Modeling and Vibration Control of a Two-Link Flexible Manipulator with ANSYS APDL

Abstract

In this study, the control of post-motion residual vibrations of a two-link flexible manipulator is investigated. The manipulator is modeled in ANSYS by using APDL (Ansys Parametric Design Language). The post-motion vibration signals are simulated by transient analysis which is performed in ANSYS based on the finite element theory. Experimental results are also presented and compared with simulation results. Trapezoidal velocity profiles are used for the motors. The acceleration, constant velocity and deceleration time intervals of the trapezoidal velocity profile are determined by considering the lowest natural frequency of the manipulator structure at the stopping position. Various starting and stopping positions are considered. The root mean square (RMS) acceleration values of the vibration signals after stopping are calculated. It is observed that the residual vibration is sensitive to the deceleration time.  The RMS values are lowest if the inverse of the deceleration time is equal to the first natural frequency.  It is highest if the inverse of the deceleration time is equal to the half of the first natural frequency. It is observed that simulation and experimental results are in good agreement.

Keywords

• Flexible Manipulator,Vibration Control,ANSYS APDL

İki Eksenli Esnek bir Manipülatörün ANSYS APDL ile Modellenmesi ve Titreşim Kontrolü

Abstract

Bu çalışmada, iki eksenli esnek bir manipülatörün hareket sonrası artık titreşimlerinin kontrolü incelenmiştir. Manipülatör ANSYS'de APDL (Ansys Parametrik Tasarım Dili) kullanılarak modellenmiştir. Hareket sonrası titreşim sinyalleri, sonlu elemanlar teorisine dayalı olarak ANSYS'de gerçekleştirilen dinamik analiz ile simüle edilir. Önceki çalışmada elde edilen deney sonuçları da sunulmuş ve benzetim sonuçları ile karşılaştırılmıştır. Tahrik motorları için trapez hız profilleri kullanılmıştır. Trapez hız profilinin ivme, sabit hız ve yavaşlama süreleri, durdurma pozisyonundaki manipülatör yapısının en düşük doğal frekansı dikkate alınarak seçilir. Çeşitli başlangıç ve durma pozisyonları değerlendirilmiştir. Hareket bittikten sonra meydana gelen artık titreşim sinyallerinin karelerinin ortalamasının karekök (RMS) değerleri hesaplanır. Artık titreşimin yavaşlama süresine duyarlı olduğu gözlemlenmiştir. RMS değerleri, yavaşlama süresinin tersi ilk doğal frekansa eşitse, en düşük değer elde edilmektedir. Yavaşlama zamanının tersi ilk doğal frekansın yarısına eşitse, en yüksek değer elde edilir. Benzetim ve deney sonuçlarının birbirleriyle uyumlu çıktığı görülmektedir.

Keywords

• Manipülatör,Titreşim Kontrolü,ANSYS APDL

References

1. [1] Benosman M., LeVey G. 2004. Control of flexible manipulators: A survey. Robotica, Cilt. 22, s. 533-545.
2. [2] Fung T.C. 1997. Unconditionally stable higher-order Newmark methods by sub-stepping procedure. Computer Methods in Applied Mechanics and Engineering, Cilt. 147, s. 61-84.
3. [3] Owren B., Simonsen H.H. 1995. Alternative integration methods for problems in structural dynamics. Computer Methods in Applied Mechanics and Engineering, Cilt. 122, s. 1-10.
4. [4] Zhang L., Zhu J.W., Zheng Z. 1999. The stochastic Newmark algorithm for random analysis of multi-degree-of-freedom nonlinear systems. Computers and Structures, Cilt. 70, s. 557-568.
5. [5] Karagülle H., Malgaca L., Öktem H.F. 2004. Analysis by active vibration control in smart structures by ANSYS, Smart Materials and Structures, Cilt. 13, s. 661–667.
6. [6] Dwivedy S.K., Eberhard P. 2006. Dynamic analysis of flexible manipulators, a literature review. Mechanism and Machine Theory, Cilt. 41, s. 749–777.
7. [7] Shin H.C., Choi S.B. 2001. Position control of a two link flexible manipulator featuring piezoelectric actuators and sensors. Mechatronics, Cilt. 11, s. 707-729.
8. [8] Gurses K., Bradley J.B., Edward J.P. 2009. Vibration control of a single-link flexible manipulator using an array of fiber optic curvature sensors and PZT actuators. Mechatronics Cilt. 19, s. 167–177.

9. [9] Mirzaee E., Eghtesad M., Fazelzadeh S.A. 2010. Maneuver control and active vibration suppression of a two-link flexible arm using a hybrid variable structure/Lyapunov control design. Acta Astronautica, Cilt. 67, s. 1218–1232.
10. [10] Zhang Q., Li J., Zhang J., Zhang J. 2017. Smooth adaptive sliding mode vibration control of a flexible parallel manipulator with multiple smart linkages in modal space. Journal of Sound and Vibration. Cilt. 411, s. 1-19.
11. [11] Pedro J.O., Smith R.V. 2017. Real-Time Hybrid PID/ILC Control of Two-Link Flexible Manipulators. IFAC-PapersOnline. Cilt. 50, s. 145-150.
12. [12] Park K.J. 2004. Flexible robot manipulator path design to reduce the endpoint residual vibration under torque constraints. Journal of Sound and Vibration, Cilt. 275, s. 1051–1068.
13. [13] Abe A. 2009. Trajectory planning for residual vibration suppression of a two-link rigid-flexible manipulator considering large deformation. Mechanism and Machine Theory, Cilt. 44, s. 1627–1639.
14. [14] Green A., Sasiadek J.Z. 2004. Dynamics and Trajectory Tracking Control of a Two-Link Robot Manipulator. Journal of Vibration and Control, Cilt. 10, s. 1415–1440.
15. [15] Singer N.C., Seering W.P. 1990. Preshaping command inputs to reduce system vibration. Journal of Dynamic Systems, Measurement and Control, Cilt. 112, s. 76-82.
16. [16] Singhose W. 2009. Command shaping for flexible systems: a review of the first 50 years. International Journal of Precision Engineering and Manufacturing, Cilt. 10, s. 153-168.
17. [17] Ouyang Y., He W., Li X. 2017. Reinforcement learning control of a single- link flexible robotic manipulator. IET Control Theory. Cilt. 11(9), s. 1426-1433.
18. [18] Ankarali A., Diken H. 1997. Vibration Control Of An Elastic Manipulator Link. Journal of Sound and Vibration, Cilt. 204, s. 162-170.
19. [19] Mimmi G., Pennacchi P. 2001. Pre-shaping Motion Input for a Rotating Flexible Link. International Journal of Solids and Structures, Cilt. 38, s. 2009-2023.
20. [20] Shan J., Liu H.T., Sun S. 2005. Modified input shaping for a rotating single-link flexible manipulator. Journal of Sound and Vibration,Cilt. 285, s. 187–207.
21. [21] Shin K., Brennan M.J. 2008. Two simple methods to suppress the residual vibrations of a translating or rotating flexible cantilever beam. Journal of Sound and Vibration, Cilt. 312, s. 140–150.
22. [22] Ozer A., Semercigil S.E. 2008. An event-based vibration control for a two-link flexible robotic arm: Numerical and experimental observations. Journal of Sound and Vibration, Cilt. 313, s. 375–394.
23. [23] Karagülle H., Malgaca L., Dirilmiş M., Akdağ M., Yavuz Ş. 2017. Vibration control of a two-link flexible manipulator. Journal of Vibration and Control, Cilt. 23, s. 2023-2034.
24. [24] ANSYS. 2018. Web adresi: http:// http://www.ansys.com/academic. Erişim Tarihi: 20.01.2018
25. [25] Thomson W.T., & Dahleh M.D. (1988). Theory of Vibration with Applications 3rd edition. Englewood Cliffs: Prentice-Hall.
26. [26] MicroStrain Inc. 2015. Web adresi: http://www.microstrain.com/wireless/sensors. Erişim tarihi: 20.01.2018.