Reduced-order Sliding Mode Observer Research Articles

Single phase second order sliding mode controller for complex interconnected systems with extended disturbances and unknown time-varying delays

<p>Novel results on complex interconnected time-delay systems with single phase second order sliding mode control is investigated. First, a reaching phase in traditional sliding mode control (TSMC) is removed by using a novel single phase switching manifold function. Next, a novel reduced order sliding mode observer (ROSMO) with lower dimension is suggested to estimate the unmeasurable variables of the plant. Then, a new single phase second order sliding mode controller (SPSOSMC) is established based on ROSMO tool to drive the state variables into the specified switching manifold from beginning of the motion and reduce the chattering in control input. Then, a stability condition is suggested based on the well-known linear matrix inequality (LMI) method to ensure the asymptotical stability of the whole plant. Finally, an illustrated example is simulated to validate the feasible application of the suggested technique.</p>

Single Phase Second Order Sliding Mode Controller for Mismatched Uncertain Systems with Extended Disturbances and Unknown Time-Varying Delays

In this paper, a novel single phase second order sliding mode controller (SPSOSMC) is proposed for the mismatched uncertain systems with extended disturbances and unknown time-varying delays. The main achievements of this study consist of three tasks: 1) a reaching phase in conventional sliding mode control (CSMC) technique is removed to ensure the global stability of the system; 2) an influence of the undesired high-frequency oscillation phenomenon in control input is vanished; 3) an exogenous perturbation is generally extended to the k-order disturbance of state variable. Firstly, a single phase switching manifold function is defined to eliminate the reaching phase in CSMC. Secondly, an unmeasurable state variable is estimated by using the proposed reduced-order sliding mode observer (ROSMO) tool. Next, a SPSOSMC is built based on the help of ROSMO tool and output information only. Then, a sufficient condition is established by employing the linear matrix inequality (LMI) technique and Lyapunov function theory such that the resulting sliding mode dynamics is asymptotically stable. Finally, a numerical example is simulated via the well-known MATLAB software to validate the effectiveness of the proposed technique.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

A Sliding Mode Observer Design for the Average State Estimation in Large-Scale Systems

In this letter the average state estimation problem on a large-scale system with only few gateway nodes available for measurements is solved as the design problem of a reduced-order sliding mode observer subjected to unmatched perturbations. Necessary and sufficient conditions to guarantee the exact estimation are derived. Still, even in the case such conditions are not fulfilled, the boundedness of the estimation error is proved. Finally, a criteria to minimize such bound, and a gain adaptation law to trade-off that bound and its convergence rate are provided. Neither the observer complexity nor the estimation error depend explicitly on the size of the system, thus making the approach scalable and computationally tractable. Simulations supporting the effectiveness of the proposed strategy and a comparison with other existing strategies are also provided.

Robust fault estimation of a blade pitch and drivetrain system in wind turbine model

In this article, a novel robust fault estimation scheme to ensure efficient and reliable operation of wind turbines has been presented. Wind turbines are complex systems with large flexible structures that work under very turbulent and unpredictable environmental conditions for a variable electrical grid. The proposed observer-based estimation scheme consists of a set of possible faults affecting the dynamics, sensors, and actuators of wind turbines. First, the pitch and drivetrain system faults occur simultaneously with process and sensor disturbances that are called unknown input signals. Second, through a series of coordinate transformations, the faulty subsystem is decoupled from the rest of the system. The first subsystem is affected by unknown inputs, and the second one is affected by faults. A reduced-order unknown input observer is designed to reconstruct states accurately, whereas a reduced-order sliding mode observer is designed for the second subsystem such that it is robust against unknown inputs and faults. Moreover, the reduced-order unknown input observer guarantees the asymptotic stability of the error dynamics using the Lyapunov theory method and completely removes unknown inputs; on the other hand, the reduced-order sliding mode observer is designed to reconstruct faults for the faulty subsystem accurately. Until now, authors only focused on an unknown input signal in the dynamics of the system, especially in nonlinear systems. The estimated fault will be adequate to accommodate the control loop, and sufficient conditions are developed to guarantee the stability of the state estimation error. In the next step, to figure the effectiveness of the proposed approach, a wind turbine benchmark system model is considered with faults and unknown inputs scenarios. The simulation results are used to validate the robustness of the proposed algorithms under noise conditions, and the results show that the algorithm could classify faults robustly.

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.

Sliding mode controller-observer pair for p53 pathway.

A significant loss of p53 protein, an anti‐tumour agent, is observed in early cancerous cells. Induction of small molecules based drug is by far the most prominent technique to revive and maintain wild‐type p53 to the desired level. In this study, a sliding mode control (SMC) based robust non‐linear technique is presented for the drug design of a control‐oriented p53 model. The control input generated by conventional SMC is discontinuous; however, depending on the physical nature of the system, drug infusion needs to be continuous. Therefore, to obtain a smooth control signal, a dynamic SMC (DSMC) is designed. Moreover, the boundedness of the zero‐dynamics is also proved. To make the model‐based control design possible, the unknown states of the system are estimated using an equivalent control based, reduced‐order sliding mode observer. The robustness of the proposed technique is assessed by introducing input disturbance and parametric uncertainty in the system. The effectiveness of the proposed control scheme is witnessed by performing in‐silico trials, revealing that the sustained level of p53 can be achieved by controlled drug administration. Moreover, a comparative quantitative analysis shows that both controllers yield similar performance. However, DSMC consumes less control energy.

Actuator and Sensor Fault Estimation for Time-Delay Markov Jump Systems With Application to Wheeled Mobile Manipulators

In this paper, fault and state estimation issue for wheeled mobile manipulators with time delay, using a novel sliding mode observer (SMO) approach has been discussed. It is well-known that the traditional SMO method, i.e., the equivalent output error injection technique cannot be simply employed to Markov jump systems (MJSs) to estimate actuator faults. In this paper, we propose a novel SMO to reconstruct the actuator and sensor faults for MJSs with time delay. First, we decouple the actuator faults from the first subsystem by utilizing coordinate transformation technique. Then, construct an augmented plant for the new system and propose a novel reduced-order SMO. By the proposed novel SMO, the state and fault can be reconstructed simultaneously. Finally, an illustrative wheeled mobile manipulator example is given to show the effectiveness of the proposed approach.

Dominant-Modes-Based Sliding-Mode Observer for Estimation of Temperature Distribution in Rapid Thermal Processing System

A novel method for the estimation of the temperature distribution in a rapid thermal processing (RTP) system is developed in this paper. The proposed method uses a proper orthogonal decomposition algorithm to extract the dominant modes of the temperature distribution and a reduced-order model is obtained. Then, a reduced-order sliding-mode observer is developed to capture the dynamics of the dominant modes. The estimated dynamics of the dominant modes can be used to reconstruct the temperature distribution. It is proved that the estimation error would be drawn into a small boundary rapidly. Test results confirm the effectiveness of the proposed observer for the RTP system.

A proton exchange membrane fuel cell with an airflow cooling system: Dynamics, validation and nonlinear control

This work synthesizes a reduced-order sliding mode observer-based sliding mode controller for a proton exchange membrane fuel cell system. This multivariable closed-loop system is dealt with two inputs (hydrogen fuel flow and cooling air flow rate) and two outputs (output voltage and stack temperature). For this, at first, we develop a nonlinear transient proton exchange membrane fuel cell model. This model is verified with the available experimental data. To maintain the fuel cell operating temperature, it is coupled with an airflow cooling fan. Then a nonlinear model-based control scheme is formulated that consists of sliding mode controller and reduced-order sliding mode observer. A special care is taken in control model against chattering response. Evaluating the sliding mode observer performance, it is integrated with sliding mode controller and the resulting hybrid control structure is compared with a traditional proportional integral controller. The nonlinear sliding mode observer-based controller shows its superiority over the proportional integral controller in rejecting the disturbance as well as tracking the set point.

Nonlinear multivariable sliding mode control of a reversible PEM fuel cell integrated system

This work proposes a reduced-order sliding mode observer (SMO) based nonlinear control to regulate a multivariable proton exchange membrane fuel cell (PEMFC) integrated system. To make this system reversible, it is integrated with an air compressor, air cooler, primary manifold, supply manifold, humidifier and return manifold. To recirculate the unreacted hydrogen fuel, an ejector and to suppress the fuel cell heat of reaction, a simple water cooled heat exchange system is modeled. Among the three measured outputs, namely output voltage (main product), compressor air flow and fuel cell body temperature, the last two are proposed to control at their desired values to avoid oxygen starvation at cathode side and adverse effect of system temperature, respectively. To increase the lifetime of proton exchange membrane fuel cell and its smooth operation, a model based sliding mode controller (SMC) is synthesized, coupling with a nonlinear sliding mode observer required to estimate the unmeasured state information. This observer is formulated based on the reduced-order process model that leads to a process/model mismatch. Further, a saturation function is included in the sliding mode control theory in order to avoid the chattering effect. The performance of the proposed nonlinear observer based sliding mode controller is finally investigated by comparing with the conventional proportional integral (PI) controller in terms of servo (output voltage and fuel cell body temperature) and regulatory (load current) responses.

Descriptor reduced-order sliding mode observers design for switched systems with sensor and actuator faults

This paper investigates the state and fault estimation problem for linear continuous-time switched systems with simultaneous disturbances, sensor and actuator faults, and two types of observer approaches are presented to solve this design issue. The first one is a linear descriptor reduced-order observer, which generates the exact estimation of state and sensor faults together with disturbances by decoupling them from the state vector without any supplementary design. The second one refers to a descriptor sliding mode observer approach, where the state, disturbances, sensor and actuator faults can be reconstructed simultaneously. In the second method, the reachability of sliding surface is not necessary to be investigated, since the actuator faults can be estimated directly without using the equivalent output error injection scheme as in traditional sliding mode observers. Therefore, both developed observer approaches avoid the sliding surface switching problem of traditional sliding mode observers in application to switched systems. Finally, an example is given to demonstrate the effectiveness of the two designed observer methods.

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.

A reduced-order nonlinear sliding mode observer for vehicle slip angle and tyre forces

In this paper, a reduced-order sliding mode observer (RO-SMO) is developed for vehicle state estimation. Several improvements are achieved in this paper. First, the reference model accuracy is improved by considering vehicle load transfers and using a precise nonlinear tyre model ‘UniTire’. Second, without the reference model accuracy degraded, the computing burden of the state observer is decreased by a reduced-order approach. Third, nonlinear system damping is integrated into the SMO to speed convergence and reduce chattering. The proposed RO-SMO is evaluated through simulation and experiments based on an in-wheel motor electric vehicle. The results show that the proposed observer accurately predicts the vehicle states.

Ultra-precision positioning system using robust sliding mode observer and control

Abstract In this paper, the robust sliding mode control based on reduced order observer is proposed to overcome the model imperfections in ultra-precision positioning system. The reduced order sliding mode observer enables the states and the estimated outputs to be available for controller design. The manifold of the sliding mode control is composed of the estimated output only instead of system states. Using the reduced order observer, the sliding mode control is designed in output feedback form. The effectiveness of the proposed control algorithm has been proved from the application of an ultra-precision stage.

Robust reduced-order sliding mode observer design

In this article, a triple state and output variable transformation-based method combined with linear matrix inequality (LMI) techniques to design a new robust reduced-order sliding mode observer for perturbed linear multiple-input and multiple-output systems is developed. The state and output variables of the original system are triple transformed into suitable canonical form coordinates to facilitate the design of a reduced-order observer. The existing transformations are summarised in this study and presented systematically. A new combined observer configuration is proposed and compared with another type of observers. Global asymptotical stability LMI and sliding mode existence conditions for the coupled observer error system are derived using Lyapunov full quadratic form. Reaching and sliding modes of motion of decoupled observer error system are discussed as well. Two numerical and simulation examples are given to illustrate the usefulness of the proposed design techniques.

Stabilizing the unstable periodic orbits of a chaotic system using model independent adaptive time-delayed controller

In this paper we deal with the control of chaotic systems. Knowing that a chaotic attractor contains a myriad of unstable periodic orbits (UPO’s), the aim of our work is to stabilize some of the UPO’s embedded in the chaotic attractor and which have interesting characteristics. First, using the input-to-state linearization method in conjunction with a time-delayed state feedback, we design a control signal that can achieve stabilization. Next, an adaptive time-delayed state feedback is proposed which shows at once efficiency and simplicity and circumvents the construction complexity of the first controller. Finally, we propose a reduced order sliding mode observer to estimate the necessary states for the design of an adaptive time delayed state feedback controller. This last controller has one main advantage, it in fact achieves UPO stabilization without using the system model. The efficacy of the proposed methods is illustrated by numerical simulations onto Chua’s system.

FULL VEHICLE ACTIVE SUSPENSION: SENSOR FAULT DIAGNOSIS AND FAULT TOLERANCE

In this paper, sensor fault detection, identification and fault tolerance model-based approach is designed for a linear full vehicle's active suspension system. The approach uses a bank of reduced order sliding mode observers to generate residuals. Residuals are defined in such a way to isolate the faulty sensor after detecting the occurrence of the fault. Once detected and isolated, the sensor fault is accommodated by replacing the faulty measurement by its estimation. In this study, sensor drift, bias and complete breakdown are considered. Simulation is made to illustrate the proposed strategy.