Time-dependent reliability based design for control of servo linkages with unknown but bounded uncertainties

- The motion error of uncertain servo mechanisms is qualified by the interval process.
- The uncertainty quantification method is proposed via the first-order Taylor expansion and interval mathematics.
- A new measure index of time-dependent reliability of servo mechanisms is presented.
- The reliability based controller design for servo linkages is conducted.

Due to the inevitable phenomena that various uncertainty factors in the servo mechanisms severely affect the output motion accuracy and the exact statistic characteristics of uncertainties may extremely difficult to be gained since the lack of sample information in practice, the non-probabilistic dynamic reliability assessment and optimization with high confidence and efficiency is of great significance for scientists and engineers. In view of this, this study develops a novel approach of non-probabilistic reliability based controller design for servo mechanisms and the related solution details are further expounded. The uncertainty quantification of dynamic response is conducted by the combination of the first-order Taylor expansion and interval mathematics. The non-probabilistic reliability with consideration of time-dependency for servo mechanisms is obtained by the first passage theory and interval process model. By comparing with the Monte-Carlo simulations (MCS) and the robust design approach, the accuracy of proposed reliability index and the applicability of the developed reliability based controller design method are demonstrated in two numerical examples.