Stabilization in a State-Dependent Model of Turning Processes

@article{Hu2012StabilizationIA,
  title={Stabilization in a State-Dependent Model of Turning Processes},
  author={Qingwen Hu and Wieslaw Krawcewicz and Janos Turi},
  journal={SIAM J. Appl. Math.},
  year={2012},
  volume={72},
  pages={1-24}
}
We consider a two-degree-of-freedom model for turning processes which involves a system of differential equations with state-dependent delay. Depending on process parameters (e.g., spindle speed, depth of cut) the cutting tool can exhibit unwanted vibrations, resulting in a nonsmooth surface of the workpiece. In this paper we propose a feedback law to stabilize the turning process for a large range of system parameters. The feedback law introduces a generic nonhyperbolic stationary point into… 

Figures and Tables from this paper

Global Stability Lobes of Turning Processes with State-Dependent Delay

The spindle speed control strategy investigated in [SIAM J. Appl. Math., 72 (2012), pp. 1--24] can provide essential improvement on the stability of turning processes with state-dependent delay, and furthermore the existence of a proper subset of the stability region which is independent of system damping is shown.

Stability of Systems with State Delay Subjected to Digital Control

Stability of linear delayed systems subjected to digital control is analyzed. These systems can typically be written in the form $$ \dot{{x}}(t)={Ax}(t)+{Bx}(t-\tau)+{Cx}(t_{j-1}) \; , \quad t \in

Stabilization of turning processes using spindle feedback with state-dependent delay

We develop a stabilization strategy of turning processes by means of delayed spindle control. We show that turning processes which contain intrinsic state-dependent delays can be stabilized by a

Positive solutions of iterative functional differential equations and application to mixed-type functional differential equations

<p style='text-indent:20px;'>In this paper we consider the existence, uniqueness, boundedness and continuous dependence on initial data of positive solutions for the general iterative functional

References

SHOWING 1-10 OF 25 REFERENCES

On the problem of linearization for state-dependent delay differential equations

The local stability of the equilibrium for a general class of statedependent delay equations of the form ẋ(t) = f ( xt, ∫ 0 −r0 dη(s)g(xt(−τ(xt) + s)) ) has been studied under natural and minimal

State dependent regenerative effect in milling processes

Summary. The mechanical model of the milling process is extended using the precise computation of the chip thickness and the time delay, which leads to a state-dependent delay differential equation.

On the zeros of a third degree exponential polynomial with applications to a delayed model for the control of testosterone secretion.

  • S. RuanJ. Wei
  • Mathematics
    IMA journal of mathematics applied in medicine and biology
  • 2001
It is shown that under certain assumptions on the coefficients the steady state of the delay model is asymptotically stable for all delay values.

Differential-Difference Equations

Publisher Summary A systematic development of the theory of differential–difference equations was not begun until E. Schimdt published an important paper about fifty years ago. The subsequent gradual

On the zeros of transcendental functions with applications to stability of delay differential equations with two delays

In this paper, we first establish a basic theorem on the zeros of general transcendental functions. Based on the basic theorem, we develop a decomposition technique to investigate the stability of

Existence of Periodic Solutions for Delay Differential Equations with State Dependent Delay

Abstract In this paper we study the existence of periodic solutions of a delay differential equation with delay depending indirectly on the state. A fixed point problem related to a Poincare operator

Normal Forms for Retarded Functional Differential Equations with Parameters and Applications to Hopf Bifurcation

Abstract The paper addresses, for retarded functional differential equations (FDEs) with parameters, the computation of normal forms associated with the flow on a finite-dimensional invariant

Introduction to Functional Differential Equations

There are different types of functional differential equations (FDEs) arising from important applications: delay differential equations (DDEs) (also referred to as retarded FDEs [RFDEs]), neutral