The describing function method accuracy in first order plants with rate-limited feedback

In this paper, the rate limiter describing function is used to analyze by harmonic balance the existence of limit cycles in first order plants. Next, by comparison with analytical results previously obtained by the authors, the accuracy of the above approximate predictions is assessed. The main conclusion is that from a qualitative point of view the harmonic balance is good enough, providing in a exact way the critical value of the bifurcation parameter, and leading to neither spurious predictions of limit cycles nor failures in their detection. Regarding the quantitative aspects, the accuracy of the method depends on certain dimensionless parameter which is intrinsic to the problem.