Descriptor Observer Research Articles

Output feedback control for a class of nonlinear systems with actuator degradation and sensor noise

This paper investigates the output feedback control problem of a class of nonlinear systems with sensor noise and actuator degradation. Firstly, by using the descriptor observer approach, the origin system is transformed into a descriptor system. On the basis of the descriptor system, a novel Proportional Derivative (PD) observer is developed to asymptotically estimate sensor noise and system state simultaneously. Then, by designing an adaptive law to estimate the effectiveness of actuator, an adaptive observer-based controller is constructed to ensure that system state can be regulated to the origin asymptotically. Finally, the design scheme is applied to address a flexible joint robot link problem.

Fault detection for discrete-time linear systems based on descriptor observer approach

This paper investigates the problem of actuator fault detection filter design for discrete-time linear systems with output disturbance. By using the descriptor observer method, an H∞ fault detection filter is designed to guarantee the residual system is admissible and satisfies the H∞ performance. By utilizing Lyapunov function approach, a sufficient condition for the admissible of the residual system is obtained in the form of linear matrix inequality (LMI). The desired fault detection filter can be designed by solving a set of LMIs. Finally, a numerical example is proposed to illustrate the effectiveness of the developed method.

Speed sensor fault tolerant controller design for induction motor drive in EV

This paper deals with the problem of speed sensor fault tolerant controller (SSFTC) design for Induction Motor (IM) drive in electric vehicle (EV). First, the Takagi-Sugeno (T-S) model approach was adopted to represent the nonlinear dynamic of IM subject to speed sensor faults and unknown bounded disturbance. Next, based on L2 robust fault detection filter design, a Modified Field Oriented Controller (MFOC) is designed. The proposed approach requires the knowledge of the occurring faults which are estimated from a descriptor observer. The observer gains are determined by solving a set of Linear Matrix Inequality (LMI). Finally, simulation results show the effectiveness of the proposed approach evaluated on 7.5kVA Induction Motor.

Reduced-order fractional descriptor observers for a class of fractional descriptor continuous-time nonlinear systems

Abstract Fractional descriptor reduced-order nonlinear observers for a class of fractional descriptor continuous-time nonlinear systems are proposed. Sufficient conditions for the existence of the observers are established. The design procedure for the observers is given and demonstrated on a numerical example.

Perfect nonlinear observers of fractional descriptor continuous-time nonlinear systems

Abstract Perfect nonlinear fractional descriptor observers for fractional descriptor continuous-time nonlinear systems are proposed. Necessary and sufficient conditions for the existence of the observers are established. The design procedure of the nonlinear fractional observers is given. It is based on the elementary row (column) operations and reducing the singular matrix of the system to upper (lower) triangular form. The effectiveness of the procedure is demonstrated on a numerical example.

Robust Sensor Fault-Tolerant Control of Induction Motor Drive

This paper presents an active fuzzy fault-tolerant control (FTC) strategy for induction motor that ensures the performances of the field-oriented control (FOC). In the proposed approach, a robust controller is synthesized in order to compensate for both the resistance variation, the load torque disturbance, and the sensor fault. The physical model of induction motor is approximated by the Takagi–Sugeno (T–S) fuzzy technique in the synchronous d-q rotating frame. Fuzzy descriptor observer is introduced to estimate simultaneously the system state and the sensor faults. A robust feedback state tracking control is proposed to guarantee the control performances by minimizing the effect of the load torque and the uncertainties. The proposed controller is based on a T–S reference model in which a desired trajectory has been specified. The performances of the trajectory tracking are analyzed using the Lyapunov theory and the \(L_2\) optimization. Observer and controller gains are obtained by solving a set of LMIs constraint. To highlight the effectiveness of the proposed control simulation, results are introduced for a 1.5 KW induction motor.

Fault-Tolerant Control for T–S Fuzzy Descriptor Systems with Sensor Faults: An LMI Approach

This paper focuses on the robust sensor fault-tolerant control of T–S fuzzy descriptor systems with unmeasurable premise variables subject to external disturbances. By introducing sensor fault as an auxiliary state vector, an augmented fuzzy descriptor system is constructed. A robust fuzzy descriptor observer is investigated to achieve simultaneous reconstruction of system states and sensor faults using descriptor approach and the \(L_2\) techniques to minimize the effect of the perturbations on the state estimation error. Based on the state estimated variables and by isolating the sensor fault, a fault-tolerant control scheme is proposed using a state feedback controller approach such that the resulting closed-loop system is stable with prescribed \(H_{\infty }\) performance. Sufficient conditions for the existence of a robust fuzzy descriptor observer and a fault-tolerant controller are derived in the sense of Lyapunov asymptotic stability and are formulated in terms of a series of linear matrix inequalities without additional constraints. Finally, a numerical example was discussed to prove the performance of the proposed approach.

Actuator and Sensor Fault Reconstructions for Uncertain Lipschitz Nonlinear Systems Based onH∞Observers

AbstractThis paper considers fault reconstruction problems for a class of uncertain Lipschitz nonlinear systems with actuator faults, sensor faults, and external disturbances. First, by extending the state vector, the original system is transformed into an augmented descriptor system before anobserver, which can decouple the disturbances, is developed. Since the sensor faults become parts of the extended state vector, the descriptor observer can provide not only state estimates but also the sensor fault reconstructions. Second, a second‐order high‐gain sliding mode observer is used to estimate the derivatives of the system outputs in a finite time. Third, using the estimates of the states and the output derivatives, an algebraic actuator fault reconstruction method is proposed. Finally, a simulation example is given to validate the proposed method.

Model REFERENCE Tracking Control for Uncertain Takagi-Sugeno Systems subject to Sensor Faults

This work concerns the model REFERENCE fault tolerant tracking Control problem for uncertain Takagi-Sugeno (T-S) models with unmeasurable premise variables. The idea is to synthesize a fault tolerant controller with a guaranteed ° performance to attenuate the tracking error for bounded REFERENCE inputs. Based on Lyapunov theory, new less conservative approach is proposed in terms of Linear Matrix Inequalities (LMIs). A descriptor observer is needed to estimate simultaneously the sensor faults and the system states in order to reconfigure the FTC law. A numerical example is considered to illustrate the effectiveness of the proposed FTC tracking performance approach.

Robust fault tolerant tracking controller design for vehicle dynamics: A descriptor approach

In this paper, an active Fault Tolerant Tracking Controller (FTTC) scheme dedicated to vehicle dynamics system is proposed. To address the challenging problem, an uncertain dynamic model of the vehicle is firstly developed, by considering the lateral forces nonlinearities as a Takagi–Sugeno (TS) representation, the sideslip angle as unmeasurable premise variables and the road bank angle as an unknown input. Subsequently, the vehicle dynamic states with the sensor faults are jointly estimated by a descriptor observer on the basis of the roll rate and the steering angle measures. Then a fault tolerant tracking controller is synthesized and solutions are proposed in terms of Linear Matrix Inequalities (LMIs). Simulation results show that the proposed FT control approach can effectively improve tracking performance of the vehicle motion.

Sensor fault estimation and accommodation for discrete‐time switched linear systems

In this study, sensor fault estimation and accommodation for discrete-time switched linear systems are investigated. By using descriptor observer method and switched Lyapunov function technique, efficient conditions to design the fault observer are obtained via a linear matrix inequality formulation. Then, based on the estimation of the sensor fault, an efficient fault-tolerant operation can be realised via sensor fault compensation. Finally, an example is given to illustrate the developed technique.

Robust Control of Stochastic Systems Against Bounded Disturbances With Application to Flight Control

This paper investigates the problems of state observer design and observer-based integral sliding-mode control (SMC) for a class of Itô stochastic systems subject to simultaneous input and output disturbances. A new type of sliding-mode-based descriptor observer method is developed to approximate the system state and disturbance vectors. An integral-type SMC scheme is proposed based on the state estimation to stabilize the overall system. The main contributions of this approach are as follows: 1) The desired estimations of state and disturbance vectors can be obtained simultaneously, and 2) in the designed sliding-mode observer, the integral term of the Itô stochastic noise is eliminated in the proposed sliding-mode surface by a matrix design; thus, the reachability of the sliding-mode surface is strictly guaranteed. Finally, the proposed approach is applied to the disturbance reconstruction problem of an F-18 aircraft model to illustrate the effectiveness and applicability.

Fault-Tolerant Trajectory Tracking Control for Takagi–Sugeno Systems with Unmeasurable Premise Variables: Descriptor Approach

This paper discusses the problem of fault-tolerant tracking control (FTTC) for fuzzy nonlinear systems with unmeasurable premise variables. To simultaneously estimate the system states and the sensor faults, a fuzzy descriptor observer is developed. Then, a fault-tolerant controller to track the desired reference trajectories is synthesized. The sufficient stability conditions of the appropriate nonlinear augmented system are derived via the Lyapunov theory and the $$H_\infty $$ H ? approach. In order to obtain both the observer and the controller gains the design conditions are formulated in Linear matrix inequality terms which can be solved using a one-step design procedure. Finally, the FTTC strategy is illustrated on a two-tank system to show its effectiveness.

Observer-Based Synchronization of a New Hybrid Chaotic System and Its Application to Secure Communications

This paper presents an interesting issue of using hybrid dynamical system to chaos synchronization and its application in secure communication using a new 5D hyperchaotic systems. The slave system is modeled by an unknown input observer, in which the unknown input issued from the hybrid system is the transmitted information. Based on the descriptor observer design, the Lyapunov stability theory and some robustness criteria, new su cient synthesis conditions are given in terms of linear matrix inequalities that we can obtain the estimations of both the hybrid system states and the transmitted signals. Numerical examples are provided to show the performances of the proposed approach.

Robust $H_{\infty} $ Sliding Mode Descriptor Observer for Fault and Output Disturbance Estimation of Uncertain Systems

A robust H∞ sliding mode descriptor observer for simultaneous state and disturbance estimation of uncertain system is developed. Inspired by a singular system theory, a descriptor observer design is presented to estimate some class of output disturbances. A sliding mode scheme is used for the observer to reconstruct the input fault based on the transformed coordinate system. Simulation study illustrates the effectiveness of the proposed method.

Design of Observers With Error Limitation in Discrete-Time Descriptor Systems: A Case Study of a Hydraulic Tank System

A novel descriptor observer structure is proposed in the context of discrete-time descriptor linear systems. On the basis of this new structure, the characterization of conditioned-invariant polyhedral sets with the purpose of limiting the estimation error is carried out. Limitation of the estimation error can be achieved by the computation of an as small as possible conditioned-invariant polyhedron, that contains the set of possible initial errors, and by a suitable output injection law. The approach is applied to an experimental tanks platform, for which a descriptor model is identified and validated. The obtained results confirm the merits of the proposed observer for applications in this kind of systems.

Sensor fault estimation and compensation for time-delay switched systems

In this article, the problems of sensor fault estimation and compensation approaches for time-delay switched systems are investigated based on a switched descriptor observer approach. First, a novel time-delay switched descriptor state observer is proposed to estimate both the state and sensor fault. The proposed observer technique is also extended to systems with nonlinearities. Then, based on the estimation of the sensor fault, an efficient fault-tolerant operation can be realised via sensor fault compensation. Finally, an example is given to show the efficiency of the developed techniques.

State and Faults Estimation for T-S Models and Application to Fault Diagnosis

In this study, we propose a method to simultaneously estimate system state and faults for nonlinear systems described by T-S (Takagi-Sugeno) model. The method uses the technique of descriptor systems by considering both sensor and actuator faults as an auxiliary state variable. Then the idea consists in developing a descriptor observer for the given augmented system. This method has the advantage to estimate the state variables and the sensor and actuator faults simultaneously. The observer gains are determined using LMI (Linear Matrix Inequality) formulation. A three tanks system is used to show the effectiveness of the given result.

Chaotic synchronization and secure communication based on descriptor observer

This paper presents an effective technique for both synchronization and secure communication of chaotic systems. A class of nonlinear chaotic systems is discussed, whose transmitted signal can be of multiple dimensions. Based on the descriptor observer design, we can obtain the accurate estimations of both the system states and the transmitted signals. Because the descriptor observer approach avoids using the derivation of the transmitted signal, the approach proposed does not need the assumption that the information signal is slowly varying. Numerical examples are given to illustrate the effectiveness of the proposed scheme.

Descriptor observer approaches for multivariable systems with measurement noises and application in fault detection and diagnosis

In this paper, new descriptor observer design approaches are presented for multivariable systems with measurement noises. If the system matrix is stable, the proposed modified proportional and derivative observer technique allows us not only to decouple the measurement noise in any forms completely, but also obtain accurate estimations of both system states and measurement noises. If the system is detectable and the noise is bounded, it has been shown that two design parameters can provide more degrees of freedom. In this context, the derivative gain parameter is chosen to reduce the amplification of the noise, and the proportional gain is then selected to guarantee the stability of the error dynamics. For systems with both measurement output noises and input disturbances, a modified proportional, derivative and integral observer is constructed to asymptotically estimate states, input disturbances, and output noises at the same time. The applications of the proposed observers for systems with actuator and sensor faults are also discussed. Numerical examples are given to illustrate the design procedures, and the simulation results show the satisfactory tracking performance.