In practical systems having separable hard nonlinearities, sustained oscillation is detected at the steady state response due to the presence of stable limit cycles. An optimization problem is proposed to tune the fractional order controller parameters for system with multiple-nonlinearity to suppress the limit cycle magnitude in addition to meet the desired closed loop specifications. To extend the applicability of the existing Nyquist plot for predicting this limit cycle, an input dependent Nyquist plot is proposed in this paper. A servo system with backlash and relay nonlinearities is considered as a case study for limit cycle prediction with obtained fractional order controllers using an input dependent Nyquist plot. The predicted limit cycle information is compared with optimization results, input dependent root locus and are validated through closed loop simulations. Further, the robustness of the designed controllers are tested under system parameter uncertainty, disturbance and measurement noise conditions.
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