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In the paper, the problem of compensation of external disturbance in multichannel systems with unmeasurable state vector and delay in the control channel is considered. It is assumed that the disturbance has a harmonic form. To solve the problem of estimating the state vector of a system, a full-order observer with Unknown Input Observer is constructed. A new observer of external disturbance is formed on the basis of the state vector estimates produced by this observer. As a result, a system is formed that uses estimates with an extended state vector. For this system, a regulator is constructed that provides compensation of the disturbance. The proposed algorithm guarantees boundedness of all signals in the closed-loop system and asymptotic stability of the output. It does not require identification of parameters of external disturbance. To demonstrate the performance and efficiency of the proposed approach, computer simulation using MATLAB Simulink software environment is performed. The developed algorithm can be effectively applied in systems with external disturbance in the form of sinusoidal signals, including systems exposed to wind, ship systems, motion control systems of robotic complexes of various types, and others.

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]

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 pφ=1, pω,unc=0.9983 and pω,cav=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.

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]

A novel anti-disturbance strategy for a class of uncertain systems is investigated. Besides the unknown frequency sinusoidal, the controlled plant is subjected to bounded noise and unknown nonlinear term simultaneously. Through the construction of auxiliary observer, the sinusoidal is represented in a parametric uncertainty form. Only one unknown scalar needs estimating to construct compensation signal, meanwhile the unwanted nonlinear operation between frequency and equivalent disturbance can be removed. By integrating a feedback control law, all the unexpected dynamics can be rejected and attenuated respectively, where the conditions on the stability and optimal performance are also provided. Finally, a computer simulation example is presented to illustrate the effectiveness and the applicability of the suggested method. [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 time-varying frequency disturbance rejection problem is addressed for a class of nonlinear uncertain system. A novel refined disturbance observer (RDO) is developed composed of auxiliary observer and calibration observer. At first, the disturbance is redescribed using auxiliary observer after coordinate transformation, which contains a parametric form about frequency and a decay term. The derivative of frequency and system uncertain are absorbed in the decay term, furthermore, the correlation between disturbance frequency and disturbance can be derived. Then the key parameter, i.e. frequency factor is estimated by calibration observer characteristic with two-degree-freedom, the decay term associated with derivative of frequency can be attenuated in feedback control loop. Thus, the composite controller including a refined disturbance observer (RDO) and a robust feedback controller is designed, which inherits the elegant feature of disturbance observer based control (DOBC). The H ∞ index performance can be guaranteed to attenuate the estimation error driven by disturbance time-varying frequency together with system uncertainty. • Firstly, an special auxiliary observer is constructed to excite the time-varying disturbance frequency property. As a result, the unwanted nonlinear operation between time-varying frequency and equivalent disturbance can be removed, which simplify the design and stability analysis. • A calibration observer is proposed to estimate the time-varying frequency parameter and reconstruct the disturbance. Meanwhile, our estimation algorithm involves only one parameter with respect to frequency, which reduce the computation complex. • The H ∞ index performance can be guaranteed to attenuate the estimation error driven by derivative of time-varying frequency, which leads to smaller design conservativeness. [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]

In this paper, performance analysis of generalized extended state observer (ESO) in handling fast-varying sinusoidal disturbances is presented. It is shown that the higher order ESO offers improvement in the tracking of fast-varying sinusoidal disturbances, if the ESO bandwidth is chosen significantly larger than the frequency of the disturbance and ensuring that it is sufficiently smaller than unmodeled high frequency dynamics. The frequency and time-domain analysis results are presented, and the findings are verified through numerical simulations and experimentation on Quanser's motion control module. [ABSTRACT FROM AUTHOR]

Motivated by practical applications such as active vibration control and noise attenuation, this paper presents an adaptive Youla ( Q ) parameterized regulation approach to reject unknown sinusoidal exogenous inputs representing disturbance or reference signals. A weighted Ritz-type Q parameter is adopted to implement the adaptation algorithm and to shape the sensitivity functions of the resulting adaptive system. The proposed regulation approach is applied to a benchmark problem involving unknown vibration attenuation in an active suspension system. Both simulation and real time experimental results are discussed and analyzed to illustrate the effectiveness of the proposed adaptive regulation approach. [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]

A lack of reliable data treatment method has been for several decades the bottleneck of viscosity measurement by disturbance amplitude damping method of shock waves. In this work the finite difference method is firstly applied to obtain the numerical solutions for disturbance amplitude damping behavior of sinusoidal shock front in inviscid and viscous flow. When water shocked to 15 GPa is taken as an example, the main results are as follows: (1) For inviscid and lower viscous flows the numerical method gives results in good agreement with the analytic solutions under the condition of small disturbance ( a / λ=0.02); (2) For the flow of viscosity beyond 200 Pa s ( η = κ) the analytic solution is found to overestimate obviously the effects of viscosity. It is attributed to the unreal pre-conditions of analytic solution by Miller and Ahrens; (3) The present numerical method provides an effective tool with more confidence to overcome the bottleneck of data treatment when the effects of higher viscosity in experiments of Sakharov and flyer impact are expected to be analyzed, because it can in principle simulate the development of shock waves in flows with larger disturbance amplitude, higher viscosity, and complicated initial flow. [ABSTRACT FROM AUTHOR]

The sensitivity of two-dimensional isothermal film casting processes to ongoing sinusoidal disturbances has been investigated by using the frequency response method with transient simulation techniques. Amplitude ratios of state variables such as cross-sectional area, film width and film thickness at the take-up position with respect to a sinusoidal disturbance show resonant peaks along the frequency domain. Effects of operating conditions, such as drawdown ratio and aspect ratio, on the process sensitivity have been examined. Increasing drawdown ratio and decreasing aspect ratio make the system more sensitive to disturbances. Also, the dichotomous behavior in the sensitivity analysis using viscoelastic Phan-Thien and Tanner fluids has been elucidated. This frequency response method can be a useful tool to optimally design process systems for better processability and product quality. [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]

This paper addresses the problem of torque and velocity ripple elimination in AC permanent magnet (PM) motor control systems. The torque ripples caused by DC offsets that are present in the current sensors of the motor driver and the digital-to-analog converters of the motion controller are studied and formulated mathematically. These torque ripples eventually generate velocity ripples at the speed output and degrade the system performance. In this paper the torque ripples are modeled as a sinusoidal function with a frequency depending on the motor speed. The internal model principle (IMP) is then used to design a controller to eliminate the torque and velocity ripples without estimating the amplitude and the phase values of the sinusoidal disturbance. A gain scheduled (GS) robust two degree of freedom (2DOF) speed regulator based on the IMP and the pole-zero placement is developed to eliminate the torque and velocity ripples and achieve a desirable tracking response. Simulation and experimental results reveal that the proposed GS robust 2DOF speed regulator can effectively eliminate the torque ripples generated by DC current offsets, and produce a velocity ripple-free output response. [ABSTRACT FROM PUBLISHER]

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]