Skip to main content
SpringerLink
Log in

Variable Fractional Order Sliding Mode Control for Seismic Vibration Suppression of Uncertain Building Structure

  • Original Paper
  • Published:
Journal of Vibration Engineering & Technologies Aims and scope Submit manuscript

Abstract

Purpose

Building structures are affected by earthquakes and uncertainties, which cause serious damage and threaten people’s lives. Thus, it is necessary to design an effective control method for uncertain buildings.

Methods

A novel variable fractional order sliding mode control (VOSMC) technique is proposed to control the vibration of building structure caused by seismic excitations, including El Centro, Hachinohe, Northridge and Kobe earthquakes. Based on the proposed variable fractional order sliding mode surface, a variable fractional order sliding control law is presented. The global asymptotic stability and finite-time convergence of the considered system are analyzed and proved by using variable fractional order Lyapunov stability theorem. Besides, the corresponding constant fractional order sliding mode control (FOSMC) method is also given. Finally, the control effects of VOSMC and FOSMC methods are discussed by four performance indices.

Results

The feasibility and rationality of the introduced methods are verified by two examples.

Conclusions

Compared with the FOSMC method, the proposed variable fractional order control method not only has lower control output, but also has higher output utilization ratio, which is beneficial to energy conservation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Muhammed ZK, Sachin B (2020) Performance evaluation of moment-resisting steel frame buildings under seismic and blast-induced vibrations. Int J Comput Appl Technol 8:1–26

    Google Scholar 

  2. Francesc P, Yolanda V, Guillem G et al (2018) Hysteretic active control of base-isolated buildings. Struct Control Health Monit 25:e2206

    Article  Google Scholar 

  3. Mohibb-e-Hussain J, Rangaraj MD, Radhe STS, Hemantha K, Sharnappa J (2021) Dynamic analysis of a quarter car model with semi-active seat suspension using a novel model for magneto-rheological (MR) Damper. Int J Comput Appl Technol 9:161–176

    Google Scholar 

  4. Wang JH, Zhu HY, Zhang CL et al (2018) Adaptive hyperbolic tangent sliding-mode control for building structural vibration systems for uncertain earthquakes. IEEE Access 6:74728–74736

    Article  Google Scholar 

  5. Aghababa MP (2013) A fractional-order controller for vibration suppression of uncertain structures. ISA Trans 52:881–887

    Article  Google Scholar 

  6. Yu Y, Royel S, Li JC et al (2016) Magnetorheological elastomer base isolator for earthquake response mitigation on building structures: modeling and second-order sliding mode control. Earthq Struct 11(6):943–966

    Article  Google Scholar 

  7. Normaisharah M, Fitri Y, Sheikh AZSS et al (2020) Seismic control of a building structure equip with hybrid mass damper using sliding mode control. Intell Manufa Mech 2:146–156

    Google Scholar 

  8. Arash YF, Touraj T (2016) Sliding mode fault detection and fault-tolerant control of smart dampers in semi-active control of building structures. Noise Control Eng J 24(12):125030

    Google Scholar 

  9. AOzer HO, Sayin A, Korkmaz N, Yagiz N, (2016) Sliding mode control optimized by genetic algorithm for building model. Int J Comput Appl Technol 4(1):13–19

    Google Scholar 

  10. Josué EZ, Gerardo SN (2016) Ground-borne vibration control in a building-like structure using multi-positive position feedback combined with sliding mode control. Noise Control Eng J 64(5):668–676

    Article  Google Scholar 

  11. Paul S, Yu W, Li X (2019) Discrete-time sliding mode for building structure bidirectional active vibration control. T I Meas Control 41(2):433–446

    Article  Google Scholar 

  12. Paul S, Yu W, Li X (2019) Fuzzy-sliding mode control of nonlinear smart base-isolated building under earthquake excitation. Struct Des Tall Spec 28(1):e1557

    Article  Google Scholar 

  13. Ken Y (2011) Seismic response control of sliding isolated buildings using adaptive fuzzy sliding mode control. Int J Phys Sci 6(20):4732–4738

    Google Scholar 

  14. Zhu HY, Chen ZC, Wang JH et al (2018) Fuzzy adaptive compensation control for uncertain building structural systems by sliding-mode technology. Complexity 2018:1–6

    MATH  Google Scholar 

  15. Normaisharah M, Fitri Y, Sheikh AZSS, Mohamed SMA (2020) Seismic vibration suppression of a building with an adaptive nonsingular terminal sliding mode control. J Vib Control 26(23–24):2136–2147

    MathSciNet  Google Scholar 

  16. Wang JH, Chen WL, Chen ZC et al (2019) Neural terminal sliding-mode control for uncertain systems with building structure vibration. Complexity 2019:1–9

    MATH  Google Scholar 

  17. Ismail Z, Varatharajoo R, Chak YC (2020) A fractional-order sliding mode control for nominal and underactuated satellite attitude controls. Adv Space Res 66(2):321–334

    Article  Google Scholar 

  18. Phuc BDH, Phung VD, You SS, Do TD (2020) Fractional-order sliding mode control synthesis of supercavitating underwater vehicles. J Vib Control 26(21–22):1909–1919

    Article  MathSciNet  Google Scholar 

  19. Zhou T, Xu YG, Wu B (2020) Smooth Fractional Order Sliding Mode Controller for Spherical Robots with Input Saturation. Appl Sci 10(6):2117

    Article  Google Scholar 

  20. Wang J, Min CL, Jaehyung K, Hyun HK (2021) Fast fractional-order terminal sliding mode control with rbfnn based sliding perturbation observer for 7-dof robot manipulator. IEEE Access 9:1

    Article  Google Scholar 

  21. Huang S, Wang J (2020) Fixed-time fractional-order sliding mode control for nonlinear power systems. J Vib Control 26(17):1425–1434

    Article  MathSciNet  Google Scholar 

  22. Lv X, Sun Y, Hu W, Dinavahi V (2021) Robust load frequency control for networked power system with renewable energy via fractional-order global sliding mode control. Iet Renew Power Gen 15(5):1046–1057

    Article  Google Scholar 

  23. Cheng C, Liu S, Wu H (2020) Sliding mode observer-based fractional-order proportional-integral-derivative sliding mode control for electro-hydraulic servo systems. P I Mech Eng C-J Mec 234(10):1887–1898

    Article  Google Scholar 

  24. Kuang Z, Gao H, Tomizuka M (2021) Precise linear-motor synchronization control via cross-coupled second-order discrete-time fractional-order sliding mode. IEEE-ASME T Mech 26(1):358–368

    Google Scholar 

  25. Zhou X, Li X (2021) Trajectory tracking control for electro-optical tracking system using ESO based fractional-order sliding mode control. IEEE Access 9:45891–45902

    Article  Google Scholar 

  26. Zhu P, Chen Y, Li M, Zhang P, Wan Z (2020) Fractional-order sliding mode position tracking control for servo system with disturbance. ISA Trans 105:269–277

    Article  Google Scholar 

  27. Guo YX (2021) Hyperbolic uncertainty estimator based fractional order sliding mode control framework for uncertain fractional order chaos stabilization and synchronization. ISA Trans 28:5

    Google Scholar 

  28. Seyede ZM, Assef Z, Majid H (2021) A new fractional sliding mode controller based on nonlinear fractional-order proportional integral derivative controller structure to synchronize fractional-order chaotic systems with uncertainty and disturbances. J Vib Control 2:1–13

    Google Scholar 

  29. Seyede ZM, Assef Z, Majid H (2020) Fuzzy logic embedding of fractional order sliding mode and state feedback controllers for synchronization of uncertain fractional chaotic systems. Comput Appl Math 39(3):182

    Article  MathSciNet  Google Scholar 

  30. Rabah K, Ladaci S (2020) A Fractional Adaptive Sliding Mode Control Configuration for Synchronizing Disturbed Fractional-Order Chaotic Systems. Circ Syst Signal Pr 39(3):1244–1264

    Article  Google Scholar 

  31. Chen Y, Yan JY, Feng J, Sareh P (2021) Particle Swarm Optimization Based Metaheuristic Design Generation of Non-Trivial Flat Foldable Origami Tessellations with Degree-4 Vertices. J Mech Design 143(1):0117031–01170312

    Article  Google Scholar 

  32. Chen Y, Yan JY, Feng J (2019) Geometric and kinematic analyses and novel characteristics of origami-inspired structures. Symmetry 11(9):1101

    Article  Google Scholar 

  33. Ma JY, You Z (2013) Energy absorption of thin-walled beams with a pre-folded origami pattern. Thin Wall Struct 73(12):198–206

    Article  Google Scholar 

  34. Dong ZX, Liu JY, Liu B, Li KN, Li X (2021) Hourly energy consumption prediction of an office building based on ensemble learning and energy consumption pattern classification. Energ Build. 241:110929

    Article  Google Scholar 

  35. Toqeer A, Asad W, Essam A (2020) Energy management of a battery storage and D-STATCOM integrated power system using fractional order sliding mode control. CSEE J Power Energy 2:1–14

    Google Scholar 

  36. Afghoul H, Krim F, Babes B et al (2018) Design and real time implementation of sliding mode supervised fractional controller for wind energy conversion system under sever working conditions. Energ Convers Manage 167(1):91–101

    Article  Google Scholar 

  37. Meng X, Wu Z, Gao C et al (2021) Finite-time Projective Synchronization Control of Variable-Order Fractional Chaotic Systems via Sliding Mode Approach. IEEE T Circuits-II 2021:1

    Google Scholar 

  38. Jiang JF, Cao DQ, Chen HT (2020) Sliding mode control for a class of variable-order fractional chaotic systems. J Franklin I 357(15):10127–10158

    Article  MathSciNet  MATH  Google Scholar 

  39. Jiang JF, Li HK, Zhao K et al (2021) (2021) Finite time stability and sliding mode control for uncertain variable fractional order nonlinear systems. Adv Differ Equ-Ny 1:1–16

    Google Scholar 

  40. Lorenzo CF, Hartley TT (2002) Variable order and distributed order fractional operators. Nonlinear Dynam 29(1–4):57–98

    Article  MathSciNet  MATH  Google Scholar 

  41. Valério D, Costa JS (2011) Variable-order fractional derivatives and their numerical approximations. Signal Process 91(3):470–483

    Article  MATH  Google Scholar 

  42. Li Y, Chen YQ, Podlubny I (2010) Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Comput Math Appl 59:1810–1821

    Article  MathSciNet  MATH  Google Scholar 

  43. Tenreiro M, Jose A, Moghaddam BP (2018) A Robust Algorithm for Nonlinear Variable-Order Fractional Control Systems with Delay. Int J Nonlin Sci Num 19(3–4):231–238

    Google Scholar 

  44. China, (2016) GB 50011–2010 Code for Seismic Design of Buildings. China Construction Industry Press, Beijing

    Google Scholar 

Download references

Acknowledgements

The authors thank the National Natural Science Foundation of China (41977240) for its support.

Author information

Authors and Affiliations

  1. School of Civil Engineering and Transportation, Hohai University, Nanjing, China

    Chunxiu Wang, Xingde Zhou, Xianzeng Shi & Yitong Jin

Authors
  1. Chunxiu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xingde Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xianzeng Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yitong Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chunxiu Wang.

Ethics declarations

Conflict of interest

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, C., Zhou, X., Shi, X. et al. Variable Fractional Order Sliding Mode Control for Seismic Vibration Suppression of Uncertain Building Structure. J. Vib. Eng. Technol. 10, 299–312 (2022). https://doi.org/10.1007/s42417-021-00377-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42417-021-00377-9

Keywords

Search

Navigation