Many high-precision measurement and control devices must be mounted on vibration-free platforms. Accuracy of those devices’ output are adversely affected by the base excitation motion, so motion of these platforms must be isolated from the excitation source. In this paper, a flexible platform, which is mounted on a car, is considered as a base on which many such measurement and control devices can be attached. To this end, mixed finite element and lumped parameter model of the platform and vehicle are used to derive the model of such a system; this results in a discrete-model with finite degree of freedom. This lumped parameter model of the system is then controlled by a linear quadratic regulator, which minimizes the amplitude of vibration at finite number of points on the platform. The mathematical model of this system was simulated on a computer and it has been shown that it is possible to minimize the vibration of this flexible platform.
QiuZcZhangXmWuHXet al.Optimal placement and active vibration control for piezoelectric smart flexible cantilever plate. J Sound Vib2007; 301: 521–543.
2.
BurkeSEHubbardJEJr. Active vibration control of a simply supported beam using a spatially distributed actuator. IEEE Control Syst Magaz1987; 7: 25–30.
3.
TangPPalazzoloABKascakAFet al.Electromechanical modeling of hybrid piezohydraulic actuator system for active vibration control. J Dyn Syst Meas Control1997; 119: 10–18.
4.
HagoodNWvon FlotowA. Damping of structural vibrations with piezoelectric materials and passive electrical networks. J Sound Vib1991; 146: 243–268.
5.
ClarkWW. Vibration control with state-switched piezoelectric materials. J Intell Mater Syst Struct2000; 11: 263–271.
6.
CorrLRClarkWW. A novel semi-active multi-modal vibration control law for a piezoceramic actuator. J Vib Acoust2003; 125: 214–222.
7.
BadelASebaldGGuyomarDet al.Piezoelectric vibration control by synchronized switching on adaptive voltage sources: Towards wideband semi-active damping. J Acoust Soc Am2006; 119: 2815–2825.
8.
FlemingAJMoheimaniSRBehrensS. Synthesis and implementation of sensor-less active shunt controllers for electromagnetically actuated systems. IEEE Trans Control Syst Technol2005; 13: 246–261.
9.
ChenC-QWangX-MShenY-P. Finite element approach of vibration control using self-sensing piezoelectric actuators. Comput Struct1996; 60: 505–512.
10.
NarayananSBalamuruganV. Finite element modelling of piezolaminated smart structures for active vibration control with distributed sensors and actuators. J Sound Vib2003; 262: 529–562.
11.
MichielsenJArteagaILNijmeijerH. LQR-based optimization of multiple tuned resonators for plate sound radiation reduction. J Sound Vib2016; 363: 166–180.
12.
TrindadeMBenjeddouAOhayonR. Piezoelectric active vibration control of damped sandwich beams. J Sound Vib2001; 246: 653–677.
13.
VasquesCRodriguesJD. Active vibration control of smart piezoelectric beams: Comparison of classical and optimal feedback control strategies. Comput Struct2006; 84: 1402–1414.
14.
Chuang CH and Wang Q. Active controllers for reducing vibration amplitude. In: American control conference, 1992, pp.1611–1615. New York: IEEE.
15.
HiramotoKDokiHObinataG. Optimal sensor/actuator placement for active vibration control using explicit solution of algebraic Riccati equation. J Sound Vib2000; 229: 1057–1075.
16.
PengFNgAHuYR. Actuator placement optimization and adaptive vibration control of plate smart structures. J Intell Mater Syst Struct2005; 16: 263–271.
17.
AbdeljaberOAvciOInmanDJ. Active vibration control of flexible cantilever plates using piezoelectric materials and artificial neural networks. J Sound Vib2016; 363: 33–53.
18.
GucluRGulezK. Neural network control of seat vibrations of a non-linear full vehicle model using PMSM. Math Comput Model2008; 47: 1356–1371.
19.
JaliliN. A comparative study and analysis of semi-active vibration-control systems. J Vib Acoust2002; 124: 593–605.
20.
ChoiSBNamMHLeeBK. Vibration control of a MR seat damper for commercial vehicles. J Intell Mater Syst Struct2000; 11: 936–944.
21.
LaiCYLiaoWH. Vibration control of a suspension system via a magnetorheological fluid damper. J Vib Control2002; 8: 527–547.
22.
Jahromi AF and Zabihollah A. Linear quadratic regulator and fuzzy controller application in full-car model of suspension system with magnetorheological shock absorber. In: 2010 IEEE/ASME international conference on mechatronics and embedded systems and applications (MESA), 2010, pp.522–528. New York: IEEE.
23.
Zhu W, Hu AP and Shen HP. Semi-active optimal control of parallel multi-DOF vibration reduction system for instrument carried by vehicle. In: Control and decision conference, CCDC’09, 2009, pp.1985–1989. New York: IEEE.
ChangCHsuC. Control performance of liquid column vibration absorbers. Eng Struct1998; 20: 580–586.
26.
GengZJHaynesLS. Six degree-of-freedom active vibration control using the Stewart platforms. IEEE Trans Control Syst Technol1994; 2: 45–53.
27.
DubayRHassanMLiCet al.Finite element based model predictive control for active vibration suppression of a one-link flexible manipulator. ISA Trans2014; 53: 1609–1619.
28.
BoscariolPGasparettoAZanottoV. Active position and vibration control of a flexible links mechanism using model-based predictive control. J Dyn Syst Meas Control2010; 132: 014506–014506.
29.
GiuaASeatzuCUsaiG. A mixed suspension system for a half-car vehicle model. Dyn Control2000; 10: 375–397.
30.
GucluR. Fuzzy logic control of seat vibrations of a non-linear full vehicle model. Nonlin Dyn2005; 40: 21–34.
31.
Liang Q, Lu Y, Wu X, et al. Analysis and semi-active control of rigid-flexible coupled system on vehicle. In: 2011 international conference on transportation, mechanical, and electrical engineering (TMEE), 2011, pp.715–718. New York: IEEE.
32.
GuZFeiSZhaoYet al.Robust control of automotive active seat-suspension system subject to actuator saturation. J Dyn Syst Meas Control2014; 136: 041022–041022.
33.
StengelRF. Optimal control and estimation, North Chelmsford, MA: Courier Corporation, 2012.
34.
JazarRN. Vehicle dynamics: Theory and application, New York: Springer Science & Business Media, 2013.
35.
ShabanaAA. Theory of vibration: Volume II: discrete and continuous systems, New York: Springer Science & Business Media, 2012.
