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RESEARCH PRODUCT

On stability of linear dynamic systems with hysteresis feedback

Michael Ruderman

subject

0209 industrial biotechnologyThermodynamic equilibriumApplied Mathematics020208 electrical & electronic engineeringMathematical analysis02 engineering and technologySystems and Control (eess.SY)Invariant (physics)Electrical Engineering and Systems Science - Systems and ControlVDP::Mathematics and natural scienses: 400Nonlinear systemHysteresis020901 industrial engineering & automationModeling and Simulation0202 electrical engineering electronic engineering information engineeringDissipative systemFOS: Electrical engineering electronic engineering information engineeringCircle criterionParallelogramVDP::Matematikk og naturvitenskap: 400Harmonic oscillatorMathematics

description

The stability of linear dynamic systems with hysteresis in feedback is considered. While the absolute stability for memoryless nonlinearities (known as Lure's problem) can be proved by the well-known circle criterion, the multivalued rate-independent hysteresis poses significant challenges for feedback systems, especially for proof of convergence to an equilibrium state correspondingly set. The dissipative behavior of clockwise input-output hysteresis is considered with two boundary cases of energy losses at reversal cycles. For upper boundary cases of maximal (parallelogram shape) hysteresis loop, an equivalent transformation of the closed-loop system is provided. This allows for the application of the circle criterion of absolute stability. Invariant sets as a consequence of hysteresis are discussed. Several numerical examples are demonstrated, including a feedback-controlled double-mass harmonic oscillator with hysteresis and one stable and one unstable poles configuration.

yearjournalcountryeditionlanguage
2020-02-09
http://arxiv.org/abs/2002.03423