Kalman Filter Observer Research Articles

Consensus formation control of wheeled mobile robots with mixed disturbances under input constraints

This paper addresses the problem of distributed consensus-based formation control for wheeled mobile robots (WMRs) under the influence of mixed disturbances, including both random noise and non-random disturbances. A consensus formation auxiliary subsystem is constructed based on the leader’s position estimated by the distributed estimator. A formation tracking subsystem for each robot is constructed based on the trajectory tracking error method. The above two subsystems are constructed into an extended formation modeling system. Further, a distributed model predictive control (DMPC) is designed to control this system without disturbance, and the controller is solved by means of a general-purpose neural network. A combination of Kalman filter (KF) and extended state observer (ESO) is intended to reduce the effect of both non-random disturbances and random noise, hence increasing the controller’s resilience to disturbances. Moreover, a composite control law is designed to ensure the controller’s effectiveness. Finally, simulation results demonstrate that the proposed control strategy is well-suited to addressing the problem, as it not only achieves accurate formation control but also effectively regulates the robot’s physical constraints while suppressing both non-random disturbances and random noise.

Gaussian-inverse gamma mixture distribution–based extended Kalman observer for dynamic positioning control system of offshore platform

Under different working conditions and control objectives, fuzzy model predictive control is used to optimize the control effect by adjusting the weight to achieve stable and accurate control for the dynamic positioning control of offshore platforms. Also, aiming at the situation where the measurement noise of dynamic positioning control may be time-varying and non-Gaussian and the statistics of the noise are not exact, this paper proposes a variational Bayesian extended Kalman filter observer. In order to model non-Gaussian noise more reasonably, the joint posterior distribution of non-Gaussian noise with state and time-varying covariance is described as the product of Gaussian and independent inverse gamma distributions. Then, the variational Bayesian (VB) method was used to simultaneously estimate the system state, the intermediate variable values of the new distribution, and the noise parameters through fixed-point iteration. The fuzzy algorithm is applied to the model predictive control, and the weight parameters of the model predictive control are adaptively changed to better adapt to the changing working conditions in the control process. The simulation results show that the variational Bayesian extended Kalman filter observer has better performance than the existing algorithms when dealing with the time-varying non-Gaussian observation noise, whose statistics are not exact. The variational Bayesian extended Kalman filter observer can significantly improve the accuracy of the control when it is used in fuzzy model predictive control.

A charge dynamics model for state-of-charge estimation by Kalman filter and lithium-ion battery parameters observation in real-vehicle

A charge dynamics model for state-of-charge estimation by Kalman filter and lithium-ion battery parameters observation in real-vehicle

Robust fault detection and adaptive fixed-time fault-tolerant control for quadrotor UAVs

This note scrutinizes an adaptive fault-tolerant control (FTC) approach tailored for unmanned aerial vehicles (UAVs), addressing the critical need for both fault accommodation and disturbance suppression. Departing from traditional reliance on robust discontinuous control strategies prone to chattering and demanding precise uncertainty bounds, our FTC method ensures fixed-time stability, guaranteeing the convergence of attitude tracking errors to zero. Central to our approach is an adaptive algorithm adept at concurrently estimating unknown actuator faults and upper bounds of lumped uncertainties. Moreover, our adaptive schemes accurately estimate the upper bound of the lumped uncertainty term, encompassing model uncertainties, external disturbances, and unmodeled dynamics, thereby eliminating the need for assuming known bounds on uncertainties. Stability analysis under the developed control law is thoroughly performed using the Lyapunov stability theory. Notably, our strategy employs an extended Kalman filter (EKF) observer for state estimation and fault detection, facilitating fault detection through an adaptive threshold technique dynamically adjusted based on real-time mean and variance of the residual signal. Through comprehensive simulation and experimental validations, our proposed methodology demonstrates significant advancements in ensuring safety and reliability in UAVs.

Discrete-time sliding mode prescribed performance controller via Kalman filter and disturbance observer for load following of a pressurized water reactor

In practical implementations, most nuclear reactors employ digital controllers to accomplish the load following operation. However, most of the pre-existing works only focus on continuous time controller design, which may yield degraded control performance when the control strategy is employed by a digital controller owing to the finite sampling frequency and the inevitable discrete-time approximations. To this end, this paper proposes a discrete-time sliding mode prescribed performance controller (DTSMPPC) via Kalman filter (KF) and disturbance observer (DO) for a pressurized water reactor (PWR), aiming to achieve an easier implementation on the practical nuclear reactor systems. Specifically, the continuous mathematical model of the PWR system with consideration of model errors and disturbances is first transformed to a discrete-time form by virtue of Euler’s discretization technique. Then, based on this transformed discrete-time model, the KF and DO, which provide the estimates of unmeasured system states (relative density of delayed neutron precursor, average fuel temperature, xenon concentration, and iodine concentration) and uncertainties, respectively, are constructed using the input/output measurement information acquired from the nuclear reactor system merely. By incorporating the observed information provided by the KF and DO into the control framework, the proposed DTSMPPC enables the load following error to fulfill the accurate and robust performance requirement even in the presence of unmeasured system states and uncertainties, while at the same time ensuring the transient and steady-state load following error within a prescribed zone described by performance functions. The system stability and the aforementioned theoretical findings are proved through rigorous analysis and simulations. Simulation results also reveal that the proposed DTSMPPC via the KF and DO yields a superior load following performance compared with some previous control strategies.

Field oriented control technique applied to the PMSM without mechanical sensor, based on the cubature KALMAN filter observer

Field oriented control technique applied to the PMSM without mechanical sensor, based on the cubature KALMAN filter observer

A data-driven hybrid sensor fault detection/diagnosis method with flight test data

Fault diagnosis of multi-source signal systems is critical for the safe and reliable operation of modern industrial systems, and accurate fault diagnosis of systems based on multi-source signals remains challenging. This study proposes a data-driven hybrid fault detection/diagnosis method to identify sensor faults in complex systems through interactions between multiple sensors. Dynamic mode decomposition with control is used to obtain the approximate model of the investigated system from multi-source signals, extract the underlying physical mechanisms, combined with the Kalman filter observer to generate the residual between the observed data and the predicted data. Then the residual (moving innovation covariance matrix V k ) is input into the k-nearest neighbor classification algorithm for fault detection and diagnosis. The effectiveness of the proposed method was evaluated using the flight test braking system dataset. The results showed that the accuracy of the proposed method in fault detection and diagnosis (with accuracies of 100% and 100%, respectively) was significantly improved than that of using raw signal data (76.6% and 6.38%) or raw signal data and Vk (80.85% and 42.55%). The analysis of different parameters including fault severity, algorithm hyperparameter k , and sensor type showed that the proposed method has high robustness, generalization ability, and practicality.

Sensorless control of permanent magnet synchronous motor for exhaust energy recovery of internal combustion engine: a comparison between Kalman filter and MRAS observer

This paper deals with the sensorless control of a Permanent Magnet Synchronous Motor (PMSM) to be employed on a turbo-generator to recover the exhaust gas energy of an Internal Combustion Engine (ICE). The main problem with this application is the high rotational speed required by the exhaust gas turbo-generator. Indeed, this implies the difficulty of installing an encoder for speed measurement and control. For this reason, sensorless control is highly recommendable, but, on the other hand, the main sensorless techniques could fail in this peculiar situation because of the high computational effort required compared with the other sensorless applications. Moreover, a good knowledge of the model parameters is necessary. Therefore, the main goal of this paper is to compare two main sensorless techniques for rotational speed measurement, both in the deterministic framework (Model Reference Adaptive System (MRAS) observer) and stochastic framework (Extended Kalman Filter (EKF)), to verify their effectiveness, their computational load, their sensitivity against parameter variation and noisy measurements, and, finally, to present the best solution for the exhaust gas energy recovery from the internal combustion engine.

Speed Tracking and Anti-Slip Control for Heavy Freight Trains Considering the Conicity of the Wheel

To ensure the safe and punctual transportation of freight trains, it is crucial for the train to travel at the targeted speed on the track. This paper proposes a scheme for speed tracking and anti-slip control for freight trains. The speed tracking is implemented through predictive auto disturbance rejection control (PADRC), which includes a flexible Smith estimation module capable of accurately predicting the output of large time delay systems, such as freight trains. The key to anti-slip control relies on the precise observation of the radial velocity and slip rate. Therefore, an unscented Kalman filter observer is designed in this article, incorporating an adaptive parameter adjustment mechanism to enhance observation accuracy. The anti-slip parameters obtained from this observer can then be used to determine the anti-slip control scheme. The effectiveness of this scheme is demonstrated through simulations of the HXD1 electric traction locomotive’s driving process, using line data from the Geku line section in China. Compared to conventional active disturbance rejection control, PADRC reduces speed fluctuation by 55%, and freight trains under anti-slip control decrease the slip speed by 90%.

Estimation of Lateral Velocity and Cornering Stiffness in Vehicle Dynamics Based on Multi-Source Information Fusion

<div>To address the challenge of directly measuring essential dynamic parameters of vehicles, this article introduces a multi-source information fusion estimation method. Using the intelligent front camera (IFC) sensor to analyze lane line polynomial information and a kinematic model, the vehicle’s lateral velocity and sideslip angle can be determined without extra sensor expenses. After evaluating the strengths and weaknesses of the two aforementioned lateral velocity estimation techniques, a fusion estimation approach for lateral velocity is proposed. This approach extracts the vehicle’s lateral dynamic characteristics to calculate the fusion allocation coefficient. Subsequently, the outcomes from the two lateral velocity estimation techniques are merged, ensuring rapid convergence under steady-state conditions and precise tracking in dynamic scenarios. In addition, we introduce a tire parameter online adaptive module (TPOAM) to continually update essential tire parameters such as cornering stiffnesses, with its effectiveness demonstrated through DLC and slalom simulation tests. Using a dual extended Kalman filter (DEKF) observer, the article allows for joint estimation of vehicle states and tire parameters. Ultimately, we offer a cost-effective estimation method of vital dynamic vehicle parameters to support the motion control module in autonomous driving.</div>

Nonlinear Time-Delayed Quorum Sensing System: State Estimation Via a Robust Observer

This paper proposes an innovative method to estimate the states in a nonlinear time-delayed quorum sensing (QS) model using an extended Kalman filter (EKF) observer. By addressing the inherent time delays in QS system which arise as a delayed response of bacteria to population fluctuations, the study introduces variable structure dynamical estimators, specifically the EKF, to approximate missing states based on available measurements. The EKF observer is applied to estimate four out of five internal non-measurable nonlinear states in a time-delayed QS model. This is the first attempt to utilize the EKF state estimation in nonlinear time delay QS models. The research contributes to the understanding of QS systems, provides insights into the communication dynamics inside biological systems, and offers a practical solution for estimating states in realistic scenarios.

ОПТИМАЛЬНІ ОЦІНКИ ВЕКТОРА СТАНУ ДЛЯ ДИСКРЕТНИХ СТОХАСТИЧНИХ СИСТЕМ З НЕВИЗНАЧЕНИМИ ЗБУРЕННЯМИ ТА ШУМОМ

Assessment of the dynamic systems state is widely used in various areas of technical activity. In practice, the most well-known and common methods of estimation are the methods of the Kalman filter and Luenberger observers. Most of the results known in the scientific literature for constructing estimates of the dynamic systems state in the presence of acting uncontrolled disturbances and noise are associated with stationary systems. The insensitivity of such estimates to the influence of accompanying uncontrolled perturbations is ensured by the introduction of certain restrictions that are imposed on a number of system matrices, and their optimality is achieved by minimizing the estimation errors covariance matrix trace due to those degrees of freedom that remained after the separation procedure was performed. The aim of the work is to develop a filter capable of generating state vector optimal estimates of a stochastic linear system with changeable parameters that are insensitive to the influence of uncontrolled inputs. In this case, the conditions that guarantee the convergence of the estimates obtained must be easily verifiable. The goal is achieved by using a one-to-one transformation of the equations of systems, followed by the application of the Kalman filter. The O'Reilly functional observer is used as the specified transformation. An example is given that illustrates the effectiveness of the proposed filter.

Intelligent Deep Learning Estimators of a Lithium-Ion Battery State of Charge Design and MATLAB Implementation—A Case Study

The main objective of this research paper was to develop two intelligent state estimators using shallow neural network (SNN) and NARX architectures from a large class of deep learning models. This research developed a new modelling design approach, namely, an improved hybrid adaptive neural fuzzy inference system (ANFIS) battery model, which is simple, accurate, practical, and well suited for real-time implementations in HEV/EV applications, with this being one of the main contributions of this research. On the basis of this model, we built four state of charge (SOC) estimators of high accuracy, assessed by a percentage error of less than 0.5% in a steady state compared to the 2% reported in the literature in the field. Moreover, these estimators excelled by their robustness to changes in the model parameters values and the initial “guess value” of SOC from 80–90% to 30–40%, performing in the harsh and aggressive realistic conditions of the real world, simulated by three famous driving cycle procedure tests, namely, two European standards, WLTP and NEDC, and an EPA American standard, FTP-75. Furthermore, a mean square error (MSE) of 7.97 × 10−11 for the SOC estimation of the NARX SNN SOC estimator and 5.43 × 10−6 for voltage prediction outperformed the traditional SOC estimators. Their effectiveness was proven by the performance comparison with a traditional extended Kalman filter (EKF) and adaptive nonlinear observer (ANOE) state estimators through extensive MATLAB simulations that reveal a slight superiority of the supervised learning algorithms by accuracy, online real-time implementation capability, in order to solve an extensive palette of HEV/EV applications.

An efficient Feed-forward compensation mechanism for NFC-based PMSM system using different observers for Load-torque estimation

Permanent magnet synchronous motor (PMSM) offers high torque and efficiency and is used in most industrial applications. This manuscript uses a feed-forward compensation mechanism to design an efficient neuro-fuzzy logic controller (NFC) based surface-mounted PMSM system. The different load-observers like Discrete Luenberger Observer (DLO), Kalman filter observer (KFO), and discrete Kalman filter observer (DKFO) are used as a feed-forward compensation method to compensate the dq stator current and also estimate performance metrics. The NFC is used as a speed controller, and two PI controllers are used for the current control mechanism. The noise is added at the actual load torque and speed of PMSM and compensated using load observers. In this work, two different design scenarios are considered to analyze the performance metrics like load torque, speed, and position. The work also explores the average error that occurred at load torque, speed, and position during estimation. The NFC-based PMSM system improves the performance and utilizes less error over the PI/FLC-based PMSM using different observers.

DTC-SVM οf Sensorless Five-phase Induction Machine Using Extended Kalman Filter

This work relates to the study of direct torque control based on space vector modulation applied on five-phase induction machine. It is well established that the conventional direct torque control using hysteresis comparators suffers from high torque ripples and variable switching frequency. The most common solution to those problems is the use of space vector modulation. In the other hand, this paper aims also to design an extended Kalman filter observer for speed/flux estimation, which improves not only the control performances by using a sensorless algorithm but also can lower the cost and increase the reliability of the system. Both theoretical principle and simulation results of the sensorless control method of multiphase drive will be conducted to verify the effectiveness of the proposed control approach.

A Parameter-Free Method for Estimating the Stator Resistance of a Wound Rotor Synchronous Machine

This paper presents a new online method based on low frequency signal injection to estimate the stator resistance of a Wound Rotor Synchronous Machine (WRSM). The proposed estimator provides a parameter-free method for estimating the stator resistance, in which there is no need to know the values of the parameters of the machine model, such as the stator and rotor inductances or the rotor flux linkage. In this method, a low frequency sinusoidal current is injected in the d axis of the stator current to produce a sinusoidal flux in the stator. In this paper, it is shown that the phase difference between the generated sinusoidal flux and the injected sinusoidal current is related to the stator resistance mismatch. Using this phase difference, the stator resistance is estimated. To validate the proposed model-free estimator, simulations were performed with Matlab Simulink and the results were compared with the extended Kalman filter observer. Finally, experimental tests, under different conditions, were performed to estimate the stator resistance of a WRSM.

Extended Kalman Filter Based Resilient Formation Tracking Control of Multiple Unmanned Vehicles via Game-Theoretical Reinforcement Learning

In this paper, we discuss the resilient formation tracking control problem of multiple unmanned vehicles (MUV). A dynamic leader-follower distributed control structure is utilized to optimize the performance of the formation tracking. For the follower of the MUV, the leader is a cooperative unmanned vehicle, and the target of formation tracking is a non-cooperative unmanned vehicle with a nonlinear trajectory. Therefore, an extended Kalman filter (EKF) observer is designed to estimate the state of the target. Then the leader of the MUV is adjusted dynamically according to the state of the target. In order to describe the interactions between the follower and dynamic leader, a Stackelberg game model is constructed to handle the hierarchical decision problems. At the lower layer, each follower responds by observing the leader's strategy, and the potential game is used to prove a Nash equilibrium among all followers. At the upper layer, the dynamic leader makes decisions depending on the response of all followers to reaching the Stackelberg equilibrium. Moreover, the Stackelberg-Nash equilibrium of the designed game theoretical model is proven. A novel reinforcement learning-based algorithm is designed to achieve the Stackelberg-Nash equilibrium of the game. Finally, the effectiveness of the method is verified by a variety of formation tracking simulation experiments.

Model-based simultaneous diagnosis of ammonia injection failure and catalyst ageing in [formula omitted] engine after-treatment systems

After-treatment systems (ATS) in vehicle powertrains are developed to achieve maximum pollutant abatement efficiency under design operating conditions. However, anomalies in the ATS may appear during real operation, such as reducing agent supply failure and catalyst ageing. As in the case of an ATS composed of a selective catalytic reduction (SCR) system plus an ammonia slip catalyst (ASC), injection failure leads to insufficient ammonia levels to reduce nitrogen oxide (NOx), and ageing decreases the ammonia storage capacity and NOx conversion efficiency, these drawbacks drive both pollutants to levels above those expected and allowed by governmental regulations. To address this problem, a novel methodology was proposed that simultaneously estimates the operational state of the ATS in terms of ammonia injection failure and ASC catalyst ageing. The approach through control-oriented models based on an artificial neural network (ANN) and sensor signal analysis (SSA), as well as an extended Kalman filter (EKF) observer, compares the current emission levels estimated by the observer in a two-dimensional probabilistic plan and a variable time-window, with those expected if the ATS were operating under normal conditions. The proposed methodology was evaluated in real driving cycles with the ATS subjected to several undesired operating conditions. As a result, the model was able to accurately estimate the levels of ammonia injection failure and catalyst ageing state. Therefore, enabling the control system to modify the ammonia injection strategy to achieve desired levels of NOx and NH3 emissions.

Coordinated Lateral Stability Control of Autonomous Vehicles Based on State Estimation and Path Tracking

This paper proposes a coordinated control system of autonomous vehicles’ lateral stability based on state estimation and path tracking, which contributes to enhancing path-tracking capability and at the same time maintaining the stability of autonomous vehicles driving in complex and dynamic road conditions. First, an extended Kalman filter observer is designed to estimate the vehicle parameters. Then, based on the single-point preview theory, an adaptive preview time model is built for the accuracy of path tracking. When designing the direct yaw-moment controller, sideslip angle and yaw rate, two critical parameters for lateral dynamic stability control are considered, and the single-wheel braking method is utilized to reasonably distribute the additional yaw moment to a certain wheel. To make full use of active front steering and direct yaw-moment control, the critical steering angle of the front wheel is determined, and a switching function is formulated. Co-simulation shows that the suggested coordinated control system can effectively strengthen maneuvering stability and simultaneously satisfy tracking accuracy.

Two Decentralized Dynamic State Estimation Schemes for Multimachine Power Systems with Transmission Losses

This article addresses the problem of estimating the state of a multimachine power system (MPS). To work with power networks with lossy transmission lines, a variation of the classical third-order MPS is proposed by considering generators’ electrical power injected into the grid as a state variable. Based on a linear decentralized estimation model (tailored for a specific purpose), the state variables of generators (load angle, relative speed, and electrical power) together with terminal voltage magnitudes are estimated in a decentralized fashion through two new robustly convergent linear Luenberger estimators, one based on load angle measurement and the other based on relative speed measurement. The new MPS estimation model includes a set of robustly quick observable states, one per machine, which allows capturing the interaction with other generators, transmission line losses, unknown disturbances, and model errors. The result is a design superior to other related estimation techniques such as the extended Kalman filter (EKF) or Sliding Modes Perturbation Observer (SMPO) in terms of (i) a conventional-like simple pole placement-based tuning, (ii) low online computational load and disturbance rejection capability, and (iii) small gain-based convergence assessment. The performance of the proposed state estimation scheme is illustrated in a 3-machine power system under different operational conditions.