Nonlinear Adaptive Observer Research Articles

Fault tolerant control for a class of nonlinear non-Gaussian singular stochastic distribution systems

New fault diagnosis and active fault tolerant control (FTC) algorithms are proposed for a class of nonlinear singular stochastic distribution control (SDC) systems in this paper. Different from general SDC systems, in singular SDC systems, the relationship between the weights and the control input is expressed by a singular state space model, which increases the difficulty in design of fault diagnosis and fault tolerant control. A non-singular state transformation is made to transform the singular dynamic system into a differential-algebraic system. An adaptive nonlinear observer is designed to estimate the size of the fault occurring in the system. Furthermore, the linear matrix inequality (LMI) approach is applied to establish sufficient conditions for the existence of the observer. Based on the estimated fault information, the active fault tolerant controller is designed to make the post-fault probability density function (PDF) still track the given distribution. At last, an illustrated example is given to demonstrate the effectiveness of the proposed algorithm, and satisfactory results have been obtained.

Fault tolerant control for a class of nonlinear non-Gaussian singular stochastic distribution systems

New fault diagnosis and active fault tolerant control (FTC) algorithms are proposed for a class of nonlinear singular stochastic distribution control (SDC) systems in this paper. Different from general SDC systems, in singular SDC systems, the relationship between the weights and the control input is expressed by a singular state space model, which increases the difficulty in design of fault diagnosis and fault tolerant control. A non-singular state transformation is made to transform the singular dynamic system into a differential-algebraic system. An adaptive nonlinear observer is designed to estimate the size of the fault occurring in the system. Furthermore, the linear matrix inequality (LMI) approach is applied to establish sufficient conditions for the existence of the observer. Based on the estimated fault information, the active fault tolerant controller is designed to make the post-fault probability density function (PDF) still track the given distribution. At last, an illustrated example is given to demonstrate the effectiveness of the proposed algorithm, and satisfactory results have been obtained.

Adaptive Backstepping-Flatness Control Based on an Adaptive State Observer for a Torque Tracking Electrohydraulic System

In practical applications, electrohydraulic servo systems (EHSSs) are known to be highly nonlinear. On account of high cost, space limitation, technical matters, etc., some of the state variables of the EHSS cannot be measured. Moreover, it is common that some of the physical parameters are uncertain. To the authors’ knowledge, it is difficult to design a controller to achieve high trajectory-tracking precision in a wide frequency range for the nonlinear EHSS with unmeasurable state variables and uncertain parameters based on a single control method, and few articles are available for this problem, thus this paper proposes a compound controller: a nonlinear adaptive backstepping-flatness controller based on a nonlinear adaptive state observer. The observer is designed for highly precise state estimations in presence of nonlinear dynamics and uncertain parameters. The flatness method is originally applied to deal with the system with estimated state variables and parameters. Based on the observer, with integration of the backstepping method and the flatness method, the proposed controller is designed with lower design complexity and fewer feedback variable derivatives that ensure the proposed controller is easy to follow for control engineers and can help to avoid serious input voltage saturation. Simulation results show effectiveness of the proposed controller; furthermore, this paper shows how to implement the proposed controller on a torque tracking EHSS prototype and experimental results demonstrate its effectiveness as the results are compared with that of three previously reported controllers.

Adaptive observer-based synchronization of two non-identical chaotic systems with unknown parameters

In this study, adaptive observer-based synchronization of chaotic systems is considered. The master and slaves systems have different dynamics and it is assumed that the master system parameters are unknown while its states are available. First, it is assumed that the slave system parameters are known but its states are not completely available. It is shown that an observer for the slave system can be designed and applied for the purpose of synchronization. Based on a Lyapunov function, an adaptive law for master parameters estimation and a control law for the synchronization goal are extracted. Stability of the entire system including the observer dynamics has been proved. Further, it is assumed that the parameters of both master and slave systems are unknown. For this case, an adaptive nonlinear observer is designed to estimate the slave system states and two adaptive laws for estimating the unknown parameters are proposed. In addition, a proper control law to achieve the synchronization goal has been suggested, and the stability of the closed-loop system is established. Finally, the effectiveness of the proposed synchronization method is shown via simulation results.

An Adaptive Observer for Recirculation-Based Solid Oxide Fuel Cells

In this paper, we present an observer design for online estimation of species concentrations in recirculation-based solid oxide fuel cell (SOFC) systems with integrated reformers. For the system considered, on-board reforming of methane results in mixture of several species of different concentrations along the fuel path. The presence of a fuel reformer gives way to coupling of system equations, in turn, increasing species interactions and complexity of the state equations. The knowledge of concentration of species at key locations in the fuel cell can help prevent cell damage and improve longevity. In this regard, the use of sensors to determine species concentration is an invasive process which is expensive to both utilize and maintain. While existing observers are designed either for chemical reactors or for a fuel cell exclusively, the proposed strategy aims to improve on that by considering a combined reformer and fuel cell and designing a nonlinear adaptive observer using readily measured concentrations and selected variables. For estimating certain critical indicators, such as fuel utilization, state transformations have been used in the design to obtain a more versatile and computationally efficient reduced order observer. The study develops detailed stability analysis of the observers and quantifies the effect of uncertainties on observer performance.

Simultaneous fault diagnosis for robot manipulators with actuator and sensor faults

This paper studies a model-based fault detection and isolation (FDI) scheme for robot manipulators with actuator and sensor faults. Without adding redundant joint sensor measurements, the multiple faults simultaneously occurring in the actuators and sensors of the manipulator are detected, estimated and isolated. Considering Lipschitz-like nonlinearities and modeling uncertainties, a nonlinear adaptive observer is presented to estimate the faulty parameters with a pre-specified estimation error bound. The performances of the proposed FD scheme, including the robustness of observers to the uncertainties, the accuracy of fault estimation and the rapidity of fault diagnosis, are rigorously analyzed. The proposed approach is verified by a simulation of Integrated Motion Inc. (IMI) two-link, revolute, direct-drive robot manipulator.

Robust adaptive nonlinear observer design via multi-time scales neural network

This paper deals with the robust adaptive observer design for nonlinear dynamic systems that have an underlying multiple time-scales structure via different time-scales neural network. The Lyapunov function method is used to develop a novel stable updating law for the multi-time scales neural networks model and prove that the state error, output estimation error and the neural network weights errors are all uniformly ultimately bounded around the zero point during the entire learning process. Furthermore, passivity-based approach is used to derive the robust property of the proposed multi-time scales neural networks observer. Compared with the other nonlinear observers without considering the time scales, the proposed observer demonstrates faster convergence and more accurate properties. Two examples are presented confirming the validity of the above approach.

Experimental validation of an actuator fault tolerant control system using virtual sensor: Application in a double pipe heat exchanger

This work presents an actuator fault tolerant control (FTC) system applied in a counter-current double pipe heat exchanger. The heat exchanger has two input variables which are, cold and hot water flow rates. The main actuator manipulates the cold water flow rate in order to control the hot water temperature. The goal of this work is to keep in continuous operation the counter-current double pipe heat exchanger, even if the main actuator is stuck-open. In case of failure on the main actuator, it is proposed to control the process with the second input variable (by manipulating the hot water flow rate). To achieve our aim, we designed an FTC system based in a fault detection and isolation (FDI) system and a Model Following Control (MFC). To develop the FDI system an adaptive nonlinear observer to estimate the flow rates in the heat exchanger for both streams (hot and cold) was implemented. The FDI is performed by the comparison between the flow rate estimation (by the adaptive nonlinear observer) and the flow rate provided by the control law. The nonlinear flow rate estimation is needed because the real plant does not have digital flowmeters to measure the flow rates online. The FDI system allows to detect and isolate the fault actuator then, the control signal and the failure accommodation is realized by the MFC. The results showed that it is possible to keep the heat exchanger in continuous operation even if the main actuator is stuck-open.

Nonlinear Adaptive Observer for a Lithium-Ion Battery Cell Based on Coupled Electrochemical–Thermal Model

Real-time estimation of battery internal states and physical parameters is of the utmost importance for intelligent battery management systems (BMS). Electrochemical models, derived from the principles of electrochemistry, are arguably more accurate in capturing the physical mechanism of the battery cells than their counterpart data-driven or equivalent circuit models (ECM). Moreover, the electrochemical phenomena inside the battery cells are coupled with the thermal dynamics of the cells. Therefore, consideration of the coupling between electrochemical and thermal dynamics inside the battery cell can be potentially advantageous for improving the accuracy of the estimation. In this paper, a nonlinear adaptive observer scheme is developed based on a coupled electrochemical–thermal model of a Li-ion battery cell. The proposed adaptive observer scheme estimates the distributed Li-ion concentration and temperature states inside the electrode, and some of the electrochemical model parameters, simultaneously. These states and parameters determine the state of charge (SOC) and state of health (SOH) of the battery cell. The adaptive scheme is split into two separate but coupled observers, which simplifies the design and gain tuning procedures. The design relies on a Lyapunov's stability analysis of the observers, which guarantees the convergence of the combined state-parameter estimates. To validate the effectiveness of the scheme, both simulation and experimental studies are performed. The results show that the adaptive scheme is able to estimate the desired variables with reasonable accuracy. Finally, some scenarios are described where the performance of the scheme degrades.

Gradient and Mass Estimation from CAN Based Data for a Light Passenger Car

We present a method for the estimation of vehicle mass and road gradient for a light passenger vehicle. The estimation method uses information normally available on the vehicle CAN bus without the addition of extra sensors. A composite parameter estimation algorithm incorporating a nonlinear adaptive observer structure uses vehicle speed over ground and driving torque to estimate mass and road gradient. A system of filters is used to avoid deriving acceleration directly from wheel speed. In addition, a novel data fusion method makes use of the regressor structure to introduce information from other sensors in the vehicle. The dynamics of the additional sensors must be able to be parameterised using the same parameterisation as the complete vehicle system dynamics. In this case we make use of an Inertial Measurement Unit (IMU) which is part of the vehicle safety and Advanced Driver Assist Systems (ADAS). Therefore, a method using some filtering and supervisory logic is employed to give a sensible update behaviour for the vehicle mass estimation algorithm. The main function of the supervisor is to reject the mass estimate produced by unsuitable available data due to unmodelled loss forces. Good estimation results are obtained from data from a vehicle which was also fitted with some additional instrumentation including GPS sensors and a high quality IMU for scientific verification purposes.

Analytical redundancy based fault diagnosis scheme for satellite attitude control systems

This paper presents an integrated fault detection and diagnosis (FDD) scheme based on analytical redundancy for satellite attitude control systems (ACS). The faults of actuators, angular rate sensors and attitude sensors are all taken into account, and the nonlinear ACS considered is subject to both space disturbance torques and sensor uncertainties. The proposed scheme is developed in two phases. In the first phase, two nonlinear observers are designed, and based on the proposed strategy which called observer redundancy the fault source (actuators, angular rate sensors or attitude sensors) can be verified. In the second phase, two banks of fault isolation observers (FIOs) activated by the previous detection results are designed to perform the diagnosis within the fault part. The first bank of FIOs are obtained based on nonlinear unknown input observers to isolate the fault actuator and the second bank of FIOs are obtained based on nonlinear adaptive observers to isolate and estimate the fault of angular rate sensor. The effectiveness of the proposed scheme is simulated on a closed-loop satellite attitude control system with some typical faults of these components.

Adaptive-gain observer-based control of a class of time-delay systems subject to output-slope non-linearities

A non-linear adaptive observer is proposed to estimate the unmeasured states of a class of time-delay non-linear systems. Irrespective of the size of the constant delay, it is shown that the observer is globally convergent if the growth rate of the system non-linearities is output dependent. The presented results generalize previous results on observation of Lipschitz time-delay systems. Subsequently, the observerbased control problem of time-delay systems, having triangular structure, is discussed for arbitrary large constant delay.

An Adaptive Nonlinear Extended State Observer for the Sensorless Speed Control of a PMSM

This paper presents a sensorless speed control strategy for a permanent-magnet synchronous motor (PMSM) based on an adaptive nonlinear extended state observer (ANLESO). In this paper, an extended state observer (ESO), which takes back-EMF (back electromotive force) as an extended state, is used to estimate the rotor position and the rotor speed because of its simpler structure and higher accuracy. Both linear ESO (LESO) and nonlinear ESO (NLESO) are considered to estimate the back-EMF of PMSM, and NLESO is finally implemented due to its obvious advantage in convergence. The convergence characteristics of the estimation error of the observer are analyzed by the Lyapunov theory. In order to take both stability and steady-state error into consideration, an adaptive NLESO is proposed, which adaptively adjusts the parameters of NLESO to a compromised value. The performance of the proposed method was demonstrated by simulations and experiments.

Evaluation of Lyapunov-based Adaptive Observer using Low-Order Lumped Model for Estimation of Production Index in Under-balanced Drilling

A distributed drift-flux model and a low-order lumped model describing a multiphase (gas-liquid) flow in the well during Under-Balanced Drilling (UBD) has been presented. This paper presents a novel nonlinear adaptive observer to estimate the total mass of gas and liquid in the annulus and production constant of gas and liquid from the reservoir into the well during UBD operations. Furthermore, it describes a joint unscented Kalman filter to estimate parameters and states for both the distributed drift-flux and lumped model by using real-time measurements of the choke and the bottom-hole pressures. The performance of the adaptive observers are evaluated for typical drilling scenarios. The results show that all adaptive observers are capable of identifying the production index, although the adaptive observers based on the low-order lumped model achieves better convergence rate than adaptive observer based on the drift-flux model. The results show that the LOL model is sufficient for the purpose of estimating the production parameters.

Adaptive Tuning Functions Tracking Control with Nonlinear Adaptive Observers

Abstract The paper is dedicated to the derivation of a unified approach for nonlinear adaptive closed loop system design with nonlinear adaptive state and parameter observers combined with tuning functions-based nonlinear adaptive control for trajectory tracking. The proposed approach guarantees asymptotic stability of the closed loop nonlinear adaptive system with respect to the tracking and state estimation errors and Lyapunov stability of the parameter estimator. The advantages of the approach are the lack of over-parametrization, resulting in a minimal number of estimator equations and the preservation of the overdamped performance specifications of the closed loop nonlinear adaptive system in its whole range of operation. The application of the approach to a permanent magnet synchronous motor driven inverted pendulum concludes with simulation of the closed loop nonlinear adaptive system time responses.

Fuzzy adaptive output feedback control for robotic systems based on fuzzy adaptive observer

In this paper, a fuzzy adaptive output feedback control scheme based on fuzzy adaptive observer is proposed to control robotic systems with parameter uncertainties and external disturbances. It is supposed that only the joint positions of the robotic system can be measured, whereas the joint velocities are unknown and unmeasured. First, a fuzzy adaptive nonlinear observer is presented to estimate the joint velocities of robotic systems, and the observation errors are analyzed using strictly positive real approach and Lyapunov stability theory. Next, based on the observed joint velocities, a fuzzy adaptive output feedback controller is developed to guarantee stability of closed-loop system and achieve a certain tracking performance. Based on the Lyapunov stability theorem, it is proved that all the signals in closed-loop system are bounded. Finally, simulation examples on a two-link robotic manipulator are presented to show the efficiency of the proposed method.

Adaptive Estimation and Control Algorithms for Certain Independent Control Axis Misalignments

Actuators are often assumed to be perfectly aligned when designing for a stable closed-loop system. In practice, small actuator misalignments can cause the system to perform poorly, or worse, become unstable. Consequently, adaptive observers can be introduced that build online estimates for the unknown misalignments and recover closed-loop stability. In this paper, the problem where the control axes are independently misaligned in three dimensions is considered. A study of the problem indicates a fundamental geometric difference between in-plane and out-of-plane misalignments. Accordingly, special attention is paid to the case where two axes are independently misaligned. New nonlinear adaptive observers are introduced for both the in-plane and out-of-plane problems that guarantee that the misalignment axis estimates remain unit vectors. Furthermore, a Lyapunov-like stability analysis is performed to show convergence of the misalignment estimates to their true values for a wide range of misalignment angles. In addition, a novel control system is developed for a representative dynamic system containing the aforementioned actuator misalignments that ensures perfect asymptotic tracking of prescribed reference trajectories. Also, an axis decoupling method is described that helps alleviate some of the inherent issues in the estimation problem. Detailed proofs and numerical simulations are presented to help illustrate the technical aspects of the work.

Simultaneous estimation of states and inputs in a planar solid oxide fuel cell using nonlinear adaptive observer design

An adaptive nonlinear observer design for the planar solid oxide fuel cell (SOFC) is presented in this work. This observer is based on a lumped parameter model of the SOFC and it can simultaneously estimate the inputs and the states of the system. Considering the inputs as unknown parameters is advantageous because some of the input parameters are not practically measurable in a SOFC stack. The asymptotic stability of the proposed observer is proven using the Lyapunov function method and is based on the concept of input-to-state stability for cascaded systems. The simulations show that the developed observer can track the temperature and species concentration profiles in the planar SOFC during step changes in the input variables and can simultaneously predict the input variables. The adaptive observer presented is valid for a wide operating range, requires fewer variables to be measured, and is robust to fluctuations in the input variables.

UAV guidance using a monocular-vision sensor for aerial target tracking

Target tracking is difficult for a Unmanned Aerial Vehicle (UAV) equipped with a monocular-vision sensor because the sensor cannot measure the range between aerial target and UAV. Since the range between UAV and target is unobservable, the target position is also unknown. A measurement model of the vision sensor is proposed based on a specific image processing technique. A nonlinear adaptive observer is designed to estimate states and parameters, and the position of the target is estimated. A guidance law for target tracking and UAV maneuvers for persistent excitation condition are also proposed. To demonstrate the effectiveness of the proposed algorithms, numerical simulations are performed.

A Neural-Network-Based Nonlinear Adaptive State-Observer for Pressurized Water Reactors

Although there have been some severe nuclear accidents such as Three Mile Island (USA), Chernobyl (Ukraine) and Fukushima (Japan), nuclear fission energy is still a source of clean energy that can substitute for fossil fuels in a centralized way and in a great amount with commercial availability and economic competitiveness. Since the pressurized water reactor (PWR) is the most widely used nuclear fission reactor, its safe, stable and efficient operation is meaningful to the current rebirth of the nuclear fission energy industry. Power-level regulation is an important technique which can deeply affect the operation stability and efficiency of PWRs. Compared with the classical power-level controllers, the advanced power-level regulators could strengthen both the closed-loop stability and control performance by feeding back the internal state-variables. However, not all of the internal state variables of a PWR can be obtained directly by measurements. To implement advanced PWR power-level control law, it is necessary to develop a state-observer to reconstruct the unmeasurable state-variables. Since a PWR is naturally a complex nonlinear system with parameters varying with power-level, fuel burnup, xenon isotope production, control rod worth and etc., it is meaningful to design a nonlinear observer for the PWR with adaptability to system uncertainties. Due to this and the strong learning capability of the multi-layer perceptron (MLP) neural network, an MLP-based nonlinear adaptive observer is given for PWRs. Based upon Lyapunov stability theory, it is proved theoretically that this newly-built observer can provide bounded and convergent state-observation. This observer is then applied to the state-observation of a special PWR, i.e., the nuclear heating reactor (NHR), and numerical simulation results not only verify its feasibility but also give the relationship between the observation performance and observer parameters.