Hamed H. Afshari

Gaussian filters for parameter and state estimation

Real-time control systems rely on reliable estimates of states and parameters in order to provide accurate and safe control of electro-mechanical systems. The task of extracting state and parametric values from systems partial measurements is referred to as state and parameter estimation. The main goal is minimizing the estimation error as well as maintaining robustness against the noise and modeling uncertainties. The development of estimation techniques spans over five centuries, and involves a large number of contributors from a variety of fields. This paper presents a tutorial on the main Gaussian filters that are used for state estimation of stochastic dynamic systems. The main concept of state estimation is firstly described based on the Bayesian paradigm and Gaussian assumption of the noise. The filters are then categorized into several groups based on their applications for state estimation. These groups involve linear optimal filtering, nonlinear filtering, adaptive filtering, and robust filtering. New advances and trends relevant to each technique are addressed and discussed in detail.

Robust fault diagnosis of an electro-hydrostatic actuator using the Novel dynamic second-order SVSF and IMM strategy

This paper introduces a new robust fault detection and identification (FDI) structure applied to an electro-hydrostatic actuator (EHA) experimental setup. This FDI structure consists of the dynamic second-order smooth variable structure filter (Dynamic second-SVSF) and the interacting multiple model (IMM) strategy. The dynamic second-order smooth variable structure filter (SVSF) is a new robust-state estimation method that benefits from the robustness and chattering suppression properties of second-order sliding mode systems. It produces robust-state estimation by preserving the first and second-order sliding conditions such that the measurement error and its first difference are pushed towards zero. Moreover, the EHA prototype works under two different operational regimes that are the normal EHA mode and the faulty EHA mode. The faulty EHA setup contains two types of faults, namely friction and internal leakage. The FDI structure contains a bank of dynamic second-order SVSFs estimating state variables based on these models. The IMM strategy combines these filters in parallel and determines the particular operating regime based on the system models and the input-output data. Experimental results demonstrate superior performance in terms of accuracy, robustness, and smoothness of state estimates.

Modeling, parameterization, and state of charge estimation of Li-Ion cells using a circuit model

This paper presents a general procedure applied for modeling, parameter identification, and state of charge (SOC) estimation of a Li-Ion battery cell. The paper explains a battery tester with a number of experiments conducted to investigate the cell physical properties. Dynamics of the Li-Ion cell are modeled using an equivalent circuit model, whereas parameters of the model are calculated using particle swarm optimization. This method minimizes the output error that is the difference between the simulated output from the model and the measured terminal voltage. The provided equivalent circuit model with optimized parameters was used for SOC estimation. Two different state estimation methods have been applied to estimate the cell SOC based on real-time measurements. The estimation methods include the extended Kalman filter (EKF), and the novel smooth variable structure filter (SVSF). The SVSF method was used as it can produce more accurate state estimates for dynamic systems with modeling and parametric uncertainties. This paper compares the performance of these two estimators for real-time SOC estimation using tester data.

A nonlinear second-order filtering strategy for state estimation of uncertain systems

Abstract In this paper, a new strategy referred to as the nonlinear second-order (NSO) filter is presented and used for estimation of linear and nonlinear systems in the presence of uncertainties. Similar to the popular Kalman filter estimation strategy, the proposed strategy is model-based and formulated as a predictor-corrector. The NSO filter is based on variable structure theory that utilizes a switching term and gain that ensures some level of estimation stability. It offers improvements in terms of robustness to modeling uncertainties and errors. The proof of stability is derived based on Lyapunov that demonstrates convergence of estimates towards the true state values. The proposed filtering strategy is based on a second-order Markov process that utilizes information from the current and past two time steps. An experimental system was setup and characterized in order to demonstrate the proposed filtering strategys performance. The strategy was compared with the popular Kalman filter (and its nonlinear form) and the smooth variable structure filter (SVSF). Experimental results demonstrate that the proposed nonlinear second-order filter provides improvements in terms of state estimation accuracy and robustness to modeling uncertainties and external disturbances.

A Review of Smooth Variable Structure Filters: Recent Advances in Theory and Applications

The smooth variable structure filter (SVSF) is a relatively new state and parameter estimation technique. Introduced in 2007, it is based on the sliding mode concept, and is formulated in a predictor-corrector fashion. The main advantages of the SVSF, over other estimation methods, are robustness to modeling errors and uncertainties, and its ability to detect system changes. Recent developments have looked at improving the SVSF from its original form. This review paper provides an overview of the SVSF, and summarizes the main advances in its theory.Copyright

Dynamic analysis of a Li-Iron Phosphate cell using the electro-chemical modelling approach

Accurate modeling of batteries has an important and challenging role in battery management systems. In this paper, dynamics of a Li-Iron Phosphate (LiFePO4) cell are simulated using an electro-chemical model. This model was obtained by simplifying a full-order electro-chemical model into the single particle model. In the single particle model the diffusion of lithium inside each electrode is modeled assuming that each electrode is a single particle. This model is then parameterized using input-output data captured from a battery test setup and by applying the genetic algorithm for optimization. The genetic algorithm calculates numeric values of parameters by minimizing the error that is the difference between the measured terminal voltage and simulated one obtained by the electro-chemical model. Dynamics of the (LiFePO4) cell are then investigated in order to determine the state of charge (SOC) of the cell over time.

Development of a sliding mode controller and higher-order structure-based estimator

Accurate and robust control methodologies are critical to the reliable and safe operation of engineering systems. Sliding mode control (SMC) is a form of variable structure control and is regarded as one of the most effective nonlinear robust control approaches. The control law is designed so that the system state trajectories are forced towards the sliding surface and stays within a region of it. The switching gain in the control signal brings an inherent amount of stability to the control process. However, the controller is only as effective as the knowledge of critical system states and parameters. Estimation strategies, such as the Kalman filter or the smooth variable structure filter (SVSF), may be employed to improve the quality of the state estimates used by control methods. A recently developed SVSF formulation, referred to as the second-order SVSF, offers robustness and chattering suppression properties of second-order sliding mode systems. It produces robust state estimation by preserving the first- and second-order sliding conditions such that the measurement error and its first difference are pushed towards zero. This paper aims to combine the SMC with the second-order SVSF in an effort to develop and offer an improved control strategy. It is proposed that this controller will offer an improvement in terms of controller accuracy without affecting its inherent stability and robustness. An electro hydrostatic actuator will be used for proof of concept, and future work will extend the application to automotive power trains.

State estimation of a faulty actuator using the second-order smooth variable structure filter (The 2 ND -order SVSF)

This paper presents the application of the new developed second-order Smooth Variable Structure Filter, 2nd-order SVSF, for fault detection under uncertain conditions. The 2nd-order SVSF is a novel modelbased state estimation method formulated in a predictor-corrector form. It produces robust state estimation under uncertain conditions, while decreasing the measurement error and its difference, at the same time. The stability of the 2nd-order SVSF is proven using the Lyapunovs stability criterion with the given bounded noise and modeling uncertainties. The corrective gain of the filter is pushing the measurement error and its difference toward zero. This results in providing higher degrees of accuracy, robustness and smoothness in state estimation under uncertain situations. Due to the robust performance of the 2nd-order SVSF for state estimation, it applies to an experimental setup of an Electro-Hydrostatic Actuator (EHA) for fault detection. Experimentation are performed for the EHA setup under the normal and faulty conditions. For the faulty EHA setup, there exists a major friction condition in the EHAs cylinders. The robustness of the new developed 2nd-order SVSF is then verified by comparing its performance with the state-of-the-art filters including the Kalman Filter (KF) and the 1st-order SVSF.

Robustness comparison of some state estimation methods with an explicit consideration of modeling uncertainties

This paper presents a comparative analysis of well-known state estimation methods that are commonly used in real systems. The aim of this research is to measure and then evaluate the robustness (i.e., a measure of performance when a small and deliberate changes are made to the method conditions) of these methods against modeling uncertainties. The state estimation methods include the Kalman Filter, the 1st-Order Smooth Variable Structure Filter (1st-order SVSF), and the new developed Dynamic 2nd-Order SVSF. A relatively new performance robustness criterion (so-called robustness index) is adopted in this work to first measure the robustness of the estimation methods, and then, evaluate their performance. The robustness index is calculated for each method when modeling uncertainties are explicitly considered. Simulation analysis is performed using the linear model of an Electro-Hydrostatic Actuator (EHA) setup under the normal and uncertain conditions. Simulation results showed the superior performance of the Dynamic 2nd-Order SVSF over other methods in terms of robustness against modeling uncertainties.

Condition Monitoring of an Electro-Hydrostatic Actuator Using the Dynamic 2nd-Order Smooth Variable Structure Filter

This paper introduces the dynamic 2nd-order Smooth Variable Structure Filter (Dynamic 2nd-order SVSF) method for the purpose of robust state estimation. Thereafter, it presents an application of this method for condition monitoring of an electro-hydrostatic actuator system. The SVSF-type filtering is in general designed based on the sliding mode theory; whereas the sliding mode variable is equal to the innovation (measurement error). In order to formulate the dynamic 2nd-order SVSF, a dynamic sliding mode manifold is defined such that it preserves the first and second order sliding conditions. This causes that the measurement error and its first difference are pushed toward zero until reaching the existence subspace. Hence, this filter benefits from the robustness and chattering suppression properties of the second order sliding mode systems. These help the filter to suppress the undesirable chattering effects without the need for approximation or interpolation that however reduces accuracy and robustness of the SVSF-type filtering. In order to investigate the performance of the dynamic 2nd-order SVSF for state estimation, it applies to an Electro-Hydrostatic Actuator (EHA) system under the normal and uncertain scenarios. Simulation results are then compared with ones obtained by other estimation methods such as the Kalman filter and the 1st-order SVSF method.Copyright