Identification of multivalued and memory nonlinearities in dynamic processes

Abstract

This paper presents a new approach to the identifica tion of multivalued and memory types of functions (such as hysteresis) in a class of nonlinear dynamic processes which can be represented by a set of ordi nary differential equations. This approach leads to the direct identification of an unknown nonlinear coefficient or unknown nonlinear term. Four examples illustrate applications of the method: a hysteresis loop, a relay with hysteresis, a second-order system with hysteresis and an unknown nonlinear "constant," and a relay with hysteresis and an unknown dead zone. This paper uses standard CSMP function notation. The four systems were simulated and identified with adequate accuracy for many engineering purposes. The method is applicable to a broad class of mechan ical processes and dynamic mechanisms, including many common vibration phenomena involving nonlinear springs and nonlinear energy dampers. A CSMP digital computer program was used to simulate the dynamics of the physical systems and to implement the identifica tion technique.