LIMIT CYCLES IN A CERTAIN CLASS OF SAMPLIEDDATA CONTROL SYSTEMS,

Abstract

This paper discusses periodic, unforced solutions (called limit cycle solutions) to the state and output equations of a certain class of nonlinear sampled-data control systems. The class of systems consists of a linear plant, a single nonlinearity, a sample and hold element and a single feedback loop. Two different methods are given for determining the possible existence and the solutions for the limit cycles. An approximate method for determining possible existence and output solutions for limit cycles is also given. Finally, a certain kind of stability of limit cycle solutions is defined, and sufficient conditions for the stability and instability of limit cycles are developed. (A limit cycle is defined as a periodic trajectory in state space; i.e., it is an unforced, periodic, steady state solution to the state space equations of the system.)

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1964
Accession Number
AD0610099

Entities

People

  • Ronald A. Werner

Organizations

  • University of Illinois Urbana–Champaign

Tags

DTIC Thesaurus Topics

  • Closed Loop Systems
  • Control Systems
  • Differential Equations
  • Equations
  • Feedback
  • Instability
  • Steady State
  • Trajectories

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.

Technology Areas

  • Space
  • Space - Spacecraft Maneuvers