Vibration attenuation of spacecraft in the presence of parametric and unmodeled dynamics uncertainties using collocated and noncollocated control: A comparative study
Restricted accessResearch articleFirst published online July, 2018
Vibration attenuation of spacecraft in the presence of parametric and unmodeled dynamics uncertainties using collocated and noncollocated control: A comparative study
µ-control synthesis offers the advantage of maintaining robust performance and stability in the presence of plant uncertainties. Expressions relating the 2-norm of the vector of regulated outputs and closed-loop modal damping to the weights used for µ-control synthesis are derived in this paper. By using these expressions, the amount of damping added to each mode can be controlled individually while maintaining equal importance for each controlled mode. Hence, the selection of weights for synthesizing a suitable µ-controller is greatly simplified. Furthermore, a comparative study of µ-controllers designed by the proposed procedure and positive position feedback (PPF) controllers designed by analytically derived optimal parameters is also presented. The techniques are compared for their vibration attenuation, energy utilization, and stability characteristics, in the presence of parametric and unmodeled dynamics uncertainties. Results for both time domain and frequency domain simulations are presented. As in some cases (sandwich plate structures etc.) the noncollocation of actuator/sensor becomes crucial for achieving good performance, the above-mentioned characteristics are evaluated for both collocated and noncollocated sensor locations.
AldraihemOJSinghTWetherholdRC (2000) Optimal size and location of piezoelectric actuator/sensors: Practical considerations. Journal of Guidance, Control, and Dynamics23(3): 509–515.
2.
AlkhatibRGolnaraghiMF (2003) Active structural vibration control: A review. Shock and Vibration Digest35(5): 367–383.
3.
Amezquita-SanchezJPDominguez-GonzalezASedaghatiRet al. (2014) Vibration control on smart civil structures: A review. Mechanics of Advanced Materials and Structures21(1): 23–38.
4.
ANSYS 14.5 help manual (2012) ANSYS, Inc.
5.
BalasGJDoyleJC (1994a) Control of lightly damped, flexible modes in the controller crossover region. Journal of Guidance, Control, and Dynamics17(2): 370–377.
6.
BalasGJDoyleJC (1994b) Robustness and performance trade-offs in control design for flexible structures. IEEE Transactions on Control Systems Technology, IEEE2(4): 352–361.
7.
BalasGJDoyleJCGloverKet al. (2001) µ-analysis and Synthesis Toolbox for use with MATLAB, Natick, MA: The MathWorks, Inc.
8.
BisplinghoffRLAshleyH (1975) Principles of Aeroelasticity, New York: Dover Publications.
9.
CaugheyTKFansonJL (1990) Positive position feedback control for large space structures. AIAA Journal28(4): 717–724.
10.
ChangWGopinathanSVVaradanVVet al. (2002) Design of robust vibration controller for a smart panel using finite element model. ASME Journal of Vibration and Acoustics124: 265–276.
11.
CloughRPenzienJ (1995) Dynamics of Structures, 3rd ed. Berkeley: Computers & Structures, Inc.
12.
DongXPengZZhangWet al. (2014) Research on spillover effects for vibration control of piezoelectric smart structures by ANSYS. Mathematical Problems in Engineering2014: 1–8.
13.
El-KhouryOAdeliH (2013) Recent advances on vibration control of structures under dynamic loading. Archives of Computational Methods in Engineering20(4): 353–360.
14.
FansonJL (1987) An Experimental Investigation of Vibration Suppression in Large Space Structures using Positive Position Feedback, PhD thesis, California: California Institute of Technology Pasadena.
15.
FeiJFangYYanC (2010) The comparative study of vibration control of flexible structure using smart materials. Mathematical Problems in Engineering2010: 1–13.
16.
FerrariGAmabiliM (2015) Active vibration control of a sandwich plate by non-collocated positive position feedback. Journal of Sound and Vibration342: 44–56.
17.
FriswellMIInmanDJ (1999) The relationship between positive position feedback and output feedback controllers. Smart Materials and Structures8(3): 285–291.
18.
GohCJCaugheyTK (1985) On the stability problem caused by finite actuator dynamics in the collocated control of large space structures. International Journal of Control41(3): 787–802.
19.
GuptaVSharmaMThakurN (2010) Optimization criteria for optimal placement of piezoelectric sensors and actuators on a smart structure: A technical review. Journal of Intelligent Material Systems and Structures21(12): 1227–1243.
20.
GuptaVSharmaMThakurN (2011) Mathematical modeling of actively controlled piezo smart structures: A review. Smart Structures and Systems8(3): 275–302.
21.
HuJXuG (2013) Vibration control of piezoelectric flexible structure using robust control methodology. Journal of Theoretical and Applied Information Technology51(2): 264–274.
22.
HuQMaG (2006) Spacecraft vibration suppression using variable structure output feedback control and smart materials. Journal of Vibration and Acoustics128(2): 221.
23.
HylandDCJunkinsJLLongmanRWet al. (1993) Active control technology for large space structures. Journal of Guidance, Control, and Dynamics16(5): 801–821.
IorgaLBaruhHUrsuI (2009) H∞ Control with µ-analysis of a Piezoelectric actuated plate. Journal of Vibration and Control15(8): 1143–1171.
26.
JiangJ-PLiD-X (2011) Robust H ∞ vibration control for smart solar array structure. Journal of Vibration & Control17(4): 505–515.
27.
JiangYHuQMaG (2008) Attitude manoeuvring and vibration reducing control of flexible spacecraft using smart materials. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering222(3): 357–367.
28.
JoshiAKhotSM (2007) Smart actuator effectiveness improvement through modal analysis. Advances in Vibration Engineering6(3): 195–208.
29.
KhotSYelveNPTomarRet al. (2012) Active vibration control of cantilever beam by using PID based output feedback controller. Journal of Vibration and Control18(3): 366–372.
30.
KumarR (2013) Enhanced active constrained layer damping (ACLD) treatment using stand-off-layer: robust controllers design, experimental implementation and comparison. Journal of Vibration and Control19(3): 439–460.
31.
LewisJAInmanDJ (2001) Finite element modeling and active control of an inflated torus using piezoelectric devices. Journal of Intelligent Material Systems and Structures12(12): 819–833.
32.
LiPChengLLiYYet al. (2003) Robust control of a vibrating plate using µ-synthesis approach. Thin-Walled Structures41(11): 973–986.
33.
Mahmoodi SN, Aagaah MR and Ahmadian M (2009) Active vibration control of aerospace structures using a modified Positive Position Feedback method. In: 2009 American control conference, St. Louis, MO, USA, 10–12 June 2009, pp.4115–4120.
34.
MalgacaLKaragülleH (2009) Numerical and experimental study on integration of control actions into the finite element solutions in smart structures. Shock and Vibration16(4): 401–415.
35.
MATLAB R2014a help manual (2014) The MathWorks, Inc.
36.
MengGYeLDongXet al. (2006) Closed loop finite element modeling of piezoelectric smart structures. Shock and Vibration13(1): 1–12.
37.
MoheimaniSORHeathWP (2002) Model correction for a class of spatio-temporal systems. Automatica38(1): 147–155.
38.
OrszulikRShanJ (2011a) Vibration control using input shaping and adaptive positive position feedback. Journal of Guidance, Control, and Dynamics34(4): 1031–1044. Available at: http://arc.aiaa.org/doi/10.2514/1.52287.
39.
Orszulik R and Shan JJ (2011b) Multi-mode adaptive positive position feedback: An experimental study. In: 2011 American control conference, San Francisco, CA, USA, 29 June–1 July 2011, pp.3315–3319.
40.
OrszulikRRShanJ (2012) Active vibration control using genetic algorithm-based system identification and positive position feedback. Smart Materials and Structures21(5): 55002.
41.
OveisiAGudarziM (2012) Robust active vibration control of smart structures; A comparison between two approaches: µ-synthesis & LMI-based design. International Journal of Aerospace Sciences1(5): 116–127.
42.
PreumontA (2011) Vibration Control of Active Structures: An Introduction (Solid Mechanics and Its Applications), 3rd ed. Heidelberg: Springer.
43.
SafonovMGChiangRY (1989) A Schur method for balanced-truncation model reduction. IEEE Transactions on Automatic Control34(7): 729–733.
44.
SethiVFranchekMSongG (2011) Active multimodal vibration suppression of a flexible structure with piezoceramic sensor and actuator by using loop shaping. Journal of Vibration and Control17(13): 1994–2006.
45.
ShanJLiuHTSunD (2005) Slewing and vibration control of a single-link flexible manipulator by positive position feedback (PPF). Mechatronics15(4): 487–503.
46.
ShanJSunDLiuD (2004) Design for robust component synthesis vibration suppression of flexible structures with on-off actuators. IEEE Transactions on Robotics and Automation20(3): 512–525.
47.
SongGAgrawalBN (2001) Vibration suppression of flexible spacecraft during attitude control. Acta Astronautica49(2): 73–83.
48.
Song GSG, Schmidt SP and Agrawal BN (1998) Experimental study of active vibration suppression of flexible structure using modular control patch. In: Aerospace Conference, 28–28 March 1998. IEEE. DOI: 10.1109/AERO.1998.686818.
49.
SrideviMMadhavasarmaP (2010) Model identification and smart structural vibration Control using H ∞ controller. International Journal on Smart Sensing and Intelligent Systems3(4): 655–671.
VasquesCMADias RodriguesJ (2006) Active vibration control of smart piezoelectric beams: Comparison of classical and optimal feedback control strategies. Computers & Structures84(22–23): 1402–1414.
52.
YaWangInmanDJ (2011) Comparison of control laws for vibration suppression based on energy consumption. Journal of Intelligent Material Systems and Structures22(8): 795–809.
53.
YounS-HHanJ-HLeeI (2000) Neuro-adaptive vibration control of composite beams subject to sudden delamination. Journal of Sound and Vibration238(2): 215–231.
