Limit Cycle Oscillation Amplitude Tailorng Based on Describing Functions and $$\mu $$ Analysis

Nonlinear Robust Approaches to Study Stability and Postcritical Behavior of an Aeroelastic Plant

“…6) or DF-µ approach (Fig. 8), whereas for the former one sensitivity analyses as the ones shown in [32] might also provide invaluable aid.…”

“…Based on the validation campaign performed, it can be affirmed that when the hypotheses underlying DF theory (mentioned in Sec. II-B and further commented in [5], [32]) to the particular system examined are fulfilled, the DF method leads to accurate quantitative predictions of the LCO phenomenon, and its use in conjunction with µ can give important indications on the effect of the uncertainties. IQC, on the other hand, can guarantee the absolute stability of the system without the same assumptions on the nature of the signal.…”

“…The DF method is instrumental in guaranteeing this connection and enabling to transfer the information coming from multiple linear flutter analyses to an LCO characterization. For the interested reader, this aspect is further addressed in [32]. Stable and unstable oscillations are depicted respectively with solid and dashed lines, according to the criterion in [33].…”

Nonlinear stability and post-critical analysis of an uncertain plant with describing functions and integral quadratic constraints

“…3. The DF method is instrumental in guaranteeing this connection and enabling to transfer the information coming from multiple linear flutter analyses to an LCO characterization [15]. Stable and unstable oscillations are depicted respectively with solid and dashed lines, according to the criterion in [16].…”

“…III to emphasize the two regions), it is evident a greater effect of the uncertainties in worsening the response. For example, assume a nominal analysis cleared the system, able to withstand oscillations of amplitude up to 1.9δ, to operate at V =16 It is important to note finally that the accuracy of the conclusions inferred with this local approach is expected to depend in general on the applicability of the hypotheses underlying DF theory to the particular system examined (these were commented on for this problem in [15]). …”