Sliding Mode Observer Design Research Articles

Dynamic event‐triggered sliding mode control of networked switched systems with imperfect transmissions

AbstractAs a significant type of dynamic systems, switched systems have been successfully applied to the construction of many engineering fields. Recently, the studies of networked switched control systems have received a lot of attention. However, the intervention of the network often causes the delay or packet loss during data transmission, resulting in incomplete data transmission. The paper studies a sliding mode observer design for above‐mentioned systems with external disturbance under an imperfect transmission communication link. By constructing a dynamic event generator, a dynamic event‐triggered mechanism between the event‐generator and controller is developed to save additional network bandwidth and improve system performance. A desirable sliding surface function is built to solve the complexity of system analysis problems caused by network‐induced delay and packet‐dropout‐induced imperfect transmission. Then, a corresponding event‐based integral‐type sliding mode observer is constructed to estimate inaccessible system states, guaranteeing the reachability of the sliding surface. Based on the augmented system dynamics, sufficient conditions are derived to guarantee exponent stability with a weighted ‐ performance level. Finally, two simulations are presented to demonstrate the feasibility and effectiveness of the proposed method.

A Review of Sliding Mode Observer Based Sensorless Control Methods for PMSM Drive

For permanent magnet synchronous machines (PMSMs), high performance control strategies rely on sensors to obtain accurate information of rotor position and speed. However, mechanical sensors are expensive and susceptible to harsh environment. Therefore, various sensorless control strategies have been proposed and intensively investigated for decades. Among them, sliding mode observer (SMO) based sensorless control method has drawn increasing attention due to its simple implementation and strong robustness. This paper presents a comprehensive review of SMO based sensorless control strategies for PMSMs reported in the literature. State-of-the-art SMO based sensorless control strategies have been reviewed and investigated, and the design of SMO under non-ideal conditions is presented as well. In addition, future research trends for SMO based sensorless control strategies are also discussed.

Jordan Canonical Form for Solving the Fault Diagnosis and Estimation Problems

The suggested methods for solving fault diagnosis and estimation problems are based on the use of the Jordan canonical form. The diagnostic observer, virtual sensor, interval, and sliding mode observer design problems are considered. Algorithms have been developed to solve these problems for both linear and nonlinear systems, considering the presence of external disturbances and measurement noise. It has been shown that the Jordan canonical form allows reducing the dimensions of interval observers and virtual sensors, thus simplifying the design process in comparison to the identification canonical form. The theoretical results are illustrated through examples.

Load frequency composite control for multi-region interconnected power systems

This paper investigates a composite controller for load frequency control (LFC) in multi-region interconnected power systems via sliding mode observer design. State observers (SOs) and disturbance observers (DOs) are implied for the LFC based on the load variations with communication delays and quantization output measurements. A nonlinear integral sliding surface combined with a composite controller is developed to optimize control performance. Moreover, a three-area power system model is used to demonstrate the effectiveness of the proposed scheme in the illustrative example, confirming that frequency deviations can be rejected despite delays, uncertainties, and quantization during transmission.

Prescribed-Time Sliding Mode Observer for Nonlinear Triangular Systems

This paper deals with the problem of prescribed-time sliding mode observer design for a class of triangular nonlinear systems. The contribution of the paper is twofold. First, we propose a new prescribed-time observer based on Super-Twisting-Algorithm (STA), for a triangular two-dimensional system. Such an STA algorithm is based on the use of two power terms, instead of only one as with the standard STA. Then we exploit this algorithm to develop a novel step-by-step arbitrary order sliding mode observer for a general class of triangular systems. An application to vehicle motion estimation in a platoon is provided to show the validity and efficiency of the proposed step-by-step sliding mode observer. For this case study, we use a third-order longitudinal kinematic linear vehicle model.

Observer-based sliding mode controller design for singular bio-economic system with stochastic disturbance

<abstract><p>In this paper, we investigate the problems of sliding mode observer design and observer-based integral sliding mode control for a class of singular bio-economic systems with stochastic disturbance. Initially, we establish a bio-economic system with the alien invasive species and stochastic disturbance. Then, a new integral sliding surface is constructed based on the multiplication of sliding variables and negative definite matrix for the error system. The advantage of this method is that it not only stabilizes the sliding variables, but also eliminates the restrictive assumptions often used in sliding mode control of the singular bio-economic systems with stochastic disturbance. Finally, an augmented system is constructed and the linear matrix inequality technique is used to determine the admissibility of the mean square exponent. Furthermore, an observer-based sliding mode controller is designed so that the reachability conditions can be guaranteed. The validity of the results is verified by a numerical simulation.</p></abstract>

On sliding mode observers for non-infinitely observable descriptor systems

This paper presents a sliding mode observer (SMO) design method to estimate the states and unknown inputs (UIs) in a class of non-infinitely observable (NIO) descriptor systems that contain UIs in both the state and output equations. Existing works on SMO design for NIO systems did not consider UIs in the output equation. In order to overcome the difficulty caused by UIs in output channels and the NIO condition, we reformulated the original system and introduced new UIs to replace the original UIs to obtain an equivalent infinitely observable descriptor system whose output does not contain any UI. Based on the developed equivalent system, a new SMO method is proposed to estimate both the states and the UIs. Subsequently, the necessary and sufficient conditions for the existence of the SMO are derived in terms of the original system matrices, which thus makes the conditions easy to be examined. Finally, an example is used to verify the effectiveness of the proposed method.

Lower triangle factor based sliding mode observers design for T–S fuzzy systems with faults

The paper mainly focuses on the fault estimation for a class of Takagi–Sugeno (T–S) fuzzy systems with faults. A synthetic estimation observer design method is proposed. The synthetic estimation observer can cover the robust observer, adaptive observer and intermediate estimation observer in the existing study work. Based on the observer design method, an LTF-based sliding mode observer (SMO) is designed for the T–S fuzzy system in consideration. Under the observer, the fault occurring in the system can be well estimated. The obtained LMI-based conditions guarantee the states of the error dynamics to be uniformly ultimately bounded. A numerical example tests the proposed method.

Generalized Sliding Mode Observers for Simultaneous Fault Reconstruction in the Presence of Uncertainty and Disturbance

In this paper, a generalized sliding mode observer design method is proposed for the robust reconstruction of sensors and actuators faults in the presence of both unknown disturbances and uncertainties. For this purpose, the effect of uncertainty and disturbance on the system has been considered in generalized state-space form, and the LMI tool is combined with the concept of an equivalent output error injection method to reduce the effects of them on the reconstruction process. The upper bound of the disturbance and uncertainty are minimized in the design of the sliding motion so that the reconstruction of the faults will be minimized. The design method is applied for actuator faults in the generalized state-space form, and then with some suitable filtering, the method extends as sensors and actuators coincidentally faults. Since in the proposed approach, the state trajectories do not leave the sliding manifold even in simultaneous sensors and actuators faults, then the faults are reconstructed based upon information retrieved from the equivalent output error injection signal. Due to the importance of the robust fault reconstruction in the wind energy conversion system (WECS), the proposed approach is successfully applied to a 5 MW wind turbine system. The simulation results verify the robust performances of the proposed approach in the presence of unknown perturbations and uncertainties.

A New Sliding Mode Observer Design for Fault Estimation in a Class of Nonlinear Fractional-Order Systems Based on the Super-Twisting Algorithm

A New Sliding Mode Observer Design for Fault Estimation in a Class of Nonlinear Fractional-Order Systems Based on the Super-Twisting Algorithm

Anti-disturbance sliding mode control for uncertain nonlinear systems

In this paper, the problem of disturbance-based nonlinear sliding mode observer design is investigated for uncertain time-delay repeated scalar nonlinear systems subject to quantisation output measurement. State and disturbance observers are constructed by using the quantised measured output. Then, an improved nonlinear sliding surface is developed, and sufficient conditions are obtained for the sliding mode dynamics to be asymptotically stable with the desired performance level. In addition, a composite nonlinear feedback control law is synthesised to guarantee the reachability of the nonlinear surface. Finally, examples and simulations are presented to demonstrate the effectiveness of the proposed new design techniques.

Adaptive sliding mode observers for sector‐bounded nonlinear systems

SummaryThis article introduces a novel sliding mode observer design for sector bounded nonlinear systems. The proposed observer can simultaneously estimate both states and unknown parameters in the presence of disturbances and measurement noise. The observer is developed by using a time‐averaged Lyapunov (TAL) functional to analyze the effect of noise (Gaussian) and to adequately reduce its effect on the system. The TAL averages the Lyapunov analysis over a small finite time interval, allowing for intuitive analysis of noises and disturbances acting on the system. The TAL is shown to satisfy all the requirements of a Lyapunov candidate function. The article focuses on the observer design for sector bounded nonlinear systems since several nonlinearities can be modeled using a sector bound. An optimization approach is also developed to provide a tight bound on the effect of the uncertainty on the estimated parameters. The conditions for the existence of the observer are presented in the form of linear matrix inequality (LMI), which can be explicitly solved offline using commercial LMI solvers. Furthermore, the LMI design is also extended to a specific case of a dissipative nonlinear system. The observer design has also been extended to the case where the input disturbance is correlated with the sensor noise.

Adaptive sliding mode observer design for semi-Markovian jump systems through dynamic event-triggered mechanism

This paper deals with the problem of network-based sliding mode observer design and stabilization for nonlinear semi-Markovian jump systems. To design the observer, an event-triggering condition relies on network framework is proposed based on the system output measurement that transmitted through communication channel. Relying on the estimated state, an integral sliding surface is proposed and corresponding sliding mode controller is constructed to guarantee finite-time reachability of predefined sliding surface. In the analysis of sliding mode dynamics and error dynamics, it is considered that the transition rate information suffer from more generally uncertain cases, especially for the type that the mode jumping information from mode to others are totally unknown. Even so, sufficient conditions are developed to ensure stochastic stability of the overall closed-loop system. Finally, a numerical example is provided to verify the effectiveness of the established method.

Fault-Tolerant Quantized Sliding Mode Observers Design for a Class of Takagi-Sugeno Fuzzy System With Unmeasurable Premise Variable

This article addresses the state and fault estimation problems for a class of quantized Takagi–Sugeno (T-S) fuzzy systems with sensor and actuator faults. Two types of observer design methods are developed for two different network transmission environments. In the first case, the signal quantization effect is only considered on the channel between sensor and controller, and a sliding mode observer is designed, which can reconstruct the actuator faults. In the second case, the quantization effects are considered in both the sensor-controller side and the controller-actuator side, which is more difficult to be dealt with compared to the first case, and the sliding mode observer method cannot be effective now since the discontinuous term is difficult to be designed. A descriptor reduced-order observer is presented to solve this problem, where the jumping behavior that resulted from the signal quantization is considered in the observer, which is novel and effective to compensate the quantization effects. Finally, simulation examples of rigid-body satellite attitude control T-S fuzzy system are presented to verify the effectiveness of the proposed observer design approaches.

Выявление неисправностей в группах мобильных роботов с использованием скользящих наблюдателей

The paper studies the emerging trends in advanced computing and information technology for efficient solutions of fault identification problem for mobile robot groups under the unmatched disturbances. The sliding mode observers are considered for mentioned problem solution. It facilitates the concept of Smart everything inside the considered robotic group during its generalized control: smart surrounding sensing, communication, processing, and scanned data storing. The suggested novel approach to sliding mode observer design is based on obtaining the reduced order model of the initial system. This allows reduce the complexity of sliding mode observer and relax restrictions imposed on the initial system.

Fault Identification in Mobile Robot Groups Using Sliding Mode Observers

The paper studies the emerging trends in advanced computing and information technology for efficient solutions of fault identification problem for mobile robot groups under the unmatched disturbances. The sliding mode observers are considered for mentioned problem solution. It facilitates the concept of Smart everything inside the considered robotic group during its generalized control: smart surrounding sensing, communication, processing, and scanned data storing. The suggested novel approach to sliding mode observer design is based on obtaining the reduced order model of the initial system. This allows reduce the complexity of sliding mode observer and relax restrictions imposed on the initial system.

State-estimation-based adaptive sliding mode control of uncertain switched systems: A novel linear sliding manifold approach

A new sliding mode observer design scheme is developed with a novel linear sliding manifold for the exponential stabilization problem of a class of uncertain switched systems in this note. Firstly, the linear sliding manifold is constructed based on a modified observer, through which a new technical approach of the underlying system analysis is exploited to devise a novel exponential stability criteria. Moreover, an associated adaptive switching controller is presented, by which the arrival condition of the designated sliding manifold is fulfilled. Ultimately, illustrative examples are conducted to confirm the feasibility of the proposed scheme.

Attractive Ellipsoid Sliding Mode Observer Design for State of Charge Estimation of Lithium-Ion Cells

This work investigates the real-time estimation of the state-of-charge (SoC) of Lithium-ion (Li-ion) cells for reliable, safe and efficient utilization. A novel attractive ellipsoid based sliding-mode observer (AESMO) algorithm is designed to estimate the SoC in real-time. The algorithm utilizes standard equivalent circuit model (ECM) of a Li-ion cell and provides reliable and efficient SoC estimate in the presence of bounded uncertainties in the battery parameters as well as exogenous disturbances. The theoretical framework of the observer design is not limited to the SoC estimation problem of Li-ion cell but applicable to a wider class of nonlinear systems with both matched and mismatched uncertainties. The main advantage of the proposed observer is to provide a fast and optimal SoC estimate based on minimization over the uncertainty bound. The proposed method is experimentally tested and evaluated for a range of temperatures using the hybrid pulse power characterization test (HPPC), EPA's Federal Test Procedure (FTP75) and Supplemental Test Procedure (US06) data, which demonstrate its effectiveness and feasibility.

Finite-Time State Estimation for an Inverted Pendulum under Input-Multiplicative Uncertainty

A sliding mode observer is presented, which is rigorously proven to achieve finite-time state estimation of a dual-parallel underactuated (i.e., single-input multi-output) cart inverted pendulum system in the presence of parametric uncertainty. A salient feature of the proposed sliding mode observer design is that a rigorous analysis is provided, which proves finite-time estimation of the complete system state in the presence of input-multiplicative parametric uncertainty. The performance of the proposed observer design is demonstrated through numerical case studies using both sliding mode control (SMC)- and linear quadratic regulator (LQR)-based closed-loop control systems. The main contribution presented here is the rigorous analysis of the finite-time state estimator under input-multiplicative parametric uncertainty in addition to a comparative numerical study that quantifies the performance improvement that is achieved by formally incorporating the proposed compensator for input-multiplicative parametric uncertainty in the observer. In summary, our results show performance improvements when applied to both SMC- and LQR-based control systems, with results that include a reduction in the root-mean square error of up to 39% in translational regulation control and a reduction of up to 29% in pendulum angular control.

Switching TS fuzzy model-based dynamic sliding mode observer design for non-differentiable nonlinear systems

This paper presents four sliding mode observers (SMOs) based on a novel approach in Takagi–Sugeno (TS) fuzzy modeling of multi-input multi-output (MIMO) non-linear systems that have non-differentiable operating points. A comprehensive approach is proposed to using the TS fuzzy model (TSFM) in the field of non-differentiable nonlinear systems, where the TSFM is an approximation with high accuracy and a negligible error (2ε) of the nonlinear model. Furthermore, the considered system can be with measurable or unmeasurable premise variables. The observers are synthesized for the above two cases and dynamic observers for state estimations of MIMO non-linear Lipschitz systems. The dynamic gain of the observer is established from inspiring state-space representation of an LTI system with error as input, internal states, and the gain of the observer as output. The dynamics used in the gain of the observer will increase the degrees of freedom in the design procedure and a generalization to the one used in previous works. The proposed method is applicable for continuous-time, but not necessarily differentiable, nonlinear systems. Considering the inherent strongly nonlinear and coupling performance of the plant, the switching method driven by states is presented. This paper presents a comparison of four SMOs and multiple-model adaptive estimation (MMAE) for benchmark hydraulic wind power transfer (HWPT). Simulation results demonstrate improvement in the state observation convergence rate and simplicity and universality of the proposed approach.