Active vibration suppression of a cantilever wing

Meirovitch, L.; Silverberg, Larry

doi:10.1016/0022-460x(84)90274-8

Cited by 31 publications

(13 citation statements)

References 3 publications

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“…The results for the openloop/closed loop control and the closed-loop control only are given for the terminal time T' = 0.075. It is noted that the difference in the energy functionals for these two cases depends on the magnitudes of the weighting factors p1 and p2 attached to the penalty functional In Figure 2 the dimensionless penalty functional Ji (see (6a)) and the dimensionless functional Ji involving the maximum values of the deflection and angle of twist (see (8)) are plotted against Ci with Ci = 0 and T' = 0.075. It is observed that the feedback parameter also has an affect on the open-loop penalty functional Ji.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In practice it is more common to use a displacement actuator than a torsional actuator. However, the energy expression (8) involves both the displacement and angle of twist and the control is exercised on both quantities. From Figure 1 it is clear that the behaviour of the cost functional with respect to the feedback parameter is highly dependent on the terminal time.…”

Section: Numerical Resultsmentioning

confidence: 99%

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Optimal open‐loop/closed‐loop control for one‐dimensional structures with several state variables

Bruch

Sadek

Adali

et al. 1993

Optim Control Appl Methods

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SUMMARYAn optimal control problem for one-dimensional structures described by a system of partial differential equations is formulated. Open-and closed-loop control mechanisms are incorporated into the formulation and a general method of solution is presented in the context of a structural vibration problem. The expenditure of control force is restricted by penalizing a functional of the open-loop control force in the performance index and by imposing a constraint on the magnitude of the closed-loop control force. The optimality condition for the open-loop control is derived by using the methods of eigenfunction expansion and variational calculus. The closed-loop control parameters are obtained from the minimization of the energy of the system. The theory is illustrated by solving a vibration control problem for a beam undergoing torsional and flexural vibrations. Numerical results are presented in a graphical form in which the behaviours of the controlled and uncontrolled beams at different terminal times are compared. The numerical results indicate the effectiveness of the proposed control mechanism for reducing excessive vibrations as measured by the energy of the beam. The minimizing value of the closed-loop control parameter associated with displacement feedback is shown to be a function of the terminal time.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

Optimal open‐loop/closed‐loop control for one‐dimensional structures with several state variables

Bruch

Sadek

Adali

et al. 1993

Optim Control Appl Methods

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“…Indeed, a vast number of solution techniques are available to solve equation (12). The method of setting…”

Section: Methods Of Solutionmentioning

confidence: 99%

“…Thus, results on the control of membranes [15], wings [12], beams [16,17], and plates [1,18] became available in the literature. A survey article [22] provides a review of the recent advances in the field of distributed parameter systems.…”

Section: Introductionmentioning

confidence: 96%

Active control of flexible systems by a mathematical programming approach

Nouri-Moghadam

Sadek

1993

Dynamics and Control

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Abstract.A class of control problems for a damped distributed parameter system governed by a system of partial differential equations with side constraints (equality and/or inequality) is considered. The proposed approach approximates each control force of the system by a Fourier-type series. In contrast to standard linear optimal control approaches, the method used here is based on the mathematical programming approach, in which the necessary condition of optimality is derived as a system of linear algebraic equations. The proposed approach is easy to apply to a large class of control problems. A vibrating beam excited by an initial disturbance is studied numerically in which the effectiveness of the control and the amount of force spent in the process are investigated in relation to the reduction to the dynamic response.

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“…Although this situation may lead to excessive vibrations under dynamic loading, the problem can be dealt with by employing structural control, in particular, active control. Applications of this type of control have recently been extended to various structures [1][2][3][4]. Since the idea of active control was first proposed for tall buildings in the 1960s [5], much progress has been made in this field.…”

Section: Introductionmentioning

confidence: 99%