Fault‐tolerant fixed‐time prescribed performance control of MEMS gyroscope

Abstract

Abstract This paper investigates a fault‐tolerant fixed‐time prescribed performance microelectromechanical system gyroscope using the adaptive backstepping method. The control protocol is designed such that not only is the system robust to even extremely harsh conditions of disturbance and actuator faults but also the performance and its settling time are user‐adjustable. Also, the system itself along with the external disturbances and actuator faults are assumed to be uncertain. Two case studies have been analyzed; the controller performance in the presence of very severe while uncertain disturbance and actuator faults, and a comparison between fixed‐time and finite‐time in this model in terms of their performance and convergence rate. First, the dynamics of the system are derived, and the prescribed performance error is defined for the analysis. Then, using the backstepping method, and adaptive estimations for the uncertainties, the algorithm is designed to converge the errors to a small set near zero with a fixed‐time convergence rate after which the stability of the system is verified via Lyapunov theory. In the end, a simulation example is presented in each case study to represent the efficacy of the proposed control scheme.