Online Frequency Estimation Research Articles

Online frequency estimation of periodic disturbance based on FFT algorithm with application in repetitive control

In this paper, a new adaptive method is proposed for online frequency estimation of a periodic disturbance by the output measurement based on the fast Fourier transform algorithm. The performance of the proposed algorithm is evaluated in the face of time varying frequency, time varying amplitude, non-sinusoidal periodic disturbance, and different plants. Also, the convergence rate of the method is compared by other estimation methods. Then, the online estimation is used in the repetitive controller structure for eliminating periodic disturbances with unknown frequencies. A new analysis is performed on RC and the stability conditions are determined in a theorem. These are illustrated in simulation results. The effectiveness of this method is shown on the application of ϕ-shaped PZT active suspension and it is compared by existing results.

Online Frequency Estimation on a Building-like Structure Using a Nonlinear Flexible Dynamic Vibration Absorber

The online frequency estimation of forced harmonic vibrations on a building-like structure, using a nonlinear flexible vibration absorber in a cantilever beam configuration, is addressed in this article. Algebraic formulae to compute online the harmonic excitation frequency on the nonlinear vibrating mechanical system using solely available measurement signals of position, velocity, or acceleration are presented. Fast algebraic frequency estimation can, thus, be implemented to tune online a semi-active dynamic vibration absorber to obtain a high attenuation level of undesirable vibrations affecting the main mechanical system. A semi-active vibration absorber can be tuned for application where variations of the excitation frequency can be expected. Adaptive vibration absorption for forced harmonic vibration suppression for operational scenarios with variable excitation frequency can be then performed. Analytical, numerical, and experimental results to demonstrate the effectiveness and efficiency of the operating frequency estimation, as well as the acceptable attenuation level achieved by the tunable flexible vibration absorber, are presented. The algebraic parametric estimation approach can be extended to add capabilities of variable frequency vibration suppression for several configurations of dynamic vibration absorbers.

An enhanced adaptive notch filtering method for online multi-frequency estimation from contaminated signals of a mechanical control system

Real-time frequency information is extremely important in many fields of mechanical engineering, such as fault diagnosis, noise and vibration control, underwater acoustic detection, vehicle communication, etc. However, sometimes frequencies cannot be directly detected, making it important to quickly and accurately estimate the frequencies from contaminated signals of a mechanical system. An adaptive notch filter (ANF) is one of the most popular methods for online frequency estimation due to its simple structure and low computational complexity. However, ANF is a biased estimation if the signal contains uncorrelated noise. An enhanced adaptive notch filtering (EANF) method, which is able to reduce the frequency estimation bias and improve the estimation speed from contaminated signals, is proposed in this paper. Firstly, the limitations of the traditional ANF method are theoretically and numerically analyzed. Then, the principles of the proposed EANF method are formulated, including key parameter optimization and uncorrelated noise compensation in the update process. Afterwards, a multiple extension of the proposed EANF method is constructed using the adaptive simultaneous structure. The results of the numerical simulation show that the proposed method is superior to traditional ones. Finally, a two-stage vibration isolation system is established for experimental validation. The experimental results also demonstrate the effectiveness of the proposed method.

Frequency-Adaptive Virtual Flux Estimator-Based Predictive Power Control With Suppression of Dc Voltage Ripples Under Unbalanced Network

This article presents a closed-loop virtual-flux (VF) estimator for grid voltage sensorless control of pulsewidth modulation (PWM) rectifier under unbalanced network. Compared with the prior open-loop VF estimator, the proposed method shows better filtering capability and improved robustness against load variation. Considering the grid frequency may deviate from the nominal value in practical application, an adaptive method is further developed for online frequency estimation. Additionally, the finite control set-model predictive power control with power compensation is implemented based on the proposed VF estimator to attenuate dc voltage ripples under unbalanced network. Theoretical analysis show that the twice-grid-frequency ripple component in the dc voltage can be effectively suppressed even with inductance mismatches. Experimental tests on a two-level PWM rectifier confirm the effectiveness of the proposed method.

Relaxation for online frequency estimator of bias‐affected damped sinusoidal signals based on Dynamic Regressor Extension and Mixing

SummaryThis paper considers the problem of continuous‐time online frequency estimation for a biased damped sinusoidal signal. The previous result for a sinusoidal signal with time‐varying amplitude requires a persistency of excitation condition for regressor, which is not satisfied in the considered case. To relax this condition, we propose to use Dynamic Regressor Extension and Mixing method on the first step to replace nth‐order regression with n first‐order regression models. On the second step, two simple relaxation methods are proposed to establish necessary excitation for the first‐order gradient‐based estimator. The efficiency of the proposed approach is demonstrated through the set of numerical simulations for the exponentially damped sinusoidal signal.

A Comparative Performance Evaluation of Extended AANF with Different Parameter Estimation Techniques for Renewable Energy Integration

This paper presents real time performance evaluation of three phase extension of an amplitude adaptive notch filter (AANF) for online estimation of frequency, amplitude, and sequence components of the input grid voltage signal. The performance of an extended AANF is compared with conventional synchronous reference frame-phase lock loop (SRF-PLL), enhanced phase lock loop (EPLL), and existing adaptive notch filter (ANF). Comparative analysis has been carried out based on their ability in extracting frequency and amplitude of input grid voltage signal under balanced and unbalanced voltage sag/swell, frequency shift and distorted grid condition. Three phase AANF method provides high degree of accuracy than SRF-PLL, EPLL, and ANF in extracting appropriate signal information for unbalanced and harmonically distorted grid condition. The important feature of this method is its amplitude adaptability, which improves its speed of response and accuracy when grid signal is of variable amplitude. OPAL-RT’s (OP4500) real time controller with an in-built Xilinx Kintex-7 FPGA processor is used for real time implementation. Experimental results validate fast and accurate performance of an extended AANF in extracting frequency, amplitude, and sequence components of the utility grid voltage signal, which can be further used for performance improvement of grid connected renewable energy systems, custom power devices, and flexible ac transmission systems (FACTS) devices.

A globally convergent frequency estimator of a sinusoidal signal with a time-varying amplitude

The paper considers the problem of continuous-time online frequency estimation for a sinusoidal signal with a time-varying amplitude, where the latter is given by a known function of time multiplied by an unknown constant. To solve the problem a novel parameterization method is applied yielding linear regression with three unknown constant parameters. Next, two estimation algorithms are proposed, where the first is based on the conventional gradient approach, and a recently presented dynamic regressor extension and mixing procedure is used for the second. Global exponential convergence of the suggested frequency estimator is established, and the obtained performance is illustrated with simulations.

Adaptive Tracking of a Multi-Sinusoidal Signal with DREM-Based Parameters Estimation

In this paper tracking of an unknown multi-sinusoidal signal with fast online frequency estimation is addressed. The latter has been achieved by the so-called dynamic regressor extension and mixing (DREM) approach, which allows to increase performance of multiple frequency estimation. Designed predictive compensation algorithm is capable to operate under presence of computational or transmission delays. The resultant controller has been implemented to a robotic arm with a computer vision system. An extensive experimental study shows undoubted advantages of the DREM-based frequency estimator in comparison to the classical gradient approach. A detailed analysis of the transient response properties is provided in the paper.

A Complex Least Squares Enhanced Smart DFT Technique for Power System Frequency Estimation

A complex-valued least-squares (CLS) framework is proposed in order to enhance the accuracy of the smart discrete Fourier transform (SDFT) algorithms for power system frequency estimation in the presence of noise and harmonic pollution. It is first established that the underlying time-series relationship among the consecutive DFT fundamental components employed by the original SDFT algorithms does not hold when noises or unexpected higher order harmonics are present, resulting in suboptimal estimation performances. To eliminate these adverse effects on the frequency estimation, the degree of the relationship breakdown is next quantified via a model mismatch error vector. The CLS technique is then employed to minimize the mean-square model deviation when the SDFT voltage modelling is suboptimal. The proposed CLS-enhanced SDFT (CLS-SDFT) methods are shown to be more accurate than the original ones in heavily noisy and harmonic-distorted environments, typical scenarios in online frequency estimation. The benefits of the SDFT framework are verified by simulations for various power system conditions, as well as for real-world measurements.

Discrete derivative method for adaptive notch filter-based frequency estimators

This paper presents a new discrete derivative method for adaptive notch filter (ANF)-based frequency estimators. ANF-based frequency estimators are widely used for online frequency estimation because of their small computation requirements and simple structures. A discrete-time derivative is usually required for the estimators because they are implemented in the discrete-time domain. However, conventional discretization processes may cause problems in calculating the derivative of the adaptive filter state. For example, a derivative needs to have a phase of 90°, but finite difference methods produce phase responses that are less than 90° in high-frequency ranges. This phenomenon causes inaccurate frequency estimation results in high-frequency ranges. A bilinear transform method can prevent the phase problem, but it has oscillating transient responses, which deteriorate the convergence properties of the estimated frequency. A new discrete derivative method that modifies the bilinear transform is proposed. The proposed method does not produce the oscillating transient response in the steady state. Moreover, the phase responses of this method remain at 90° even in high-frequency ranges. Therefore, the frequency estimators that use the proposed derivative method can accurately estimate the frequencies of input signals in various frequency ranges.

Online frequency estimation with applications to engine and generator sets

Frequency and spectral analysis based on the discrete Fourier transform is a fundamental task in signal processing and machine diagnostics. This paper aims at presenting computationally efficient methods for real-time estimation of stationary and time-varying frequency components in signals. A brief survey of the sliding time window discrete Fourier transform and Goertzel filter is presented, and two filter banks consisting of: (i) sliding time window Goertzel filters (ii) infinite impulse response narrow bandpass filters are proposed for estimating instantaneous frequencies. The proposed methods show excellent results on both simulation studies and on a case study using angular speed data measurements of the crankshaft of a marine diesel engine-generator set.

Power System Frequency Estimation Method in the Presence of Harmonics

A frequency estimation method with good resistance to harmonics is proposed in this paper. In the proposed method, a new sequence is constructed using the summation of the samples in the original sampling sequence. The amplitude ratio of the new sequence and the original sequence is used to calculate the fundamental frequency deviation. The effects of negative fundamental component, harmonics, and interharmonics are studied. A preprocessing procedure is also proposed to eliminate the effects of the interharmonics with frequency near the fundamental frequency. Theoretical analysis and simulations validate that the proposed method has good immunity to harmonics. Due to its low required processing effort and high precision, this method is a good candidate for online frequency estimation in the presence of harmonics.

Adaptive Road Profile Estimation in Semiactive Car Suspensions

The enhancement of passengers’ comfort and their safety are part of the constant concerns for car manufacturers. Semiactive damping control systems have emerged to adapt the suspension features, where the road profile is one of the most important factors determining the automotive vehicle performance. Because direct measurements of the road profile represent expensive solutions and are susceptible to contamination (e.g. using laser and other visual sensors), this paper proposes a novel road profile estimator that offers the essential information (road roughness and its frequency) for the adjustment of the vehicle dynamics using conventional sensors, such as accelerometers or displacement/velocity sensors easy to mount, cheap, and useful to estimate all suspension variables. Based on the ${Q}$ -parametrization approach, an adaptive observer estimates the dynamic road signal; afterward, a Fourier analysis is used to compute the road roughness condition online and to perform an International Organization for Standardization (ISO) 8608 classification. Experimental results on the rear-left corner of a 1:5 scale vehicle, equipped with electro-rheological (ER) dampers, have been used to validate the proposed road profile estimation method. Different ISO road classes evaluate the performance of the proposed algorithm, whose results show that any road can be identified successfully at least 70% of the time with a false alarm rate lower than 5%; the general accuracy of the road classifier is 95%. A second test with variable vehicle velocity shows the importance of the online frequency estimation to adapt the road estimation algorithm to any driving velocity; in this test, the road is correctly estimated in 868 of 1042 m (an error of 16.7%). Finally, the adaptability of the parametric road estimator to the semiactiveness property of the ER damper is tested at different damping coefficients.

Online Hop Timing Detection and Frequency Estimation of Multiple FH Signals

This paper addresses the problem of online hop timing detection and frequency estimation of multiple frequency-hopping (FH) signals with antenna arrays. The problem is deemed as a dynamic one, as no information about the hop timing, pattern, or rate is known in advance, and the hop rate may change during the observation time. The technique of particle filtering is introduced to solve this dynamic problem, and real-time frequency and direction of arrival estimates of the FH signals can be obtained directly, while the hop timing is detected online according to the temporal autoregressive moving average process. The problem of network sorting is also addressed in this paper. Numerical examples are carried out to show the performance of the proposed method.

Multivariable Repetitive Sliding Mode Control with Frequency Estimator: Rejection of Sinusoidal Disturbances with Time Varying Frequency

In this paper a repetitive sliding mode control (RSMC) with frequency estimator for discrete multivariable systems to reject unknown sinusoidal disturbances is proposed. The RSMC can reject only the harmonic disturbances with known frequency. When, this frequency is unknown or varying in time, we use a new strategy based on the combination between the multivariable RSMC and an on-line frequency estimator. The simulation results are satisfactory and show a good performances in terms of tracking reference trajectories in spite of the presence of sinusoidal disturbances with time varying frequency.

Adaptive Online Frequency Estimation of Sinusoid with Unknown Frequency

In this short paper the problem of continuous time online estimation of frequency of a mixture of sinusoidal signal is considered. A simple estimator based on minimization of a Lyapunov function is suggested for the solution of this problem. For given a sinusoid signal consisting of many frequencies, the results show that estimator is globally convergent which can be applied for any initial condition and frequency values.

Shifting Window Average Method for Accurate Frequency Measurement in Power Systems

A shifting window average method (SWAM) is proposed to enhance the accuracy of the widely implemented discrete Fourier transform (DFT)-based algorithm in power system frequency measurements. First, the authors have comprehensively analyzed the error induced in the DFT-based algorithm. The SWAM is then introduced to improve frequency measurement accuracy by examining the analytic form of the error. Test results have validated that it achieves higher accuracy compared to the DFT-based algorithm. Due to its high accuracy and low required processing effort, the SWAM is a valuable candidate for online frequency estimation in real-life power systems, especially when harmonics, uncharacteristic harmonics, noises, and large frequency excursions exist.

Adaline-based approaches for time-varying frequency estimation in power systems

Two new neural approaches for on-line frequency estimation of a sinusoidal signal perturbed by harmonic distortions and random noise are presented in this paper. These approaches are based on an iterative formulation of the signal which is learned by Adaline neural networks. Adalines are very simple and efficient artificial neural networks, they can be easily implemented on a digital signal processor. The proposed approaches are therefore suitable for real-time implementations and their performance and robustness are evaluated by numerical simulations and experimentally under different severe operating conditions. The proposed neural estimators are favorably compared to the classical zero-crossing method, to an active notch filter method, and to a previous Adaline based-method. Furthermore, all these methods are also evaluated in terms of computational costs.

A fast on-line frequency estimator of lightly damped vibrations in flexible structures

A significant research effort has been conducted in the past to achieve a reliable on-line vibration mode estimator. Frequently, pure sinusoidal models of the underlying mechanical system have been used to accomplish the estimation task. In this paper, an algebraic approach is proposed for the fast and reliable, on-line identification of the natural frequency of a flexible-link manipulator. The proposed method uses the pure sinusoidal model in combination with the algebraic derivative method for parameter identification. The method leads, in the time domain, to an exact computation formulae for the unknown frequency parameter. This formula is synthesized in terms of time-varying linear unstable filters in combination with classical low-pass filters of the Butterworth type. The computations are performed in a quite small-time interval which is only a small fraction of the first full cycle of the measured sinusoidal signal. The proposed method is verified to be robust with respect to un-modeled small attenuations, present in the flexible structure, and to measurement noise. An experimental setup has been developed as a benchmark to test and compare the proposed method with other recently developed parameter estimation techniques.

Stability analysis of periodic orbit of an adaptive notch filter for frequency estimation of a periodic signal

Online frequency estimation of a sinusoidal signal is a classical problem and has many practical applications. Recently an adaptive notch filter (ANF) with global convergence property has been developed for frequency estimation of a pure sinusoidal signal. This paper addresses a modified ANF structure that can estimate the fundamental frequency of any periodic signal including pure sinusoidal signals. To prove the stability of the modified ANF, the paper introduces a new theorem that shows for any periodic signal, there exists a locally asymptotically stable periodic orbit of this ANF by which the frequency estimation becomes feasible. This alternative stability proof is simple and uses widely known mathematical tools, and therefore alleviates the problem complexity even when the input signal is a pure sinusoidal signal. A further contribution of this paper is obtaining a necessary and sufficient condition in terms of design parameters for local asymptotical stability of the modified ANF. This condition, obtained from the numerical study of Floquet multipliers of a linear time-varying periodic system, provides a strict stability region in the modified ANF design parameters space.