Measures of modal controllability and observability in vibration control of flexible structures

Optimal Locations of Dampers/Actuators in Vibration Control of a Truss-Cored Sandwich Plate

“…It is also known that the goal of actuator optimization is not just simply to meet the condition of controllability. The extent of controllability that can provide a quantitative measurement on the physical actuator force vector needed for a given modal control force vector is also of great interest [21]. For a modal control force vector designed to achieve the expected control effect, it is highly expected that through actuator placement optimization, smaller physical control forces will be required to realize a more controllable system.…”

“…Lammering [20] proposed an optimization method for the actuator placement by using the trace of matrix   To illustrate the relationship among modal control forces, singular values and physical control forces, we introduce a new modal coordinate {η} through the coordinate transformation [21]:…”

Quantitative Measures of Modal Controllability and Observability in Vibration Control of Defective and Near-Defective Systems

“…In the following, we try to extend the idea presented in reference [5] to the case of the defective or near-defective systems with repeated or close eigenvalues. Taking the SVD of the modal controllable matrix, P K in equation (25), yields…”

“…Reference [5] presented a criterion for the quantitative measures for modal controllability and observability of non-defective systems with repeated eigenvalues. In the following, we try to extend the idea presented in reference [5] to the case of the defective or near-defective systems with repeated or close eigenvalues.…”

“…The singular-value decomposition (SVD) technique was widely used to deal with the control problems. Recent papers in this "eld include the measures of modal controllability and observability for non-defective systems with repeated eigenvalues [5,6], indirect adaptive periodic control [7], controllability analysis of thermally coupled distillation systems [8], stability and modal control for multi"ngers robot band [9], the controllability and observability analysis for adaptive optical systems [10], and the index of controllability and observability of a given mode [11].…”