2-DOF Fractional Order PID Control Based on BP Neural Network for Atomic Force Microscope
Shujun Chang*,, Chao Peng**, Shiqiang Dai**, and Jianyu Wang**
*Zhongshan Institute, University of Electronic Science and Technology of China
1 Xueyuan Road, Shiqi District, Zhongshan City, Guangdong 528400, China
**School of Automation Engineering, University of Electronic Science and Technology of China
2006 Xiyuan Avenue, West Hi-Tech Zone, Chengdu, Sichuan 611731, China
To enhance trajectory tracking performance of atomic force microscope system, a two-degree of freedom fractional order PID (2-DOF FOPID) control approach based on back propagation (BP) neural network is proposed in this paper. At first, principle and structure of the proposed control approach is presented. Then, 2-DOF FOPID controller is designed, including in feedforward and feedback controller, fractional calculus and approximation of fractional operator. Meanwhile, the parameters of controller are analyzed. Based on them, a BP neural network is built to adjust the parameters in this control structure according to the error between the reference trajectory and the actual output. Finally, the proposed control approach is conducted in atomic force microscope tracking control experiment, experimental results verify the effectiveness and improvement of the proposed control approach.
-  M. Marrese, V. Guarino, and L. Ambrosio, “Atomic force microscopy: a powerful tool to address scaffold design in tissue engineering,” J. of Functional Biomaterials, Vol.8, No.1, Article No.7, 2017.
-  A. Ikai et al., “Atomic force microscope as a nano- and micrometer scale biological manipulator: A short review,” Seminars in Cell & Developmental Biology, Vol.73, pp. 132-144, 2018.
-  Y.-X. Ding et al., “Mechanical characterization of cervical squamous carcinoma cells by atomic force microscopy at nanoscale,” Medical Oncology, Vol.32, No.3, Article No.71, 2015.
-  Y. Wang et al., “Nanomanipulation of Individual DNA Molecules Covered by Single-Layered Reduced Graphene Oxide Sheets on a Solid Substrate,” J. of Physical Chemistry B, Vol.122, No.2, pp. 612-617, 2017.
-  M. H. Korayem, H. Khaksar, and H. J. Sharahi, “Modeling and simulation of contact parameters of elliptical and cubic nanoparticles to be used in nanomanipulation based on atomic force microscope,” Ultramicroscopy, Vol.206, Article No.112808, 2019.
-  G.-Y. Gu et al., “Modeling and control of piezo-actuated nanopositioning stages: A survey,” IEEE Trans. on Automation Science and Engineering, Vol.13, No.1, pp. 313-332, 2016.
-  W. Lv and F. Wang, “Finite-time adaptive fuzzy tracking control for a class of nonlinear systems with unknown hysteresis,” Int. J. of Fuzzy Systems, Vol.20, No.3, pp. 782-790, 2018.
-  W. Liu et al., “Displacement Control of Piezoelectric Actuator Based on Fuzzy Fractional Order PID,” 5th Int. Conf. on Control, Automation and Robotics (ICCAR), pp. 495-500, 2019.
-  W. Zhu and X.-T. Rui, “Hysteresis modeling and displacement control of piezoelectric actuators with the frequency-dependent behavior using a generalized Bouc-Wen model,” Precision Engineering, Vol.43, No.C, pp. 299-307, 2016.
-  J. Gan, X. Zhang, and H. Wu, “A generalized Prandtl-Ishlinskii model for characterizing the rate-independent and rate-dependent hysteresis of piezoelectric actuators,” Review of Scientific Instruments, Vol.87, No.3, Article No.035002, 2016.
-  X. Song et al., “Modeling and identification of hysteresis with modified Preisach model in piezoelectric actuator,” IEEE Int. Conf. on Advanced Intelligent Mechatronics (AIM), pp. 1538-1543, 2017.
-  B. Ding and Y. Li, “Hysteresis Compensation and Sliding Mode Control with Perturbation Estimation for Piezoelectric Actuators,” Micromachines, Vol.9, No.5, Article No.241, 2018.
-  L. Zhi, J. Shan, and U. Gabbert, “Inverse compensation of hysteresis using Krasnoselskii-Pokrovskii model,” IEEE/ASME Trans. on Mechatronics, Vol.23, No.2, pp. 966-971, 2018.
-  E. Y. Bejarbaneh et al., “A new adjusting technique for PID type fuzzy logic controller using PSOSCALF optimization algorithm,” Applied Soft Computing, Vol.85, Article No.105822, 2019.
-  J. I. Chowdhury et al., “Control of supercritical organic Rankine cycle based waste heat recovery system using conventional and fuzzy self-tuned PID controllers,” Int. J. of Control, Automation and Systems, Vol.17, No.11, pp. 2969-2981, 2019.
-  S. Zeng et al., “Nonlinear adaptive PID control for greenhouse environment based on RBF network,” Sensors, Vol.12, No.5, pp. 5328-5348, 2012.
-  B. Yang et al., “Adaptive fractional-order PID control of PMSG-based wind energy conversion system for MPPT using linear observers,” Int. Trans. on Electrical Energy Systems, Vol.29, No.1, Article No.e2697, 2019.
-  A. S. Chopade et al., “Design and implementation of digital fractional order PID controller using optimal pole-zero approximation method for magnetic levitation system,” IEEE/CAA J. of Automatica Sinica, Vol.5, No.5, pp. 977-989, 2018.
-  K. Sundaravadivu, S. Sivakumar, and N. Hariprasad, “2DOF PID controller design for a class of FOPTD Models – An analysis with heuristic algorithms,” Procedia Computer Science, Vol.48, pp. 90-95, 2015.
-  H. B. Huo, X. J. Zhu, and G. Y. Cao, “Design for two-degree-of-freedom PID regulator based on improved generalized extremal optimization algorithm,” J. of Shanghai Jiaotong University (Science), No.2, pp. 148-152, 2007.
-  Y. Wu and Q. Zou, “Iterative control approach to compensate for both the hysteresis and the dynamics effects of piezo actuators,” IEEE Trans. on Control Systems Technology, Vol.15, No.5, pp. 936-944, 2007.
-  S. C. Ashley et al., “Hysteresis inverse iterative learning control of piezoactuators in AFM,” IFAC Proc. Volumes, Vol.41, No.2, pp. 8269-8274, 2008.
-  V. M. Alfaro, R. Vilanova, and O. Arrieta, “Considerations on set-point weight choice for 2-DoF PID controllers,” IFAC Proc. Volumes, Vol.42, No.11, pp. 721-726, 2009.
-  E. Yumuk, M. Güzelkaya, and İ. Eksin, “Analytical fractional PID controller design based on Bode’s ideal transfer function plus time delay,” ISA Trans., Vol.91, pp. 196-206, 2019.
-  M. Koseoglu et al., “An effective analog circuit design of approximate fractional-order derivative models of M-SBL fitting method,” Engineering Science and Technology, an Int. J., Vol.33, Article No.101069, 2022.
-  R. Stanisławski, M. Rydel, and Z. Li, “A New Reduced-Order Implementation of Discrete-Time Fractional-Order PID Controller,” IEEE Access, Vol.10, pp. 17417-17429, 2022.
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.