Document Type : Research Paper


Laboratoire d'Ingenierie des Systemes Industriels et des Energies Renouvelables (LISIER), The National Higher Engineering School of Tunis (ENSIT), BP 56, 1008 Tunis, Tunisia


This paper addresses the problems caused by an inappropriate selection of sliding surface parameters in fuzzy sliding mode controllers via an optimization approach. In particular, the proposed method employs the parallel distributed compensator scheme to design the state feedback based control law. The controller gains are determined in offline mode via a linear quadratic regular. The particle swarm optimization is incorporated into the linear quadratic regular technique for determining the optimal weight matrices. Consequently, an optimal sliding surface is obtained using the scalar $sign$ function. This latter is used to design the proposed control law. Finally, the effectiveness of the proposed fuzzy sliding mode controller based on parallel distributed compensator and using particle swarm optimization is evaluated by comparing the obtained results with other reported in literature.


[1] F. Allouani, D. Boukhetala and F. Boudjema, Particle swarm optimization based fuzzy sliding
mode controller for the twin rotor mimo system, 16th IEEE Mediterranean Electrotechnical
Conference (MELECON), (2012), 1063{1066.
[2] P. P. Bonissone, V. Badami, K. Chaing, P. Khedkar, K. Marcelle and M. Schutten, Industrial
applications of fuzzy logic at general electric, Proceedings of the IEEE, 83(3) (1995), 450{
[3] A. Boubaki, F. Boudjema, C. Boubakir and S. Labiod, A fuzzy sliding mode controller using
nonlinear sliding surface applied to the coupled tanks system, International Journal of Fuzzy
Systems, 10(2) (2008), 112{118.
[4] W. Chang, J. B. Park, Y. H. Joob and G. Chen, Design of robust fuzzy-model- based controller
with sliding mode control for siso nonlinear systems, Fuzzy Sets and Systems, 125(1) (2002),
[5] L. Chaouech and A. Chaari, Design of sliding mode control of nonlinear system based on
Takagi-Sugeno fuzzy model, World Congress on Computer and Information Technology (WCCIT),
(2013), 1{6.
[6] L. Chaouech, M. Soltani, S. Dhahri and A. Chaari, Design of new fuzzy sliding mode con-
troller based on parallel distributed compensation controller and using the scalar sign func-
tion, Mathematics and Computers in Simulation, 132 (2017), 277{288.
[7] P. C. Chen, C. W. Chen and W. L. Chiang, GA-based fuzzy sliding mode controller for
nonlinear systems, Mathematical Problems in Engineering, 2008 (2008), 1{16.
[8] C. M. Dorling and A. S. I. Zinober, Two approaches to hyperplane design in multivariable
variable structure control systems, International Journal of Control, 44(1) (1986), 65{82.
[9] P. Durato, C. Abdallah and V. Cerone, Linear quadratic control: An introduction, Prentice
Hall, USA, 1995.
[10] S. El Beid and S. Doubabi, DSP-Based implementation of fuzzy output tracking control for
a boost converter, IEEE Transactions on Industrial Electronics, 61(1) (2014), 196{209.
[11] P. Guan, X. J. Liu and J. Z. Liu, Adaptive fuzzy sliding mode control for
exible satellite,
Engineering Applications of Arti cial Intelligence, 18(4) (2005), 451{459.
[12] S. Hong and R. Langari, Robust fuzzy control of a magnetic bearing system subject to har-
monic disturbances, IEEE Transactions on Control Systems Technology, 8 (2) (2000), 366{
[13] Z. Hongbing, P. Chengdong, K. Eguchi and G. Jinguang, Euclidean particle swarm opti-
mization, Second International Conference on Intelligent Networks and Intelligent Systems,
Tianjin (2009), 669{672.
[14] Y. J. Huang and H. K. Wei, Sliding mode control design for discrete multivariable systems
with time-delayed input signals, International Journal of Systems Science, 33(10) (2002),
[15] L. Hung, H. Lin and H. Chung, Design of self-tuning fuzzy sliding mode control for TORA
system, Expert Systems with Applications, 32 (1) (2007), 201{212.
[16] E. Iglesias, Y. Garcia, M. Sanjuan, O. Camacho and C. Smith, Fuzzy surface-based sliding
mode control, ISA Transactions, 43(1) (2007), 73{83.
[17] A. Isidoti, Nonlinear Control Systems, Springer, Berlin, 1989.
[18] K. Jafar, B. M. Mohammad and K. Mansour, Feedback-linearization and fuzzy controllers
for trajectory tracking of wheeled mobile robots, Kybernetes, 39(1) (2010), 83{106.
[19] K. Jafar and B. M. Mohammad, From Nonlinear to Fuzzy Approaches in Trajectory Tracking
Control of Wheeled Mobile Robots, Asian Journal of Control, 14 (4) ( 2012), 960{973.
[20] A. Khosla, S. Kumar and K. R. Ghosh, A comparison of computational e orts between
particle swarm optimization and genetic algorithm for identi cation of fuzzy models, Fuzzy
Information Processing Society, (2007), 245{250.
[21] R. J. Lian, Adaptive self-organizing fuzzy sliding-mode radial basis-function neural-network
controller for robotic systems, IEEE Transactions on Industrial Electronics, 61(3) (2014),
[22] C. Liang and J. P. Su, A new approach to the design of a fuzzy sliding mode controller, Fuzzy
Sets and Systems, 139(1) (2003), 111{124.
[23] Z. Liang, Y. Yang and Y. Zeng, Eliciting compact T-S fuzzy models using subtractive clus-
tering and coevolutionary particle swarm optimization, Neuro-computing, 72(10-12) (2009),
[24] M. Mohamed, M. Anis, L. Majda, S. N. Ahmed and B. A. Ridha, Fuzzy discontinuous term
for a second order asymptotic dsmc: An experimental validation on a chemical reactor, Asian
Journal of Control, 13(3) (2010), 369{381.
[25] R. M. Nagarale and B. M. Patre, Decoupled neural fuzzy sliding mode control of nonlinear
systems, IEEE International Conference on Fuzzy Systems, (2013), 1{8.
[26] T. Niknam and B. Amiri, An ecient hybrid approach based on PSO, ACO and k-means for
cluster analysis, Applied Soft Computing, 10(1) (2010), 183{197.
[27] V. Panchal, K. Harish and K. Jagdeep, Comparative study of particle swarm optimization
based unsupervised clustering techniques, International Journal of Computer Science and
Network Security, 9(10) (2009), 132{140.
[28] K. Saji and K. Sasi, Fuzzy sliding mode control for a PH process, IEEE International Conference
on Communication Control and Computing Technologies, (2010), 276{281.
[29] A. Shahraz and R. B. Boozarjomehry, A fuzzy sliding mode control approach for nonlinear
chemical processes, Control Engineering Practice, 17(5) (2009), 541{550.
[30] S. F. Shehu, D. Filev and R. Langari, Fuzzy Control: Synthesis and Analysis, John Wiley
and Sons LTD, USA, 1997.
[31] L. Shieh, Y. Tsay and R. Yates, Some properties of matrix sign function derived from contin-
ued fractions, IEEE Proceedings of Control Theory and Applications, 130 (1983), 111{118.
[32] M. Singla, L. S. Shieh, G. Song, L. Xie and Y. Zhang, A new optimal sliding mode controller
design using scalar sign function, ISA Transactions, 53(2) (2014), 267{279.
[33] M. Soltani and A. Chaari, A PSO-Based fuzzy c-regression model applied to nonlinear data
modeling, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems,
23(6) (2015), 881{892.
[34] M. Sugeno and G. Kang, Fuzzy modeling and control of multilayer incinerator, Fuzzy Sets
and Systems, 18 (3) (1986), 329{345.
[35] T. Takagi and M. Sugeno, Fuzzy identi cation of systems and its application to modeling
and control, IEEE Transactions on Systems, Man and Cybernetics, 15(1) (1985 ), 116{132.
[36] K. Tanaka and M. Sugeno, Stability analysis and design of fuzzy control systems, Fuzzy Sets
and Systems, 45(2)(1992), 135{156.
[37] V. I. Utkin, Variable structure systems with sliding mode, IEEE Transactions on Automatic
Control, 26(2) (1977), 212{222.
[38] S. Vishnu Teja, T. N. Shanavas and S. K. Patnaik, Modi ed PSO based sliding-mode controller
parameters for buck converter, Conference on Electrical, Electronics and Computer Science
(SCEECS), (2012), 1{4.
[39] R. Wai, C. Lin and C. Hsu, Adaptive fuzzy sliding-mode control for electrical servo drive,
Fuzzy Sets and Systems, 143(2) (2004), 295{310.
[40] H. O. Wang, K. Tanaka and M. F. Grin, An approach to fuzzy control of nonlinear systems:
Stability and design issues, IEEE Transactions on Fuzzy Systems, 4(1) (1996), 14{23.
[41] H. O. Wang, K. Tanaka and M. F. Grin, Parallel distributed compensation of nonlinear
systems by Takagi-Sugeno fuzzy model, Proceedings FUZZY- IEEE/IFES, (1995), 531{538.
[42] G. O. Wang, K. Tanaka and T. Ikeda, Fuzzy modeling and control of chaotic systems, IEEE
Symposium Circuits and Systems, Atlanta, USA 3 (1996), 209{212.
[43] T. Wang, W. Xie and Y. Zhang, Sliding mode fault tolerant control dealing with modeling
uncertainties and actuator faults, ISA Transactions, 51(3) (2012), 386{392.
[44] J. Wu, M. Singla, C. Olmi, L. Shieh and G. Song, Digital controller design for absolute value
function constrained nonlinear systems via scalar sign function approach, ISA Transactions,
49(3) (2010), 302{310.
[45] Y. Xinghuo, Z. Man and B. Wu, Design of fuzzy sliding-mode control systems, Fuzzy Sets
and Systems, 95 (3) (1998), 295{306.
[46] F. K. Yeh and C. M. Chen, J. J. Huang, Fuzzy sliding-mode control for a MINI-UAV, IEEE
International Symposium on Computational Intelligence in Scheduling, (2010), 3317{3323.
[47] K. Young, V. I. Utkin and U. Ozguner, A control engineer's guide to sliding mode control,
IEEE Transactions on Control Systems Technology, 7(3) (1999), 328{342.
[48] Y. Zhang, D. Huang, M. Ji and F. Xie, Image segmentation using PSO and PCM with
mahalanobis distance, Expert Systems with Applications, 38(7) (2011), 9036{9040.