Modelling and control of a shell structure based on a finite dimensional variational formulation

Mathematical control theory: nonlinear dynamics and engineering applications

“…Для варіаційної форми задачі про коливання оболонки запропоновано аналітико-чисельну схему визначення коефіцієнтів скінченновимірних наближених систем відповідно до узагальненого методу Гальоркіна. Створено програмну реалізацію цієї схеми при чисельному заданні власних форм оболонки [29]. Результати пройшли апробацію на керованій оболонковій конструкції Stuttgart SmartShell, спорудженій в Університеті Штутгарта для експериментів з надлегкими будівельними конструкціями (рис.…”

Modeling and Stabilization of a Rotating Mechanical System with Elastic Plates

“…Let us consider the first flexible mode only (m 1 = m 2 = 1) and apply the Ritz-Galerkin method (cf. [22]) for the nonlinear closed-loop system (7)-(9), (20), (24), (29) to derive its finite-dimensional approximation of the forṁ…”

“…For the Cartesian frames (g 1 , g 2 , g 3 ) and (e 1 , e 2 , e 3 ) of the same orientation, the system of differential equations (7), (8), (9), (18), (22) has the following particular solution with f 1 = f 2 = f 3 = 0:…”

“…To study the stabilization problem for the equilibrium (23), we introduce new variables g ij (t) = g ij (t) − δ ij and consider the equations of perturbed motion for (22):…”

Reduced‐Order Observers for Nonlinear State Estimation in Flexible Multibody Systems

“…In contrast, the direct measurement of all the state variables is rarely feasible or convenient [9], so the unmeasured state variables should be estimated by means of state observers that exploit a smaller set of measurements, ensuring the system observability and an accurate system model. Most of the contributions in the literature have been focused on the state estimation in rigidbody multibody systems [10][11][12], in flexible structures [13] or in single-link flexible mechanisms [2,[14][15][16][17]. Complexity is significantly exacerbated in the case of multilink flexible systems where state estimation is, to date, still a challenging task, mainly because of the complex and large dimensional models used to represent these systems that make cumbersome the synthesis of observers.…”