Kalman Observer Research Articles

Finite-control-set model predictive control of interleaved DC-DC boost converter Based on Kalman observer

A finite control set model predictive control (FCS-MPC) method combining with a Kalman observer is proposed to control an interleaved DC-DC boost converter. The optimal switching control signals are obtained by the FCS-MPC to keep the minimal inductor current error with the advantage of fast calculation. The time delay from sampling is compensated in FCS-MPC. And a Kalman observer is designed to obtain the load variation for model correction, which can diminish the disturbance. Moreover, it can estimate the voltage error and its integration, which is used to dynamically compensate the current reference calculated from power balance equation. In this way, the robustness of the FCS-MPC can be improve. The proposed control method is validated both by simulation and experiment. The results show that compared with PI and ST controllers, the robustness of the proposed approach is improved both in load and input voltage changes. • The converter's discrete time model is built to predict future behavior of the state variables. • Delay compensation strategy is designed to compensate the time delay between the sampling time and switching time. • A Kalman observer is established to compensate the current reference and modify predictive model. • A disturbance suppression method is proposed.

Синтез наблюдателя Калмана системы нелинейного электропривода оптико-механического комплекса

The electric drive of the optical-mechanical complex is considered as a three-mass elastic system. The coefficients of elasticity in this case cannot be measured by the sensor and are not fixed by the operating time of the device. The synthesis of observers using the adaptive extended Kalman filter, estimating variables in a three-mass elastic system, is a necessity in electric drive control systems of the optical-mechanical complex. The mathematical model of the three-mass electric drive system of the optical-mechanical complex is built with taking into account nonlinear elastic factors. The Kalman observer is built in combination vector control system with a permanent magnet synchronous motor. This is an important part before the synthesis of the nonlinear predictive controller for electromechanical drive system of the optical-mechanical complex. Simulation results are executed in the MatLab/Simulink environment.

Kernel representation of Kalman observer and associated H-matrix based discretization

In deterministic estimation, applying a Kalman filter to a dynamical model based on partial differential equations is theoretically seducing but solving the associated Riccati equation leads to a so-called curse of dimensionality for its numerical implementation. In this work, we propose to entirely revisit the theory of Kalman filters for parabolic problems where additional regularity results proves that the Riccati equation solution belongs to the class of Hilbert-Schmidt operators. The regularity of the associated kernel then allows to proceed to the numerical analysis of the Kalman full space-time discretization in adapted norms, hence justifying the implementation of the related Kalman filter numerical algorithm with H-matrices typically developed for integral equations discretization.

A Switching Observer for a Class of Nonuniformly Observable Systems via Singular Time-Rescaling

We present a switching observer for a class of nonuniformly observable systems that are affine in the unmeasured states and nonlinear in the measured output. Using a singular time-rescaling, the dynamics of the estimation error is transformed into that of a bimodal switched linear system. Sufficient conditions that guarantee the observer’s uniform asymptotic stability are provided; these are stated in terms of persistency of excitation and dwell-time of the (output-dependent) time-scaling function evaluated along the trajectories of the system. Unlike most results on switching observers, our approach does not rely on the solution of a set of linear matrix inequalities to compute the observer gain. In addition, we compare our scheme against the Kalman observer in a particular, but meaningful, case-study of observer-based control in automotive systems.

Sensor Selection and State Estimation for Unobservable and Non-Linear System Models.

To comply with the increasing complexity of new mechatronic systems and stricter safety regulations, advanced estimation algorithms are currently undergoing a transformation towards higher model complexity. However, more complex models often face issues regarding the observability and computational effort needed. Moreover, sensor selection is often still conducted pragmatically based on experience and convenience, whereas a more cost-effective approach would be to evaluate the sensor performance based on its effective estimation performance. In this work, a novel estimation and sensor selection approach is presented that is able to stabilise the estimator Riccati equation for unobservable and non-linear system models. This is possible when estimators only target some specific quantities of interest that do not necessarily depend on all system states. An Extended Kalman Filter-based estimation framework is proposed where the Riccati equation is projected onto an observable subspace based on a Singular Value Decomposition (SVD) of the Kalman observability matrix. Furthermore, a sensor selection methodology is proposed, which ranks the possible sensors according to their estimation performance, as evaluated by the error covariance of the quantities of interest. This allows evaluating the performance of a sensor set without the need for costly test campaigns. Finally, the proposed methods are evaluated on a numerical example, as well as an automotive experimental validation case.

Kalman observers in estimating the states of chaotic neurons for image encryption under MQTT for IoT protocol

Kalman observers in estimating the states of chaotic neurons for image encryption under MQTT for IoT protocol

Estimation of Vehicle Longitudinal Speed Based on Improved Kalman Filter

Estimation of vehicle longitudinal acceleration is very important in vehicle active safety control system. In this paper, two driving conditions of a 4WD off-road vehicle are divided by vehicle signals such as steering angle. Under different working conditions, different estimation algorithms are adopted. In the straight driving condition, the longitudinal speed was estimated by adjusting the variance weight of acceleration Kalman observation noise based on kinematics method. For steering conditions, in order to obtain the longitudinal velocity at the center of mass, by dynamic method, a lateral state estimator was designed and tire sideslip dynamics was modeled. The CarSim-Simulink co-simulation results show that the proposed algorithm has high accuracy and strong practicability.

Kalman Observer Contribution to a Second Order Sliding Mode Control for Wind Turbine Based on DFIG During the Network Voltage Dip

Kalman Observer Contribution to a Second Order Sliding Mode Control for Wind Turbine Based on DFIG During the Network Voltage Dip

Online diagnosis of supercapacitors using extended Kalman filter combined with PID corrector

<span>Supercapacitors are electrical energy storage devices with a high specific power density, a long cycle life and a good efficiency, which make them attractive alternative storage devices for various applications. However, supercapacitors are subject to a progressive degradation of their perfor-mance because of aging phenomenon. Therefore, it is very important to be able to estimate their State-of-Health during operation. Electrochemical Impedance Spectroscopy (EIS) is a very recog-nized technique to determine supercapacitors’ state-of-health. However, it requires the interrup-tion of system operation and thus cannot be performed in real time (online). In this paper, a new online identification method is proposed based on extended Kalman observer combined with a complementary PID corrector. The proposed method allows to accurately estimating supercapacitor resistance and capacitance, which are the main indicators of supercapacitor state-of-health. The new online identification method was applied for two voltage/current profiles using two different supercapacitors. The resistance/capacitance estimated by the new method and the conventional EKF were compared with those obtained by an experimental offline method. In comparison with conventional EKF, the capacitance obtained by the new method is significantly more accurate.</span>

Impulsive adaptive observer design for a class of hybrid ODE–PDE cascade systems with uncertain parameters

In this paper, an impulsive adaptive observer is proposed for online estimates of a class of hybrid cascade systems with uncertain parameters. The hybrid cascade system is formed by an ordinary differential equation (ODE) coupled with a partial differential equation (PDE) with uncertain parameters. In the hybrid cascade system, the state of the connection point between the two subsystems cannot be directly available, which makes it difficult to obtain online estimates of the inaccessible states. To deal with the complex observation problem, an impulsive adaptive observer is designed using the backstepping approach and the extended Kalman observer. In addition, the convergence of the proposed observer is examined. The backstepping transformation plays a crucial role in the convergence proof. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.

Hybrid Learning Approach to Sensor Fault Detection with Flight Test Data

Data-driven algorithms are developed to fully automate sensor fault detection in systems governed by underlying physics, with a particular focus on the flight test setting. The proposed machine learning method uses a time series of typical behavior to approximate the evolution of measurements of interest by a linear time-invariant system. Given additional data from related sensors, a Kalman observer is used to maintain a separate real-time estimate of the measurement of interest. Sustained deviation between the measurements and the estimate is used to detect anomalous behavior. A decision tree, informed by integrating other sensor measurement values, is used to determine the amount of deviation required to identify a sensor fault. The method is validated by applying it to three test systems exhibiting various types of sensor faults: commercial flight test data, an unsteady aerodynamics model with dynamic stall, and a model for longitudinal flight dynamics forced by atmospheric turbulence. In the latter two cases, fault detection was tested for several prototypical failure modes. The combination of a learned dynamic model with the automated decision tree accurately detects sensor faults in each case.

Leak diagnosis in pipelines based on a Kalman filter for Linear Parameter Varying systems

This paper proposes a new approach for the leak diagnosis problem in pipelines based on the use of a Kalman filter for Linear Parameter Varying (LPV) systems. Such a filter considers the availability of flow and pressure measurements at each end of the pipeline. The proposed methodology relies on an LPV model derived from the nonlinear description of the pipeline. For the Kalman filter design purposes, the LPV model is transformed into a polytopic representation. Then, using such a representation, the LPV Kalman filter is designed by solving a set of Linear Matrix Inequalities (LMIs) offline. In the online implementation, the observer gain is calculated as an interpolation of those gains previously computed at the vertices of the polytopic model. The main advantages of this approach are: a) the embedding of the nonlinearities in the varying parameters allows the quasi-LPV system to be obtained which is equivalent to the original nonlinear one, and; b) the use of the well-known LMIs to compute the Kalman gain allows the extension to the LPV case. Those aspects are the main advantages with respect to the classic design of the Extended Kalman Filter (EKF) that requires a linearization procedure and the solution of the Ricatti equation at each iteration. To illustrate the potential of this method, a test bed plant built at Cinvestav-Guadalajara is used. Additionally, the results presented are compared with those results obtained through the classical EKF showing that LPV Kalman observer outperforms the classical EKF.

Autonomous Vehicles Sideslip Angle Estimation: Single Antenna GNSS/IMU Fusion With Observability Analysis

Taking advantage of available measurement in Internet of Things (IoT) for intelligent transportation systems, a sideslip angle estimation method for autonomous vehicles is presented and experimentally verified by fusing global navigation satellite system (GNSS) and inertial measurement unit (IMU), and by constructing an observability index (OI). The correlation between the vehicle sideslip error and the inertial navigation system (INS) heading error is presented first. Then, the observability for the heading error in a velocity-based Kalman filter is discussed and a novel index is defined to check the observability of the heading error. The course from a single antenna GNSS in an autonomous vehicle is augmented to estimate the heading error when the observability of the heading error is low. To reject the course measurement for scenarios that include sideslip movement, a binary hypothesis test approach is applied to indicate whether the vehicle is sidesliping. In addition, based on the OI and the sideslip indicator, a hybrid feedback strategy is designed for the heading error correction. To improve the convergence rate of the heading error in the velocity-based Kalman filter, a tuning strategy is presented. The stochastical observability of the designed Kalman observer is investigated for known and stochastic initial conditions. Finally, the proposed sideslip angle estimator is experimentally validated through a vehicle test platform in critical driving scenarios. The results confirm that the proposed OI can effectively identify when the heading error is observable, and also corroborate the effectiveness of the hybrid feedback strategy and adaptation method in the Kalman observer.

Bond Graph Modeling and Kalman Filter Observer Design for an Industrial Back-Support Exoskeleton

This paper presents a versatile approach to the synthesis and design of a bond graph model and a Kalman filter observer for an industrial back-support exoskeleton. Actually, the main purpose of developing a bond graph model is to investigate and understand better the system dynamics. On the other hand, the design of the Kalman observer always should be based on a model providing an adequate description of the system dynamics; however, when back-support exoskeletons are considered, the synthesis of a state observer becomes very challenging, since only nonlinear models may be adopted to reproduce the system dynamic response with adequate accuracy. The dynamic modeling of the exoskeleton robotic platform, used in this work, comprises an electrical brushless DC motor, gearbox transmission, torque sensor and human trunk (biomechanical model). On this basis, a block diagram model of the dynamic system is presented and an experimental test has been carried out for identifying the system parameters accordingly. Both the block diagram and bond graph dynamic models are simulated via MATLAB and 20-sim software (bond graph simulation software) respectively. Furthermore, the possibility of employing the Kalman filter observer together with a suitable linear model is investigated. Subsequently, the performance of the proposed Kalman observer is evaluated in a lifting task scenario with the use of a linear quadratic regulator (LQR) controller with double integral action. Finally, the most important simulation results are presented and discussed.

Continuous model predictive control of interleaved boost converter with current compensation

An interleaved DC–DC boost converter is widely used in DC power systems such as fuel cell systems or other systems requiring high-power quality for increasing and stabilising the output voltage. The performance of the converter can be affected by the control strategy. In this study, a robustness continuous control set model predictive control (CCS-MPC) for an interleaved DC–DC boost converter is proposed to achieve optimised transient dynamics and steady performance. To deal with unknown load variation and systems uncertainties, an extended Kalman observer is designed to estimate the lumped disturbance, including the load variation and unmodelled part. Based on the disturbance estimation, a dynamic current reference with the disturbance and the integrated voltage error is formulated for the optimal voltage tracking. Also, a prediction-accuracy-enhanced CCS-MPC for a wide range of operation points and multi-parameter disturbance is obtained. The proposed approach could stabilise the output voltage with good robustness under external disturbance and operation point change. Compared with other existing controllers, i.e. a proportional–integral controller, a sliding mode controller, and a finite control set model predictive controller, both the steady and transient performances are validated by a simulation and experimental test bench.

Improved nonlinear observable degree analysis using data fusion

For nonlinear Kalman filtering, process noise and observation noise affect the accuracy of system filtering, and filtering accuracy is related to observable degree. That is, the calculation of observable degree will be affected by process noise and observation noise. Traditional solutions for observable degree of nonlinear systems do not take noise into account. In this paper, the observable degree theory is solved by using the Cramer-Rao Lower Bound and the Lie derivative in differential geometry theory. The process noise and the observation noise are taken into account in the calculation matrix of the nonlinear observable degree. The paper proposes a new method based on condition number fusion. The iterative algorithm is used to make the condition number of the fused matrix reach the minimum value. In the result, the error of observable degree calculation can be reduced. The validity of the proposed method is verified by simulation, and the calculation theory of nonlinear observable degree is improved.

On the convergence of the unscented Kalman filter

A convergence analysis of the modified unscented Kalman filter (UKF), used as an observer for a class of nonlinear deterministic continuous time systems, is presented. Under certain conditions, the extended Kalman filter (EKF) is an exponential observer for non-linear systems, i.e., the dynamics of the estimation error is exponentially stable. It is shown that unlike the EKF, the UKF is not an exponentially converging observer. A modification of the UKF – the unscented Kalman observer – is proposed, which is a better candidate for an observer.This paper is a first step towards a proof of the global convergence of the high-gain version of the UKO.

A multiobjective optimization approach for linear quadratic Gaussian/loop transfer recovery design

SummaryThis article bestows the linear quadratic Gaussian (LQG)/Loop Transfer Recovery (LTR) optimal controller design for a perturbed linear system having insufficient information about systems states through a multiobjective optimization approach. A Kalman filter observer is required to estimate the unknown states at the output from the noisy data. However, the main downside of the LQG controller's is that its robustness cannot be guaranteed because it consists of linear quadratic regulator (LQR) and Kalman observer, and due to observer incorporation within the LQR framework results in loss of robustness which is undesirable. Therefore, it is necessary to recover the robustness by tuning the controller which further plays havoc with system performance and control effort for certain plants. The present work addresses the investigation of the trade‐off between multiobjective indexes (formulated on the basis of robustness, optimal control, and performances) through three multiobjective optimization algorithms as NSGA‐II, multiobjective simulated annealing and multiobjective particle swarm optimization. The tuned parameters meet the competitive multiobjective performance indexes that are verified through simulation results. The Pareto front with multiple solutions helps to design a robust controller depending on the weightage given to the respective performance indexes. Simulation results reveal that the proposed multiobjective control strategy helps in recovering the characteristics of LQG/LTR.

Diagnosis of Lithium Ion Batteries for Power Electronic Applications

This poster presents a lithium ion battery State-of-charge (SOC) and the capacity estimation technique for electric vehicle applications. The proposed strategy achieves online parameter estimation by making use of adaptive control theory and Kalman observer. The convergence and stability are guaranteed by Lyapunov’s direct method. The estimation strategy takes into account the surface temperature variation. Experiments have been carried-out under different operating temperature conditions and various discharge currents. The effectiveness of the proposed method is verified by experiments for different aging states.State-of-Health (SOH) is an important aspect in Battery Management Systems (BMS) since it is considered, as the battery’s energy. Therefore, bad SOH estimation ultimately results in damaging the battery and reducing its lifespan. Similar to other chemical-based energy storage systems, the battery’s use generates irreversible physical and chemical changes and hence, its performance tends to deteriorate gradually over its lifetime. Several studies have been presented for lithium-ion battery calendar aging and show an internal resistance increase and a capacity decrease. So, the definition of the End-of-Life (EoL) of the battery depends on these aging indicators. The limit is generally set to 80% of the nominal capacity.In our case, the cells are prepared at different State-of-Charge (SOC) values and stressed with different temperatures. The cell parameters as the internal resistance and the capacity are measured periodically with well-defined discharge conditions. In this study, a 20Ah, 3.2V Lithium iron phosphate battery, LiFePO4, is used in the experiments. The battery is characterized, initially and after each aging phase, at different constant currents and at different operating temperatures.In order to study the evolution of the OCV-SOC characterization during the battery lifetime, we have compared the OCV-SOC characterization for different aging states. The results shown that the different between the OCV-SOC estimation and measured is negligible from one aging state to another.Using the experimental protocol results for a constant current, the internal resistance and the capacity evolution for different currents and the different operating temperatures are measured and estimated, and compared.Conclusion : In this study, an online SoC and SOH estimation method is presented for lithium-ion batteries. The proposed strategy capitalizes on the capabilities of Kalman filtering for the design of an extended Kalman observer to estimate SOC. Moreover, the adaptive estimation technique achieves online robust SoH estimation. Unlike other methods, this paper presents an online diagnosis method considering the surface temperature variation of the battery. Moreover, only voltage, current and temperature measurements are required, which reduces the number of sensors compared to other methods. The effectiveness of the proposed online observer is shown through a set of experiments. Results highlight its good performance in parameters estimation for different conditions of operating temperature, discharging current and battery lifetime.

DSP in the Loop Implementation of Sliding Mode and Super Twisting Sliding Mode Controllers Combined with an Extended Kalman Observer for Wind Energy System Involving a DFIG

This paper presents the conception and the implementation of a robust non-linear control technique on a TMS320F28335 Digital Signal Processor as Hardware in the Loop (HIL). The control law is a sliding mode controller (SMC), synthesized in order to optimize, via back-to-back power converters, the output power of a grid-connected doubly fed induction generator. Besides, the Maximum Power Point Tracking strategy to extract the optimal electromagnetic torque is designed by combining an extended Kalman observer, in order to estimate the mechanical torque, and a super twisting sliding mode controller (STSMC). The performance of the proposed strategy is compared to the one of the conventional Proportional-Integral (PI) controller under the same scenario. The results of the DSP in the Loop implementation present the best performances in terms of setpoint tracking, speed response, and robustness concerning sudden variations in the generator parameters.