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Robust adaptive vibration control for a general class of structures in the presence of time-varying uncertainties and disturbances

Koofigar H. R., Amelian S.

Journal of Theoretical and Applied Mechanics

2013

Vol. 51 nr 3

533--541

The problem of active vibration suppression in a wide class of smart structures is addressed. The dynamical model of a structure may be perturbed by uncertain time-varying parameters and external disturbances. A novel adaptive-based control algorithm is presented here to satisfy robustness properties with respect to model uncertainties and environmental disturbances. Reflecting practical situations, the upper bound of perturbations is not required for controller design. The analytical stability of a closed-loop system is presented based on the Lyapunov stability theorem. Furthermore, numerical analysis is also provided to show the effectiveness of the proposed method.

Algorytm odpornego sterowania adaptacyjnego - DACDM

Giernacki W.

Pomiary Automatyka Kontrola

2012

R. 58, nr 12

1100-1104

W artykule przedstawiono studium przypadku nad nową, autorską metodą odpornego sterowania adaptacyjnego - DACDM. Celem proponowanego algorytmu jest wyznaczenie regulatora odpornego na niepewność parametryczną, pracującego w układzie adaptacyjnym. Novum w syntezie regulatora stanowi wykorzystanie trójstopniowej kontroli odporności układu. Przeprowadzone badania numeryczne potwierdzają skuteczność proponowanego rozwiązania.

The paper presents a case study on a new, original, robust adaptive control method - DACDM [1]. The design of a controller robust to parametric uncertainty and working in the adaptive system is an aim of proposed algorithm. The DACDM procedure combines advantages of both control techniques - robust and adaptive. A novelty in the controller synthesis is the use of three stage system robustness control (by the use of coefficient diagram [2], optional step of the robustness index optimization [3], the use of adaptation mechanisms [4]). The case study is performed for the linear model SMFNO (stable, minimum-phase, non-oscillatory) described by equation 1 in the structure of the control system of Figure 1. The proposed algorithm from Figure 2 uses table 2 [5] for the selection of controller structure and design specifications [2] specified by equations 4 and 6. The use of the equation 16 enables to introduce the averaged model to the adaptive control system and the change of parametric uncertainty vector. The case study highlights the clarity of the design procedure. The coefficient diagram analysis (Fig.3) and results of conducted numerical studies (Fig. 4, Fig. 5, Fig. 8) confirm the effectiveness of the proposed solution in relation to the selected SMFNO model.