Existence of periodic modes in automatic control system with a three-position relay

ABSTRACT

We consider an automatic control system with a three-position relay of hysteresis type and a continuous periodic external disturbance. The purpose of the paper is to define the values of the system parameters at which periodic modes exist. A theorem on the existence of periodic solutions is proved. We provide an application with a numerical example to support the theorem.

KEYWORDS:

• Automatic control system
• three-position relay
• hysteresis
• periodic external disturbance
• periodic solutions

AMS SUBJECT CLASSIFICATIONS:

• 34A34
• 34A36
• 34H05
• 93C73
• 34C25

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Alexander M. Kamachkin  http://orcid.org/0000-0001-5934-4033

Dmitriy K. Potapov  http://orcid.org/0000-0002-4781-252X

Victoria V. Yevstafyeva  http://orcid.org/0000-0001-7449-7089