Sliding Mode Estimator Research Articles

Control Based on Nonlinear Estimators of Parametric Uncertainties Applied to an Agricultural Tractor Equipped with a Towed Implement System

This article presents a nonlinear control strategy designed to address parametric uncertainties in an agricultural tractor system coupled to a towed implement. The controller ensures accurate tracking of lateral and yaw velocities relative to desired reference trajectories, even under the presence of parametric variations and external disturbances. The reference trajectories are derived from an “ideal” tractor model, excluding the effects of the towed implement. A High-Order Sliding Mode (HOSM) estimator is employed to provide an estimation of disturbances, which are subsequently mitigated by the controller to maintain system stability and precision. The effectiveness of the proposed control strategy is validated through Matlab-Simulink simulations, which include a double-step steer maneuver. This maneuver tests the system’s ability to handle abrupt steering changes, providing insight into the controller’s robustness and its capacity to ensure accurate trajectory tracking in demanding conditions.

Distributed adaptive prescribed-time orbit containment control for satellite cluster flight

The distributed prescribed-time orbit containment control for the satellite cluster flight with multiple dynamic leaders is investigated. The directed information communication topology between followers is taken into account in the overall paper. When the satellite mass is assumed to be constant, a distributed prescribed-time orbit containment controller is, firstly, presented to drive the followers into the dynamic convex hull produced by multiple leaders. Then, the parameter uncertainty is considered, and a prescribed-time sliding mode estimator is introduced to estimate the desired velocity of each follower. Based on the estimated state, a novel distributed adaptive prescribed-time orbit containment control scheme is proposed. The Lyapunov stability theory is utilized to prove the prescribed-time stability of the closed-loop system. Finally, several numerical simulations and comparison of different control methods are provided to verify the effectiveness and superiority of the proposed control method.

Fixed-time sliding mode estimator-based distributed formation control for multiple nonholonomic mobile robots

This paper proposes a fixed-time estimator-based distributed formation controller for a system consisting of multiple nonholonomic mobile robots, taking into consideration the stability of individuals and the effectiveness of internal communication. The desired trajectory of the formation is given by the virtual leader whose state is available only to some followers, and the information interaction within the followers is localized. To begin with, a distributed fixed-time sliding mode estimator is designed for each follower to estimate the state information of the virtual leader within a fixed time. Subsequently, based on the estimator, a formation controller is designed according to the trajectory tracking error of each follower. In addition, the Lyapunov function is constructed for stability analysis. Finally, simulation experiments are conducted in MATLAB/Simulink to demonstrate the effectiveness of the proposed estimator and controller, and the robustness of the control system is further verified by combining the actual situation of communication interruption and external disturbance.

Chattering-Free Second Order Robustness Sliding Mode Controller for Complex Interconnected Systems: A Moore-Penrose Inverse Technique

In this paper, a novel second order sliding mode control approach is extended toa class of complex interconnected systems with mismatched interconnections and unknown perturbations. The key contribution of this paper is to cancel two common restrictions clogging the application of the variable structure control to complex interconnected systems: 1) all of state variables must be accessible; 2) the control input is affected by chattering problems. First, a novel reduced-order sliding mode estimator (ROSME) is proposed to estimate the unmeasurable variables. Second, based on Moore-Penrose inverse technique and ROSME tool, a new decentralized chattering-free second order robustness sliding mode controller (CSORSMC) is developed to force the system states to stay in a sliding surface from the initial period instance and attenuate the chattering phenomenon in the control signal. Besides, a novel appropriate linear matrix inequality (LMI) requirement is proved such that the plant in sliding mode is asymptotically stable. Lastly, a mathematical model including two subsystems is simulated which confirms the usefulness and advantages of proposed technique.

Formation control of multi-agent systems with actuator saturation via neural-based sliding mode estimators

In this paper, the formation control problem for second-order multi-agent systems with model uncertainties and actuator saturation is investigated. An estimator-based robust formation controller is developed to ensure boundedness of the system’s formation tracking error. To estimate uncertain factors without prior knowledge of their Lipschitz constants, two new estimator designs that combine the neural-based estimation process and the sliding mode technique are proposed. Finite-time stability is achieved by introducing a new terminal estimation surface. Regarding the formation controller design, we provide a new framework to study the combined effect of input saturation and input coupling. Both an adaptive compensator and an input regulation algorithm are employed to attenuate state fluctuation led by the reverse effect. Comparative simulations regarding a multi-robot system are conducted to demonstrate the effectiveness of the proposed estimators and the estimator-based controller.

Nonlinear observer-based adaptive control of ground vehicles with uncertainty estimation

In this work, a nonlinear observer-based controller is designed for the attitude control of a ground vehicle with uncertainty estimation. This controller ensures the tracking of desired references in the presence of environmental disturbances and parametric uncertainties, making use of high-order sliding-mode estimators to estimate these perturbations. Furthermore, the controller incorporates a kinematic observer reconstructing the lateral vehicle velocity, based on a novel high-order sliding-mode observer. The proposed controller ensures good performance and better transient behavior with respect to existing controllers when parametric uncertainties and environmental disturbances are present. Its performance is evaluated by numerical simulation in CarSim, considering a challenging double turn maneuver, which is described in the ISO-3888 specifications.

Adaptive Gain Tuning Rule for Nonlinear Sliding-Mode Speed Control of Encoderless Three-Phase Permanent Magnet Assisted Synchronous Motor

In this paper, an adaptive gain tuning rule is designed for the nonlinear sliding mode speed control (NSMSC) in order to enhance the dynamic performance and the robustness of the permanent magnet assisted synchronous reluctance motor (PMa-SynRM) with considering the parameter uncertainties. A nonlinear sliding surface whose parameters are altering with time is designed at first. The proposed NSMSC can minimize the settling time without any overshoot via utilizing a low damping ratio at starting along with a high damping ratio as the output approaches the target set-point. In addition, it eliminates the problem of the singularity with the upper bound of an uncertain term that is hard to be measured practically as well as ensures a rapid convergence in finite time, through employing a simple adaptation law. Moreover, for enhancing the system efficiency throughout the constant torque region, the control system utilizes the maximum torque per ampere technique. The nonlinear sliding surface stability is assured via employing Lyapunov stability theory. Furthermore, a simple sliding mode estimator is employed for estimating the system uncertainties. The stability analysis and the experimental results indicate the effectiveness along with feasibility of the proposed speed estimation and the NSMSC approach for a 1.1-kW PMa-SynRM under different speed references, electrical and mechanical parameters disparities, and load disturbance conditions.

Model-based observer for vehicle proton exchange membrane fuel cell humidity based on adaptive sliding mode estimation technique

Real-time humidity acquisition for vehicle proton exchange membrane fuel cell (PEMFC) facilitates humidity control to avoid membrane flooding or drying, improving its efficiency and stability. However, due to the frequent changes of actual vehicle conditions and expensive as well as unreliable humidity sensors, it is difficult to obtain real-time water content in PEMFC, which brings obstacles to closed-loop control of humidity. To this end, a model-based observer is proposed to obtain real-time humidity. Specifically, a dimensionless third-order model of relative humidity for PEMFC was established, which includes the dynamic of membrane water content. Based on the proposed model, an adaptive sliding mode convergence algorithm was designed to approach real-time humidity using measurable signals (voltage, current, pressure, flow rate, and temperature). The exploration of proposed adaptive sliding mode observer (ASMO) performance was compared with non-adaptive sliding mode observer (SMO) and classical ASMO by using a real 80 kW commercial fuel system experimental data. The experimental results show that compared with second-order humidity model, proposed third-order humidity model reduced recovery time under small step condition, where 250 s for cathode humidity estimation and 200 s for anode humidity estimation. In addition, under the small step condition, the average error of the three observers was less than 3%, which is accurate for engineering application. Moreover, proposed ASMO had the minimum static error, with 4% for cathode humidity estimation and 9% for anode humidity estimation under large step conditions as well as MAE, MSE, RMSE with 4%, 1.90%, 4.39% for cathode relative humidity estimation, 8.19%, 0.89%, 9.44% for anode relative humidity estimation respectively. The comprehensive results indicate that the proposed ASMO with adaptive parameters tuning has better dynamic performance than non-adaptive SMO as well as classical ASMO in terms of robustness and estimated accuracy.

State Estimation in a Biodigester via Nonlinear Logistic Observer: Theoretical and Simulation Approach

The state variables in a biodigester are predicted using an unstructured model, and this study offers an analytical design of a Non-Linear Logistic Observer (NLLO), subsequently comparing its performance to that of other prominent state estimators. Because of variables such as temperature, pH, high pressure, volumetric organic load (VOC), and hydraulic retention time (HRT), among others, biodigester samples can be affected by the use of physical sensors, which are not always practical owing to their sensitivity to the type of sampling and external disturbances. The use of virtual sensors represents one approach to solving this issue. In this work, we suggest experimentally validating a mathematical model, then analytically designing a novel NLLO observer, and finally comparing the results to those obtained using a sliding-mode estimator and a Luenberger observer. By including online CH4 and CO2 measurements as inputs to the proposed observer, the local observability analysis demonstrated that all state variables were recoverable. After showing how well the suggested observer performs in numerical experiments, a proof based on the Lyapunov theory is offered. The primary innovation of this study is the incorporation of a novel algorithm that has been empirically validated and has output resilience to input parametric perturbations.

DO-Based Adaptive Consensus Control for Multiple MUAVs With Dynamic Constraints

This article investigates the adaptive consensus control problem for a group of multirotor unmanned aerial vehicles (MUAVs) subject to dynamic state constraints and unmatched external disturbances. An adaptive inner–outer loop controller is devised based on the backstepping method, where the issue of “explosion of complexity” is solved via a first-order sliding-mode differentiator. By introducing a barrier function-based state transformation technique into the outer loop controller design, the dynamic constraints covering different types of time-varying state constraints can be addressed without reconfiguring the controller structure. Meanwhile, a neural-network-based disturbance observer is constructed to estimate the external disturbances. Consequently, the applicability and robustness of controller are improved, such that the position tracking control can be implemented in severe environments. Moreover, the inner loop controller is established by virtue of a distributed sliding-mode estimator so as the consensus control for attitude systems of multiple MUAVs can be realized rapidly. Finally, a simulation example is presented to demonstrate the validity and superiority of the proposed control strategy.

A distributed predefined-time attitude coordination control scheme for multiple rigid spacecraft

In this paper, the distributed predefined-time attitude coordination control problem is investigated for multiple rigid spacecraft systems when only a subset of spacecraft has access to the reference attitude and angular velocity. Two sliding mode estimators are proposed to estimate the reference attitude and angular velocity, respectively. It is proved that the states of the two proposed estimators can converge to zero in a predefined time. Then, a predefined-time control scheme is designed for the multiple rigid spacecraft systems subject to inertial uncertainty and external disturbance. The practical predefined-time stability is proved for the multiple rigid spacecraft system under the presented controller. It should be pointed out that the most important feature of the proposed estimators and controller is the tunable settling time characteristic. To be specific, based on ensuring that the settling time is less than the predefined value, the actual settling time of the system states can be further adjusted for different task requirements by a tunable parameter. Finally, some simulations are conducted to illustrate the effectiveness and advantages of the proposed tunable predefined-time control scheme.

Integral Sliding-Mode Fault-tolerant Pitch Control of Wind Turbines

In this paper, an integral sliding-mode fault-tolerant pitch control of wind turbines is presented. The proposed approach uses a fault diagnosis strategy which consists of a sliding-mode fault diagnosis observer. This observer is based on using an integral sliding-mode estimation scheme by using a suitable Lyapunov functional. Based on the previous fault diagnosis strategy, an integral sliding mode controller is designed by selecting an appropriate sliding mode surface in order to obtain the fault tolerant-control law obtained by also selecting appropriated Lyapunov functional. A wind-turbine case study is used to validate in simulation the the proposed approach.

Adaptive resilient containment control for nonlower triangular multiagent systems with time-varying delay and sensor faults

This paper investigates the adaptive resilient containment control for nonlinear multiagent systems (MASs) with time-varying delay, unmodeled dynamics and sensor faults. To solve the coupling problem of unknown state delays and sensor faults in a nonlower triangular structure, we develop an effective method by using a new lemma and the Lyapunov-Krasovskii functional. Then, to reduce the negative impact of unknown sensor faults, a novel adaptive resilient containment control method is designed based on a distributed sliding-mode estimator, which can effectively improve the transient performance of the MASs. Moreover, by using a dynamic signal, the problem of unmodeled dynamics is solved. The proposed control scheme can not only drive all followers suffering from sensor faults to converge to the convex hull formed by the leaders but also relatively reduce the undesired chattering phenomenon. Finally, a comparative simulation example is given to illustrate the effectiveness of the proposed strategy.

Humidity estimation of vehicle proton exchange membrane fuel cell under variable operating temperature based on adaptive sliding mode observation

Active humidity control of vehicle fuel cell requires real-time and accurate estimation of actual humidity. However, the vehicle operation conditions change rapidly, which makes the accuracy of transient estimation become the difficulty of estimation algorithm with operation condition deviation. In order to solve this problem, an adaptive sliding mode estimation algorithm based on dimensionless modelling method is designed. The experiment on a real 80 kW commercial fuel cell system proves that compared with the classical sliding mode observation algorithm, the adaptive scheme can reduce the absolute estimation error of humidity by about 5% on average, and the absolute estimation error can be reduced by 17% in some transients.

Online power and efficiency estimation of a fuel cell system for adaptive energy management designs

The temporal changes of power and efficiency in a fuel cell (FC) stack can cause malperformance in the energy management strategy (EMS) of a FC hybrid electric vehicle. Therefore, the online estimation of these physical attributes is becoming an integral part of any EMS. This paper aims to utilize a two-step method to extract the maximum power and efficiency points of a FC system online. In this respect, an online parameter estimation technique, composed of smooth variable structure filter (SVSF) and Kalman filter (KF), is utilized in the first step to estimate the parameters of a FC semi-empirical voltage model. KF generates statistically optimal estimates for a linear, well-designed system model in the existence of Gaussian noise. However, these assumptions do not always hold in real applications and can lead to unstable estimation. A practical solution to deal with these instabilities is to enforce boundaries on the state estimates through SVSF which is based on sliding mode estimation concept. Hence, unlike the other similar studies, this paper synthesizes the robustness of SVSF with the precision of KF to enhance the characteristics estimation process of a FC stack. In the second step, the updated voltage model is utilized to extract the efficiency and power curves of the real FC system. To corroborate the potential of the proposed approach, a thorough comparison with KF, as an attested estimation method, is performed. The experimental tests on a 500-W FC stack indicate the superior performance of the SVSF-KF compared to that of KF.

Induction motor sliding mode estimators with known fluxes

Induction motor sliding mode estimators with known fluxes

Induction motor sliding mode estimators with known fluxes

Induction motor sliding mode estimators with known fluxes

Adaptive sliding mode estimation of state of charge implemented on a field programmable gate array Spartan‐6 Xilinx device

AbstractThis paper presents the implementation of adaptive sliding mode estimation (ASME) of the state of charge of a battery on a field programmable gate array (FPGA). The study is conducted in two steps: in the first step, we design an adaptive sliding mode observer by taking into account an electrical equivalent circuit describing the battery's behavior and identify the parameters of this equivalent circuit by using the recursive least squares estimation method. In the second step, we study the implementation of this ASME on an FPGA card.

MRAS-Based Super-Twisting Sliding-Mode Estimator Combined With Block Control and DTC of Six-Phase Induction Motor for Ship Propulsion Application

This article presents the block control (BC) approach combined with the direct torque control (DTC) through employing a model reference adaptive system (MRAS) based on the super-twisting sliding-mode (STSM) speed estimator of a six-phase induction motor (6PIM) for ship propulsion application. The BC is a robust speed controller that is employed for regulating the 6PIM speed. The closed-loop approach is designed in an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">αβ</i> -reference frame as well as is based on the linearization BC approach. The flux estimator is based on the super-twisting technique that is a second-order sliding-mode approach. This observer is utilized as a reference model throughout the MRAS-based speed estimator for discarding the chattering problem of the conventional sliding-mode technique. Two STSM controllers are used for controlling the torque along with the stator flux and improving the drive system performance throughout external load disruptions. Furthermore, the STSM estimator estimates the torque and stator flux in a robust response with discarding the chattering problem. The proposed MRAS-based STSM speed estimator performance is investigated experimentally for the 750-W 6PIM as well as compared with the traditional DTC approach throughout various speed references, load disruptions, and low-speed command/low loading torque conditions.

Identification of the dynamics of the drivetrain and estimating its unknown parts in a large scale wind turbine

In this paper, the drivetrain identification problem of a horizontal axis gear-driven wind turbine has been considered. The identification problem leads to a precise model of the drivetrain of the wind turbines which plays a key role in the production and transmission of electrical energy. This process consists of two stages: First, offline identification which needs the input–output data from the drivetrain system. These data are obtained from the FAST code. FAST (Fatigue, Aerodynamics, Structures, and Turbulence) is a valid aeroelastic code in the simulation aeroelastic field of offshore and onshore wind turbines. In region 2 (wind velocity is between the cut-in and rated velocities), the generator torque is input, and rotor speed is output. It is supposed that the wind velocity is neglected in the identification process (the identification process is not considered in the presence of wind or done in the low wind velocities bellower than the cut-in wind velocity). In the second stage, after completion of the offline identification process, the drivetrain model of the wind turbine is obtained but the aerodynamic torque in the real performance of the wind turbine is still unknown. In this stage, to estimate the aerodynamic torque, high order sliding mode estimator is used and the unknown states are estimated by using the Extended Kalman Filter (EKF)