Discrete-Time Model Predictive Controller Using Laguerre Functions for Active Flutter Suppression of a 2D wing with a Flap
Abstract
:1. Introduction
2. Theory and Methods
2.1. The Aeroelastic Model
2.2. Discrete Time MPC Using Laguerre Fnctions
2.3. Discrete Time Kalman Filter
2.4. Simulation Results Analysis
- The 10–90% rise time to give an indication of the speed of the response.
- The present overshoot, , which measures the similarity with which the actual response matches the step input.
- The settling time, , which indicates how quickly the system settles within 2% of the input amplitude.
3. Results and Discussion
3.1. The Open Loop System Analysis
3.2. Closed Loop MPC Using Laguerre Functions
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Appendix B
; | The ratio of the total wing’s mass to the mass of the air affected by the wing |
; | The dimensionless radius of gyration of the wing about the elastic axis |
; | The dimensionless radius of gyration of the control surface about its hinge |
; | The plunge structural stiffness, where is uncoupled plunge fre-quency |
; | The pitch structural stiffness, where is uncoupled pitch fre-quency |
; | The control surface structural stiffness, where is uncoupled control surface frequency |
; | The ratio of uncoupled plunge and pitch natural frequencies |
; | The reduced velocity, or the dimensionless free stream speed of air |
; | The plunge structural damping, where is the plunge damping ratio |
; | The pitch structural damping, where is the pitch damping ratio |
; | The control surface structural damping, where is the control sur-face damping ratio |
; | The dimensionless time |
Appendix C
Geometric Parameters | |
Chord | 0.254 m |
Span | 0.52 m |
Semi-chord, b | 0.127 m |
Elastic axis, a with respect to b | −0.5 |
Hinge line, c with respect to b | 0.5 |
Mass Parameters | |
Mass of the wing | 0.62868 kg |
Mass of the aileron | 0.18597 kg |
Mass/length of the wing-aileron | 0.1558 kg/m |
Mass of support blocks | 0.47485 × 2 kg |
Inertial Parameters | |
Sα (per span) | 0.08587 kg m |
Sβ (per span) | 0.00395 kg m |
xα | 0.434 |
xβ | 0.01996 |
Iα (per span) | 0.01347 kg m2 |
Iβ (per span) | 0.0003264 kg m2 |
rα | 0.7321 |
rβ | 0.11397 |
κ | 0.03984 |
Stiffness Parameters | |
Kα (per span) | 14,861 1/s2 |
Kβ (per span) | 155 1/s2 |
Kh (per span) | 1809 1/s2 |
Damping Parameters | |
ζα (log-dec) | 0.01626 |
ζβ (log-dec) | 0.0115 |
ζh (log-dec) | 0.0113 |
W.P. Jones’ Approximation | |
λ1 | 0.014 |
δ1 | 0.165 |
λ2 | 0.320 |
δ2 | 0.335 |
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Trial No. | R | u(deg) Input Const. | du/dt Input Const. | Ts for h | ISE for h | Ts for α | ISE for α | Ts for β | ISE for β | ISU | u(deg) max. | du/dt max. |
---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 25 | No | No | 0.6 | 0.02 | 0.7 | 0.02 | 0.5 | 0.16 | 0.14 | 11.8 | 2000 |
2 | 50 | No | No | 0.8 | 0.03 | 0.8 | 0.02 | 0.6 | 0.17 | 0.15 | 7.9 | 1194 |
3 | 25 | 10 | 105 | 0.8 | 0.03 | 0.8 | 0.02 | 0.7 | 0.13 | 0.16 | 3.9 | 105 |
4 | 50 | 10 | 105 | 0.8 | 0.03 | 0.8 | 0.02 | 0.8 | 0.14 | 0.16 | 3.7 | 105 |
Trial No. | R | u(deg) Input Const. | du/dt Input Const. | ISE for β | Tr | P.O. % | Ts | ISU | u(deg) max. | du/dt max. |
---|---|---|---|---|---|---|---|---|---|---|
1 | 25 | No | No | 0.04 | 0.08 | 21 | 0.46 | 0.17 | 7.6 | 332 |
2 | 50 | No | No | 0.04 | 0.08 | 19 | 0.47 | 0.17 | 7.5 | 263 |
3 | 25 | 10 | 105 | 0.05 | 0.09 | 20 | 0.47 | 0.18 | 7.6 | 105 |
4 | 50 | 10 | 105 | 0.06 | 0.09 | 18 | 0.48 | 0.18 | 7.5 | 105 |
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Darabseh, T.; Tarabulsi, A.; Mourad, A.-H.I. Discrete-Time Model Predictive Controller Using Laguerre Functions for Active Flutter Suppression of a 2D wing with a Flap. Aerospace 2022, 9, 475. https://doi.org/10.3390/aerospace9090475
Darabseh T, Tarabulsi A, Mourad A-HI. Discrete-Time Model Predictive Controller Using Laguerre Functions for Active Flutter Suppression of a 2D wing with a Flap. Aerospace. 2022; 9(9):475. https://doi.org/10.3390/aerospace9090475
Chicago/Turabian StyleDarabseh, Tariq, Abdallah Tarabulsi, and Abdel-Hamid I. Mourad. 2022. "Discrete-Time Model Predictive Controller Using Laguerre Functions for Active Flutter Suppression of a 2D wing with a Flap" Aerospace 9, no. 9: 475. https://doi.org/10.3390/aerospace9090475
APA StyleDarabseh, T., Tarabulsi, A., & Mourad, A.-H. I. (2022). Discrete-Time Model Predictive Controller Using Laguerre Functions for Active Flutter Suppression of a 2D wing with a Flap. Aerospace, 9(9), 475. https://doi.org/10.3390/aerospace9090475