Optimal Integral Sliding Mode Controller Design for Micro Gyroscope Based on Time Delay Estimation
DOI:
https://doi.org/10.18196/jrc.v5i6.23676Keywords:
MEMS Gyroscope, Sliding Mode Control, Arithmetic Optimization Algorithms, Time Delay Control, Model Free Controllers.Abstract
Controlling Micro-Electro-Mechanical Systems (MEMS) gyroscopes often involves dealing with uncertainties and external disturbances, which can complicate control strategies. This article proposes a novel control strategy that integrates Integral Sliding Mode Control (ISMC) with Time Delay Estimation (TDE) and Arithmetic Optimization Algorithm (AOA) to enhance control performance. The proposed controller, OTDISMC, is designed to eliminate chattering and improve robustness against disturbances without relying on system dynamics. Contrary to the conventional controllers structures which depended on the system dynamic in their schemes, a model free controller is formulated without using system dynamics in its formulation. Time delay estimation technique has been undertaken as an efficient approximating strategy to approximate and compensate the lumped uncertain dynamics of the system. AOA has been undertaken to determine the optimum solutions of the coefficients of proposed control approach. The stability has been analyzed and investigated using the Lyapunov stability criterion. To show the effectiveness and validity of the developed controller, computer simulations in nominal and robustness scenarios have been carried out and compared with TDISMC that tuned by trial and error and PSO-TDISMC that tuned by particle swarm optimization (PSO). Simulation results demonstrate that OTDISMC significantly reduces tracking errors and improves robustness. The results indicate the superiority of the proposed controller as compared with traditional TDISMC tuned by classical methods and PSO-TDISMC tuned by particle swarm optimization (PSO).References
W. A. Gill, I. Howard, I. Mazhar, and K. McKee, “A review of MEMS vibrating gyroscopes and their reliability issues in harsh environments,” Sensors, vol. 22, no. 19, p. 7405, 2022.
M. A. Faraj, N. Derbel, and B. Maalej, “Optimal fractional order pd controller for MEMS gyroscope,” in 2024 21st International MultiConference on Systems, Signals & Devices (SSD), pp. 266–271, 2024.
M. Rahmani, M. H. Rahman, and M. Nosonovsky, “A new hybrid robust control of mems gyroscope,” Microsystem Technologies, vol. 26, no. 3, pp. 853–860, 2020.
M. Rahmani, “MEMS gyroscope control using a novel compound robust control,” ISA Trans., vol. 72, pp. 37–43, Jan. 2017.
Y. Fang, W. Fu, C. An, Z. Yuan, and J. Fei, “Modeling, simulation and dynamic sliding mode control of a MEMS gyroscope,” Micromachines, vol. 12, no. 2, p. 190, 2021.
H. Wang, L. Hua, Y. Guo, and C. Lu, “Control of z-axis mems gyroscope using adaptive fractional order dynamic sliding mode approach,” IEEE Access, vol. 7, pp. 133008–133016, 2019.
Y. Fang, J. Fei, and Y. Yang, “Adaptive backstepping design of a micro gyroscope,” Micromachines, vol. 9, no. 7, p. 338, 2018.
J. Fei and X. Liang, “Adaptive backstepping fuzzy neural network
fractional-order control of microgyroscope using a nonsingular
terminal sliding mode controller,” Complexity, pp. 1–12, Sep. 2018.
J. Fei, Y. Fang, and Z. Yuan, “Adaptive fuzzy sliding mode control for a micro gyroscope with backstepping controller,” Micromachines, vol. 11, no. 11, p. 968, 2020.
S. B. Fazeli Asl and S. S. Moosapour, “Fractional order fuzzy dynamic backstepping sliding mode controller design for triaxial MEMS gyroscope based on high-gain and disturbance observers,” IETE Journal of Research, vol. 67, no. 6, pp. 799–816, 2021.
L. Zhang, Z. Wen, C. Lu, Y. Guo, X. Zhang, and L. Luo, “Improved
fully adjusted neural network based recursive terminal sliding mode
control for MEMS gyroscopes,” in 2022 5th International Conference on Robotics, Control and Automation Engineering (RCAE), pp. 11–16, 2022.
M. Rahmani, M. H. Rahman, and J. Ghommam, “Compound fractional integral terminal sliding mode control and fractional pd control of MEMS gyroscope,” New Trends in Robot Control, pp. 359–370, 2020.
Y. Guo, B. Xu, and R. Zhang, “Terminal sliding mode control of MEMS gyroscopes with finite-time learning,” IEEE Transactions on Neural Networks and Learning Systems, vol. 32, no. 10, pp. 4490–4498, 2020.
K. Kant, R. K. Paswan, I. Ahmad, and A. P. Sinha, “Digital control and readout of MEMS gyroscope using second-order sliding mode control,” IEEE Sensors Journal, vol. 22, no. 21, pp. 20 567–20 574, 2022.
R. Zhang, B. Xu, S. Li, and G. Gao, “Recursive integral terminal sliding mode control with combined extended state observer and adaptive kalman filter for MEMS gyroscopes,” International Journal of Robust and Nonlinear Control, vol. 34, no. 9, pp. 5706–5718, 2024.
V. Giap, H. Vu, Q. Nguyen, and S.-C. Huang, “Chattering-free sliding mode control-based disturbance observer for mems gyroscope system,” Microsystem Technologies, vol. 28, no. 8, pp. 1867–1877, 2022.
V. N. Giap, Q. D. Nguyen, N. K. Trung, and S.-C. Huang, “Time-varying disturbance observer based on sliding-mode observer and double phases fixed-time sliding mode control for a ts fuzzy micro-electro-mechanical system gyroscope,” Journal of Vibration and Control, vol. 29, no.7-8, pp. 1927–1942, 2023.
M. Jafari, S. Mobayen, H. Roth, and F. Bayat, “Nonsingular terminal
sliding mode control for micro-electro-mechanical gyroscope based on disturbance observer: Linear matrix inequality approach,” Journal of Vibration and Control, vol. 28, no. 9-10, pp. 1126–1134, 2022.
M. Rahmani and S. Redkar, “Fractional robust data-driven control of
nonlinear MEMS gyroscope,” Nonlinear Dynamics, vol. 111, no. 21, pp. 19 901–19 910, 2023.
J. Fei and Z. Wang, “Multi-loop recurrent neural network fractional order terminal sliding mode control of MEMS gyroscope,” IEEE Access, vol. 8, pp. 965–974, 2020.
Y. Fang, W. Fu, H. Ding, and J. Fei, “Modeling and neural sliding
mode control of MEMS triaxial gyroscope,” Advances in Mechanical
Engineering, vol. 14, no. 3, 2022.
Z. Wang and J. Fei, “Double loop neural fractional-order terminal
sliding mode control of MEMS gyroscope,” in 2021 Second International Symposium on Instrumentation, Control, Artificial Intelligence, and Robotics (ICA-SYMP), pp. 1–4, 2021.
Z. Feng and J. Fei, “Super-twisting sliding mode control for micro gyroscope based on RBF neural network,” IEEE Access, pp. 1–13, 2019.
J. Fei and Z. Feng, “Fractional-order finite-time super-twisting sliding
mode control of micro gyroscope based on double-loop fuzzy neural network,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 51, no. 12, pp. 7692–7706, 2020.
J. Fei and Z. Feng, “Adaptive fuzzy super-twisting sliding mode control for microgyroscope,” Complexity, vol. 2019, no. 6, pp. 1–13, 2019.
P. Gao, X. Lv, H. Ouyang, L. Mei, and G. Zhang, “A novel model-free intelligent proportional-integral super twisting nonlinear fractional-order sliding mode control of PMSM speed regulation system,” Complexity, vol. 2020, no. 1, p. 8405453, 2020.
D. Elleuch and T. Damak, “Robust model-free control for robot manipulator under actuator dynamics,” Mathematical Problems in Engineering, vol. 2020, no. 1, p. 7417314, 2020.
H. Wang, G. I. Mustafa, and Y. Tian, “Model-free fractional-order sliding mode control for an active vehicle suspension system,” Advances in Engineering Software, vol. 115, pp. 452–461, 2018.
P. Gao, G. Zhang, and X. Lv, “Model-free control using improved
smoothing extended state observer and super-twisting nonlinear sliding mode control for pmsm drives,” Energies, vol. 14, no. 4, p. 922, 2021.
S. Ahmed, A. T. Azar, and I. K. Ibraheem, “Model-free scheme using
time delay estimation with fixed-time FSMC for the nonlinear robot
dynamics,” AIMS Mathematics, vol. 9, no. 4, pp. 9989–10009, 2024.
S. Ahmed, H. Wang, and Y. Tian, “Model-free control using time delay estimation and fractional-order nonsingular fast terminal sliding mode for uncertain lower-limb exoskeleton,” Journal of Vibration and Control, vol. 24, no. 22, pp. 5273–5290, 2018.
A. Rezoug and M. Hamerlain, “Adaptive neural super twisting controller based on terminal sliding mode and time delay estimation method for robotic manipulator,” International Journal of Digital Signals andSmart Systems, vol. 1, no. 4, pp. 348–364, 2017.
M. Taefi and M. A. Khosravi, “A model free adaptive-robust design
for control of robot manipulators: Time delay estimation approach,”
International Journal of Robust and Nonlinear Control, 2024.
S. Liu and W. Xu, “Model-free robust adaptive control of overhead
cranes with finite-time convergence based on time-delay control,” Transactions of the Institute of Measurement and Control, vol. 45, no. 6, pp. 1037–1051, 2023.
J. Sun, J. Wang, P. Yang, and S. Guo, “Fractional-order prescribed performance sliding-mode control with time-delay estimation for wearable exoskeletons,” IEEE Transactions on Industrial Informatics, vol. 19, no. 7, pp. 8274–8284, 2022.
J. Baek and J. Jung, “A model-free control scheme for attitude stabilization of quadrotor systems,” Electronics, vol. 9, no. 10, p. 1586, 2020.
H. V. A. Truong, M. H. Nguyen, D. T. Tran, and K. K. Ahn, “A
novel adaptive neural network-based time-delayed estimation control for nonlinear systems subject to disturbances and unknown dynamics,” ISA transactions, vol. 142, pp. 214–227, 2023.
Y. Kali, M. Ayala, J. Rodas, M. Saad, J. Doval-Gandoy, R. Gregor,
and K. Benjelloun, “Time delay estimation based discrete-time supertwisting current control for a six-phase induction motor,” IEEE Transactions on Power Electronics, vol. 35, no. 11, pp. 12 570–12 580, 2020.
Y. Kali, M. Saad, J. F. Boland, and C. Fallaque, “Walking control using TDE-based Backstepping SM of position-commanded Nao biped robot with matched and unmatched perturbations,” Journal of Control, Automation and Electrical Systems, vol. 33, no. 6, pp. 1633–1642, 2022.
M. Boukattaya, N. Mezghani, and T. Damak, “Adaptive nonsingular
fast terminal sliding-mode control for the tracking problem of uncertain dynamical systems,” ISA transactions, vol. 77, pp. 1–19, 2018.
F. Massaoudi, D. Elleuch, and T. Damak, “Robust control for a two dof robot manipulator,” Journal of Electrical and Computer Engineering, vol. 2019, no. 1, p. 3919864, 2019.
M. A. Faraj, B. Maalej, and N. Derbel, “Optimal sliding mode controller for lower limb rehabilitation exoskeleton in constrained environments,” Indonesian Journal of Electrical Engineering and Computer Science, vol. 30, no. 3, pp. 1458–1469, 2023.
D. Meng, H. Xu, H. Xu, H. Sun, and B. Liang, “Trajectory tracking
control for a cable-driven space manipulator using time-delay estimation and nonsingular terminal sliding mode,” Control Engineering Practice, vol. 139, p. 105649, 2023.
Z. Wen, Y. Guo, L. Zhang, X. Zhang, C. Lu, and L. Luo, “Adaptive
sliding mode control for MEMS gyroscopes based on immersion and
invariance manifold,” in 2023 9th International Conference on Information, Cybernetics, and Computational Social Systems (ICCSS), pp.6–11, 2023.
R. Sarkar, S. M. Amrr, J. K. Bhutto, A. S. Saidi, A. Algethami, and
A. Banerjee, “Finite time fractional order ISMC with time delay estimation for re-entry phase of RLV with enhanced chattering suppression,” Acta Astronautica, vol. 202, pp. 130–138, 2023.
J. Hui, “Coordinated discrete-time super-twisting sliding mode controller coupled with time-delay estimator for PWR-based nuclear steam supply system,” Energy, vol. 301, p. 131536, 2024.
Z. Song, L. Wang, J. Ling, L. Wang, J. Duan, Y. Wang, and B. Chen,
“Time-delay control scheme with adaptive fixed-time convergent super twisting fractional-order nonsingular terminal sliding mode for piezoelectric displacement amplifier,” ISA transactions, vol. 146, pp. 99–113, 2024.
S. Han, H. Wang, and Y. Tian, “Model-free based adaptive nonsingular fast terminal sliding mode control with time-delay estimation fora12DOF multi-functional lower limb exoskeleton,” Advances in Engineering Software, vol. 119, pp. 38–47, 2018.
M. A. Faraj, B. Maalej, N. Derbel and O. Naifar, “Adaptive fractional order super-twisting sliding mode controller for lower limb rehabilitation exoskeleton in constraint circumstances based on the grey wolf optimization algorithm,” Mathematical Problems in Engineering, vol. 2023, 2023.
A. Rezoug, J. Iqbal, and M. Tadjine, “Extended grey wolf optimization–based adaptive fast nonsingular terminal sliding mode control of a robotic manipulator,” Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 236, no. 9, pp. 1738–1754, 2022.
M. A. Faraj and A. M. Abbood, “Fractional order PID controller tuned by bat algorithm for robot trajectory control,” Indonesian Journal of Electrical Engineering and Computer Science, vol. 21, no. 1, pp. 74–83,2021
L. Abualigah, A. Diabat, S. Mirjalili, M. Abd Elaziz, and A. H.
Gandomi, “The arithmetic optimization algorithm,” Computer methods in applied mechanics and engineering, vol. 376, p. 113609, 2021.
M. Issa, “Enhanced arithmetic optimization algorithm for parameter estimation of PID controller,” Arabian Journal for Science and Engineering, vol. 48, no. 2, pp. 2191–2205, 2023.
Y. Fang, C. An, W. Juan, and J. Fei, “Adaptive h-infinity tracking control for microgyroscope,” Advances in Mechanical Engineering, vol. 12, no. 6, p. 1687814020927832, 2020.
J. Fei, Z. Wang, and X. Liang, “Robust adaptive fractional fast terminal sliding mode controller for microgyroscope,” Complexity, vol. 2020, no. 1, p. 8542961, 2020.
J. Xie, J. Fei, and C. An, “Gated recurrent fuzzy neural network slidingmode control of a micro gyroscope,” Mathematics, vol. 11, no. 3, p. 509, 2023
K. Youcef-Toumi and O. Ito, “A time delay controller for systems with unknown dynamics,” Journal of Dynamic Systems, Measurement, and Control, vol. 112, p. 133, 1990.
T. C. Hsia and L. Gao, “Robot manipulator control using decentralized linear time-invariant time-delayed joint controllers,” in Proceedings., IEEE International Conference on Robotics and Automation, pp. 2070–2075, 1990.
S. Ahmed, I. Ghous, and F. Mumtaz, “TDE based model-free control for rigid robotic manipulators under nonlinear friction,” Scientia Iranica, vol. 31, no. 2, pp. 137–148, 2024.
Y. Kali, M. Saad, K. Benjelloun, and C. Khairallah, “Super-twisting
algorithm with time delay estimation for uncertain robot manipulators,” Nonlinear Dynamics, vol. 93, pp. 557–569, 2018.
M. A. Faraj, B. Maalej, and N. Derbel, “Fractional order based con-trollers for lower limb exoskeleton in contact environments,” in 202320th International Multi-Conference on Systems, Signals & Devices (SSD), pp. 705–710, 2023.
M. A. Faraj, B. Maalej, and N. Derbel, “Sliding mode control for lowerlimb rehabilitation exoskeleton contacting with floor,” in 2023 20th International Multi-Conference on Systems, Signals & Devices (SSD), pp. 109–115, 2023.
M. A. Faraj, B. Maalej, and N. Derbel, “Design and analysis of
nonsingular terminal super twisting sliding mode controller for lower
limb rehabilitation exoskeleton contacting with ground,” in State Estimation and Stabilization of Nonlinear Systems: Theory and Applications, pp. 367–386, 2023.
E. S. Ghith and F. A. A. Tolba, “Tuning PID controllers based on hybrid arithmetic optimization algorithm and artificial gorilla troop optimization for micro-robotics systems,” IEEE access, vol. 11, pp. 27138–27154, 2023.
G. Hu, J. Zhong, B. Du, and G. Wei, “An enhanced hybrid arithmetic
optimization algorithm for engineering applications,” Computer Methods in Applied Mechanics and Engineering, vol. 394, p. 114901, 2022.
K. G. Dhal, B. Sasmal, A. Das, S. Ray, and R. Rai, “A comprehensive
survey on arithmetic optimization algorithm,” Archives of Computational Methods in Engineering, vol. 30, no. 5, pp. 3379–3404, 2023.
M. Ahmadipour, M. M. Othman, R. Bo, M. S. Javadi, H. M. Ridha,
and M. Alrifaey, “Optimal power flow using a hybridization algorithm of arithmetic optimization and aquila optimizer,” Expert Systems with Applications, vol. 235, p. 121212, 2024.
A. Znidi, A. S. Nouri, and N. Derbel, "Trajectory Tracking of Lower Limb Exoskeletons using Fractional Order Sliding Mode Control," 2023 IEEE International Workshop on Mechatronic Systems Supervision (IW_MSS), pp. 1-6, 2023.
A. Q Al-Dujaili, A. Falah, D. A. Pereira, and I. K. Ibrahim, “Optimal super-twisting sliding mode control design of robot manipulator: design and comparison study,” Int. J. Adv. Robotic Syst., vol. 17, no. 6, 2020.
A. J. Humaidi and H. M. Badr, “Linear and Nonlinear Active
Disturbance Rejection Controllers for single-link flexible joint robot manipulator based on PSO tuner,” J. Eng. Sci. Technol. Rev., vol. 1, no. 3, pp. 133–8, 2018.
Downloads
Published
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
This journal is based on the work at https://journal.umy.ac.id/index.php/jrc under license from Creative Commons Attribution-ShareAlike 4.0 International License. You are free to:
- Share – copy and redistribute the material in any medium or format.
- Adapt – remix, transform, and build upon the material for any purpose, even comercially.
The licensor cannot revoke these freedoms as long as you follow the license terms, which include the following:
- Attribution. You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- ShareAlike. If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
- No additional restrictions. You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
• Creative Commons Attribution-ShareAlike (CC BY-SA)
JRC is licensed under an International License
