Partial pole assignment with time delay by the receptance method using multi-input control from measurement output feedback

Active control of vibrational systems is a topic that has been widely studied over the past few decades. Assigning poles by state-feedback control is one of the classical control methods. Conventional pole assignment problems are usually solved using finite element (FE) models or theoretical models. However, FE models have several disadvantages, e.g., a difficulty in obtaining precise damping models of real structures, especially for structures with many forms of damping (such as friction and viscosity). Theoretical models unavoidably involve errors with respect to practical systems. To overcome these shortcomings, the receptance method for linear active vibration control has recently been developed. One remarkable advantage of this method is that it is entirely based on data from modal testing with no need to know the exact mass, damping and stiffness matrices, which are typically obtained using the FE method.

Skipping the process of modelling, namely eliminating largely approximations, assumptions and modelling errors, makes the receptance method feasible and effective for practical structures. Plenty of research has proved its effectiveness and superiority for active vibration control of linear systems both theoretically and experimentally since its first introduction. Considering that time delays in control loops are inevitable because of the dynamics involved in the actuators, sensors, and controllers, partial pole assignment by single-input for time-delay systems using the receptance method has been achieved. As a counterpart, however, how to accomplish the same goal by multi-input control has remained unstudied.

This paper originally formulates the partial pole assignment of multi-input time-delay systems using the receptance method from measurement output feedback (i.e., acceleration, velocity and displacement). We achieve partial assignment of the desired poles with no spillover using the assigned and unchanged poles and the corresponding eigenvectors of the closed-loop system. In addition, the effects of time delay on partial pole assignment and modal constraints assignment are presented theoretically and numerically. Our theoretical results could be applicable for active vibration control of practical multi-input time-delay system, e.g. active flutter suppression of time-delay aeroelastic systems with multiple control surfaces.