Second-order Sliding Mode Observer Research Articles

A novel PV-MPPT method based on a second order sliding mode gradient observer

Leading PV system operation at its Maximum Power Point (MPP) is crucial to improve the overall system efficiency and reduce the solar energy cost. In such a sense, this paper presents a closed-loop Maximum Power Point Tracking (MPPT) method based on the combination of a Second Order Sliding Mode Observer (SOSMO) and a traditional PI controller. The particular SOSMO proposed is especially appropriate to deal with finite time power gradient estimation even in the presence of unmodeled dynamics and external perturbations. Based on this estimation, the PI controller is used to quickly drive the PV system to operate on its MPP and tracking its variations. The resulting closed-loop scheme presents a fast tracking dynamics during rapidly changing environmental conditions having good accuracy and a moderate computational burden. The closed-loop system performance is evaluated using representative computer simulations and corroborated through experimental tests.

A Robust Load Frequency Control Scheme for Power Systems Based on Second-Order Sliding Mode and Extended Disturbance Observer

This paper proposes a new robust load frequency control (LFC) scheme for multiarea power systems based on the second-order sliding mode control and an extended disturbance observer. First, a reduced-order model of the power system LFC is derived. In this model, the load variations and net exchange tie-line power deviations are combined as a lumped disturbance which can be estimated by the extended disturbance observer. Second, a novel sliding surface is designed with the new transformed state variables obtained from the estimated disturbance. The system dynamics can be indicated by sliding surface design using the eigenvalue assignment or the optimal sliding manifold technique. The sliding variable is driven to the sliding surface with a second-order sliding mode algorithm named supertwisting algorithm. The stability of the proposed LFC scheme and the extended disturbance observer is proved using Lyapunov method. The merits of the scheme include faster response speed, stronger robustness against disturbances arising from power system parameter errors, and unmodeled dynamics, and the full consideration of tie-line power flow scheduling variations. Finally, numerical simulations verify the effectiveness of the LFC scheme and reveal its advantages over the state of the arts.

Adaptive fault tolerant control and thruster fault reconstruction for autonomous underwater vehicle

This paper investigates adaptive fault tolerant control and fault reconstruction problem for AUV subject to ocean current disturbance and modelling uncertainty. At first, a virtual closed-loop system based adaptive fault tolerant control method is developed. In this method, the constructed virtual closed-loop system is mainly used to deal with the influence of the initial tracking error in an ideal environment and avoid the serious chattering phenomenon in control output. Then with respect to fault reconstruction in the framework of fault tolerant control, an improved second-order sliding mode observer is constructed to estimate the thruster fault effect. The feedback of the developed observer consists of different functions of the estimation errors, including fractional function, signature function and integral function etc. Furthermore, the stability analysis is given based on Lyapunov theory. Finally, a series of simulations are performed on an over-actuated AUV for different desired trajectories and different types of thruster faults under the condition of the simulated ocean current environment. The comparative simulation results demonstrate the effectiveness and feasibility of the new design.

Re-adhesion control strategy based on the optimal slip velocity seeking method

In the railway industry, re-adhesion control plays an important role in attenuating the slip occurrence due to the low adhesion condition in the wheel–rail interaction. Braking and traction forces depend on the normal force and adhesion coefficient at the wheel–rail contact area. Due to the restrictions on controlling normal force, the only way to increase the tractive or braking effect is to maximize the adhesion coefficient. Through efficient utilization of adhesion, it is also possible to avoid wheel–rail wear and minimize the energy consumption. The adhesion between wheel and rail is a highly nonlinear function of many parameters like environmental conditions, railway vehicle speed and slip velocity. To estimate these unknown parameters accurately is a very hard and competitive challenge. The robust adaptive control strategy presented in this paper is not only able to suppress the wheel slip in time, but also maximize the adhesion utilization performance after re-adhesion process even if the wheel–rail contact mechanism exhibits significant adhesion uncertainties and/or nonlinearities. Using an optimal slip velocity seeking algorithm, the proposed strategy provides a satisfactory slip velocity tracking ability, which was demonstrated able to realize the desired slip velocity without experiencing any instability problem. The control torque of the traction motor was regulated continuously to drive the railway vehicle in the neighborhood of the optimal adhesion point and guarantee the best traction capacity after re-adhesion process by making the railway vehicle operate away from the unstable region. The results obtained from the adaptive approach based on the second-order sliding mode observer have been confirmed through theoretical analysis and numerical simulation conducted in MATLAB and Simulink with a full traction model under various wheel–rail conditions.

Output-Feedback Stabilization of the PVTOL Aircraft System Based on an Exact Differentiator

An output-feedback control strategy for the regulation of a planar vertical take-off and landing aircraft is presented here. The strategy consists of two controllers that work simultaneously. The first controller stabilizes the vertical variable, and is based on a simple feedback-linearization procedure, in combination with a nonlinear controller (which behaves as a terminal slide mode). The other controller stabilizes the horizontal and angular variables to the desired rest position, and was designed using an energy-control method. The velocities were exactly estimated with a second-order sliding-mode observer. Because this observer computes the velocities in finite time, the control strategy can be designed independently. The effectiveness of the closed-loop system was tested through numerical simulations and compared with other control strategies.

Health Parameter Estimation with Second-Order Sliding Mode Observer for a Turbofan Engine

In this paper the problem of health parameter estimation in an aero-engine is investigated by using an unknown input observer-based methodology, implemented by a second-order sliding mode observer (SOSMO). Unlike the conventional state estimator-based schemes, such as Kalman filters (KF) and sliding mode observers (SMO), the proposed scheme uses a “reconstruction signal” to estimate health parameters modeled as artificial inputs, and is not only applicable to long-time health degradation, but reacts much quicker in handling abrupt fault cases. In view of the inevitable uncertainties in engine dynamics and modeling, a weighting matrix is created to minimize such effect on estimation by using the linear matrix inequalities (LMI). A big step toward uncertainty modeling is taken compared with our previous SMO-based work, in that uncertainties are considered in a more practical form. Moreover, to avoid chattering in sliding modes, the super-twisting algorithm (STA) is employed in observer design. Various simulations are carried out, based on the comparisons between the KF-based scheme, the SMO-based scheme in our earlier research, and the proposed method. The results consistently demonstrate the capabilities and advantages of the proposed approach in health parameter estimation.

Sensorless Control of Permanent Magnet Synchronous Machine Based on Second-Order Sliding-Mode Observer With Online Resistance Estimation

In this paper, a supertwisting algorithm based second-order sliding-mode observer (STA-SMO) with online stator resistance ( $ R_{s}$ ) estimation for sensorless control of a nonsalient permanent magnet synchronous machine is proposed. A stator current observer is designed based on an STA to estimate the back electromotive force. A discontinuous sign function in the conventional SMO is replaced by a supertwisting function. The chattering problem, unavoidable in conventional SMO, is eliminated by reducing the amplitude of switching function of an STA-SMO. Meanwhile, a parallel online $ R_{s}$ estimation scheme is presented based on a modified SMO. Because mismatch between actual and set resistance may lead to estimation error and even system instability. The Lyapunov stability theorem is used to obtain the stable conditions of the proposed online $ R_{s}$ observer at both motoring and generating mode. With the help of online $ R_{s}$ observer, resistance uncertainties caused by temperature variation can be taken into account, which means robustness and stability of an STA-SMO can be improved. At the same time, higher position and speed estimation accuracy is obtained and operation range of sensorless control is extended. Finally, the proposed method is validated and compared with a conventional method by simulations and experiments.

Nonlinear observation of internal states of fuel cell cathode utilizing a high-order sliding-mode algorithm

Abstract A scheme for designing a second-order sliding-mode (SOSM) observer that estimates critical internal states on the cathode side of a polymer electrolyte membrane (PEM) fuel cell system is presented. A nonlinear, isothermal dynamic model for the cathode side and a membrane electrolyte assembly are first described. A nonlinear observer topology based on an SOSM algorithm is then introduced, and equations for the SOSM observer deduced. Online calculation of the inverse matrix produces numerical errors, so a modified matrix is introduced to eliminate the negative effects of these on the observer. The simulation results indicate that the SOSM observer performs well for the gas partial pressures and air stoichiometry. The estimation results follow the simulated values in the model with relative errors within ± 2% at stable status. Large errors occur during the fast dynamic processes (

Consensus of second-order nonlinear multi-agent systems via sliding mode observer and controller

This paper investigates the consensus problem of second-order nonlinear multi-agent systems (MASs) via the sliding mode control (SMC) approach. The velocity of each agent is assumed to be unmeasurable. A second-order sliding mode observer is designed to estimate the velocity. Then a distributed discontinuous control law based on first-order SMC is presented to solve the consensus problem. Moreover, to overcome the chatting problem, two controllers based on the boundary layer method and the super-twisting algorithm respectively are presented. It is shown that the MASs will achieve consensus under some given conditions. Some examples are provided to demonstrate the effectiveness of the proposed control laws.

Direct yaw-moment control for 4WID electric vehicle via finite-time control technique

This paper is concerned with the yaw-moment stabilization for four-wheel independent-drive electric vehicle. A second-order sliding mode observer is first designed to estimate the required sideslip angle in a finite time. Then, the finite-time control technique and nonlinear disturbance observer are applied to construct the upper controller to drive both yaw rate and sideslip angle to their desired values. Finally, the lower controller is developed to distribute the torques to the independent four wheels according to the desired yaw moment obtained by the given upper controller. Comparisons among linear, discontinuous and nonsmooth controllers under different working conditions are given by using CarSim software.

New fault-tolerant control architectures based on voting algorithms for electric vehicle induction motor drive

In this paper, we present a comparative study of four voting algorithms in two observer-based fault-tolerant control (FTC) architectures for an electric vehicle (EV) induction motor drive. The first architecture, called output FTC, is based on the mechanical sensor, an EKF and a second-order sliding mode observer (SMO2). The second one, input FTC, is based on three controllers (PI, H∞ loop shaping and the generalized internal model control), the most appropriate being selected to ensure good behaviour in presence of a multiplicative sensor fault (the fault is modelled as an exponential type emulating a bias). A third architecture, called hybrid FTC, based on the previous output and input fault-tolerant schemes, is built to mitigate simultaneous faults. Simulation and experimental results for a 7.5-kW induction motor drive show the efficiency of the approaches and their robustness against parametric variations for different load conditions.

Closed-loop growth-rate regulation in fed-batch dual-substrate processes with additive kinetics based on biomass concentration measurement

This paper deals with the design of feeding rates for dual-substrate fed-batch processes where the main control objective is the regulation of the microbial growth rate. To this end, feedback of the growth rate error is incorporated to a biomass proportional dual feeding law. A second-order sliding mode observer is used to estimate the growth rate, so that no additional sensors are required. Stability conditions are derived and robustness against several disturbances such as yield uncertainty, measurement errors and kinetic model mismatch is analytically and numerically evaluated. The advantages of the proposal include: minimal measurement requirements, regulation with fast convergence to the desired growth rate and reduced regulation error in the presence of disturbances.

Finite-time consensus control for second-order multi-agent systems without velocity measurements

ABSTRACTThis paper investigates the finite-time consensus problem for second-order multi-agent systems with unknown velocities and disturbances. By introducing the second-order sliding mode observer, two novel distributed finite-time protocols with only relative position measurements are proposed for the both cases with known and unknown boundaries of disturbances. On the basis of Lyapunov stability theorem and homogeneous theory, it is proved that the consensus can be achieved in finite time. Simulation examples are provided to show the effectiveness of the theoretical results.

Fault estimation and adaptive fault tolerant control for dynamic systems based on the second-order sliding mode observer

This article is concerned with observer-based fault estimation and adaptive fault tolerant control for a class of continuous-time dynamical systems. First, a second-order sliding mode observer is proposed, which is capable to eliminate chattering effects for fault estimation caused by the conventional sliding mode observer. Second, in order to avoid the cumbersome stability proving process by the geometric method, a Lyapunov function is adopted to prove the observer error dynamical system. Third, based on the estimated fault information by the proposed observer, an adaptive fault tolerant control law is developed to guarantee the stability of the faulty system. Finally, the proposed method is applied to the Boeing 747-100/200 flight control system, and the simulation results verify the effectiveness of the proposed scheme.

Robust Observer for a Class of Nonlinear SISO Dynamical Systems

A procedure to design an asymptotically stable second-order sliding mode observer for a class of single input single output (SISO) nonlinear systems in normal form is presented. The observer converges to the system state in spite of the existence of bounded disturbances and parameter uncertainties affecting the system dynamics. At the same time, the observer estimates the disturbances without the use of an additional filter to recover the equivalent control. The observer design is modular; each module of the observer is applied to each equation of state of the plant. Because of this, the proposed observer can be applied to a broader class of dynamic systems. The performance of the observer is illustrated in numerical and experimental form.

A Second-Order Sliding Mode Observer for Fault Detection and Isolation of Turbocharged SI Engines

This paper proposes a novel method for detection and isolation of wastegate (WG) faults in a turbocharged (TC) gasoline engine. This paper starts with a fault effect analysis on the WG faults, including WG stuck open and stuck closed, which is an early step in a detection strategy design. Then, a second-order sliding-mode observer (SOSMO) is proposed to capture the exhaust manifold dynamics. The observer uses experimentally validated engine models to estimate the WG position and a virtual force. The virtual force represents the external disturbances that disrupt the WG operation and enables the proposed SOSMO to estimate the WG position robust to the faults. Using this force, a detection and isolation algorithm is presented and experimentally verified on a modern TC gasoline engine. Test bench results show that the proposed strategy can successfully detect and isolate the two different WG faults.

Micro-satellite angular rate estimation using second-order sliding mode observer

Development of computationally efficient and accurate attitude rate estimation algorithm using low-cost commercially available star sensor arrays and processing unit for micro-satellite mission is presented. Our design reduces the computational load of least square (LS)-based rate estimation method while maintaining the same accuracy compared to other rate estimation approaches. Furthermore, rate estimation accuracy is improved by using recently developed fast and accurate second-order sliding mode observer (SOSMO) scheme. It also gives robust estimation in the presence of modeling uncertainties, unknown disturbances, and measurement noise. Simulation study shows that rate estimation accuracy achieved by our LS-based method is comparable with other methods for a typical commercially available star sensor array. The robustness analysis of SOSMO with respect to measurement noise is also presented in this paper. Simulation test bench for a practical scenario of satellite rate estimation uses moment-of-inertia variation and environmental disturbances affecting a typical micro-satellite at 500 km circular orbit. Comparison studies of SOSMO with 1-SMO and pseudo-linear Kalman filter show that satisfactory estimation accuracy is achieved by SOSMO.

Fault Estimation for Nonlinear Dynamic System Based on the Second-Order Sliding Mode Observer

This paper is concerned with the problem of fault estimation for a class of Lipschitz nonlinear systems. In order to settle the chattering problem caused by traditional sliding mode observer for fault estimation, a second-order sliding mode observer is proposed on the basis of the super-twisting algorithm. Firstly, linear coordinate transformations are introduced to decouple the fault signal from the system. Secondly, the Lyapunov function approach is applied to derive the criteria guaranteeing the stability of the observer error dynamic system. The obtained results eliminate the cumbersome proving process for the stability of the super-twisting algorithm by the geometric method. Thirdly, an estimation of the fault is generated by the proposed second-order sliding mode observer. Furthermore, only the output information of the system and observer is necessary for fault estimation. Finally, a robotic arm system is employed to show the effectiveness of the proposed fault estimation method.

Observer-based state estimation and unknown input reconstruction for nonlinear complex dynamical systems

This paper considers the issues of both state estimation and unknown information reconstruction for a class of uncertain complex dynamical networks subject to unknown inputs. First, a robust adaptive sliding mode observer which can be used to estimate the states of complex networks through available measurement outputs is developed by employing both adaptive technique and sliding mode control approach. Second, a high-gain second-order sliding mode observer is considered to exactly estimate the derivatives of the output vectors in a finite time. Third, by using the estimates of the states and output derivatives, a kind of algebraic unknown input reconstruction method is proposed. Finally, some numerical simulation examples are given to illustrate the effectiveness of the proposed methods.

Distributed finite-time tracking of multiple Euler-Lagrange systems without velocity measurements

Summary This paper investigates the distributed finite-time tracking problem of networked agents with multiple Euler–Lagrange dynamics. To achieve finite-time tracking, a distributed finite-time protocol is first proposed on the basis of both relative position and relative velocity measurements. By using tools from homogeneous theory, it is theoretically shown that the proposed protocol can guarantee finite-time tracking in the presence of control input constraints. On the basis of the state feedback analysis and with the aid of second-order sliding-mode observer approach, a new class of finite-time tracking protocols based only on the relative position measurements is developed and employed. It is proved that the multiple agents equipped with the designed protocols can track the target location in finite time. Furthermore, a decentralized finite-time protocol based on a distributed estimator is proposed to solve the finite-time tracking problems with a dynamic leader. The effectiveness of the theoretical results is finally illustrated by numerical simulations. Copyright © 2014 John Wiley & Sons, Ltd.