Study of Active Vibration Control using the Method of Receptances
Using the Method of Receptance, it is possible in general to assign 2_x0002_ poles (i.e. n conjugate pairs) of an axially vibrating rod of variable cross section by sensing the state at _x0002_ points along the rod. Using the sensor data, closed loop feedback control gains can be calculated by solving a simple set of linear equations. The feedback gains can be applied to generate the required control force using an actuator. This partial pole assignment can be done without continuous or discrete analytical modeling. Therefore, the physical parameters such as the rigidity, the density, and the variable cross-sectional area of the rod may be considered unknown for calculating the gains for the control force. These control gains are purely determined by the measurement of receptances between the point of actuation and the points of sensing, which may be conducted experimentally. In the analytical arena, the estimates for the receptances are exact and therefore the assignment of the desired poles is also exact and suffers from no discretization or model reduction errors. However, in practical implementation, the control force affects the poles of the closed loop system. In practical implementation, the control force may also shift some of the poles which are not intended to be desirably placed or to remain unchanged. Although in this dissertation, the analysis is carried on an axially vibrating rod for simplicity, the Method of Receptances is generally applicable to other linear elastic structures of higher dimensions.
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