, I., Musyafa, A., Soeprijanto, A., Type-2 Fuzzy Logic Controller Based PV Passive Two-Axis Solar Tracking System, (2015) International Review of Electrical Engineering (IREE), 10 (3), pp. 390-398.
http://dx.doi.org/10.15866/iree.v10i3.6090

Shouman, M., El Bayoumi, G., Adaptive Robust Control of Satellite Attitude System, (2015) International Review of Aerospace Engineering (IREASE), 8 (1), pp. 35-42.
http://dx.doi.org/10.15866/irease.v8i1.5322

Kaddari, F., Mazari, B., Mihoub, Y., Harmonic Currents Extraction Techniques for a Fix and Adaptive Fuzzy Hysteresis Controlled Shunt Active Power Filter, (2015) International Review on Modelling and Simulations (IREMOS), 8 (6), pp. 670-678.
http://dx.doi.org/10.15866/iremos.v8i6.7942

Mellouli, E., Chalh, Z., Alfidi, M., Boumhidi, I., A New Robust Adaptive Fuzzy Sliding Mode Controller for a Variable Speed Wind Turbine, (2015) International Review of Automatic Control (IREACO), 8 (5), pp. 338-345.
http://dx.doi.org/10.15866/ireaco.v8i5.7192

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