Control of a class of second-order linear vibrating systems with time-delay: Smith predictor approach

This paper presents an innovative approach to the design of feedback control in second-order symmetric linear systems under long input time-delay. Recent works have presented design techniques for second order-systems. However, most of them carry out an a posteriori analysis to check if the target eigenvalues are correctly assigned. An inaccurate eigenvalue assignment can occur due to infinite dimensional nature of the characteristic polynomial for systems with time-delay, and, eventually, the target eigenvalues can be assigned as secondary ones, with unstable, dangerous primary eigenvalues entering the picture. The proposal uses a Smith Predictor based approach to compensate the time-delay by providing a nominal characteristic polynomial without delay. The prediction is obtained by employing the versatile receptance approach in the conception of the predictor, and thus the design is entirely made at the frequency domain. The proposal uses a filtered prediction error which can be applied to attenuate the undesired effect of the poorly damped eigenvalues and ensure the internal stability of the marginally stable case. Some numerical experiments are given to illustrate the effectiveness of the proposed approach.