Computation of Limit Cycle in a Nonlinear Fractional-Order Feedback Control Plant with Time Delay

This paper predicts the presence of the limit cycle for a class of nonlinear fractional-order feedback control plants with separable nonlinearities. The concept of describing function along with the Nyquist contour is extended to evaluate the amplitude and frequency of such periodic oscillations for a fractional-order time-delay system. The critical value of plant gain is evaluated below which the system response shows convergence and oscillations fail to sustain. The accuracy of the proposed technique has been substantiated by comparing it with the results from MATLAB/SIMULINK applications.