Keywords: uncertainty, smart beam, stochastic load, robust performance, robust analysis, robust synthesis.

In this paper we apply and investigate the technology of robust control in smart structures. A smart structure can be defined as a structure with integrated sensors and actuators, together with a control system which aids the structure in reacting automatically to external stimuli acting upon it. The control system aims at suppressing undesirable effects and/or enhancing desirable effects. We study an example of such a structure: an intelligent beam with integrated piezoelectric actuators, the goal of which is to suppress oscillations under deterministic and stochastic loads [1].

Firstly we examine the H_infinity criterion. The control problem is to keep the beam in equilibrium to face the external disturbances, such as wind and noise under the presence of model inaccuracies, using the available measurements and controls [2]. Also of interest is the maximum disturbance the system can handle, given its piezoelectric voltage limits. The advantage of the H_infinity criterion is in its ability to take into account in the computations the worst result of uncertain disturbances or noise in the system [3]. It is possible to synthesize a H_infinity controller which will be robust with respect to a predefined number of uncertainties in the model. The results are very good: the oscillations were suppressed even for a real aeolian load, with the piezoelectric component voltages within their endurance limits.

Then, by taking into account the non-linearity of the system which was not considered in the model, our inaccurate knowledge of the model's values and parameters, and their physiological variations over the course of the structures' operation, we introduce modeling uncertainties [4]. A robust m-controller was analyzed and synthesized, using the D-K iterative method. The results using the various controllers are compared and commented upon.

We propose a new method of robust fault detection that is insensitive to the disturbances caused by unknown modeling errors while it is highly sensitive to the component failures. It is shown by numerical simulations that the proposed methods suppresses the disturbances due to model errors and markedly improves the detection performance. The suitability of the H_infinity and the D-K design technique in the modeling of uncertainties and in evaluating the robust performance of the system was demonstrated.

1

G. Foutsitzi, D. Marinova, E. Hadjigeorgiou, G. Stavroulakis, "Finite element modelling of optimally controlled smart beams", 28th Summer School: Applications of Mathematics in Engineering and Economics, Sozopol, Bulgaria, 2002.

2

G.E. Stavroulakis, G. Foutsitzi, E. Hadjigeorgiou, D. Marinova, C.C. Baniotopoulos, "Design and robust optimal control of smart beams with application on vibrations suppression", Advances in Engineering Software, 36(11-12), 806-813, 2005. doi:10.1016/j.advengsoft.2005.03.024

3

A. Pouliezos, "MIMO control systems", class notes, 2008. http://pouliezos.dpem.tuc.gr

4

D. Marinova, G.E. Stavroulakis, D. Foutsitzi, E. Hadjigeorgiou, E.C. Zacharenakis, "Robust design of smart structures taking into account structural defects", Summer School Conference Advanced Problems in Mechanics Russian Academy of Sciences, D.A. Indeitsev, (Editor), 288-292, 2004.

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