Bifurcations in Systems with a Rate Limiter

Limit cycles analysis of feedback systems with rate limiters in the actuator 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 for limit cycles in such control systems. Three examples with three different bifurcations (saddle-node bifurcation of limit cycles, subcritical Hopf bifurcation at infinity and supercritical Hopf-like bifurcation) are included. The method is approximate but its main advantage is that intuition is gained into a difficult problem.