Control of second-order asymmetric systems with time delay: Smith predictor approach

Abstract

Abstract The feedback control for systems modeled as second-order linear dynamics with time delays is a challenge that received crescent attention nowadays. Flexible structures and structural systems are some remarkable examples that can be modeled as second-order dynamics. In the presence of delays, the well-known pole/eigenvalue assignment may fail due to the infinite-dimensional nature of the characteristic polynomials: the dominant eigenvalues can be erroneously placed in positions near to the imaginary axis, or even in unstable locations, that is, in the right-half plane. Recently, the authors have proposed a receptance-based delay compensation strategy that merges remarkable properties of receptance description and Filtered Smith Predictor (FSP). The obtained results outperformed pure pole/eigenvalue assignment techniques since the undesired delay effect is removed from the nominal characteristic equation. Hence, standard design strategies can be directly applied to control second-order systems with time delay based on a receptance model with no delay. In this work, these results are extended to deal with unstable second-order systems, an issue widespread in aeroelastic or friction-induced vibration systems. The FSP structure design is carried out in the discretized models of the system receptance to ensure internal stability as a consequence of particular filter design and implementation strategy. This procedure is possible due to a stable implementation structure for the receptance-based predictor in its digital form. Two typical examples, namely, aeroelastic flutter control and friction-induced vibration control, are used as benchmarks to verify the efficacy of the proposal.