Controle PID de vibrações em sistemas de segunda ordem com atraso usando receptância com estabilidade robusta e otimização de desempenho

Abstract

Phenomena such as mechanical vibrations, resonance and oscillations can be mathematically described by second-order differential equation systems, commonly referred to as second-order systems. Working with this type of model, instead of first-order state models, brings numerical benefits, but there are inherent difficulties in determining their physical parameters. The challenges become even more significant when considering the existence of delays between state measurements and actuation signals, leading some approaches to require post-analysis for determining the stability of calculated solutions. An alternative to overcoming the difficulties of parameter measurement is the frequency response approach which utilizes models based on receptance. In view of the issue, this work focuses on the design of PID controllers (Proportional-Integral-Derivative) for linear dynamic systems with delay, modeled by second-order matrix differential equations. It adopts the receptance approach because it is based on the frequency response of the system, enabling precise treatment of closed-loop stability, without the need for approximations or back-testing of delay terms. To ensure robustness and performance, as well as minimize the Absolute Error Integral relative to the tracking of a constant reference, it formules an optimization problem for the determination of controller gains. Also, it takes into account a pre-established stability margin. To solve the optimization problem, it implements a Genetic Algorithm. Unlike related works in the literature, the proposed method can be equally applied to systems with open-loop poles in the right half-plane.