Partial Pole Assignment in Second-Order Multiple-Input Systems with Time Delay using Receptance
Second Order Systems, Time-Delay, Partial Pole Assignment, Receptance, Frequency Response, Robustness.
Structures subject to vibrations such as bridges, buildings, highways, vehicles, among others, can be mathematically modeled by second-order differential equations with finite element discretization from complex distributed parameter models. This way, working with these models, despite the numerical benefits, brings inherent difficulties in determining their physical parameters. The challenges are even more significant when considering the existence of delays between the states' measurements and actuation signals, which leads some approaches to the need for an "a posteriori" analysis to avoid instability with the calculated solutions. An alternative to avoid such obstacles is to obtain representations directly from experimental data, as in the approach by receptance. This proposal consists of developing a numerical technique to solve partial pole placement problems for second-order multiple-input systems with delay, very common in vibration control in structures. The proposal is based on the concept of receptance and deals with the problems caused by the delay's presence, eliminating any need to approximate the exponential term. Closed-loop stability shall be ensured by the Nyquist criterion, with a robustness index given by the maximum peak of the sensitivity function defined by the so-called Ms circle. Solutions obtained for single-input models are extended to the multiple-input case. The generalized Nyquist criterion shall be used to establish stability with the so-called eigenloci. The control problem addressed here is split into two subproblems: the partial assignment of a set of desired poles, and closed-loop stabilization. The solution to the proposed problem can be found by a heuristic method using search algorithms. For this research, the versatile genetic algorithm was chosen as the search method.