Yeroglu C.Tan N.2024-08-042024-08-0420150324-8569https://hdl.handle.net/11616/90589This paper presents extensions of some results, obtained for the analysis of classical nonlinear control systems, to the nonlinear fractional order systems. It is shown that the results related to limit cycle prediction using describing function method can be applied to the fractional order plants. The frequency and the amplitude of the limit cycle are used for auto-tuning of the PID controller for nonlinear control systems with fractional order transfer functions. Fractional order control system with parametric uncertainty is also considered for the nonlinear case. On the other hand, a new method is provided for stability margin computation for fractional order nonlinear control system with parametric uncertainty structure using the Nyquist envelopes of the fractional order uncertain plant and the describing function that represents the nonlinearity of the system. Maximum perturbation bounds of the parameters of the fractional order plant are computed. Numerical examples are included to illustrate the methods presented.eninfo:eu-repo/semantics/closedAccessDescribing functionFractional order controlLimit cycleNonlinear systemsRelay auto-tuningStability marginArticle4422332552-s2.0-85018838439Q4