Fault-Tolerant Terminal Sliding Mode Control with Disturbance Observer for Vibration Suppression in Non-Local Strain Gradient Nano-Beams
This research investigates the stabilization and control of an uncertain Euler–Bernoulli nano-beam with fixed ends. The governing partial differential equations of motion for the nano-beam are derived using Hamilton’s principle and the non-local strain gradient theory. The Galerkin method is then ap...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-02-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/3/789 |
| _version_ | 1797623835370979328 |
|---|---|
| author | Hajid Alsubaie Amin Yousefpour Ahmed Alotaibi Naif D. Alotaibi Hadi Jahanshahi |
| author_facet | Hajid Alsubaie Amin Yousefpour Ahmed Alotaibi Naif D. Alotaibi Hadi Jahanshahi |
| author_sort | Hajid Alsubaie |
| collection | DOAJ |
| description | This research investigates the stabilization and control of an uncertain Euler–Bernoulli nano-beam with fixed ends. The governing partial differential equations of motion for the nano-beam are derived using Hamilton’s principle and the non-local strain gradient theory. The Galerkin method is then applied to transform the resulting dimensionless partial differential equation into a nonlinear ordinary differential equation. A novel fault-tolerant terminal sliding mode control technique is proposed to address the uncertainties inherent in micro/nano-systems and the potential for faults and failures in control actuators. The proposed controller includes a finite time estimator, the stability of which and the convergence of the error dynamics are established using the Lyapunov theorem. The significance of this study lies in its application to the field of micro/nano-mechanics, where the precise control and stabilization of small-scale systems is crucial for the development of advanced technologies such as nano-robotics and micro-electromechanical systems (MEMS). The proposed control technique addresses the inherent uncertainties and potential for faults in these systems, making it a valuable choice for practical applications. The simulation results are presented to demonstrate the effectiveness of the proposed control scheme and the high accuracy of the estimation algorithm. |
| first_indexed | 2024-03-11T09:34:27Z |
| format | Article |
| id | doaj.art-6e3fe1ceaa94460d94d0d3c294053904 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T09:34:27Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6e3fe1ceaa94460d94d0d3c2940539042023-11-16T17:24:37ZengMDPI AGMathematics2227-73902023-02-0111378910.3390/math11030789Fault-Tolerant Terminal Sliding Mode Control with Disturbance Observer for Vibration Suppression in Non-Local Strain Gradient Nano-BeamsHajid Alsubaie0Amin Yousefpour1Ahmed Alotaibi2Naif D. Alotaibi3Hadi Jahanshahi4Department of Mechanical Engineering, College of Engineering, Taif University, Taif 21944, Saudi ArabiaDepartment of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697, USADepartment of Mechanical Engineering, College of Engineering, Taif University, Taif 21944, Saudi ArabiaCommunication Systems and Networks Research Group, Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mechanical Engineering, University of Manitoba, Winnipeg, MB R3T 5V6, CanadaThis research investigates the stabilization and control of an uncertain Euler–Bernoulli nano-beam with fixed ends. The governing partial differential equations of motion for the nano-beam are derived using Hamilton’s principle and the non-local strain gradient theory. The Galerkin method is then applied to transform the resulting dimensionless partial differential equation into a nonlinear ordinary differential equation. A novel fault-tolerant terminal sliding mode control technique is proposed to address the uncertainties inherent in micro/nano-systems and the potential for faults and failures in control actuators. The proposed controller includes a finite time estimator, the stability of which and the convergence of the error dynamics are established using the Lyapunov theorem. The significance of this study lies in its application to the field of micro/nano-mechanics, where the precise control and stabilization of small-scale systems is crucial for the development of advanced technologies such as nano-robotics and micro-electromechanical systems (MEMS). The proposed control technique addresses the inherent uncertainties and potential for faults in these systems, making it a valuable choice for practical applications. The simulation results are presented to demonstrate the effectiveness of the proposed control scheme and the high accuracy of the estimation algorithm.https://www.mdpi.com/2227-7390/11/3/789robust adaptive controlnon-local strain gradient theoryfault-tolerant terminal sliding mode controlfinite time disturbance observernonlinear vibrationsHamiltonian principle |
| spellingShingle | Hajid Alsubaie Amin Yousefpour Ahmed Alotaibi Naif D. Alotaibi Hadi Jahanshahi Fault-Tolerant Terminal Sliding Mode Control with Disturbance Observer for Vibration Suppression in Non-Local Strain Gradient Nano-Beams Mathematics robust adaptive control non-local strain gradient theory fault-tolerant terminal sliding mode control finite time disturbance observer nonlinear vibrations Hamiltonian principle |
| title | Fault-Tolerant Terminal Sliding Mode Control with Disturbance Observer for Vibration Suppression in Non-Local Strain Gradient Nano-Beams |
| title_full | Fault-Tolerant Terminal Sliding Mode Control with Disturbance Observer for Vibration Suppression in Non-Local Strain Gradient Nano-Beams |
| title_fullStr | Fault-Tolerant Terminal Sliding Mode Control with Disturbance Observer for Vibration Suppression in Non-Local Strain Gradient Nano-Beams |
| title_full_unstemmed | Fault-Tolerant Terminal Sliding Mode Control with Disturbance Observer for Vibration Suppression in Non-Local Strain Gradient Nano-Beams |
| title_short | Fault-Tolerant Terminal Sliding Mode Control with Disturbance Observer for Vibration Suppression in Non-Local Strain Gradient Nano-Beams |
| title_sort | fault tolerant terminal sliding mode control with disturbance observer for vibration suppression in non local strain gradient nano beams |
| topic | robust adaptive control non-local strain gradient theory fault-tolerant terminal sliding mode control finite time disturbance observer nonlinear vibrations Hamiltonian principle |
| url | https://www.mdpi.com/2227-7390/11/3/789 |
| work_keys_str_mv | AT hajidalsubaie faulttolerantterminalslidingmodecontrolwithdisturbanceobserverforvibrationsuppressioninnonlocalstraingradientnanobeams AT aminyousefpour faulttolerantterminalslidingmodecontrolwithdisturbanceobserverforvibrationsuppressioninnonlocalstraingradientnanobeams AT ahmedalotaibi faulttolerantterminalslidingmodecontrolwithdisturbanceobserverforvibrationsuppressioninnonlocalstraingradientnanobeams AT naifdalotaibi faulttolerantterminalslidingmodecontrolwithdisturbanceobserverforvibrationsuppressioninnonlocalstraingradientnanobeams AT hadijahanshahi faulttolerantterminalslidingmodecontrolwithdisturbanceobserverforvibrationsuppressioninnonlocalstraingradientnanobeams |