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It is achieved in link with modal controllability and observability considerations.
This paper addresses this issue by extending the concepts of modal controllability and observability norm developed for linear systems to weakly non-linear systems that exhibit non-linear normal modes.
Using the singular-value decomposition of input matrix B and output matrix C in the modal subspace, the quantitative measures of modal controllability and observability of defective systems are discussed.
Based on the dynamic finite element (FE) model and a linear-quadratic-Gaussian (LQG) model of vibration control for an adaptive truss, an integrated optimization model is built in which an improved quadratic performance index is adopted as the objective function and the mode closed-loop damping ratio, modal controllability and actuator number are selected as the constraints.
Using modal decomposition to discretize the spatial coordinate, and the notions of spatial and modal controllability and observability, the semi-infinite optimization problem is formulated as a nonlinear optimization problem in an abstract space, which is subsequently solved using standard search algorithms.
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Beside the analysis of the inherent dynamics of this system in terms of eigenvalues and vectors, the influence of centrifugal stiffening on the modal controllability of the blade is discussed.
Although there are a number of design configurations of distributed actuators, e.g., segmentation and shaping, been investigated over the years, this study is to explore a new actuator configuration spatially bonded on the surface of shell structures to enhance the spatial modal controllability.
Moreover, the time-varying modal matrices, used for the modal decoupling, are also used for controllability and observability analyses in order to achieve optimal actuator and sensor placement in the system.
We have developed the approach proposed earlier in Dugarova and Smagina (Avtomat. i Telemech. 11 (1990) 176) and proved a direct correlation between interval system controllability and existence of robust modal P-regulator.
The modal masses can be obtained based on the fact that the multiplication of the controllability and observability matrices does not change with the type of the system matrices, including the modal space ones.
To evaluate the performance of this control structure, we quantified its degree of controllability and stability (Fig. 5b).
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