Angular Speed Estimation Research Articles

Comprehensive wheel cylinder pressure estimation based on systematic hydraulic control unit model

Wheel cylinder pressure (WCP) is a crucial state for vehicles, directly influencing safety, comfort, and fuel economy. Serving as the foundation for sensor-less control and sensor redundancy, WCP estimation is a promising work for brake-by-wire systems (BBW). Nevertheless, WCP estimation is a challenging problem due to the nonlinear characteristics and intricate coupling within the hydraulic control unit (HCU). To enhance the performance of BBW, this paper proposes a comprehensive WCP estimation scheme based on the systematic HCU model. Component models including direct current (DC) motor pump and normally open valve (NOV) are established first. Considering the pulsation of the plunger pump, a modified nonlinear observer (MNO) is used to observe the angular speed of the DC motor. Inspired by the critical state, the linear pressure-drop relationship of NOV is analyzed and the NOV is simplified as a relief valve model expressed by algebraic equations. Dividing the HCU into the pump front part, pump rear part, and cylinder part, the systematic HCU model is then established, based on which, the comprehensive cause-based WCP estimation scheme is proposed. Next, simulations utilizing Amesim validate the angular speed estimator, while bench experiments prove the NOV model. Finally, vehicle tests under active and passive pressure regulating conditions are conducted. The results indicate the proposed scheme exhibits satisfactory performance while preserving computational efficiency.

Accurate and Efficient Instantaneous Angular Speed Estimation Method for Rolling Bearing Under Time-Varying Speed

Accurate and Efficient Instantaneous Angular Speed Estimation Method for Rolling Bearing Under Time-Varying Speed

Instantaneous angular speed estimation in gas foil bearings from vibration signal

Instantaneous angular speed estimation in gas foil bearings from vibration signal

An enhanced instantaneous angular speed estimation method by multi-harmonic time–frequency realignment for wind turbine gearbox fault diagnosis

Gearboxes are one of the most critical transmission devices in wind turbines (WTs). Order tracking (OT) of variable-speed WT gear is a powerful means to carry out fault diagnosis. Since it is difficult to install a tachometer or encoder for gearboxes with limited structural space, it is impossible to obtain the instantaneous angular speed (IAS) of the gearbox. In recent years, many tacholess techniques have been presented to estimate instantaneous phase from vibration signals for OT. However, their performance needs to be further improved to get a more exact diagnosis result. To solve this issue, this paper presents an enhanced IAS estimation approach for WT tacholess order tracking (TLOT), which is available for accurate IAS estimation of the rotating shaft, so that TLOT can be more effectively conducted under conditions of large speed variation and background noise. An improved cost function algorithm is designed to extract the IAS from the vibration signal. A Vold–Kalman filter and Hilbert transform are combined to calculate the instantaneous phase. Afterwards, the raw non-stationary vibration signal is resampled at an equal angle increment, and the envelope order spectrum is calculated from the resampled signal for fault diagnosis of the WT gearbox. The main innovating idea of this approach is to improve the traditional cost function ridge-extraction method by introducing gradient information based on probability and multi-harmonic time–frequency realignment, which makes the IAS estimation process more accurate and overcomes the limitations of traditional IAS estimation techniques. The effectiveness of the presented approach is demonstrated by using a vibration signal measured from real-world WT gearboxes, and the validation results demonstrate that the presented approach surpasses some state-of-the-art methods in IAS estimation accuracy and efficiency.

Erratum to “On Angular Speed Estimation of Rigid Bodies”

We fix errata due to misprints occurred in the printed version of F. Ferrante and G. Besançon “On Angular Speed Estimation of Rigid Bodies” published in IEEE Control Systems Letters, vol. 6, 2022, pages 1394–1399.

On Angular Speed Estimation of Rigid Bodies

The problem of estimating the angular speed of a solid body from attitude measurements is addressed. To solve this problem, we propose an observer whose dynamics are not constrained to evolve on any specific manifold. This drastically simplifies the analysis of the proposed observer. Using Lyapunov analysis, sufficient conditions for global asymptotic stability of a set wherein the estimation error is equal to zero are established. In addition, the proposed methodology is adapted to deal with angular speed estimation for systems evolving on the unit circle. The approach is illustrated through several numerical simulations.

Research on a PMSM control strategy for electric vehicles

This paper proposes a novel state estimation based permanent magnet synchronous motor (PMSM) control method for electric vehicle (EV) driving. Firstly, a state feedback decoupling control with disturbance feed-forward (SFDCDF) is described. As motor angular speed and rotary angle are key information for the proposed control algorithm and park’s transformation, a novel observer based angular speed estimator (OBASE) is proposed for angular speed estimation. Moreover, an extended Kalman filter (EKF) based rotary angle estimator (EBRAE) is used for rotary angle estimation with information of the estimated angular speed. The convergence of angular speed estimation is proven through Lyapunov stability theory. Simulation results also indicate that the proposed algorithms can control PMSM torque, current, and angular speed to accurately follow reference values without severe fluctuation. In addition, in order to provide SFDCDF with load torque information, the OBASE is slightly modified to work as a vehicle load estimator (VLE) so PMSM responds more rapidly and speed fluctuates more slightly when the load suddenly changes. Then a series of hardware in the loop (HIL) simulations are carried out. Results indicate that the proposed control strategy can precisely estimate PMSM’s angular speed and rotor angle. Also, it can improve the driving performance of PMSM used on EVs.

Multi-harmonic phase demodulation method for instantaneous angular speed estimation using harmonic weighting

Phase demodulation is arguably the most used technique for the estimation of the instantaneous angular speed from vibration signals measured on rotating machinery. Although phase demodulation offers a straightforward approach to determine accurately the rotation speed of a particular shaft in a rotating machine, it does have strict limitations that can hinder the estimation accuracy and its overall reliability. In general, phase demodulation relies on the presence of a single harmonic with a high signal-to-noise ratio for the full duration of the measured vibration signal. Such a precondition hinders its applicability for a generic speed estimation approach for rotating machinery. There are copious real-world scenarios where this requirement is not met, especially given the increasing complexity and dynamic operating range of rotating machines nowadays. In such complex rotating systems, the deterministic signals are not necessarily all harmonically related to a fundamental harmonic. The presence of crossing harmonic orders from non-synchronous rotating components or of lightly damped structural resonances can significantly skew the instantaneous phase demodulation. This paper proposes a novel approach towards phase demodulation by both incorporating multiple harmonics in the demodulation process and also giving the individual harmonic phases time-dependent weighting. This combination of incorporating multiple harmonics and weighting them allows for fully exploiting the information contained within the vibration signal while also promising to be more robust to changing operating regimes. The proposed multi-harmonic demodulation method is investigated thoroughly by assessing its performance on simulated data, on two benchmark experimental data sets, and on a large wind turbine vibration data set consisting of thousands of vibration measurements.

High frequency demodulation technique for instantaneous angular speed estimation

This paper adapts the super-heterodyne method from telecommunication field to speed estimation from an optical encoder signal. After a presentation of our gear box test bench and the associated electronic devices, the paper explains the classical methods for Instantaneous Angular Speed (IAS) estimation from an optical encoder. Firstly, elapsed time method that measures the interval between consecutive (rising) edges of an optical encoder is investigated: aliasing problem and quantification effect are explained. Secondly, frequency demodulation technique based on temporally sampled optical encoder signal is investigated. An analysis of this signal shows its imperfections (crosstalk, presence of a second order harmonic, …). The necessity of a high-sampling frequency, the aliasing problem and the noise impact are also illustrated. Next, this method is compared with elapsed time. In the second section, a new method is proposed: high frequency demodulation. This method uses an analog frequency shifting before sampling the signal. Therefore, the required sampling frequency is reduced and linked with the speed fluctuation frequency. Spectrum of optical encoder signal is analysed and used to explain how to set up the frequency shift and limitations. Finally, a comparison is made with elapsed time.

An Improved Viterbi Algorithm for Adaptive Instantaneous Angular Speed Estimation and Its Application Into the Machine Fault Diagnosis

It is a very challenging task to diagnose the fault of rotating machinery under variable speed condition. The traditional tacholess order tracking (TLOT) method still has the problems of high computation complexity and low adaptability. Aiming at these problems, a new adaptive instantaneous angular speed (IAS) estimation method based on the improved Viterbi algorithm (VA) and the energy centrobaric correction method is developed. Since the traditional VA cannot process the long time series and find the fundamental order automatically, an improved penalty function for ridge search is proposed. Meanwhile, the search band of IAS is adaptively optimized to accelerate the speed of ridge search. Furthermore, an energy centrobaric correction approach is used for improving the accuracy of instantaneous frequency estimation and the antinoise performance. With the obtained IAS, the nonstationary time-domain vibration signal is resampled as the stationary angle-domain vibration signal by the Vold–Kalman filtering and the Hilbert transform. Finally, the envelope order spectrum is used to diagnose the mechanical faults of a civil aircraft engine. With the datasets of aircraft engine, rolling bearing, and wind turbine, the experimental results show that the improved VA can adaptively estimate IAS faster and achieve higher accuracy of fault detection than the typical IAS estimation methods. Meanwhile, its antinoise ability is verified.

An accurate instantaneous angular speed estimation method based on a dual detector setup

Instantaneous angular speed (IAS), or ‘true IAS’, is an inherent signature directly related to the mechanical dynamics of rotor systems and has been employed extensively in different rotating machines. Due to various uncertainties, such as manufacturing error or the inaccurate installation of encoders, the acquired IAS signals often contains significant contents of ‘false IAS’ which can mask the small variations of IAS, lead to low accuracy and consequently affect the understanding of the dynamic behaviour of a rotor system. This study proposes a dual detector method to minimize the influence of encoder errors and hence obtain more accurate IAS estimation. Through theoretical study, it is proved that the false IAS induced by encoder errors from the two detectors have the same amplitudes but with a phase difference, whereas the true IAS components from the two detectors are identical. On this basis, an algorithm is developed firstly to acquire the encoder errors through a phase alignment operation and then estimate the true IAS after removing the estimated encoder errors. The proposed method is evaluated by both numerical simulations and experimental studies. The results show that the proposed method can more significantly suppress the encoder errors associated with encoder eccentricities in comparison with conventional reference methods, thereby yielding an accurate true IAS from the measurement. The proposed method can be particularly effective when the encoder has very low accuracy, allowing a more cost-effective IAS monitoring system to be achieved.

Missing value recovery for encoder signals using improved low-rank approximation

Rotary encoders have been increasingly equipped in high precision machinery, and their data missing may pose great challenges for both numeric control and health monitoring. In view of this limitation, a new methodology, termed improved low-rank approximation (ILRA), is proposed for encoder signal recovery. In this approach, phase space representation (PSR) is first introduced to transform the one-dimensional encoder signal into a matrix for low-rank exploration. Bidirectional centralization with cumulative energy ratio is then proposed to identify and extract the principal components embedded in phase space. Finally, an improved low-rank approximation scheme is employed to recover the missing values in an iterative manner. The performance of the proposed ILRA is evaluated by both simulation and experimental analysis. The results show that the proposed method can recover the missing values efficiently. Furthermore, the method yields satisfactory results for subsequent instantaneous angular speed estimation. Therefore, it may offer a promising tool for numerical data recovery in industrial applications.

Adaptive Estimation of Instantaneous Angular Speed for Wind Turbine Planetary Gearbox Fault Detection

Planetary gearbox faults are the leading causes of downtime in wind turbines (WTs). In recent years, numerous and various vibration-based approaches have been put forward for WT gearbox fault detection. In the vibration-based techniques, order tracking-based methods, which by identifying fault orders in gearbox drivetrains, are regarded as very promising and powerful techniques. In the currently available order tracking methods, auxiliary devices are required to accurately obtain the instantaneous angular speed (IAS) of drivetrain. To tackle this problem, instantaneous angular speed estimation from vibration signals has been studied and some tacho-less order tracking (TLOT) approaches have been developed. However, many vital parameters for IAS estimation in the currently available TLOT algorithms need to be manually selected, which raise the question of user-friendliness, even result in a false diagnosis. As mentioned earlier, aiming at the shortcomings, a novel TLOT method based on adaptive IAS estimation is proposed for WT planetary gearbox fault diagnosis. In the proposed method, the nonlinear mode decomposition (NMD) method is improved, and its computational burden is reduced. And, the tachometer information of the drivetrain is adaptively extracted by the improved NMD method from generator vibration signal for gearbox vibration signal resampling. A field test is conducted, and the vibration signal of WT planetary gearbox with the compound fault is used for further investigation. The experimental validation results demonstrate that the planetary gearbox compound fault can be successfully detected, and the proposed method outperforms the traditional method based on generalized demodulation.

Sensorless control system for assistive robotic ankle-foot

This article presents a novel sensorless control system of assistive robotic ankle-foot prosthesis, two estimation algorithms were developed and an analogy between them has been made. The system actuator’s motor is a permanent magnet synchronous motor, unlike other powered ankle-foot, where the brushless DC motor and DC motor were used. Utilizing the permanent magnet synchronous motor will reduce the torque ripples and increase system ability to be overloaded compared to systems which utilize the brushless DC motor. Moreover, the ability of the machine to operate in all speed range makes this machine more suitable for the application. Both estimation algorithms are built using C-code and assessed in MATLAB Simulink. The estimation algorithms are used to provide motor and powered ankle-foot’s angular speed and position. Two-level control system is used to evaluate the estimation algorithms; the control system role is to mimic biological ankle-foot performance during normal ground level walking speed. Based on the result of this article the unscented Kalman filter (UKF) is applicable for the application, as a result of the observer ability to estimate the motor load and angular position. On the other hand, extended Kalman filter (EKF) accuracy is affected by the load applied to the motor. Furthermore, the angular position is evaluated by integration of the angular speed which means integration of angular speed estimation error.

Effective estimation of angular speed of synchronous generator based on stator voltage measurement

Estimation of the parameters of the power generators are important part of a power system modeling and simulation. A reliable estimation of a synchronous generator parameters can be done using waveforms measured directly on the terminals of the machine. The waveforms are recorded during a carefully chosen disturbance tests of the generating unit. One of the quantities necessary to determine the generator parameters is the deviation of the generator angular speed. However, because of the safety reasons, it is very difficult to get access to the direct measurement of this quantity on a operating generating unit. Angular speed estimation based on a generator stator voltage seems to be an alternative solution to the problem.The aim of the paper is to find a computationally efficient and accurate method of indirect angular speed estimation of a synchronous generator which is based on the recording of its stator voltage during a load rejection test. The algorithms evaluated in the paper are based on Prony’s estimator, zero-crossing detection, least-square data fitting and layer recurrent neural network. Paper contains literature survey, mathematical model of the considered generator, analysis of its stator voltage recorded in a power plant, description of the selected algorithms and results of the algorithms estimation using a signal with known frequency variation. Performed algorithms evaluation allows to choose the best solution in terms of accuracy and computational effort.

Vibration-based angular speed estimation for multi-stage wind turbine gearboxes

Most processing tools based on frequency analysis of vibration signals are only applicable for stationary speed regimes. Speed variation causes the spectral content to smear, which encumbers most conventional fault detection techniques. To solve the problem of non-stationary speed conditions, the instantaneous angular speed (IAS) is estimated. Wind turbine gearboxes however are typically multi-stage gearboxes, consisting of multiple shafts, rotating at different speeds. Fitting a sensor (e.g. a tachometer) to every single stage is not always feasible. As such there is a need to estimate the IAS of every single shaft based on the vibration signals measured by the accelerometers. This paper investigates the performance of the multi-order probabilistic approach for IAS estimation on experimental case studies of wind turbines. This method takes into account the meshing orders of the gears present in the system and has the advantage that a priori it is not necessary to associate harmonics with a certain periodic mechanical event, which increases the robustness of the method. It is found that the MOPA has the potential to easily outperform standard band-pass filtering techniques for speed estimation. More knowledge of the gearbox kinematics is beneficial for the MOPA performance, but even with very little knowledge about the meshing orders, the MOPA still performs sufficiently well to compete with the standard speed estimation techniques. This observation is proven on two different data sets, both originating from vibration measurements on the gearbox housing of a wind turbine.

Angular speed estimation and fault diagnosis based on an adaptive high-order sliding-mode observer

Digitally controlled electromechanical actuators with d.c. motors have been installed on a growing number of luxury vehicles, improving the vehicle performance significantly. However, the installation space and the cost issues of speed sensors in d.c. motors have limited the application of electromechanical actuators on medium-size and compact vehicles. In this paper, a novel adaptive high-order sliding-mode observer, which is based on the hybrid sliding-mode method and adaptive theory, is proposed. By integration of two adaptive gains with a high-order sliding-mode observer, the proposed observer facilitates application without the use of a filter, reduces the estimation oscillations and strengthens the system’s robustness. The effectiveness of the proposed adaptive observer was validated by simulations and experimental data.

Performance Improvement of a Field-Oriented Induction Motor Drive via Fuzzy Control

This paper presents a fuzzy slip angular speed estimator for improving the efficiency of an indirect field-oriented (IFO) induction motor drive. The proposed estimator consists of a fuzzy detuning correction controller (FDCC) and a fuzzy excitation controller (FEC). At heavy load, the rated flux excitation of motor is set and the nominal slip angular speed is augmented by a tuning signal generated by the proposed FDCC such that the motor drawn line current is significantly reduced, and thus the field-orientation characteristics can also be much improved. At steady-state of light load, for reducing the line drawn current more effectively, the nominal slip angular speed is set and the flux current command is reduced from its rated value by the FEC. As the transient due to command or load change occurs, the flux current command is restored to its rated value to increase the torque generating capability. Finally, a simple reference model following controller is designed to further yield good rotor speed dynamic response. The design methodology of the proposed controller is detailedly described, and the performance of the resulted motor drive is demonstrated experimentally.