Order Sliding Mode Observer Research Articles

Exact docking flight controller for autonomous aerial refueling with back-stepping based high order sliding mode

Abstract Autonomous aerial refueling (AAR) exact docking control has always been an intractable problem due to the strong nonlinearity, the tight coupling of the 6 DOF aircraft model and the complex disturbances of the multiple environment flows. In this paper, the strongly coupled nonlinear 6 DOF model of the receiver aircraft which considers the multiple flow disturbances is established in the affine nonlinear form to facilitate the nonlinear controller design. The items reflecting the influence of the unknown flow disturbances in the receiver dynamics are taken as the components of the “lumped disturbances” together with the items which have no linear correlation with the virtual control variables. These unmeasurable lumped disturbances are estimated and compensated by a specially designed high order sliding mode observer (HOSMO) with excellent estimation property. With the compensation of the estimated lumped disturbances, a back-stepping high order sliding mode based exact docking flight controller is proposed for AAR in the presence of multiple flow disturbances. Extensive simulation results demonstrate the feasibility and superiority of the proposed docking controller.

Torque ripple reductions for non-sinusoidal BEMF Motor : An observation based control approach

Torque ripples are usually found in brushless DC (BLDC) motor control applications. This article presents the design of non-sinusoidal back electromotive forces (BEMF) observer for a BLDC motor in order to reduce electromechanical torque ripples. For their robustness quality, a high order sliding mode observer is used to observe the non-sinusoidal BEMF which allows to determine magnetic field angular relative position leading to a so-called extended Park’s transformation. Using this extended transformation, speed and torque vector control can be made with better performances than the classical Park’s transformation. Simulation results are performed to show the effectiveness of the proposed approach.

Oscillatory Global Output Synchronization of Nonidentical Nonlinear Systems

In this work, we study a global output synchronization problem for nonidentical nonlinear systems having relative degree 2 or higher. The synchronization uses a partial projection of individual subsystems into the Brockett oscillators. Our approach is based on output feedback and uses a higher order sliding mode observer to estimate the states and perturbations of the synchronized nonlinear systems. Simulation results are provided to illustrate the performance of the proposed synchronization scheme.

Finite time state and disturbance estimation for robust performance of motion control systems using sliding modes

ABSTRACTIn this paper, simultaneous state and disturbance estimation of a drive system composed of motor connected to a load is proposed. Such a system is represented by a two mass model realising in a fourth-order plant. Backlash is introduced as the nonlinear disturbance in gears which is proposed to be estimated and in turn compensated. For this motion control system, a two-stage higher order sliding-mode observer is proposed for state and backlash estimation. The novelty lies in the fact that for this fourth-order system, output is considered from the motor end only, i.e. its angular displacement. The unmeasured states consisting of output derivative, load-side angular displacement and its derivative along with backlash are estimated in finite time. This disturbance due to backlash is unmatched in nature. The estimated states and disturbance are used to devise a robust sliding-mode control. This proposed scheme is validated in simulation and experimentation.

A novel observer algorithm of voltages across capacitors based on the higher sliding mode control: application to multi-cells converter

In this paper, advanced automatic sliding mode observers are applied to multi-cells converter. The technique facilitates the generation of the voltages image across capacitors of the converter simply by measuring the current. Also, the technique possesses the finite time convergence error. The validity of the controller is demonstrated through simulation results in both the mentioned properties of the technique. Furthermore, a topology with a higher order sliding mode observer for multi-cell converters applications are proposed.

A novel observer algorithm of voltages across capacitors based on the higher sliding mode control: application to multi-cells converter

In this paper, advanced automatic sliding mode observers are applied to multi-cells converter. The technique facilitates the generation of the voltages image across capacitors of the converter simply by measuring the current. Also, the technique possesses the finite time convergence error. The validity of the controller is demonstrated through simulation results in both the mentioned properties of the technique. Furthermore, a topology with a higher order sliding mode observer for multi-cell converters applications are proposed.

Flexible Manipulator State Reconstruction Using Luenberger and First Order Sliding Mode Observers Under Parametric Uncertainties

This paper deals with the problem of state reconstruction fora one-link flexible manipulator using Luenberger Observer (LO) and First Order Sliding Mode Observer (FOSMO) under parametric uncertainties.The design techniques and the comparison of the state observers are presented.The mechanical equations of the system are derived using the Lagrangian approach, and the elastic movement is approximated by the assumed modes method for an Euler-Bernoulli beam. The sliding mode observer is derived based on the available outputs, and it is compared to the classical Luenberger one. The simulation results included in the paper evaluate the observers’ ability to reconstruct the state, to lower the error of estimation and to shorten the required time for the error to converge.

State of charge estimation of lithium-ion batteries using fractional order sliding mode observer

This paper presents a state of charge (SOC) estimation method based on fractional order sliding mode observer (SMO) for lithium-ion batteries. A fractional order RC equivalent circuit model (FORCECM) is firstly constructed to describe the charging and discharging dynamic characteristics of the battery. Then, based on the differential equations of the FORCECM, fractional order SMOs for SOC, polarization voltage and terminal voltage estimation are designed. After that, convergence of the proposed observers is analyzed by Lyapunov’s stability theory method. The framework of the designed observer system is simple and easy to implement. The SMOs can overcome the uncertainties of parameters, modeling and measurement errors, and present good robustness. Simulation results show that the presented estimation method is effective, and the designed observers have good performance.

Rollover Index Estimation in the Presence of Sensor Faults, Unknown Inputs, and Uncertainties

The rollover status of a vehicle indicated by the lateral load transfer (LTR) as the vehicle traverses over various driving scenarios is critical in the implementation of antirollover control procedures. The determination of LTR is often carried out by the measurements of the roll angle, the lateral acceleration, vertically acting suspension forces, etc. In all these measurements, sensor faults may occur, which lead to a faulty computation of the rollover status, raising a false alarm. In this work, a scheme based on a robust higher order sliding-mode observer is proposed to estimate the states of a nonlinear two-wheel vehicular system affected by road disturbances, uncertainties in the height of the vehicle's center of gravity, and possible multiple sensor faults. Applying the proposed approach, the unknown inputs and sensor faults are reconstructed. To perform the estimations, adaptive sliding-mode-based observers that do not require the knowledge of the bounds of the uncertainties and unknown inputs are designed. Consequently, the true rollover status of the vehicle is determined, in spite of the presence of sensor faults. The validity of the proposed scheme has been assessed on the vehicle simulation software CarSim as the vehicle undergoes a double lane change maneuver.

Implementation of Super-Twisting Control: Super-Twisting and Higher Order Sliding-Mode Observer-Based Approaches

In this paper, an output feedback stabilization of perturbed double-integrator systems using super-twisting control (STC) is studied. It is shown that when STC is implemented based on super-twisting observer (STO), then it is not possible to achieve second-order sliding mode (SOSM) using continuous control on the chosen sliding surface. Two methodologies are proposed to circumvent the above-mentioned problem. In the first method, control input is discontinuous, which may not be desirable for practical systems. In the second method, continuous STC is proposed based on higher order sliding mode observer (HOSMO) that achieves SOSM on the chosen sliding surface. For simplicity, we are considering here only the perturbed double integrator, which can be generalized for an arbitrary-order systems. Numerical simulations and experimental validation are also presented to show the effectiveness of the proposed method.

Robust output feedback control design for autonomous spacecraft rendezvous with actuator faults

This article documents a new output feedback guidance scheme for autonomous spacecraft rendezvous in the presence of actuator faults. The proposed approach is essentially a compound control methodology, which consists of higher order sliding mode observer and fast nonsingular terminal sliding mode technique. More specifically, the higher order sliding mode observer is used to estimate the relative velocity between two spacecraft while the fast nonsingular terminal sliding mode controller is used to regulate the relative position and the relative velocity to a small region around zero in finite time. The stability and performance of the closed-loop system are also analyzed using finite-time bounded function and Lyapunov function methods. Finally, numerical simulations are performed to demonstrate the robustness and effectiveness of the proposed method.

State estimation based on fractional order sliding mode observer method for a class of uncertain fractional-order nonlinear systems

State estimation of dynamic systems is quite significant in many research areas, such as state-based control and stabilization, state-based monitoring and fault detection. This paper is concerned with the problem of observer-based state estimation for a class of fractional-order (FO) nonlinear dynamic systems. The objective is to consider the state estimation of FO nonlinear system with the sliding mode control (SMC) technique, and conduct the asymptotic stability analysis for the estimate error dynamic system. Firstly, the considered FO nonlinear system models with constant and uncertain parameters are both presented. Fractional order sliding mode observer (FOSMO) structures are established for the FO nonlinear system models. Then, the asymptotic stability of the estimate error dynamic systems are analyzed via employing the Lyapunov stability analysis method for FO systems, and the sufficient conditions of asymptotic stability are derived. FOSMOs design for FO nonlinear systems of Caputo׳s and Riemann–Liouville׳s differential operators are both investigated, and the corresponding asymptotic stability sufficient conditions of the error dynamic systems are presented to insure the estimation accuracy of FOSMOs. Finally, multiple simulation examples are provided to demonstrate the effectiveness of the presented FOSMOs.

An Adaptive Controller with An Orthogonal Neural Network and A Third Order Sliding Mode Observer for Robot Manipulators

An Adaptive Controller with An Orthogonal Neural Network and A Third Order Sliding Mode Observer for Robot Manipulators

Robust software sensor design for the state estimation in a sulfate-reducing bioreactor

The goal of this work is to present a class of state observer in order to infer unavailable concentrations in a sulfate-reducing bioreactor containing an anoxic culture of Desulfovibrio alaskensis 6SR from the measurements of the sulfate concentration. The methodology is applied to the corresponding sulfate-reducing model considering modeling uncertainties. The proposed observer design presents a proportional term plus a sigmoid function structure. The model’s observability was locally analyzed by the observability matrix test, concluding that the sulfate-reducing bioreactor is detectable. A sketch of proof of the observer’s convergence is depicted in order to show the asymptotic convergence characteristics. Numerical experiments provide an overview about the superior performance of the proposed observer methodology compared to a sliding-mode and high order sliding mode observers.

Observabilty singularities and observer design: dual immersion approach

It is well-known that, for nonlinear systems, the observability is often only a local property and depends on the input. Moreover, it is often required that the observer be of the same dimension as the original system. A direct consequence of this requirement is that it enlarges the set of observability singularities. If, on one hand, it is impossible to observe the state variables that are structurally unobservable, it is, however, possible to overcome the observability singularities introduced by the constraints on the observer design. In this paper, we propose a novel dual immersion method which allows to reduce the set of observability singularities. In addition, a step by step design of a high order sliding mode observer based on the proposed dual immersion approach is presented. Finally, a thorough analysis and discussion on the simulation results with respect to a non-autonomous system is given.

Active FTC for waterjets propelled ships based on Adaptive Estimator and Sliding Techniques

Abstract: This paper focuses on the design and validation of an active Fault Tolerant Control (FTC) approach dealing with sensor and actuator faults for a ship propelled by two water jets. The proposed FTC relies on an adaptive estimation to reconstruct sensor faults and a second order sliding mode observer based on an adaptive super twisting algorithm to reconstruct the actuator faults. A nonlinear model of the considered ship, issued by a previous work, is used to prove the effectiveness of the proposed FTC in the path following maneuvers, speed regulation, and tracking course. The inputs of this model are the command orders to apply to the water jets including the two engines, the steering and reversing units for each jet. Details of the design process of the faults reconstruction and reconfiguration are given. The stability of the closed-loop system and uniform boundedness of the tracking error are proved based on Lyapunov theory. Simulations with many faults scenario are carried out. Results show that the proposed controller can successfully accommodate faults associated with sensors and actuators.

Implementation of Super-Twisting Control on Higher Order Perturbed Integrator System using Higher Order Sliding Mode Observer

Abstract: This paper presents the implementation of super-twisting control (STC) on nth-order perturbed integrator system using higher order sliding mode observer (HOSMO). It is shown that if nth-order SMO is used, either super-twisting algorithm structure is not achieved using continuous controller or the resulting controller is discontinuous. The discontinuous control action is not desirable for practical applications. A method for implementing STC using (n+1) th-order SMO is proposed. The controller proposed based on this observer design is continuous. Sliding surface is designed for handling relative degree problem and the controller is designed such that second order sliding mode (SOSM) is achieved on the sliding surface. Simulation results are also shown using practical example of Insulin-Glucose regulation dynamical model to illustrate the effectiveness of the proposed method.

Fault detection based on higher‐order sliding mode observer for a class of switched linear systems

This study considers the fault detection problem for a class of switched linear systems when the observer matching condition is not satisfied. Without using decoupling transformations, a residual signal, based on reduced order sliding mode observers, is introduced for the detection of faults which occur on the continuous part of the system. Two numerical simulations on the cascade multicellular converter and on the boost converter illustrate the effectiveness of the proposed fault detection scheme.

Nonlinear extremum seeking inspired on second order sliding modes

We present a new Extremum Seeking algorithm that uses Super-Twisting like nonlinear terms in order to improve its precision. In addition, the algorithm is combined with Second Order Sliding Mode observers to build an optimization framework for uncertain dynamic systems in which the variable to optimize is not measured and needs to be estimated. The relevance of the proposed framework is illustrated in the problem of biomass optimization of a biological reactor with uncertain kinetics.

Active Fault Tolerant Control Based on Fault Estimation

For the chattering problem in the traditional sliding mode observer-based fault estimation, a second order sliding mode observer based on the Super-twisting algorithm was proposed. In order to avoid the cumbersome process of proving the stability of the Super-twisting algorithm, a Lyapunov function was adopted. An active fault tolerant control law was designed based on the fault estimation. Finally, simulation show the effectiveness of the proposed approach.