Reliable and accurate algorithm to compute the limit cycle locus for uncertain nonlinear systems

Robust prevention of limit cycle for nonlinear control systems with parametric uncertainties both in the linear plant and nonlinearity

“…Usually, the overall picture turns out to be the proper tuning of the adjustable parameters to effectively suppress or to remove the limit cycle. To achieve this, the extensions of the describing function method-based limit cycle analysis to nonlinear systems with parametric uncertainties have recently been proposed [14][15][16][17][18][19][20]. In one of such works, Barmish and Khargonekar attempted to address the former point in [14].…”

“…It should be emphasized that a family of admissible controller gain sets, instead of just one, can be selected from the Kharitonov region, which provides a flexible choice of controller coefficients. Existing techniques provide just one controller gain set [16][17][18][19][20]. Further, since the choices are multiple, the controller gains can be properly scheduled to guarantee robustness even in the case of controller implementation uncertainty.…”

“…The request is that the nonlinearities should be separable. Further, the intervalanalysis-based algorithm presented in [20] is useful in gaining insight into the effect of one of the uncertain parameters on the limit cycle behavior by fixing other parameters to be timeinvariant.…”

“…This approach enables the designer to explicitly detect the presence of possible limit cycles including the range of their frequencies and the range of their amplitudes. Recently, a reliable and accurate algorithm for computing the limit cycle locus for nonlinear systems with nonlinear parametric uncertainty has been proposed in [20]. The request is that the nonlinearities should be separable.…”

Limit Cycle Predictions of Nonlinear Multivariable Feedback Control Systems with Large Transportation Lags

“…In general, real and imaginary parts of the characteristic equation are used as two simultaneous equations to find the solution of the limit cycle for single-input singleoutput (SISO) nonlinear feedback control systems [11][12][13][14][15][16][17]. Therefore, single nonlinearity in the system can be solved easily to find two parameters, that is, oscillation amplitude (A) and frequency (ω) of a limit cycle.…”