Limitations of the describing function method

Kou, Shauying R.; Han, Kuang-Wei

doi:10.1109/tac.1975.1100922

“…There are examples, e.g., [10], in which the describing function method predicts there are no limit cycles but the system does have an oscillation. For further comments on the example in [10], see [24]. Further, there are examples, e.g., [35], in which the describing function method predicts a limit cycle and the system does not have a limit cycle.…”

Section: Liteeaidke Reviewmentioning

confidence: 99%

Oscillations of nonlinear feedback systems which contain tightly coupled subsystems in cascade

Hoeflin

¹

,

Miller

²

1986

Circuits Systems and Signal Process

2

0

View full text Add to dashboard Cite

This reproduction was made from a copy of a document sent to us for microfilming. While the most advanced technology has been used to photograpii and reproduce this document, the quality of the reproduction is heavily dependent upon the quality of the material submitted.The following explanation of techniques is provided to help clarify markings or notations which may appear on this reproduction. 1.The sign or "target" for pages apparently lacking from the document photographed is "Missing Page(s)". If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting through an image and duplicating adjacent pages to assure complete continuity, 2. When an image on the film is obliterated with a round black mark, it is an indication of either blurred copy because of movement during exposure, duplicate copy, or copyrighted materials that should not have been filmed. For blurred pages, a good image of the page can be found in the adjacent frame. If copyrighted materials were deleted, a target note will appear listing the pages in the adjacent frame.3. When a map, drawing or chart, etc., is part of the material being photographed, a definite method of "sectioning" the material has been followed. It is customary to begin filming at the upper left hand comer of a large sheet and to continue from left to right in equal sections with small overlaps. If necessary, sectioning is continued again-beginning below the first row and continuing on until complete. PLEASE NOTE:In all cases this material has been filmed in the best possible way from the available copy. Problems encountered with this document have been identified here with a check mark V . 1984Signature was redacted for privacy.Signature was redacted for privacy.Signature was redacted for privacy. IMIROliDCTlONThe analysis of nonlinear feedback systems presents many more difficulties than the analysis of linear feedback systems. Essentially, these difficulties arise in solving a coupled nonlinear system of ordinary differential equations as opposed to a linear coupled system.In many cases one can not solve the general nonlinear system easily, if at all. Thus, we must either restrict the type of system studied or do a qualitative analysis. In qualitative analyses we seek to answer the questions of existence or nonexistence of limit cycles, give estimates of amplitudes and frequencies of these limit cycles, and determine the limit cycle stability. To use the describing function method in the case of one nonllnearity, what is done is to first replace the nonllnearity in the system by a "linear" term, then analyze the "linear" system to predict limit cycles and stability for the nonlinear system. In the case of multiple nonlinearitles, each of the nonllnearltles is replaced by a "linear" term, and the "linear" system is analyzed.We consider a feedback system containing J linear plants and J nonlinear parts in cascade, as in Figure 1. We give an exact analysis of r=0 ?H©- Unfortunate...

show abstract

“…There are examples, e.g., [10], in which the describing function method predicts there are no limit cycles but the system does have an oscillation. For further comments on the example in [10], see [24]. Further, there are examples, e.g., [35], in which the describing been given, e.g., [2], [3], and [22].…”

Section: Liteeaidke Reviewmentioning

confidence: 99%

Oscillations of nonlinear feedback systems which contain tightly coupled subsystems in cascade

Hoeflin

¹

0

View full text Add to dashboard Cite

This reproduction was made from a copy of a document sent to us for microfilming. While the most advanced technology has been used to photograpii and reproduce this document, the quality of the reproduction is heavily dependent upon the quality of the material submitted. The following explanation of techniques is provided to help clarify markings or notations which may appear on this reproduction. 1.The sign or "target" for pages apparently lacking from the document photographed is "Missing Page(s)". If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting through an image and duplicating adjacent pages to assure complete continuity, 2. When an image on the film is obliterated with a round black mark, it is an indication of either blurred copy because of movement during exposure, duplicate copy, or copyrighted materials that should not have been filmed. For blurred pages, a good image of the page can be found in the adjacent frame. If copyrighted materials were deleted, a target note will appear listing the pages in the adjacent frame. 3. When a map, drawing or chart, etc., is part of the material being photographed, a definite method of "sectioning" the material has been followed. It is customary to begin filming at the upper left hand comer of a large sheet and to continue from left to right in equal sections with small overlaps. If necessary, sectioning is continued again-beginning below the first row and continuing on until complete. 4. For illustrations that cannot be satisfactorily reproduced by xerographic means, photographic prints can be purchased at additional cost and inserted into your xerographic copy. These prints are available upon request from the Dissertations Customer Services Department. 5. Some pages in any document may have indistinct print. In all cases the best available copy has been filmed.

show abstract

“…Other related papers include Blackmore [8], Duncan and Johnson [14], Knyazev [23], Kou and Kan [24], Swern [41] and an important early paper by Bass [4] . Z c, exp(ikut), T = 2IT/U| .…”

Section: Review Of Related Literaturementioning

confidence: 99%

On the stability in oscillations in a class of nonlinear feedback systems containing numerator dynamics

Krenz

¹

0

View full text Add to dashboard Cite

I. INTRODUCTION 64 II. RELATED RESULTS 66 III. STATEMENT OF MAIN RESULT 71 IV. ANALYSIS OF THE FEEDBACK SYSTEM 78 V. EXAMPLES 93 VI. CONCLUDING REMARKS 101 VII. REFERENCES 110 ill CONCLUSION REFERENCES ACKNOWLEDGEMENTS g APPENDIX A: THE INTEGRAL MANIFOLD THEOREM APPENDIX B |(j)(tQ)-y^l <6, the solution ^^t.tg.y^) exists for t > tg and satisfies |*(t)-il/Ct.tQ.y^) ] < e, for t > t^. The solution $(t) is said to be asymptotically stable if it is stable and if there exists 6 > 0 such that whenever j^Ctg)-y^j <6, the solution ipCtjl^.y^) approaches the solution 4(t) as t ^ ®. A T-periodic solution <}>(t) is said to be orbitally stable if there is a 6 > 0 such that any solution 'J'(t,tQ .yg), with jfCtg)-y^j <6, tends to the orbit {*(t): t^ < t < t^+T}. The solution $(t) is said to be unstable in the sense of Lyapunov, if it is not stable. The Describing Function Originally, the single-input sinusoidal describing function, simply referred to as the describing function, was physically motivated. The following heuristic derivation can be found in [15, pp. 49-52, 110-120]: Assume that n(») is an odd nonlinearity, i.e., n(-y) =-n(y), and that y = A sin u)t. Then, the output of n(A sin lot) can be represented by the Fourier series n(A sin ojt) = I A

show abstract

Limitations of the describing function method

Cited by 13 publications

References 1 publication

Oscillations of nonlinear feedback systems which contain tightly coupled subsystems in cascade

Oscillations of nonlinear feedback systems which contain tightly coupled subsystems in cascade

Oscillations of nonlinear feedback systems which contain tightly coupled subsystems in cascade

On the stability in oscillations in a class of nonlinear feedback systems containing numerator dynamics

Contact Info

Product

Resources

About