Search

Frequency-dependent adaptive noise cancellation-based tracking controller (ANC-TC) is a known technique for the stabilization of several nonlinear dynamical systems. In recent years, this control strategy has been introduced and applied for the stabilization of a flexible rotor supported on full-lubricated journal bearings. This paper proposes a theoretical investigation, based on robust immersion and invariance (I&I) theory, of a novel ANC-frequency estimation (FE) technique designed to stabilize a flexible rotor shaft affected by self-generated sinusoidal disturbances, generalized to the case of unknown frequency. A structural proof, under assumptions on closed-loop output signals, shows that the sinusoidal disturbance rejection is exponential. Numerical simulations are presented to validate the mathematical results in silico. The iterative Inexact Newton method is applied to the disturbance frequency and phase estimation error point series. The data fitting confirms that the phase estimation succession has an exponential convergence behavior and that the asymptotical frequency estimation is a warm-up phase of the overall close-loop disturbance estimation process. In two different operating conditions, the orders of convergence obtained by phase and frequency estimate timeseries are p φ = 1 ,   p ω , u n c = 0.9983 and p ω , c a v = 1.005 . Rejection of the rotor dynamic disturbance occurs approximately 76% before in the cavitated than in the uncavitated condition, 2 (s) and 8.5 (s), respectively. [ABSTRACT FROM AUTHOR]

A disturbance rejection approach is presented for a class of uncertain systems subject to sinusoidal disturbance with unknown frequency. The proposed disturbance estimation method includes two types of observers that are connected in cascade form. The disturbance property is excited through an auxiliary filter, and then a frequency factor observer is constructed to generate the information required by full-order state observer. Thus, with the disturbance and system state estimation values, the composite control structure including a cascade disturbance observer (CDO) and a robust feedback controller is designed. As a result, the uncertain system with unknown-frequency sinusoidal component can be controlled within the disturbance observer-based control (DOBC) framework, where the asymptotic stability performance can be guaranteed. [ABSTRACT FROM AUTHOR]

Tracking sinusoidal references with high precision and rejection of sinusoidal disturbances is a challenging task in the motion control practice. In order to deal with this control problem, a new resonant extended state observer is proposed and introduced in the active disturbance rejection control concept. The frequency analysis shows that an appropriate selection of resonant frequency provides complete rejection of sinusoidal disturbance and ideal reference tracking in the steady state. Further, it is shown that the proposed structure achieves better performances than generalised extended state observer based system in the wide frequency range. Moreover, in order to improve the system performances in transient period, the optimal parameter tuning method is developed. The results demonstrate that the optimally tuned system achieves better performances than the conventionally tuned one by about 25%, with the same robustness and noise sensitivity. The experimental validation of the new controller is carried out on the laboratory model of the didactic three-axis radar platform in fast sinusoidal reference tracking mode. [ABSTRACT FROM AUTHOR]

The problem of optimal control of systems disturbed by sinusoidal signals for infinite control time is considered. To evaluate the control laws, a modified mean-square performance index with an infinite control time was proposed. It is based on the proposed method for the decomposition of control signals on the interval from zero to infinity into the sum of sinusoidal components with selected frequencies and an additional auxiliary signal. The performance index was formulated in such a way that each sinusoidal component corresponds to a separate weight matrix. It was shown that there are infinitely many solutions for these optimization problems. Optimal control was selected in such a way that it should be independent of the state vector, and should depend only on the disturbance signal vector. The controller was synthesized for vibration reduction system. The paper presents results of numerical and laboratory studies of the designed vehicle active suspension system. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to simulate numerical solutions of nonlinear Burgers' equation with two well-known problems in order to verify the accuracy of the cubic B-spline differential quadrature methods. Design/methodology/approach – Cubic B-spline differential quadrature methods have been used to discretize the Burgers' equation in space and the resultant ordinary equation system is integrated via Runge-Kutta method of order four in time. Numerical results are compared with each other and some former results by calculating discrete root mean square and maximum error norms in each case. A matrix stability analysis is also performed by determining eigenvalues of the coefficient matrices numerically. Findings – Numerical results show that differential quadrature methods based on cubic B-splines generate acceptable solutions of nonlinear Burgers' equation. Constructing hybrid algorithms containing various basis to determine the weighting coefficients for higher order derivative approximations is also possible. Originality/value – Nonlinear Burgers' equation is solved by cubic B-spline differential quadrature methods. [ABSTRACT FROM AUTHOR]

In this paper, we design a robust track- following controller that satisfies transient response specifications and diminishes the influence of sinusoidal disturbance. To this end, a robust control problem with the multiple constraints is considered We show that a sufficient condition satisfying the multiple constraints can be expressed by linear matrix inequalities. Finally, the robust track- following controller can be designed by solving an LMI optimization problem. The effectiveness of the proposed controller design method is verified though experiments. [ABSTRACT FROM AUTHOR]

In this work, a new robust control algorithm is introduced for uncertain systems with harmonic disturbances of unknown frequencies. The proposed solution works under the active disturbance rejection control (ADRC) framework and utilizes a specialized observer for sinusoidal uncertainties, aided with an on-line harmonic disturbance frequency estimator. The entire governing structure is derived in a convenient error-based domain, easily deployable in various industrial control software. The idea behind the introduced approach is general, but is conveyed here using solely a three degrees-of-freedom torsional system, which is considered a benchmark for vibration phenomenon in many mechanical systems. The efficacy of the proposed control scheme is validated with a set of experiments on a laboratory testbed and a theoretical analysis based on theory of singular perturbation. [ABSTRACT FROM AUTHOR]