Saddle-node bifurcation of limit cycles in a feedback system with rate limiter

Limit cycles analysis of feedback systems with rate limiters can be implemented by a classical method in the frequency domain, the harmonic balance method. In this paper, the rate limiter describing function is obtained and applied to the search of limit cycles. Finally, the describing function method has been applied to a nonlinear plant with two stable poles and a rate-limiter nonlinearity in the actuator. This study allows the detection of a saddle-node bifurcation of limit cycles.