Stabilizability diagram for turning processes subjected to digital PD control

David Lehotzky, Janos Turi, T. Insperger

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Stabilizability of the turning process subjected to a digital proportional-derivative controller is analyzed. The governing equation involves a term with continuous-time point delay due to the regenerative effect and terms with piecewise-constant arguments due to the zero-order hold of the digital control. The resulting hybrid system can be represented as a delay-differential equation with time-periodic delay, for which the stability properties are analyzed using the semi-discretization method. The critical depth of cut is determined, which limits the stabilizability of the machining process for a given spindle speed in the sense that machining operation at larger than the critical depth of cut cannot be stabilized by the applied digital controller for a fixed sampling period. The resulted stabilizability diagram shows some similarities to the traditional stability lobe diagram of machining processes.

Original languageEnglish
Pages (from-to)46-54
Number of pages9
JournalInternational Journal of Dynamics and Control
Volume2
Issue number1
DOIs
Publication statusPublished - Mar 1 2014

Fingerprint

Digital Control
Stabilizability
Machining
Diagram
Piecewise Constant Argument
Controller
Semidiscretization
Controllers
Discretization Method
Term
Delay Differential Equations
Hybrid systems
Hybrid Systems
Continuous Time
Governing equation
Differential equations
Directly proportional
Sampling
Derivatives
Derivative

Keywords

  • Machine tool chatter
  • PD controller
  • Regenerative delay
  • Sampling effect
  • Semi-discretization
  • Stabilizability

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Control and Systems Engineering
  • Electrical and Electronic Engineering
  • Mechanical Engineering
  • Control and Optimization
  • Modelling and Simulation

Cite this

Stabilizability diagram for turning processes subjected to digital PD control. / Lehotzky, David; Turi, Janos; Insperger, T.

In: International Journal of Dynamics and Control, Vol. 2, No. 1, 01.03.2014, p. 46-54.

Research output: Contribution to journalArticle

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