The describing function method is applied to characterize the steady state behavior of the linear sampled data systems stabilized by a second-order sliding mode algorithm. A describing function of the nonlinearity including a sample and hold element is derived. The proposed method allows to predict the amplitude, frequency and phase of occurring limit cycles caused by the discrete time implementation of discontinuous control algorithms. It is shown that the derived describing function is closely related to its classical continuous time counterpart. The proposed approach is demonstrated using a numerical simulation example as well as a real world experiment.
|Title of host publication||Decision and Control (CDC), 2016 IEEE 55th Conference on|
|Number of pages||7|
|Publication status||Published - 29 Dec 2016|
|Event|| 55th IEEE Conference on Decision and Control - ARIA Resort & Casino, Las Vegas, United States|
Duration: 12 Dec 2016 → 14 Dec 2016
|Conference||55th IEEE Conference on Decision and Control|
|Period||12/12/16 → 14/12/16|