Sliding Mode Observer Design Research Articles

Using sliding mode observers to estimate BtuB concentration from measured vitamin B12 concentration.

A simple model for the B12-riboswitch regulatory network in Escherichia coli is first described and the same analysis is applied when changing the strain to Salmonella enterica. Model validation is undertaken by linking the dynamics of the riboswitch model to bacterial growth and comparing the results obtained with in vivo experimental measurements. Measurements of bacterial growth are relatively straightforward to obtain experimentally, but experimental measurements relating to the operation of the riboswitch are more difficult. Using the validated model, sliding mode observer design methods are used to estimate BtuB given measurements of the concentration of vitamin B12. The sliding mode approach is selected because of its inherent robustness properties as well as for the ease of implementation. Validation of the estimates of BtuB produced by the observer is undertaken by comparing the BtuB and vitamin B12 concentrations estimated from the observer with green fluorescent protein production and the concentration of vitamin B12 obtained experimentally. These experimental results also provide further validation of the underpinning mathematical model. The results establish that using a sliding mode observer as a soft sensor is a useful approach to explore the operation of a vitamin B12 riboswitch given measurements of the concentration of vitamin B12.

Robust dynamic sliding mode observer design for a class of nonlinear systems

In this paper, a novel method for the design of robust nonlinear observer in the [Formula: see text] framework for Lipschitz nonlinear systems is proposed. For this purpose, a new dynamical structure is introduced that ensures the stability of observer error dynamics. Design innovation is the use of dynamic gain in the sliding mode observer. The additional degree of freedom provided by this dynamic formulation is exploited to deal with the nonlinear term. The performance of this stable [Formula: see text] observer is better than conventional static gain observers and the dynamic Luenberger observer. The compensator is designed in such a way that, while ensuring the stability of the closed-loop system, it prevents performance loss in the presence of the nonlinearities. By the proposed approach, the observer is robust to nonlinear uncertainties because of increasing the Lipschitz constant. Also, the design procedure in the presence of system and measurement noises is addressed. Finally, the simulation of our methodology is conducted on a nonlinear system to illustrate the advantage of this work in comparison with other observers.

Integrated fault tolerant tracking control for rigid spacecraft using fractional order sliding mode technique

In this study, the integrated fault estimation (FE) and fault tolerant control (FTC) design problem is investigated for the attitude system of a rigid spacecraft with inertia uncertainty, Lipschitz nonlinearity, external disturbance and multiple type actuator faults. An adaptive sliding mode observer design approach, which does not require the known upper bound of generalized perturbation, is proposed to obtain the estimation of unknown actuator faults. On this basis, a fault tolerant attitude tracking control scheme is developed for the faulty rigid spacecraft attitude system by combining the fractional order sliding mode control and backstepping control with adaptive fuzzy approximation technique. The stability of faulty closed loop attitude system under the designed FTC strategy is analyzed using Lyapunov approach. Finally, simulation results are given to show the superiority of the proposed integrated FE and FTC compared with some existing results.

Observer-based passive control for polynomial fuzzy singular systems with time-delay via sliding mode control

This paper is concerned with the problem of sliding mode observer design and observer-based sliding mode controller synthesis for polynomial fuzzy singular systems with time-delay. The polynomial fuzzy model is constructed for singular nonlinear system to eliminate the upper and lower bounds restriction of states in the system and reduce the calculation quantity. An integral-type sliding surface function, which has a stabilizing effect on the sliding variable, is proposed for the observer system. In terms of sum-of-squares approach, observer-based sliding mode passive controller is designed for the system with unknown membership functions, which drives the system trajectories onto the predefined sliding surface in a finite time, meanwhile, the stability and robust passivity of the closed-loop system are guaranteed. The information of membership functions is included in the stability conditions, which can reduce the conservatism. Finally, an example is performed to verify the merits of the method proposed.

On design of robust sliding mode observer for nonlinear networked time-delay systems with communication constraints

For a class of nonlinear discrete-time networked systems with time-delay and communication constraints, this paper is concerned with the design of robust sliding mode observer (SMO), where only one sensor node is allowed to transmit information to remote observer. We focus on the design of SMO to guarantee the exponentially stable of estimation error system and have a desired H∞ disturbance attenuation level in presence of communication constraints. Firstly, a sensor selector is introduced such that only one sensor node is chosen and its measurement can be transmitted to remote SMO at each time instant. Then, a sufficient condition is derived by introducing a piece-wise Lyapunov functional and using the Jensen’s Inequality, which ensures the prescribed performance of estimation error system in the sliding mode surface that we have defined. Moreover, the observer gain matrices can be obtained through solving some matrix inequalities given in the main results. Finally, a simulation study performed on the F404 aircraft engine state monitoring is introduced to validate the robust SMO design.

Robust sliding mode observer design for simultaneous fault reconstruction in perturbed Takagi-Sugeno fuzzy systems using non-quadratic stability analysis

Appearing faults in a practical system is dispensable, and if it is not compensated, it results in poor system performance or even dysfunction of the system. The fault detection has become a promising challenging issue to guarantee the safety and reliability of systems. In this paper, a novel fuzzy-based sliding mode observer for the simultaneous actuator and sensor fault reconstruction of nonlinear systems subjected to external disturbance is proposed. The proposed approach employs the Takagi-Sugeno fuzzy model, sliding mode observer and non-quadratic Lyapunov function. First, by filtering the system output, a fictitious system whose actuator faults are the original actuator and sensor faults is constructed. Then, by considering the performance criteria, the effect of disturbance on the state estimations is minimized. It is proved that the estimations asymptotically converge to their actual values for non-perturbed systems. In the process of designing the observer gains, some transformation matrices are obtained by solving linear matrix inequalities. The proposed approach has some superiority over the existing methods. First, considering the non-quadratic Lyapunov function leads to relaxed results and good estimation performance. Second, using the sliding mode observer makes the proposed approach insensitive to the uncertainties and unknown inputs and determines the shape and size of the fault. Third, assuming the premise variables are immeasurable makes the presented approach more applicable. In conclusion, two practical systems are considered and simulation results illustrate the merits of the proposed approach in comparison with the recent methods from the fast and precise fault detection performance viewpoints.

Design and Simulation of Direct and Indirect Back EMF Sliding Mode Observer for Sensorless Control of PMSM

Abstract This article compares two sensorless control algorithms for a permanent magnet synchronous machine (PMSM) based on the back-EMF sliding mode observer (SMO). Indirect SMO (I-SMO) treats the back-EMF voltages as a disturbance. Direct SMO (D-SMO) considers back-EMF voltages as state-space variables. The same phase-locked loop (PLL) is used for both observers for extraction of the rotor position and speed values from the observed back-EMF voltages. In a sensorless control, the observed speed is used as feedback for the PI controller, and the observed position is used in the Park transformations. Both observers have been implemented and tested with standard field-oriented control. Simulation results indicate rather comparable speed and position estimation precision for both, but the D-SMO indicates slightly higher precision in steady-state. Even more, a tuning procedure of the D-SMO is more straightforward when compared to the I-SMO. Thus, the D-SMO was further verified experimentally with the OP 5600 rapid prototyping device and with a 350 W PMSM drive. Experimental results of the D-SMO are included at the end of the paper.

Port-Hamiltonian Sliding Mode Observer Design for a Counter-current Heat Exchanger

This paper presents a sliding mode observer (SMO) for estimating temperatures in a heat exchanger. First a port-Hamiltonian formulation for a countercurrent heat exchanger is proposed. It is so as to guarantee convergence of the observer. It is shown that the Stokes-Dirac structure obtained by opening only the dissipation ports due to the convection phenomenon, is conservative. Secondly, a SMO based on an interconnected structure of port-Hamiltonian systems is designed. The convergence of the dynamics of the estimation error is proven. The simulation results illustrate the effectiveness of this estimation strategy.

Event-triggered sliding mode control of nonlinear dynamic systems

In this work, the problem of sliding mode observer design is investigated for a class of repeated scalar nonlinear systems via dynamic event-triggered approach. By constructing an event-triggered observer and a sliding mode surface, the system dynamics is obtained and an event-triggered controller is designed to ensure that the closed-loop system trajectories are restricted to the pre-specified sliding region. Sufficient conditions are provided to guarantee that the system dynamics is asymptotically stable with a desired H∞ performance level. Two illustrative examples are provided to demonstrate the effectiveness and potential of the proposed design method.

Observer-Based Sliding Mode Control for Uncertain Fuzzy Systems via Event-Triggered Strategy

This paper investigates the problem of sliding mode observer design for a class of uncertain fuzzy time-delay systems based on an event-triggered strategy. The objective is to design an event-triggered mechanism by utilizing the information of system output and observer function. Based on the delay partitioning method and the Lyapunov–Krasovskii function approach, delay-dependent sufficient conditions are proposed to guarantee the overall system, including sliding mode dynamics and error dynamics, to be asymptotically stable with an $\mathcal {H}_{\infty }$ performance. Furthermore, an event-triggered sliding mode controller is synthesized to ensure that the system dynamics can be driven to the sliding region near the equilibrium point in finite time. Finally, a verification example is provided to demonstrate the feasibility and efficiency of the theoretical results presented.

Reduced-Order Sliding-Mode-Observer-Based Fault Estimation for Markov Jump Systems

This paper is concerned with the fault and state estimation problem for Markovian jump systems (MJSs) with simultaneous actuator and sensor faults. To deal with the design issues, we propose a novel descriptor reduced-order sliding mode observer (SMO), based on which the estimation of the actuator faults, sensor faults, and the states can be obtained simultaneously. Compared with the traditional SMO design issues in MJSs, we reconstruct the actuator faults directly without employing the equivalent output error injection method. Thus, the reachability analysis of the sliding surface is not necessary. The superiority of this kind of the SMO method is that the sliding surface switching problem is avoided. Finally, the effectiveness (as suggested by the theoretical results) of the approach described is tested on a mobile manipulator by simulation studies.

An H∞non‐fragile observer‐based adaptive sliding mode controller design for uncertain fractional‐order nonlinear systems with time delay and input nonlinearity

AbstractIn this paper the problem of non‐fragile adaptive sliding mode observer design is addressed for a class of nonlinear fractional‐order time‐delay systems with uncertainties, external disturbance, exogenous noise, and input nonlinearity. An H∞ observer‐based adaptive sliding mode control considering the non‐fragility of the observer is proposed for this system. The sufficient asymptotic stability conditions are derived in the form of linear matrix inequalities. It is proven that the sliding surface is reachable in finite time. An illustrative example is provided which corroborates the effectiveness of the theoretical results.

State and Fault Observer Design for Switched Systems via an Adaptive Fuzzy Approach

This article investigates the state and fault estimation problem for switched systems with external disturbances, unknown nonlinear dynamics, and actuator and sensor faults. In this article, a new adaptive fuzzy-based observer is designed, where the prior knowledge of the nonlinearities, disturbances, and faults is not required. In contrast to the sliding mode observer (SMO), the proposed observer can guarantee the convergence of the error trajectory through the online adaptive mechanism, avoiding the sliding surface switching problem in SMO design. The accurate state asymptotic estimations can also be provided by the developed design approach subject to the simultaneous additive and multiplicative faults. Finally, a simulation example is presented to show the effectiveness of the proposed method.

Adaptive Sliding Mode Observer Design for a Class of T–S Fuzzy Descriptor Fractional Order Systems

This paper investigates the problem of sliding mode observer (SMO) design for Takagi-Sugeno (T-S) fuzzy descriptor fractional order systems (FOSs) with fractional order $0<; \alpha <; 1$. First, an SMO is designed for the T-S fuzzy descriptor FOS. Then, a fuzzy fractional order integral-type sliding surface is constructed. By utilizing the fuzzy sliding surface, the assumption that all local input matrices are identical in most existing results about sliding mode control (SMC) for T-S fuzzy systems, can be removed. Then, a new sufficient condition is proposed in terms of linear matrix inequalities (LMIs), which guarantees the admissibility of the sliding mode dynamics. Moreover, adaptive SMC strategy is used such that the reachability condition can be guaranteed. Finally, three examples are given to verify the effectiveness of our results.

Sliding mode observer design for fault and disturbance estimation using Takagi–Sugeno model

This paper presents an actuator fault and disturbance estimation scheme using sliding mode observer (SMO) based on Takagi–Sugeno (TS) fuzzy system model. The TS model is first transformed in order to decouple disturbance and faults. Then a TS fuzzy SMO is developed for the transformed system. Finally, the disturbance and the fault are estimated using equivalent output error. The stability of the proposed observer is analyzed and its performances are tested for a doubly fed induction generator with actuator fault and disturbance.

Sliding mode observer design for fault and disturbance estimation using Takagi-Sugeno model

Abstract This paper presents an actuator fault and disturbance estimation scheme using sliding mode observer (SMO) based on Takagi–Sugeno (TS) fuzzy system model. The TS model is first transformed in order to decouple disturbance and faults. Then a TS fuzzy SMO is developed for the transformed system. Finally, the disturbance and the fault are estimated using equivalent output error. The stability of the proposed observer is analyzed and its performances are tested for a doubly fed induction generator with actuator fault and disturbance.

A sliding mode observer design for uncertain fractional Ito stochastic systems with state delay

ABSTRACTThis paper addresses the robust observer design problem for uncertain time-delay fractional Ito stochastic systems. A sliding surface is proposed and it is shown that state estimates converge towards it and remain there for the subsequent time. Additionally, by constructing a novel Lyapunov functional, a sufficient condition for the stability of the sliding motion of the estimated states is given in the form of Linear Matrix Inequalities (LMIs). It is demonstrated that the state estimates are stabilizable in probability provided that the LMI is feasible. Moreover, a finite-time sliding mode control law based on the estimated states is proposed. Simulation examples are given to show the validity and effectiveness of the results.

Sliding Mode Observer Design for a Parabolic PDE in the Presence of Unknown Inputs

AbstractThis paper considers observer design for systems modeled by linear partial differential equations (PDEs) of parabolic type, which may be subject to unknown inputs. The system is assumed to have only one spatial dimension, over which it is discretised to obtain what is referred to as the lattice system, which is a set of linear time invariant (LTI) ordinary differential equations (ODEs) having a canonical Toeplitz‐like structure with a specific sparsity pattern. This lattice structure is shown to be particularly appropriate for step‐by‐step sliding mode observer design that can reconstruct the state estimates at the points of discretisation and estimate the unknown input. Simulation results for both stable and unstable PDEs show that accurate state estimates can be provided at the points of discretisation. An approach to reconstruct the unknown input is demonstrated.

Sliding-mode observer design and finite-time control of one-sided Lipschitz nonlinear systems with time-delay

This paper is concerned with finite-time observer-based control of time-delay systems with one-sided Lipschitz nonlinearity and unknown energy-bounded exogenous disturbances. For this purpose, first, a robust sliding-mode observer is designed and the dynamical equations of the observer error are obtained. Then, the observer-based controller is designed to yield the finite-time boundedness of the time-delay closed-loop system and also satisfies the passivity performance index. By selecting the appropriate Lyapunov–Krasovskii functional, which is function of both systems states and observer error, the sufficient conditions are derived for robust finite-time boundedness of the closed-loop nonlinear one-sided Lipschitz system. In this regard, two theorems are given and the sufficient conditions are derived in terms of feasibility testing of the extracted linear matrix inequalities. Finally, computer simulations are performed to verify the theoretical achievements.

Robust H∞ sliding mode observer design for a class of Takagi–Sugeno fuzzy descriptor systems with time-varying delay

This paper focuses on the problem of robust H∞ sliding mode observer (SMO) design for a class of Takagi–Sugeno (T–S) fuzzy descriptor systems with time-varying delay. A SMO is designed by taking the control input and the measured output into account. Then a novel integral-type sliding surface, which involves the SMO gain matrix, is constructed for the error system. By using an appropriate Lyapunov–Krasovskii functional, a delay-dependent sufficient condition is established in terms of linear matrix inequality (LMI), which guarantees the sliding mode dynamic to be robustly admissible with H∞ performance and determines the SMO gain matrix. Moreover, a sliding mode control (SMC) law is synthesized such that the reachability can be ensured. Finally, simulations are presented to show the effectiveness of our results.