Active vibration suppression by pole-zero placement using measured receptances

The paper addresses the problem of pole-zero assignment using the receptance method in active vibration control and has applications particularly in vibration absorption and detuning of structures to avoid resonance. An output feedback approach is described that makes use of measured receptances, there being no requirement at all for the M, C, K matrices usually obtained by finite elements. Therefore, in the controller design, the approximations, assumptions and other modelling errors are largely eliminated. In addition, the method does not require the use of model reduction techniques or the estimation of unmeasured states by an observer. An advantage of the output feedback method, over state feedback, is that collocated actuator–sensor arrangements become possible. However this is achieved at the expense of creating characteristic equations nonlinear in the control gains. Numerical examples are provided to illustrate the working of the method. This is followed by a series of experimental tests carried out using collocated accelerometers and inertial actuators on a T-shaped plate. In a series of experiments poles and zeros are assigned separately and simultaneously. Stability robustness is demonstrated by applying a constraint to the singular values of the matrix return difference.