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Abstract:
A novel semi-active control method for mitigating structural vibration is studied. The method relies on distributed state information patterns and the solution to a suboptimal control problem that aims at replicating the switched structures of the optimal open-loop stabilizing controls. The optimality conditions and the method of solution of the suboptimal problem are discussed. The performance of this method is examined by means of numerical experiments performed for a double cantilever system equipped with a set of semi-active elastomers with controlled viscoelastic properties. The experiments were carried out for different controller architectures and a series of initial conditions. In terms of the assumed objectives, the proposed distributed control strategy significantly outperforms the passive damping strategies and is competitive with a standard centralized control. The proposed approach is general to a class of bilinear control systems concerned with smart structural elements. The practical aspects of the designed distributed controller are highlighted.

Keywords:
distributed control, optimal control, bilinear system, stabilization, semi-active structure

Abstract:
The problem of adaptive optimal semiactive control of a structure subjected to a moving load is studied. The control is realised by a change of damping of the structure's supports. The results presented in the previous works of the authors demonstrate that switched optimal controls can be very efficient at reducing the vibration levels of the structure. On the other hand, these controls exhibit a high sensitivity to changes of the speed of the travelling load. The aim of this paper is to develop an algorithm that enables real-time adaptation of the optimal controls according to both the measured speed of the travelling load and the estimated state of the structure. The control objective is to provide smooth passage for the vehicles and reduce the material stresses on the carrying structures. The designed adaptive algorithm uses reference optimal controls computed for constant speeds and a set of functions describing the sensitivity of the system dynamics to the measured parameters. The convergence of the algorithm, as well as aspects of its implementation, is studied. The performance of the proposed method is validated by means of numerical simulations conducted for different travelling speed scenarios. In the assumed objective functional, the proposed adaptive controller can outperform the reference optimal solutions by over 50%. The practicality of the proposed method should attract the attention of practising engineers.

Keywords:
adaptive control, moving load, online optimal control, sensitivity analysis, structural vibration control

Abstract:
The paper deals with the adaptive optimal semi-active control of the slender vibrating structures subjected to the moving loads. The deflection of the structure is governed by Euler-Bernoulli beam equation approximated by the system of bilinear ordinary differential equations. The damping function of the structure support is chosen as the control function. The optimal control problem consists in finding such bang-bang control function to minimize the energy as well as the vibrations of the carrying structure. Although the switched optimal control is a very efficient tool in the reduction of structure vibrations it is very sensitive with respect to changes of the speed of the traveling load. This paper deals with the development of the adaptive descent type algorithm that enables the update of the optimal controls in real time based on the measured speed of the traveling load or structure's state. The proposed algorithm uses reference optimal controls computed for the constant speeds and the set of functions describing the sensitivity of the system dynamics with respect to the measured parameters. Numerical computations are carried out for different speed scenarios of the moving load. The obtained numerical results indicate that the proposed adaptive controller can significantly outperform the reference optimal solutions.

Abstract:
In this paper, the problem of the optimal control of a structure subjected to a moving load has been studied. In contrast to the previous works of the authors, focused on open-loop strategies, this paper has been devoted to an adaptive closed-loop control, where the switched damping strategy is subject to real-time adaptation according to the measured speed of the moving load. The proposed adaptive controller has been designed based on the use of the reference optimal solutions computed for a given constant velocity and a set of functions describing the sensitivity of the system dynamics to a change in the speed and the initial state. All these data are pre-computed offline and stored in the controller's memory. As a result, the online computational algorithm, based on a simple gradient descent loop, uses a minimal calculation effort. This allows almost immediate updating of the optimal controls, even with the use of a standard PC. The method has been validated by means of numerical experiments carried out for a wide range of the velocity perturbation scenarios. The proposed scheme is general for a class of time-varying bilinear control systems and can be implemented to a wide range of problems concerned with smart structural elements.