An Observer-Based Direct Adaptive Fuzzy Sliding Control with Adjustable Membership Functions
In this paper, an observer-based direct adaptive fuzzy sliding mode (OAFSM) algorithm is proposed. In the proposed algorithm, the zero-input dynamics of the plant could be unknown. The input connection matrix is used to combine the sliding surfaces of individual subsystems, and an adaptive fuzzy algorithm is used to estimate an equivalent sliding mode control input directly. The fuzzy membership functions, which were determined by time consuming try and error processes in previous works, are adjusted by adaptive algorithms. The other advantage of the proposed controller is that the input gain matrix is not limited to be diagonal, i.e. the plant could be over/under actuated provided that controllability and observability are preserved. An observer is constructed to directly estimate the state tracking error, and the nonlinear part of the observer is constructed by an adaptive fuzzy algorithm. The main advantage of the proposed observer is that, the measured outputs is not limited to the first entry of a canonical-form state vector. The closed-loop stability of the proposed method is proved using a Lyapunov-based approach. The proposed method is applied numerically on a multi-link robot manipulator, which verifies the performance of the closed-loop control. Moreover, the performance of the proposed algorithm is compared with some conventional control algorithms.
[1] Mohsen Farahani, Soheil Ganjefar, Intelligent power system stabilizer design using adaptive fuzzy sliding mode controller, Neurocomputing, 226, (2017), 135-144.
[2] A. Al-khazraji, N. Essounbouli, A. Hamzaoui, F. Nollet, J. Zaytoon, Type-2 fuzzy sliding mode control without reaching phase for nonlinear system, Engineering Applications of Artificial Intelligence 24 (1) (2011) 23 – 38.
[3] O. Cerman, P. Huek, Adaptive fuzzy sliding mode control for electrohydraulic servo mechanism, Expert Systems with Applications (0) (2012).
[4] Samir Zeghlache, Tarak Benslimane, Abderrahmen Bouguerra, Active fault tolerant control based on interval type-2 fuzzy sliding mode controller and nonlinear adaptive observer for 3-DOF laboratory helicopter, ISA Transactions, (2017).
[5] Lanwei Zhou, Guoping Chen, Fuzzy sliding mode control of flexible spinning beam using a wireless piezoelectric stack actuator, Applied Acoustics, 128, (2017), 40-44.
[6] S.-C. Lin, Y.-Y. Chen, Design of adaptive fuzzy sliding mode for nonlinear system control, in: IEEE International Conference on Fuzzy Systems, Vol. 1, 1994, pp. 35–39.
[7] B. Yoo, W. Ham, Adaptive fuzzy sliding mode control of nonlinear system, IEEE Transactions on Fuzzy Systems 6 (2) (1998) 315–321.
[8] A. Gholami, Amir H.D. Markazi, Direct adaptive fuzzy sliding observation and control, Transactions of the Canadian Society for Mechanical Engineering, Vol. 36, No. 4, 2012.
[9] J. Wang, A. Rad, P. Chan, Indirect adaptive fuzzy sliding mode control: Part i: Fuzzy switching, Fuzzy Sets and Systems 122 (1) (2001) 21–30.
[10] R.Wai, C. Lin, C. Hsu, Adaptive fuzzy sliding-mode control for electrical servo drive, Fuzzy Sets and Systems 143 (2) (2004) 295–310.
[11] R. Wai, Fuzzy sliding-mode control using adaptive tuning technique, IEEE Transactions on Industrial Electronics 54 (1) (2007) 586–594.
[12] Z. Chen, C. Shan, H. Zhu, Adaptive fuzzy sliding mode control algorithm for a non-affine nonlinear system, IEEE Transactions on Industrial Informatics 3 (4) (2007) 302–311.
[13] R. Wai, M. Kuo, J. Lee, Design of cascade adaptive fuzzy sliding mode control for nonlinear two-axis inverted-pendulum servomechanism, IEEE Transactions on Fuzzy Systems 16 (5) (2008) 1232–1244.
[14] J. Hwang, H. Kwak, G. Park, Adaptive interval type-2 fuzzy sliding mode control for unknown chaotic system, Nonlinear Dynamics (2010) 1–12.
[15] H. S. Haghighi, A. H. Markazi, Chaos prediction and control in mems resonators, Communications in Nonlinear Science and Numerical Simulation 15 (10) (2010) 3091 – 3099.
[16] S. Tong, H.-X. Li, Fuzzy adaptive sliding-mode control for mimo nonlinear systems, IEEE Transactions on Fuzzy Systems 11 (3) (2003) 354– 360.
[17] S. Aloui, O. Pages, A. El Hajjaji, A. Chaari, Y. Koubaa, Improved fuzzy sliding mode control for a class of mimo nonlinear uncertain and perturbed systems, Applied Soft Computing Journal 11 (1) (2011) 820– 826.
[18] A. Poursamad, A. Markazi, Adaptive fuzzy sliding-mode control for multi-input multi-output chaotic systems, Chaos, Solitons and Fractals 42 (5) (2009) 3100–3109.
[19] J. Park, G. Park, Adaptive fuzzy observer with minimal dynamic order for uncertain nonlinear systems, IEE Proceedings: Control Theory and Applications 150 (2) (2003) 189–197.
[20] Atta Oveisi, Tamara Nestorović, Robust observer-based adaptive fuzzy sliding mode controller, Mechanical Systems and Signal Processing, 76–77, (2016), 58-71.
[21] Jun He, Minzhou Luo, Qingqing Zhang, Jianghai Zhao, Linsen Xu, Adaptive Fuzzy Sliding Mode Controller with Nonlinear Observer for Redundant Manipulators Handling Varying External Force, Journal of Bionic Engineering, 13 (4), (2016), 600-611.
[22] T.-H. S. Li, Y.-C. Huang, MIMO adaptive fuzzy terminal sliding-mode controller for robotic manipulators, Information Sciences 180 (2010) 4641–4660.
[23] Ramy Rashad, Ayman El-Badawy, Ahmed Aboudonia, Sliding mode disturbance observer-based control of a twin rotor MIMO system, ISA Transactions, 69, (2017), 166-174.
[24] Donghong Ning, Shuaishuai Sun, Lidui Wei, Bangji Zhang, Haiping Du, Weihua Li, Vibration reduction of seat suspension using observer based terminal sliding mode control with acceleration data fusion, Mechatronics, (44), (2017), 71-83.
[25] S. Tong, H. Li, W. Wang, Observer-based adaptive fuzzy control for siso nonlinear systems, Fuzzy Sets and Systems 148 (3) (2004) 355–376.
[26] S. Sastry, M. Bodson, Adaptive Control: Stability, Convergence, and Robustness, Prentice-Hall, New-Jersey, 1989.
[27] M. Biglarbegian, W. Melek, J. Mendel, Design of novel interval type- 2 fuzzy controllers for modular and reconfigurable robots: Theory and experiments, IEEE Transactions on Industrial Electronics 58 (4) (2011) 1371–1384.
[28] F. Lewis, L. K., A. Yesildirek, Neural net robot controller with guaranteed tracking performance, IEEE Transactions on Neural Networks 6 (3) (1995) 703–715.
[29] Z. Iwai, I. Mizumoto, L. Liu, S. Shah, H. Jiang, Adaptive stable pid controller with parallel feedforward compensator, in: 9th International Conference on Control, Automation, Robotics and Vision, no. pt 1, 2007, pp. 1–6.
[1] Mohsen Farahani, Soheil Ganjefar, Intelligent power system stabilizer design using adaptive fuzzy sliding mode controller, Neurocomputing, 226, (2017), 135-144.
[2] A. Al-khazraji, N. Essounbouli, A. Hamzaoui, F. Nollet, J. Zaytoon, Type-2 fuzzy sliding mode control without reaching phase for nonlinear system, Engineering Applications of Artificial Intelligence 24 (1) (2011) 23 – 38.
[3] O. Cerman, P. Huek, Adaptive fuzzy sliding mode control for electrohydraulic servo mechanism, Expert Systems with Applications (0) (2012).
[4] Samir Zeghlache, Tarak Benslimane, Abderrahmen Bouguerra, Active fault tolerant control based on interval type-2 fuzzy sliding mode controller and nonlinear adaptive observer for 3-DOF laboratory helicopter, ISA Transactions, (2017).
[5] Lanwei Zhou, Guoping Chen, Fuzzy sliding mode control of flexible spinning beam using a wireless piezoelectric stack actuator, Applied Acoustics, 128, (2017), 40-44.
[6] S.-C. Lin, Y.-Y. Chen, Design of adaptive fuzzy sliding mode for nonlinear system control, in: IEEE International Conference on Fuzzy Systems, Vol. 1, 1994, pp. 35–39.
[7] B. Yoo, W. Ham, Adaptive fuzzy sliding mode control of nonlinear system, IEEE Transactions on Fuzzy Systems 6 (2) (1998) 315–321.
[8] A. Gholami, Amir H.D. Markazi, Direct adaptive fuzzy sliding observation and control, Transactions of the Canadian Society for Mechanical Engineering, Vol. 36, No. 4, 2012.
[9] J. Wang, A. Rad, P. Chan, Indirect adaptive fuzzy sliding mode control: Part i: Fuzzy switching, Fuzzy Sets and Systems 122 (1) (2001) 21–30.
[10] R.Wai, C. Lin, C. Hsu, Adaptive fuzzy sliding-mode control for electrical servo drive, Fuzzy Sets and Systems 143 (2) (2004) 295–310.
[11] R. Wai, Fuzzy sliding-mode control using adaptive tuning technique, IEEE Transactions on Industrial Electronics 54 (1) (2007) 586–594.
[12] Z. Chen, C. Shan, H. Zhu, Adaptive fuzzy sliding mode control algorithm for a non-affine nonlinear system, IEEE Transactions on Industrial Informatics 3 (4) (2007) 302–311.
[13] R. Wai, M. Kuo, J. Lee, Design of cascade adaptive fuzzy sliding mode control for nonlinear two-axis inverted-pendulum servomechanism, IEEE Transactions on Fuzzy Systems 16 (5) (2008) 1232–1244.
[14] J. Hwang, H. Kwak, G. Park, Adaptive interval type-2 fuzzy sliding mode control for unknown chaotic system, Nonlinear Dynamics (2010) 1–12.
[15] H. S. Haghighi, A. H. Markazi, Chaos prediction and control in mems resonators, Communications in Nonlinear Science and Numerical Simulation 15 (10) (2010) 3091 – 3099.
[16] S. Tong, H.-X. Li, Fuzzy adaptive sliding-mode control for mimo nonlinear systems, IEEE Transactions on Fuzzy Systems 11 (3) (2003) 354– 360.
[17] S. Aloui, O. Pages, A. El Hajjaji, A. Chaari, Y. Koubaa, Improved fuzzy sliding mode control for a class of mimo nonlinear uncertain and perturbed systems, Applied Soft Computing Journal 11 (1) (2011) 820– 826.
[18] A. Poursamad, A. Markazi, Adaptive fuzzy sliding-mode control for multi-input multi-output chaotic systems, Chaos, Solitons and Fractals 42 (5) (2009) 3100–3109.
[19] J. Park, G. Park, Adaptive fuzzy observer with minimal dynamic order for uncertain nonlinear systems, IEE Proceedings: Control Theory and Applications 150 (2) (2003) 189–197.
[20] Atta Oveisi, Tamara Nestorović, Robust observer-based adaptive fuzzy sliding mode controller, Mechanical Systems and Signal Processing, 76–77, (2016), 58-71.
[21] Jun He, Minzhou Luo, Qingqing Zhang, Jianghai Zhao, Linsen Xu, Adaptive Fuzzy Sliding Mode Controller with Nonlinear Observer for Redundant Manipulators Handling Varying External Force, Journal of Bionic Engineering, 13 (4), (2016), 600-611.
[22] T.-H. S. Li, Y.-C. Huang, MIMO adaptive fuzzy terminal sliding-mode controller for robotic manipulators, Information Sciences 180 (2010) 4641–4660.
[23] Ramy Rashad, Ayman El-Badawy, Ahmed Aboudonia, Sliding mode disturbance observer-based control of a twin rotor MIMO system, ISA Transactions, 69, (2017), 166-174.
[24] Donghong Ning, Shuaishuai Sun, Lidui Wei, Bangji Zhang, Haiping Du, Weihua Li, Vibration reduction of seat suspension using observer based terminal sliding mode control with acceleration data fusion, Mechatronics, (44), (2017), 71-83.
[25] S. Tong, H. Li, W. Wang, Observer-based adaptive fuzzy control for siso nonlinear systems, Fuzzy Sets and Systems 148 (3) (2004) 355–376.
[26] S. Sastry, M. Bodson, Adaptive Control: Stability, Convergence, and Robustness, Prentice-Hall, New-Jersey, 1989.
[27] M. Biglarbegian, W. Melek, J. Mendel, Design of novel interval type- 2 fuzzy controllers for modular and reconfigurable robots: Theory and experiments, IEEE Transactions on Industrial Electronics 58 (4) (2011) 1371–1384.
[28] F. Lewis, L. K., A. Yesildirek, Neural net robot controller with guaranteed tracking performance, IEEE Transactions on Neural Networks 6 (3) (1995) 703–715.
[29] Z. Iwai, I. Mizumoto, L. Liu, S. Shah, H. Jiang, Adaptive stable pid controller with parallel feedforward compensator, in: 9th International Conference on Control, Automation, Robotics and Vision, no. pt 1, 2007, pp. 1–6.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:77723", author = "Alireza Gholami and Amir H. D. Markazi", title = "An Observer-Based Direct Adaptive Fuzzy Sliding Control with Adjustable Membership Functions", abstract = "In this paper, an observer-based direct adaptive fuzzy sliding mode (OAFSM) algorithm is proposed. In the proposed algorithm, the zero-input dynamics of the plant could be unknown. The input connection matrix is used to combine the sliding surfaces of individual subsystems, and an adaptive fuzzy algorithm is used to estimate an equivalent sliding mode control input directly. The fuzzy membership functions, which were determined by time consuming try and error processes in previous works, are adjusted by adaptive algorithms. The other advantage of the proposed controller is that the input gain matrix is not limited to be diagonal, i.e. the plant could be over/under actuated provided that controllability and observability are preserved. An observer is constructed to directly estimate the state tracking error, and the nonlinear part of the observer is constructed by an adaptive fuzzy algorithm. The main advantage of the proposed observer is that, the measured outputs is not limited to the first entry of a canonical-form state vector. The closed-loop stability of the proposed method is proved using a Lyapunov-based approach. The proposed method is applied numerically on a multi-link robot manipulator, which verifies the performance of the closed-loop control. Moreover, the performance of the proposed algorithm is compared with some conventional control algorithms.
", keywords = "Adaptive algorithm, fuzzy systems, membership functions, observer. ", volume = "12", number = "7", pages = "747-11", }
