In this study, adaptive prescribed finite-time stabilisation of uncertain single-input and single-output non-linear systems is considered in the presence of unknown states, unknown parameters, external load disturbance, and non-symmetric input saturation. A prescribed finite time disturbance observer is designed to approximate the unmeasured external disturbance. Also, a non-singular prescribed finite time terminal sliding mode control is proposed for the closed-loop control of the system with the non-symmetric input saturation. Extended Kalman filter algorithm is employed for the real-time estimations of the states and unknown parameters of the system. Moreover, a particle swarm optimisation algorithm is used to obtain the design parameters of the proposed disturbance observer and controller. To show the performance of designed control scheme, the proposed approach is employed to guarantee prescribed finite time stabilisation of non-linear vibration of a non-local strain gradient nanobeam. The Galerkin projection method is used to reduce the non-dimensional form of the governing non-linear partial differential equation of Euler–Bernoulli nanobeam to the ordinary differential equation. Finally, numerical simulations are performed to illustrate the effectiveness and performance of the developed adaptive control scheme for the vibration control of nanobeam in comparison with the conventional sliding mode control.

References

1. 1)
  - 22. Heo, J.S., Lee, K.Y., Garduno-Ramirez, R.: ‘Multiobjective control of power plants using particle swarm optimization technique’, IEEE Trans. Energy Convers., 2006, 21, (2), pp. 552–561.
2. 2)
  - 9. Yousefpour, A., Jahanshahi, H., Munoz-Pacheco, J.M., et al: ‘A fractional-order hyper-chaotic economic system with transient chaos’, Chaos Solitons Fractals, 2020, 130, p. 109400.
3. 3)
  - 39. Zhu, C., Fang, X., Liu, J.: ‘A new approach for smart control of size-dependent nonlinear free vibration of viscoelastic orthotropic piezoelectric doubly-curved nanoshells’, Appl. Math. Model., 2020, 77, pp. 137–168.
4. 4)
  - 40. Yu, X., Zhihong, M.: ‘Fast terminal sliding mode control design for nonlinear dynamical systems’, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 2002, 49, (2), pp. 261–264.
5. 5)
  - 33. Lu, L., Zhu, L., Guo, X., et al: ‘A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells’, Appl. Math. Mech., 2019, 40, (12), pp. 1695–1722.
6. 6)
  - 29. Bahaadini, R., Hosseini, M.: ‘Flow-induced and mechanical stability of cantilever carbon nanotubes subjected to an axial compressive load’, Appl. Math. Model., 2018, 59, pp. 597–613.
7. 7)
  - 24. Jiao, Z., Zhang, L., Xu, M., et al: ‘Coverage control algorithm-based adaptive particle swarm optimization and node sleeping in wireless multimedia sensor networks’, IEEE Access, 2019, 7, pp. 170096–170105.
8. 8)
  - 17. Pai, M.C.: ‘Disturbance observer-based global sliding mode control for uncertain time-delay nonlinear systems’, IETE J. Res., 2020, pp. 1–10.
9. 9)
  - 7. Feng, Y., Yu, X., Man, Z.: ‘Non-singular terminal sliding mode control of rigid manipulators’, Automatica, 2002, 38, (12), pp. 2159–2167.
10. 10)
  - 34. Lu, L., Guo, X., Zhao, J.: ‘A unified size-dependent plate model based on nonlocal strain gradient theory including surface effects’, Appl. Math. Model., 2019, 68, pp. 583–602.
11. 11)
  - 38. Jha, A.K., Dasgupta, S.S.: ‘Fractional order PID based optimal control for fractionally damped nonlocal nanobeam via genetic algorithm’, Microsyst. Technol., 2019, 25, (11), pp. 4291–4302.
12. 12)
  - 37. Mobki, H., Sabegh, A.M., Azizi, A., et al: ‘On the implementation of adaptive sliding mode robust controller in the stabilization of electrically actuated micro-tunable capacitor’, Microsyst. Technol., 2020, 26, pp. 3903–3916.
13. 13)
  - 14. Kayacan, E., Peschel, J.M., Chowdhary, G.: ‘A self-learning disturbance observer for nonlinear systems in feedback-error learning scheme’, Eng. Appl. Artif. Intell., 2017, 62, pp. 276–285.
14. 14)
  - 31. Vatankhah, R., Kahrobaiyan, M.H., Alasty, A., et al: ‘Nonlinear forced vibration of strain gradient microbeams’, Appl. Math. Model., 2013, 37, pp. 8363–8382.
15. 15)
  - 42. Huang, R., Patwardhan, S.C., Biegler, L.T.: ‘Robust stability of nonlinear model predictive control based on extended Kalman filter’, J. Process Control, 2012, 22, pp. 82–89.
16. 16)
  - 3. Aliakbari, S., Ayati, M., Osman, J.H.S., et al: ‘Second-order adaptive robust sliding mode fault-tolerant control in combined cycle power plants’, Appl. Therm. Eng., 2013, 50, pp. 1326–1338.
17. 17)
  - 30. Ghayesh, M.H., Farokhi, H., Farajpour, A.: ‘Pulsatile vibrations of viscoelastic microtubes conveying fluid’, Microsyst. Technol., 2019, 25, (9), pp. 3609–3623.
18. 18)
  - 41. Golubev, A.E., Krishchenko, A.P., Tkachev, S.B.: ‘Separation principle for a class of nonlinear systems’, IFAC Proc. Vol., 2002, 35, (1), pp. 447–452.
19. 19)
  - 8. Xiong, J.J., Zhang, G.B.: ‘Global fast dynamic terminal sliding mode control for a quadrotor UAV’, ISA Trans., 2017, 66, pp. 233–240.
20. 20)
  - 2. Mustafa, A., Dhar, N.K., Verma, N.K.: ‘Event-triggered sliding mode control for trajectory tracking of nonlinear systems’, IEEE/CAA J. Autom. Sin, 2019, 7, (1), pp. 307–314.
21. 21)
  - 36. Badkoubeh, A., Zheng, J., Zhu, G.: ‘Flatness-based deformation control of an Euler–Bernoulli beam with in-domain actuation’, IET Control Theory Appl., 2016, 10, (16), pp. 2110–2118.
22. 22)
  - 4. Homaeinezhad, M.R., Yaqubi, S., Gholyan, H.M.: ‘Control of MIMO mechanical systems interacting with actuators through viscoelastic linkages’, Mech. Mach. Theory, 2020, 147, p. 103763.
23. 23)
  - 32. Tajaddodianfar, F., Pishkenari, H.N., Hairi-Yazdi, M.R., et al: ‘Size-dependent bistability of an electrostatically actuated arch NEMS based on stain gradient theory’, J. Phys. D: Appl. Phys., 2015, 48, p. 245503.
24. 24)
  - 12. Hou, C., Liu, X., Wang, H.: ‘Adaptive fault tolerant control for a class of uncertain fractional order systems based on disturbance observer’, Int. J. Robust Nonlinear Control, 2020, 30, (8), pp. 3436–3450.
25. 25)
  - 26. Djuric, Z., Jokic, I., Peles, A.: ‘Fluctuations of the number of adsorbed molecules due to adsorption–desorption processes coupled with mass transfer and surface diffusion in bio/chemical MEMS sensors’, Microelectron. Eng., 2014, 124, pp. 81–85.
26. 26)
  - 6. Rajaei, A., Vahidi-Moghaddam, A., Ayati, M., et al: ‘Integral sliding mode control for nonlinear damped model of arch microbeams’, Microsyst. Technol., 2019, 25, (1), pp. 57–68.
27. 27)
  - 1. Suarez, O.J., Vega, C.J., Sanchez, E.N., et al: ‘Neural sliding mode pinning control for output synchronization for uncertain general complex networks’, Automatica, 2020, 112, p. 108694.
28. 28)
  - 25. Soltanpour, M.R., Khooban, M.H.: ‘A particle swarm optimization approach for fuzzy sliding mode control for tracking the robot manipulator’, Nonlinear Dyn., 2013, 74, pp. 467–478.
29. 29)
  - 18. Ayati, M., Khaloozadeh, H.: ‘A stable adaptive synchronization scheme for uncertain chaotic systems via observer’, J. Chaos Solitons Fractal, 2009, 42, pp. 2473–2483.
30. 30)
  - 16. Mustafa, A., Dhar, N.K., Agrawal, P., et al: ‘Adaptive backstepping sliding mode control based on nonlinear disturbance observer for trajectory tracking of robotic manipulator’. Int. Conf. on Control and Robotics Engineering (ICCRE), Bangkok, Thailand, 2017, pp. 29–34.
31. 31)
  - 27. Ghane, M., Saidi, A.R., Bahaadini, R.: ‘Vibration of fluid-conveying nanotubes subjected to magnetic field based on the thin-walled Timoshenko beam theory’, Appl. Math. Model., 2020, 80, pp. 65–83.
32. 32)
  - 13. Zhen, W., Xinhe, W., Jianwei, X., et al: ‘Adaptive sliding mode output tracking control based-FODOB for a class of uncertain fractional-order nonlinear time-delayed systems’, Sci. China Technol. Sci., 2020, 63, pp. 1854–1862.
33. 33)
  - 10. Jiao, Q., Modares, H., Xu, S., et al: ‘Multi-agent zero-sum differential graphical games for disturbance rejection in distributed control’, Automatica, 2016, 69, pp. 24–34.
34. 34)
  - 23. Alfi, A., Modares, H.: ‘System identification and control using adaptive particle swarm optimization’, Appl. Math. Model., 2011, 35, (3), pp. 1210–1221.
35. 35)
  - 21. Phogat, K.S., Chang, D.E.: ‘Invariant extended Kalman filter on matrix Lie groups’, Automatica, 2020, 114, p. 108812.
36. 36)
  - 20. Vatankhah, R., Karami, F., Salarieh, H.: ‘Observer-based vibration control of non-classical microcantilevers using extended Kalman filters’, Appl. Math. Model., 2015, 39, pp. 5986–5996.
37. 37)
  - 28. Vahidi-Moghaddam, A., Rajaei, A., Vatankhah, R., et al: ‘Analytical solution for nonlinear vibration of a new arch micro resonator model’, J. Phys. D: Appl. Phys., 202053, p. 285503.
38. 38)
  - 35. Krysko-Jr, V.A., Awrejcewicz, J., Papkova, I.V.: ‘Complex vibrations of flexible beam NEMS elements, taking into account Casimir's forces under additive white noise’.
39. 39)
  - 5. Rajaei, A., Vahidi-Moghaddam, A., Chizfahm, A., et al: ‘Control of malaria outbreak using a non-linear robust strategy with adaptive gains’, IET Control Theory Appl., 2019, 13, (14), pp. 2308–2317.
40. 40)
  - 19. Chen, Y., Li, H., Qiu, Z., et al: ‘Improved extended Kalman filter estimation using threshold signal detection with an MEMS electrostatic microscanner’, IEEE Trans. Ind. Electron., 2019, 67, pp. 1328–1336.
41. 41)
  - 15. Meng, X., Yu, H., Wu, H., et al: ‘Disturbance observer-based integral backstepping control for a two-tank liquid level system subject to external disturbances’, Math. Probl. Eng., 2020.
42. 42)
  - 11. Tatari, F., Vamvoudakis, K.G., Mazouchi, M.: ‘Optimal distributed learning for disturbance rejection in networked non-linear games under unknown dynamics’, IET Control Theory Appl., 2018, 13, (17), pp. 2838–2848.

Adaptive prescribed-time disturbance observer using nonsingular terminal sliding mode control: Extended Kalman filter and particle swarm optimization

References

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