22
2 Literature Review
genetic algorithm. Besides, the negative velocity proportional feedback control law,
Lyapunov feedback control [30, 54, 248–250] and bang-bang control [52, 223] were
also investigated by many researchers.
Many studies were implemented optimal control laws into simulations of vibration control of smart structures. Linear quadratic regulator (LQR) control is a full
state feedback control, investigated by Kang et al. [253], Narayanan and Balamurugan [54], Balamurugan and Narayanan [30], Raja et al. [263], Vasques and
Rodrigues [261], Valliappan and Qi [264] and Xu and Koko [265]. LQR control is
an ideal method, which assumes that all the state variables should be measurable
and fed back to the controller. However, state variables can not be all measured in
real applications. Therefore, linear quadratic Gaussian (LQG) control was applied to
smart structures by Stavroulakis et al. [266], Vasques and Rodrigues [261], Dong et
al. [267]. In LQG control, the state variables are not necessarily measured, but can
be estimated by an observer. Furthermore, Marinaki et al. [55] proposed a particle swarm optimization based controller for vibration suppression of beams. Roy
and Chakraborty [268] developed a genetic algorithm based LQR control for smart
composite shell structures.
2.7.2 Advanced Control Strategies
Conventional controls are with easy implementation, but they have low control efficiency and robustness. To improve the control effect, Chen and Shen [269], Lin and
Nien [270] developed an independent modal space control for vibration suppression of smart structures. Bhattacharya et al. [271] proposed an independent modal
space based LQR control strategy for vibration control of laminated spherical shell
with various fiber orientation and curvature radius. Furthermore, Manjunath and
Bandyopadhyay [272] developed a discrete sliding mode control scheme, Valliappan
and Qi [264] proposed a prediction control algorithm for smart beams with bonded
piezoelectric patches. Zhang et al. developed disturbance rejection control with both
proportional-integral (PI) [273, 274] and generalized-proportional-integral (GPI)
observers [274] for vibration suppression of smart structures. Later, in the framework of disturbance rejection control, Zhang et al. [275], Zhang et al. [276] developed
generalized disturbance rejection control with PI observer for smart beams.
Considering finite element models with geometric nonlinearities, very less papers
can be found in the literature dealing with control simulations. Due to the complexity
of nonlinear numerical models, most of the studies were applying very simple control
schemes, Zhou and Wang [277] applied a negative velocity or displacement feedback control for vibration suppression of beams. In addition, Schmidt and Vu [125],
Vu [278], Lentzen and Schmidt [134, 135] investigated the same control schemes
for vibration suppression of piezoelectric bonded plate structures based on von Kármán type nonlinear FE models, while Gao and Shen [114] studied based on a fully
geometrically nonlinear FE plate model with FOSD hypothesis.
2 Literature Review
genetic algorithm. Besides, the negative velocity proportional feedback control law,
Lyapunov feedback control [30, 54, 248–250] and bang-bang control [52, 223] were
also investigated by many researchers.
Many studies were implemented optimal control laws into simulations of vibration control of smart structures. Linear quadratic regulator (LQR) control is a full
state feedback control, investigated by Kang et al. [253], Narayanan and Balamurugan [54], Balamurugan and Narayanan [30], Raja et al. [263], Vasques and
Rodrigues [261], Valliappan and Qi [264] and Xu and Koko [265]. LQR control is
an ideal method, which assumes that all the state variables should be measurable
and fed back to the controller. However, state variables can not be all measured in
real applications. Therefore, linear quadratic Gaussian (LQG) control was applied to
smart structures by Stavroulakis et al. [266], Vasques and Rodrigues [261], Dong et
al. [267]. In LQG control, the state variables are not necessarily measured, but can
be estimated by an observer. Furthermore, Marinaki et al. [55] proposed a particle swarm optimization based controller for vibration suppression of beams. Roy
and Chakraborty [268] developed a genetic algorithm based LQR control for smart
composite shell structures.
2.7.2 Advanced Control Strategies
Conventional controls are with easy implementation, but they have low control efficiency and robustness. To improve the control effect, Chen and Shen [269], Lin and
Nien [270] developed an independent modal space control for vibration suppression of smart structures. Bhattacharya et al. [271] proposed an independent modal
space based LQR control strategy for vibration control of laminated spherical shell
with various fiber orientation and curvature radius. Furthermore, Manjunath and
Bandyopadhyay [272] developed a discrete sliding mode control scheme, Valliappan
and Qi [264] proposed a prediction control algorithm for smart beams with bonded
piezoelectric patches. Zhang et al. developed disturbance rejection control with both
proportional-integral (PI) [273, 274] and generalized-proportional-integral (GPI)
observers [274] for vibration suppression of smart structures. Later, in the framework of disturbance rejection control, Zhang et al. [275], Zhang et al. [276] developed
generalized disturbance rejection control with PI observer for smart beams.
Considering finite element models with geometric nonlinearities, very less papers
can be found in the literature dealing with control simulations. Due to the complexity
of nonlinear numerical models, most of the studies were applying very simple control
schemes, Zhou and Wang [277] applied a negative velocity or displacement feedback control for vibration suppression of beams. In addition, Schmidt and Vu [125],
Vu [278], Lentzen and Schmidt [134, 135] investigated the same control schemes
for vibration suppression of piezoelectric bonded plate structures based on von Kármán type nonlinear FE models, while Gao and Shen [114] studied based on a fully
geometrically nonlinear FE plate model with FOSD hypothesis.