Recursive Least-squares Method Research Articles

Combined estimation of the state of charge of a lithium battery based on a back-propagation– adaptive Kalman filter algorithm

The precise estimation of the battery’s state of charge is one of the most significant and difficult techniques for battery management systems. In order to improve the accuracy of estimation of the state of charge, the forgetting-factor recursive least-squares method is used to achieve online identification of the model parameters based on the first-order RC battery model, and a back-propagation neural-network-assisted adaptive Kalman filter algorithm is proposed. A back-propagation neural network is established by using the MATLAB neural network toolbox and is trained offline on the basis of the battery test data; then the trained back-propagation neural network is used to realize the online optimized results of an adaptive Kalman filter algorithm for estimation of the state of charge. The proposed methodology for estimation of the state of charge is demonstrated using experimental lithium-ion battery module data in dynamic stress tests. The results indicate that, in comparison with the common adaptive Kalman filter algorithm, the back-propagation–adaptive Kalman filter algorithm significantly improved precise estimation of the state of charge.

Development of algorithms for commercial vehicle mass and road grade estimation

Estimation algorithms for road slope angle and vehicle mass are presented for commercial vehicles. It is well known that vehicle weight and road grade significantly affect the longitudinal motion of a commercial vehicle. However, it is very difficult to measure the weight and road slope angle in real time because of lack of sensor technology. In addition, the total weight of a commercial vehicles varies depending on the freight. In this study, the road grade and vehicle mass estimation algorithms are proposed using the RLS (Recursive Least Square) method and only the in-vehicle sensors. The proposed algorithms are verified in experiments using a commercial vehicle under various conditions.

A nonlinear generalized predictive control for pumped storage unit

In this paper, the control problem of pumped storage unit (PSU) has been studied. A nonlinear generalized predictive control (NGPC) method has been applied to design the controller for a PSU. The NGPC controller is designed based on instantaneous linearization model of the control system, and the parameters of the linearized model are identified online by the recursive least square method (RLSM). Besides, in order to minimize the modelling error on initial state, a prior-knowledge learning method has been proposed to get the initial parameters for control model estimation. To verify the effectiveness of the NGPC controller, we chose a pumped-storage hydropower plant in China as the experimental subject and the simulation experiments respect to the control system are designed. The processes of start-up and speed disturbance under no-load condition have been simulated to testify the robustness and efficiency of the NGPC controller. Comparative experiments have been conducted, while the NGPC controller, a PID controller and a fractional order PID (FOPID) controller have been compared. Experimental results show that the designed NGPC could effectively restrain the oscillation of rotational speed in different working conditions of PSU and demonstrates higher robustness and stability than both the PID and FOPID controllers.

Accurate approach to the temperature effect on state of charge estimation in the LiFePO4 battery under dynamic load operation

This paper presents a simple approach to estimate the state of charge of the LiFePO4 batteries in electric vehicles under dynamic loads and variable temperature, which are inevitable during practical working conditions. This approach employs a highly adaptive estimation algorithm based on the recursive least-squares method and an original simple model of the open circuit voltage to the state of charge over a wide range of temperature. The modeling and the estimation in this approach are based on a new term for the state of charge, which is defined based on experimental findings to take into account the battery recovery capacity due to temperature variations. The proposed approach is validated through Urban Dynamometer Driving Schedule experiments including harsh temperature conditions, which have been mostly overlooked in previous research. The obtained results show that this approach maintains an accurate state of charge estimation, with an error of less than 5.2% under such conditions. The accuracy and the simplicity of the proposed algorithm are crucial for a feasible battery management system to be used in electric vehicles.

Three-parameter transmission gear-shifting schedule for improved fuel economy

Traditionally the transmission gear-shifting schedule is based upon the throttle position and the vehicle (or engine) speed. This paper proposes to add a third parameter, called the terrain coefficient, to form a three-parameter gear-shifting schedule for improving the fuel economy of a vehicle. The terrain coefficient is a compound parameter consisting of the road grade and the rolling resistance coefficient. It can be estimated in real time by the proposed multi-step recursive least-squares method. The dynamic programming and the moving least-squares method are adopted to optimize the gear sequences and to generate the three-parameter gear-shifting schedule. The proposed gear-shifting schedule is evaluated against the traditional two-parameter gear-shifting schedule via Simulink simulations and on-road experiments using a heavy-duty vehicle. The simulation results for the Urban Dynamometer Driving Schedule and the US06 Supplemental Federal Test Procedure driving cycles show that the fuel economies of the proposed gear-shifting schedule are improved by 3.3% and 2.7% respectively over that of the traditional two-parameter schedule. The experimental results indicate that the three-parameter gear-shifting schedule improves the fuel economy by 3.5% over the traditional schedule with a satisfactory acceleration performance.

Real-Time Parameter Estimation of DC–DC Converters Using a Self-Tuned Kalman Filter

To achieve high-performance control of modern dc–dc converters, using direct digital design techniques, an accurate discrete model of the converter is necessary. In this paper, a new parametric system identification method, based on a Kalman filter (KF) approach is introduced to estimate the discrete model of a synchronous dc–dc buck converter. To improve the tracking performance of the proposed KF, an adaptive tuning technique is proposed. Unlike many other published schemes, this approach offers the unique advantage of updating the parameter vector coefficients at different rates. The proposed KF estimation technique is experimentally verified using a Texas Instruments TMS320F28335 microcontroller platform and synchronous step-down dc–dc converter. Results demonstrate a robust and reliable real-time estimator. The proposed method can accurately identify the discrete coefficients of the dc–dc converter. This paper also validates the performance of the identification algorithm with time-varying parameters, such as an abrupt load change. The proposed method demonstrates robust estimation with and without an excitation signal, which makes it very well suited for real-time power electronic control applications. Furthermore, the estimator convergence time is significantly shorter compared to many other schemes, such as the classical exponentially weighted recursive least-squares method.

Estimation of Torques Transmitted by Twin-Clutch of Dry Dual-Clutch Transmission During Vehicle's Launching Process

The key to the launching control of a dual-clutch transmission (DCT) lies in the coordination control of the engine and dual clutches, along with the accurate closed-loop control of the torque transmitted by each clutch and the output torque of the engine. The implementation feasibility and precision of the clutch torque closed-loop control are completely dependent on the effective real-time estimation of the clutch torque, which cannot be directly measured. Therefore, the high-order sliding-mode observer and unknown input observer are used to estimate the transmitted torque of the twin clutches on the basis of the self-designed control strategy and estimation of the vehicle drag torque. First, for the launching clutch slipping phase, an improved engine constant speed control is proposed based on the dynamic equations of a dry DCT with dual intermediate shafts, and the minimum value principle is applied to achieve the optimum launching control of the clutches. Meanwhile, the separating conditions of the separated clutch and the torque distribution are determined to ensure approximate friction work and avoid power cycle, and the target curve of the clutch-transmitted torque is obtained according to different conditions. Then, the vehicle drag torque is estimated using the recursive least-square method with a double forgetting factor, the angular acceleration of the engine and output shaft is refactored utilizing a high-order sliding-mode observer algorithm, and the transmitted torque of the twin clutches are estimated using the unknown input observer. Then, the DCT launching process is simulated under different driving conditions on the MATLAB/Simulink software platform. Finally, the bench test is conducted to verify the effectiveness of the self-designed clutch torque estimation method. The simulation and hardware-in-the-loop (HIL) test results show that the proposed methods of high-order sliding-mode observer and unknown input observer can effectively estimate the clutch-transmitted torque and lay a solid foundation for the subsequent development of the launching control strategy for a real vehicle with a DCT.

Improvement in the vehicle stability of distributed-drive electric vehicles based on integrated model-matching control

This paper presents a vehicle dynamic stability controller for distributed-drive electric vehicles. A hierarchical control structure is adopted for the proposed controller. An upper controller is designed on the basis of integrated model-matching control. It consists of a feedforward component plus a feedback component to calculate the desired external yaw moment to achieve the desired vehicle motion. The feedforward control aims at compensating the effect caused by the variation in the linear cornering stiffnesses of the tyres during the life cycle of the tyres. It provides a rapid response under common driving conditions. The linear cornering stiffnesses of the tyres are estimated in real time by the adaptive forgetting-factor recursive least-squares method. Since many vehicle parameters have strongly non-linear and time-varying characteristics, adaptive sliding mode control is used as the feedback component to make the controller robust against systematic uncertainties. To combine the outputs of feedforward and feedback together and to avoid probable conflict, a weight gain coefficient is obtained. Additionally, a conventional sliding-mode controller is introduced as a comparative upper control strategy. The lower controller is utilized to allocate the required yaw moment and traction to the four independent motors, taking into account the tyre grip margins. Simulations for a low- g manoeuvre and a high- g manoeuvre are carried out to evaluate the proposed control algorithm. The results show that the proposed vehicle stability controller can significantly stabilize the vehicle motion and greatly reduce the driver’s workload in comparison with with the conventional sliding-mode controller.

Modelling of wind power forecasting errors based on kernel recursive least-squares method

Forecasting error amending is a universal solution to improve short-term wind power forecasting accuracy no matter what specific forecasting algorithms are applied. The error correction model should be presented considering not only the nonlinear and non-stationary characteristics of forecasting errors but also the field application adaptability problems. The kernel recursive least-squares (KRLS) model is introduced to meet the requirements of online error correction. An iterative error modification approach is designed in this paper to yield the potential benefits of statistical models, including a set of error forecasting models. The teleconnection in forecasting errors from aggregated wind farms serves as the physical background to choose the hybrid regression variables. A case study based on field data is found to validate the properties of the proposed approach. The results show that our approach could effectively extend the modifying horizon of statistical models and has a better performance than the traditional linear method for amending short-term forecasts.

Kernel online sequential ELM algorithm with sliding window subject to time-varying environments

Extreme learning machine (ELM) is an emerging machine learning algorithm with single-hidden-layer feedforward neural networks (SLFNs). The key strength of ELM algorithm is the significantly fast training speed and good generalization performance since the learning parameters of hidden nodes are generated randomly. The kernel online sequential ELM (KOS-ELM) is a straightforward extension of the well-known recursive least-squares method to the ELM framework. KOS-ELM is a good choice for the online learning of stationary applications. However, there are lots of situations and applications which are time varying quickly. It is unreasonable and inaccurate to pay equal emphasis on both old and new observations. In this paper, we proposed a modified KOS-ELM algorithm with forgetting mechanism (KOS-ELMF) to deal with the time-sensitive applications. A sliding window is applied to limit the active training data in order to ’forget’ the old observations. The size of the sliding window can change based on the forecast error automatically. The automatic determination of model parameters can avoid human interference and save training time. Empirical study of KOS-ELMF on several benchmark applications shows that the proposed approach achieves more satisfied and robust performance, compared with other ELM-related algorithms.

A Comparative Study of Adaptive Order Tracking Techniques for Rotating Machinery Analysis: Computer Experiments and Practical Implementations

This paper presents and investigates recursive order tracking (OT) techniques based on the least mean-square (LMS) method and the Vold–Kalman (VK) algorithm with a one pole structural equation, both of which could be realized as real-time applications. Additionally, for comparisons, two common adaptive OT filters are considered: the recursive least-squares (RLS) method and the VK algorithm with a two pole structural equation. The numerical implementations of the considered methods, through simulations on a representative noisy synthetic signal, including both close and crossing orders spectral components, are performed. The results indicate a possible degradation in the tracking performance of the RLS algorithm and the effectiveness of the simple LMS method, as well as both considered VK algorithms, for OT and distinguishing. The influence of the sampling frequency on the choosing of a weighting factor for the VK recursive OT filters is further investigated to extend the guidelines from the literature for using these methods. Two examples of practical implementations of the considered recursive OT methods are given: (i) the separation of the crossing orders arising in the laboratory test bench of the two unbalanced rotors rotating at independent frequencies and (ii) the one engineering application of fault diagnosis in the massive reduction gear on an excavator with a cable crowd, based on the distinguishing and separation of close orders. The experimental results justify the implementation of the proposed techniques as OT tools in industrial applications.

Combined Estimation and Optimal Control of Batch Membrane Processes

In this paper, we deal with the model-based time-optimal operation of a batch diafiltration process in the presence of membrane fouling. Membrane fouling poses one of the major problems in the field of membrane processes. We model the fouling behavior and estimate its parameters using various methods. Least-squares, least-squares with a moving horizon, recursive least-squares methods and the extended Kalman filter are applied and discussed for the estimation of the fouling behavior on-line during the process run. Model-based optimal non-linear control coupled with parameter estimation is applied in a simulation case study to show the benefits of the proposed approach.

Оценивание параметров линейных статистических объектов с использованием рекуррентного метода наименьших квадратов в среде Simulink

Оценивание параметров линейных статистических объектов с использованием рекуррентного метода наименьших квадратов в среде Simulink

State-of-health estimation of lithium-ion battery packs in electric vehicles based on genetic resampling particle filter

Power battery packs are the energy source of battery electric vehicles (BEVs). A precise state-of-health (SOH) estimation for batteries is crucial to ensure the operational security and stability of BEVs. This paper employs an equivalent circuit model of battery pack in SOH estimation. Since a battery pack is a complex and nonlinear system, the equivalent circuit model of battery pack is always complicated. To balance estimation accuracy and computational complexity, the equivalent circuit model of battery pack should be simplified. However, much noise is produced in the simplified model. In addition, the errors during SOH estimation are from various sources so that SOH estimation is a non-Gaussian problem. Given the genetic resampling particle filter (GPF) performs efficiently in solving non-Gaussian problems, this paper proposes a new GPF-based method for battery SOH dynamic estimation when accuracy of the equivalent circuit model is not high. First, a second-order equivalent circuit model of Resistance–Capacitance (RC) circuit for the battery pack is developed. The unknown parameters are identified using the recursive least-squares method with forgetting factor. Second, a state-space model of the GPF is developed based on the equivalent circuit model. Finally, a case study is conducted using real data collected from operating electric taxis in Beijing to investigate the estimation performance of the proposed model. Estimation results show that the proposed GPF model outperforms the particle filter method in the SOH estimation problem.

Coordinative traction control of vehicles based on identification of the tyre–road friction coefficient

Traction control, which can be performed by different types of chassis control system, plays an important role in vehicle motion control. Since the propulsive force is actually produced by the friction between the tyre and road, information on the tyre–road friction is crucial for traction control. In this paper, a robust and effective tyre–road friction coefficient identification algorithm for straight acceleration is proposed, and a coordinative traction control method is designed by integrated usage of gear shifting control, engine control and braking control. For different driving conditions, the tyre forces were observed by a sliding-mode observer or calculated from the states of the vehicle directly, and the tyre–road friction coefficients were estimated by the recursive least-squares method or calculated from the linear characteristics between the friction coefficient and the slip ratio consequently. Based on the estimated tyre–road information, a practical and systematic coordinative traction control algorithm was designed to integrate shifting control, engine torque control and braking pressure control. Finally, the proposed methods are verified by both simulations and road tests. The results show that the estimation algorithms can identify the variation in the road conditions with considerable accuracy and response speed, and the controller successfully adjusted the slip ratios of the driving wheels in the stable region with good performances on different types of road.

Effects of Milling Feed Rate and Tool Diameter on Cutting Forces and Cutting Coefficient for Medium Carbon Steel (S45C)

In this study, a prediction method for the milling cutting force and cutting coefficient for medium carbon steel (S45C) is developed. Two prediction methods for cutting force – the average cutting force method and the recursive least-squares method – are introduced, and then, the prediction results of cutting forces obtained by these methods are compared with experimentally measured cutting forces. Following acquisition of accurate cutting force coefficients, the cutting parameters, i.e. the friction angle and shear stress, are estimated using the oblique cutting theory. The estimation results reveal good agreement between the forces predicted by the recursive least-squares method and the experimentally measured forces. With an increase in the feed per tooth, the cutting force increases and the cutting coefficient becomes smaller in the case of shearing forces in tangential directions. Additionally, the magnitude of the friction angle is found to remain unchanged under varying feed per tooth and tool diameter.

Low Sampling Rate Online Parameters Monitoring of DC–DC Converters for Predictive-Maintenance Using Biogeography-Based Optimization

Pulse width-modulated dc–dc converters are widely used in the renewable power systems. In practice, their reliability is of major concern. To identify the converter system, the Walsh–Hadamard transformation and recursive least square (RLS) methods are used in some previous works. However, the accuracy of the identified parameters is degraded under measurement noise. In this paper, a new approach for the full parameter estimation of a dc–dc buck converter is proposed. The new approach is realized using the biogeography-based optimization. Unlike the traditional RLS method, the proposed method is based on a state-space model with full-state observation. Therefore, the performance of parameter estimation under different measurement noise levels is improved. Both simulation and experimental results are presented to validate the effectiveness of the new estimation scheme.

Low speed control and implementation of permanent magnet synchronous motor for mechanical elastic energy storage device with simultaneous variations of inertia and torque

The spiral torsion spring-based mechanical elastic energy storage (MEES) device presented previously with inherent characteristic of simultaneous variations of inertia and torque is disadvantage to be actuated by conventional control method. This study proposes an improved non-linear backstepping control scheme based on combination of recursive least squares (RLS) and differential evolution (DE) optimisation to regulate permanent magnet synchronous motor (PMSM) at a very low speed and control MEES device effectively. For this presented control scheme, first, a single RLS method with forgetting factor is presented to simultaneously estimate the time-varying inertia and torque of MEES device. Second, on the basis of estimation results, an improved non-linear backstepping control algorithm considering parameter variations in derivation process is proposed to drive PMSM to operate at a very low speed. Finally, a self-adaptive parameter DE method is designed to optimise the several control parameters. The performance of the proposed methodology is verified through simulations and experiments.

Study on stiffness visualization and safety control based on will-consensus building for tele-palpation robot system

This paper proposes a method for visualizing the stiffness of a soft object in a palpation-support information system by the teleoperation of a robot hand. It is important that a palpation system display a body's shape and stiffness. In our method, the stiffness of the contact area between the soft object and the robot finger is estimated by a recursive least-squares method with forgetting factor that uses an impedance dynamics model. With the estimated stiffness and direction of contact force, we calculate the scalar parameter for visualization of stiffness. Moreover, we propose a safety control method for the palpation system, which is part of a tele-control method based on will-consensus building. The system configuration, estimated algorithm, and experimental results are presented.

A Novel Online Multivariate Identification for Autotuning Speed Control in PMSM Drives

A novel online algorithm to identify the moment of inertia, viscous friction coefficient, and load torque of PMSM (Permanent Magnet Synchronous Motor) drives and a distinctive autotuning speed control scheme are presented. The proposed identification algorithm does not require motors run in a particular trajectory and only needs a short identification time. A Luenberger speed observer is introduced to eliminate noises which are generated by the detection of position signal and to improve the accuracy of identified parameters. Parameters of the speed controller are optimized by analyzing the mathematical model of the system and the formula of the PI controller. Compared to a standard recursive least squares method (RLSM) and traditional PI algorithm, the effectiveness of the proposed identification algorithm and autotuning speed control scheme are validated through simulations and experiments.