Rapid and Approximate Evaluation of Jump Frequencies in Feedback Systems Containing a Piecewise-Linear Nonlinearity

Abstract

Numerous methods exist for the evalution of jump resonance conditions in nonlinear feedback systems. However almost all of the known methods are graphical in nature and are extremely laborious. This paper presents certain geometric properties of Hatanka's graphical method and shows how jump resonance conditions can be approximately evaluated by a very simple graphical method in which circular arcs and straight lines need to be drawn apart from utilizing the Nyquist response of the linear part of the system. The proposed method can be useful in a quick assessment of jump conditions in the design of nonlinear systems. Two examples are included for illustrating the procedure.

Indexing Terms:

• Nonlinear Systems
• Describing Function
• Jump Resonance

Additional information

Notes on contributors

S. S. Lamba

LAMBA, S S (Dr): Received B. Tech (Hons.) in Electrical Engineering and M. Tech in Control Systems from IIT Kharagpur in 1958 and 1959 respectively. In 1959 he was awarded Senior Fellowship of the Govt. of India for Technical Teacher Training at the University of Roorkee. He joined the IIT Delhi as a faculty member in 1962. In 1965, he was awarded the Commonwealth Research Fellowship for research at the University of New Brunswick, Canada from where he received his PhD in 1968. In 1971, he was awarded the National Research Council of Canada Visiting summer fellowship forrese arch for three consecutive years at the University of New Brunswick. In 1974, he spent his sabbatical leave as senior visiting fellow in the Department of Electrical and Control Engineering, Liverpool Polytechnic, Liverpool.

Since 1975, he is working as a Professor in EE Department of IIT Delhi. His research interests are in Nonlinear Systems, Multivariable System Theory, Hybrid Computation and Computer Process Control. He has participated in many international conferences and has published over 35 technical papers. He is a senior member of IEEE and a member of the Computer Society of India.