Sensor and actuator design methods in active vibration control for distributed parameter structures

Abstract

The efficiency of active structures is determined by their design. An important part of the design process is the placement and shaping of sensors and actuators necessary for the control. This paper focuses on placement and shaping methods for distributed parameter structures, such as plates and shells. The methods are based on a modal representation of the structural vibration. According to the standards of control theory and signal processing the state space formulation is used to collect modal data into matrices and to describe the dynamics of the system. For the normalization of these matrices the H ₂ and H _∞ norms are used. The actuators are considered to be distributed piezoelectric sheets which are bonded to the surface of the structure. The efficiency of the actuators is expressed in scalar performance indices. The calculation of these indices requires the normalization of the input matrix and the generation of a so-called placement matrix. An example is presented for a plate to demonstrate the design process for distributed actuators. For the detection of modal displacements and velocities the concept of point sensors is applied which requires a positioning of sensors into an array. To obtain an appropriate sensor layout the placement of each sensor with respect to the vibration amplitude and the correlation of each sensor within the array has to be considered. The sensor performance is also expressed by scalar indices, which are calculated by the sane formulas as for the actuators. The sensor correlation is investigated by the condition of the output matrix. A comparison of different point sensor arrays is carried out for the mentioned plate example.