Pilot-induced oscillation analysis with rate limiter

Abstract

This paper proposes a describing function method for limit cycle analysis of a system with a rate limiter. First, the rate limiter is defined and its describing function is derived in a strict manner. Then, the stability analysis using the describing function of the rate limiter is executed. In many cases of limit cycles, the output of the rate limiter becomes triangular, and in order to deal with such cases by the describing function, a new method to modify an open-loop transfer function is introduced. This method can predict the limit cycle occurrence more exactly, which is applicable to a prediction of a rate-limiter based PIO (Pilot-Induced Oscillation) of an aircraft.