We develop an adaptive output-feedback controller for a wave PDE in one dimension with actuation on one boundary and with an unknown anti-damping term on the opposite boundary. This model is representative of a torsional stick–slip instability in drillstrings in deep oil drilling, as well as of various acoustic instabilities. The key feature of the proposed controller is that it requires only t...

A librating cylinder consists of a rotating cylinder whose rate of rotation is modulated. When the mean rotation rate is large compared with the viscous damping rate, the flow may support inertial waves, depending on the frequency of the modulation. The modulation also produces time-dependent boundary layers on the cylinder endwalls and sidewall, and the sidewall boundary layer flow in particul...

Abstract. The telegraph equation is employed to model wave fields taking into account energy dissipation and media stiffness. The timeharmonic scattered waves generated by a line source incident upon cylindrical obstacles of arbitrary cross-section are studied. Solutions are found to depend strongly on the relative values of the frequency, damping, and stiffness coefficients. These coefficients...

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The paper presents robust controller design for systems with uncertain transport delays. Robust PI controllers are designed using approach, which combines the method based on plotting the stability boundary locus in the (kp, ki)-plane with the pole-placement method. The approach enables to assure robust stability of the closed loop as well as the quality of the control response prescribed by th...

Based on dynamic fourth order partial differential equations, we present an iterative finite difference algorithm. With C++ language and OpenGL graphics library, we implement the finite difference algorithm into a user interface and develop shape control parameters, density, damping coefficient, boundary tangents and external forces into user handles for dynamic manipulation of surface deformat...

We study the initial-boundary problem of dissipative symmetric regularized long wave equations with damping term by finite difference method. A linear three-level implicit finite difference scheme is designed. Existence and uniqueness of numerical solutions are derived. It is proved that the finite difference scheme is of second-order convergence and unconditionally stable by the discrete energ...

For complex valued sequences {ωn}∞n=1 of the form ωn = an + ibn with an ∈ R and bn ≥ 0, we prove inequalities of the form ∫ T 0 | ∑∞ n=p xne itωn |2dt 3 ∞n=p |xn|/(1+bn), for all sequences {xn} with ∑∞ n=1 |xn|/(1 + bn) < ∞. We apply these to prove exact null-controllability for a class of hinged beam equations with mild internal damping with either boundary control or internal control.

This paper deals with feedback stabilization of a flexible beam clamped at a rigid body and free at the other end. We assume that there is no damping and the rigid body rotates with a nonconstant angular velocity. To stabilize this system, we propose a feedback law which consists of a control torque applied on the rigid body and either a dynamic boundary control moment or a dynamic boundary con...