Chapter 7 Conclusion and future work
7.2 Future work
The research has potential applications in many industries and can be developed further into many directions of research. The basic theories for partial pole placement with inaccessible degrees of freedom and block decoupling vibration control in linear time invariant systems, and global robust flutter suppression in under-actuated nonlinear aeroelastic systems are developed and presented in this thesis. Also, semi- analytical and numerical investigation of the effects of softening nonlinearity on aeroelastic systems is presented. Other aspects that can be considered as further work may be summarised here:
1. The method of receptances, originally developed in [8, 9] and further developed in this thesis [128, 129], is based on the assumption of distinct eigenvalues in both open- and closed-loop systems. In practice, systems with closely spaced eigenvalues, which are close to being defective, are common. Developing the method of receptances in defective systems is an interesting line of research.
2. Experiments for block decoupling vibration control in large flexible smart structures with embedded piezo-based actuators and sensors may be carried out.
3. The Boeing Joined-Wing SensorCraft is a concept proposed to serve as a next-generation, high altitude, long endurance reconnaissance unmanned aircraft. Buckling is considered to be a critical constraint for its aeroelastic performance [149]. It is of significant importance to comprehensively
176
investigate the effects of softening nonlinearity experimentally, due to buckling of the aerodynamic responses of joined-wing sensor-crafts.
4. Experiments for robust passivity-based sliding mode control may be carried out on a nonlinear wing section at the University of Liverpool.
177 References
[1] C.M. Denegri, Limit cycle oscillation flight test results of a fighter with external stores, Journal of Aircraft, 37 (2000) 761-769.
[2] Denegri C.M, Jr., M.R. Johnson, Limit cycle oscillation prediction using artificial neural networks, Journal of Guidance, Control, and Dynamics, 24 (2001) 887-895. [3] J. Croft, Airbus elevator flutter: Annoying or dangerous?, Aviation Week & Space
Technology, 155 (2001) 41.
[4] L. Librescu, G. Chiocchia, P. Marzocca, Implications of cubic physical/aerodynamic non-linearities on the character of the flutter instability boundary, International Journal of Non-Linear Mechanics, 38 (2003) 173-199.
[5] O. Cuvalci, A. Ertas, S. Ekwaro-Osire, I. Cicek, Nonlinear-linear vibration absorber for a system under sinusoidal and random excitation: experiments, Journal of Sound and Vibration, 249 (2002) 701-718.
[6] Y.S. Lee, A.F. Vakakis, L.A. Bergman, D.M. McFarland, G. Kerschen, Suppressing
aeroelastic instability using broadband passive targeted energy transfers, part 1:Theory, AIAA Journal, 45 (2007) 693-711.
[7] Y.S. Lee, G. Kerschen, D. Michael McFarland, W. Joel Hill, C. Nichkawde, T.W. Strganac, L.A. Bergman, A.F. Vakakis, Suppressing aeroelastic instability using broadband passive targeted energy transfers, part 2: Experiments, AIAA Journal, 45 (2007) 2391-2400.
[8] Y.M. Ram, J.E. Mottershead, Receptance method in active vibration control, AIAA
Journal, 45 (2007) 562-567.
[9] Y.M. Ram, J.E. Mottershead, Multiple-input active vibration control by partial pole placement using the method of receptances, Mechanical Systems and Signal Processing, 40 (2013) 727-735.
[10] E.H. Dowell, D. Tang, Nonlinear aeroelasticity and unsteady aerodynamics, AIAA Journal, 40 (2002) 1697-1707.
[11] Y.Q. Tu, G.T. Zheng, On the vibration isolation of flexible structures, Journal of Applied Mechanics, 74 (2006) 415-420.
[12] P. Gardonio, S.J. Elliott, R.J. Pinnington, Active isolation of structural vibration on a multiple-degree-of-freedom system, Part 1: The dynamics of the system, Journal of Sound and Vibration, 207 (1997) 61-93.
178
[13] P. Gardonio, S.J. Elliott, R.J. Pinnington, Active isolation of structural vibration on a multiple-degree-of-freedom system, Part II: Effectiveness of active control strategies, Journal of Sound and Vibration, 207 (1997) 95-121.
[14] P. Gardonio, S.J. Elliott, Passive and active isolation of structural vibration transmission between two plates connected by a set of mounts, Journal of Sound and Vibration, 237 (2000) 483-511.
[15] B.H.K. Lee, S.J. Price, Y.S. Wong, Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos, Progress in Aerospace Sciences, 35 (1999) 205-334.
[16] D.S. Woolston, H.L. Runyan, T.A. Byrdsong, Some effects of system nonlinearities
in the problem of aircraft flutter, in: NACA TN-3539, 1955.
[17] J.S. Vipperman, J.M. Barker, R.L. Clark, G.J. Balas, Comparison of mu- and H2- Synthesis Controllers on an experimental typical section, Journal of Guidance, Control, and Dynamics, 22 (1999) 278-285.
[18] J.J. Block, T.W. Strganac, Applied active control for a nonlinear aeroelasticstructure, Journal of Guidance, Control, and Dynamics, 21 (1998) 838-845.
[19] L. Yang, Y. Hongnian, H. Yu, Y. Liu, A survey of underactuated mechanical systems, IET Control Theory & Applications, 7 (2013) 921-935.
[20] R. Xu, Ü. Özgüner, Sliding mode control of a class of underactuated systems, Automatica, 44 (2008) 233-241.
[21] H.K. Khalil, Nonlinear systems, Upper Saddle River, N.J. : Prentice Hall, 2002. [22] R. Alkhatib, M.F. Golnaraghi, Active structural vibration control: A review, Shock
and Vibration Digest, 35 (2003) 367-383.
[23] J.E. Mottershead, Y.M. Ram, Inverse eigenvalue problems in vibration absorption: Passive modification and active control, Mechanical Systems and Signal Processing, 20 (2006) 5-44.
[24] W.M. Wonham, On pole assignment in multi-input controllable linear systems, Automatic Control, IEEE Transactions on, 12 (1967) 660-665.
[25] E.J. Davison, On pole assignment in linear systems with incomplete state feedback, Automatic Control, IEEE Transactions on, 15 (1970) 348-351.
[26] H. Kimura, Pole assignment by gain output feedback, Automatic Control, IEEE Transactions on, 20 (1975) 509-516.
[27] E.Y. Shapiro, J.C. Chung, Application of eigenvalue/eigenvector assignment by constant output feedback to flight control system design, in: 15th Annual Conference on Information Sciences and Systems,, Johns Hopkins University, Baltimore, Maryland, 1981, pp. 164-169.
[28] A.N. Andry, E.Y. Shapiro, J.C. Chung, eigenstructure assignment for linear systems, Aerospace and Electronic Systems, IEEE Transactions on, AES-19 (1983) 711-729. [29] L.R. Fletcher, J.F. Magni, Exact pole assignment by output feedback. Part 1,