A novel fractional order PID navigation guidance law by finite time stability approach

Abstract

In this paper, a novel fractional order proportional–integral–differential navigation guidance law utilizing finite time stability approach is presented in order to achieve robust performance for intercepting incoming targets. The proposed guidance law is designed following three-loop guidance and control scheme, considering the interceptor’s nonlinear 6 degrees-of-freedom model. In the outer loop, normal acceleration commands are generated by the proposed guidance law. In the intermediate loop, these commands are converted into equivalent body rate commands, which are tracked by dynamic inversion based autopilot in the inner loop. A fractional order circle criterion is developed for the finite time stability analysis of this proposed guidance law, whose stability conditions give an analytical bound for the flight up time in which stability can be insured. Extensive 6 degrees-of-freedom simulations and a variety of comparison studies against maneuvering targets are implemented to demonstrate the effectiveness of the proposed guidance law. The simulation results show that the proposed guidance law has better performance when comparing with the proportional navigation and proportional–integral–differential navigation guidance laws.