High-order Sliding Mode Differentiator Research Articles

Second-order sliding-mode differentiators: an experimental comparative analysis using Van der Pol oscillator

ABSTRACTThis article provides a comparative study of four different second-order sliding-mode (SOSM) differentiators proposed in the literature, namely, standard higher-order sliding-mode (HOSM) differentiator, non-homogeneous HOSM differentiator, uniform robust exact differentiator and hybrid fixed-time differentiator. Based on sliding-mode principles, these differentiators can provide robust exact differentiation with finite/fixed-time convergence. First, a comprehensive summary of the different methods is provided. Then, the differentiators are applied experimentally to estimate the states of a Van der Pol oscillator. Through experiments, it is shown that the different differentiators outperformed a Kalman-like observer, high-gain differentiator and extended Kalman filter. Finally, some suggestions are provided on the selection of SOSM differentiators for various applications.

Hypersonic Missile Adaptive Sliding Mode Control Using Finite- and Fixed-Time Observers

Finite- and fixed-settling time differentiators utilizing a nonrecursive higher order sliding mode (HOSM) observer are studied. Fixed convergence time estimation is achieved independent of initial conditions of the differentiation errors. The corresponding convergence/settling times are estimated. The finite- and fixed-time HOSM differentiators’ performance is compared against the Levant recursive one via a hypersonic missile control simulation case study during the missile's terminal phase of flight. A continuous adaptive HOSM control is utilized. The double-layer adaptive algorithm is based on an equivalent control concept and does not allow overestimation of the control gains that mitigates control chattering. The robustness and high-accuracy output tracking in the presence of matched and unmatched external disturbances and missile model uncertainties is demonstrated for both the differentiators and the controller.

Output-feedback variable gain super-twisting algorithm for arbitrary relative degree systems

ABSTRACTThis paper presents an output-feedback control strategy based on the variable gain super-twisting algorithm. The proposal achieves robust global/semi-global exact tracking results for plants with arbitrary relative degree. This is ensured in spite of parametric uncertainties and disturbances that may be state-dependent and time-varying. The construction of such controller is based on a (non)homogeneous higher order sliding-mode differentiator with dynamic gains. The gain adaptation schemes for the controller and differentiator are based on norm observers to overcome the lack of state measurement. The continuous nature of the obtained control signal alleviates the chattering phenomenon. The stability properties of the proposed controller are demonstrated by means of a Lyapunov function-based analysis. The theoretical results are verified through a simulation example, and experimentally tested on a seesaw module.

HOSM Differentiator with Varying Gains for Global/Semi-Global Output Feedback

This paper develops a higher-order sliding mode (HOSM) differentiator with adaptive gains to address the exact tracking control problem using only input-output information of a wider class of nonlinear systems with disturbances and parametric uncertainties. The complete state of the plant is assumed unmeasured so that a norm state estimator is constructed to norm bound the state-dependent disturbances and dynamically update the gains of the proposed differentiator. Global/semi-global stability properties and robust exact tracking can be achieved when the proposed adaptive HOSM based differentiator is applied to output-feedback purposes. Numerical simulations are presented for different sliding mode control designs, such as: (a) first-order sliding mode control, (b) non-singular terminal sliding modes, (c) second order sliding mode (SOSM) algorithms (twisting and super-twisting) as well as (d) quasi-continuous HOSM finite-time controllers.

Finite‐ and fixed‐time differentiators utilising HOSM techniques

Finite- and fixed-settling time of real-time differentiators utilising a higher-order sliding mode (HOSM) observer based on both non-recursive and recursive algorithm formulations are studied using constant observer gains. Fixed convergence time estimation is achieved independent of initial conditions of the differentiation errors. The corresponding convergence/settling times are estimated. The HOSM differentiators are compared with the ideal differentiation formulation and MATLAB's differentiator. The analysis incorporates input noise to demonstrate via simulations the improved performance for real-time noisy input signals.

A Robust Backstepping High-Order Sliding Mode Control Strategy for Grid-Connected DG Units With Harmonic/Interharmonic Current Compensation Capability

This paper presents a new nonlinear current control strategy based on backstepping control and high-order sliding mode differentiator in order to employ distributed generation (DG) unit interfacing converters to actively compensate harmonics/interharmonics of local loads. The converter-based DG unit is connected to a weak grid (with uncertain impedance) and local load (that can be parametrically uncertain and topologically unknown) through an LCL filter. The proposed strategy robustly regulates the inverter output currents and delivers pure sinusoidal, three-phase balanced currents to the grid. The new controller demonstrates the robust performance and robust stability of the DG unit system with respect to the filter parameters uncertainties, grid impedance, grid frequency, and grid voltage as well as the unknown load dynamics that include unbalanced loads and nonlinear loads with harmonic and interharmonic currents. We should remark that the local compensation of the loads with interharmonic current using a DG unit system is first proposed in this paper. When compared with the popular parallel proportional resonant control technique, the proposed controller offers smoother transient responses and a lower level of current distortion. The performance of the proposed control strategy is verified in MATLAB/SimPowerSystems toolbox.

Higher order sliding-mode observers with scaled dissipative stabilisers

ABSTRACTThis paper proposes a global theoretically exact finite-time convergent observer for a class of nonlinear systems, which are not necessarily bounded-input-bounded-state with respect to the unknown inputs. With this aim, a scaled dissipative stabiliser is suggested ensuring that the highest derivative of the output estimation error is independent from the stabiliser gains. After this, a higher order sliding-mode differentiator with the gains adjusted to the upper bound of the unknown inputs is applied achieving finite-time convergence.

A backstepping high-order sliding mode voltage control strategy for an islanded microgrid with harmonic/interharmonic loads

This paper presents a new nonlinear voltage control strategy based on backstepping control and a high-order sliding mode differentiator for an islanded microgrid. The microgrid consists of multiple distributed generation (DG) units with an arbitrary configuration that can be parametrically uncertain or topologically unknown. The proposed controller robustly regulates the microgrid voltages in the presence of parametric uncertainties, unmodeled dynamics, load imbalances, and nonlinear loads with harmonic/interharmonic currents. In contrast to existing methods, the controller does not need to know the frequency of harmonic and interharmonic current of microgrid loads that lead to the reduction of the steady-state error of the voltage controller in the frequency of unknown harmonics and interharmonics. The MATLAB/SimPowerSystems toolbox has verified the proposed control strategy's performance.

Fault detection and isolation for nonlinear non-affine uncertain systems via sliding-mode techniques

ABSTRACTThis paper considers the fault detection and isolation problem for nonlinear uncertain non-affine systems. The proposed approach is based on an output-feedback stabilisation strategy, which exploits a Luenberger-like nonlinear observer. As a main result, a residual-based fault detection and isolation approach is developed, which relies on the measurable output, some of its derivatives, which are provided exactly by a uniform high-order sliding-mode differentiator, and the observer’s state. The proposed methodology is able to detect some possible components and actuators faults, and to isolate, under some mild conditions, the actuator faults from those ones in components. Simulation results illustrate the feasibility of the proposed approach.

Coordinated excitation and steam valve control for multimachine power system using high order sliding mode technique

This paper presents a decentralized coordinated excitation and steam valve adaptive control combined with a high-order sliding mode differentiator. The aim is to obtain high performance for the terminal voltage and the rotor speed simultaneously under a sudden fault and a wide range of operating conditions. The methodology adopted is based on second order sliding mode technique using the supper twisting algorithm. The proposed scheme requires only local information on the physically available measurements of relative angular speed, active electric power and terminal voltage with the assumption that the power angle and mechanical power input are not available for measurement. It can be implemented locally and dispersedly for individual generators and is convenient for industrial applications. Simulation results in the case of the Kundur 4-machines 2-area power system show the effectiveness, robustness and superiority of the proposed scheme over the classical AVR/PSS controller and steam valve PI regulator.

Decentralized nonlinear coordinated excitation and steam valve adaptive control for multi-machine power systems

Abstract In this paper, a decentralized nonlinear coordinated excitation and steam valve adaptive control combined with a modified high-order sliding mode differentiator is designed for multi-machine power system stability enhancement. The proposed control scheme is based on Lyapunov’s direct method and requires only local information on the physically available measurements of relative angular speed, active electric power and terminal voltage with the assumption that the power angle and mechanical power input are not available for measurement. Each synchronous generator is considered as a classical fifth order model that includes turbine dynamics. The simplicity of the proposed scheme and its robustness with respect to large perturbations, change in operating point and parameter uncertainties constitute the main positive features. Simulation results in the case of the Kundur 4-machines 2-area power system show the effectiveness, robustness and superiority of the proposed scheme over the classical AVR/PSS.

Dynamic Gains Differentiator for Hydraulic System Control

This paper deals with online numerical differentiation of a noisy time signal where new higher order sliding mode differentiators are proposed. The key point of these algorithms is to include a dynamic on the differentiator parameters. These dynamics tune-up automatically the algorithm gains in real-time. Convergence properties of the new schemes are derived using a Lyapunov approach. Their effectiveness is illustrated via simulations and experimental tests, where comparative studies are performed between classical schemes and the new ones. Such algorithms are also used in the feedback control of an electrohydraulic system.

Composite guidance laws using higher order sliding mode differentiator and disturbance observer

This paper has proposed a new composite robust guidance law to intercept maneuvering targets without line-of-sight (LOS) angular rate information. The presented guidance law is constructed through a combination of second-order sliding mode, higher-order sliding mode (HOSM) differentiator, and finite-time convergent disturbance observer (FTDOB). More specifically, the HOSM differentiator is used to extract the LOS angular rate information from LOS angle measurement, while the FTDOB is used to estimate and compensate the unknown target maneuvers. The finite-time stability of the closed-loop guidance system is established using finite-time bounded function and Lyapunov function methods. Next, the proposed guidance law is applied to three-dimensional homing engagement, where the FTDOB is used to estimate the target maneuver as well as the cross-coupling terms between the elevation and the azimuth motions. Numerical simulations with some comparisons are carried out to demonstrate the superiority of the proposed method.

Neural Active Disturbance Rejection Output Control of Multimotor Servomechanism

In this brief, the problems of stability and tracking control for multimotor servomechanism with unmodeled dynamics are addressed by neural active disturbance rejection control. For realizing output feedback, an extended state observer based on high-order sliding mode (HOSM) differentiator is designed to estimate the unmeasured velocity. Moreover, HOSM differentiator is introduced to modify the traditional dynamic surface control method. The designed controller solves the contradiction between rapidness and overshoot, which comes from the traditional proportional-integral-derivative that deals with a large number of practical systems with unknown disturbances. In addition, unknown functions, including friction and disturbances, are approximated by Chebyshev neural networks (CNNs), in which adaptive laws are provided by Lyapunov method. Especially, steady state and transient performance of closed-loop system are maintained by performance function in theoretical analysis. Finally, extensive experimental results are provided to illustrate our proposed approach.

Estimating rotor parameters in induction motors using high‐order sliding mode algorithms

A good estimate of the rotor's parameters is essential in high-performance control of induction motors. It is shown that the structural impediment that prevents applying a usual adaptive observer to estimate these parameters is that the relative degree between the measured output and the unknown parameters is not one. Then, the high-order sliding mode differentiator is used to circumvent this restriction allowing the construction of a usual adaptive observer. Simulation results are presented to illustrate the performance of the proposed observer under ideal conditions and in the presence of measurement noises.

Modified neural dynamic surface approach to output feedback of MIMO nonlinear systems.

We report an adaptive output feedback dynamic surface control (DSC), maintaining the prescribed performance, for a class of uncertain nonlinear systems with multiinput and multioutput. Designing neural network observers and modifying the DSC method achieves several control objectives. First, to achieve output feedback control, the finite-time echo state networks (ESN) observer with fast convergence is designed to obtain the online system states. Thus, the immeasurable states in traditional state feedback control are estimated and the unknown functions are approximated by ESN. Then, a modified DSC approach is developed by introducing a high-order sliding mode differentiator to replace the first-order filter in each step. Thus, the effect of filter performance on closed-loop stability is reduced. Furthermore, the input to state stability guarantees that all signals of the whole closed-loop system are semiglobally uniformly ultimately bounded. Specifically, the performance functions make the tracking errors converge to a compact set around equilibrium. Two numerical examples illustrated the proposed control scheme with satisfactory results.

Velocity estimation of valve movement in oysters for water quality surveillance

The measurements of valve opening activity in a population of oysters under natural environmental conditions are used to estimate the velocity of their valve movement activity. Three different differentiation schemes were used to estimate the velocity, namely an algebraicbased differentiator method, a non-homogeneous higher order sliding mode differentiator and a homogeneous finite-time differentiator. The estimated velocities were then used to compare the performances of these three different differentiators. We demonstrate that this estimated velocity can be used for water quality monitoring as the differentiators can detect very rapid change in valve movements of the oyster population resulting from some external stimulus or common input.

PEM fuel cell air-feed system observer design for automotive applications: An adaptive numerical differentiation approach

In this paper, an adaptive algebraic observer is proposed for a Polymer Electrolyte Membrane Fuel Cell (PEMFC) air-feed system, based on Higher Order Sliding Mode (HOSM) differentiators. The goal is to estimate oxygen and nitrogen partial pressures in the fuel cell cathode side, using measurements of supply manifold pressure and compressor mass flow rate. As the proposed technique requires the time derivatives of the states, Lyapunov-based adaptive HOSM differentiators are synthesized and implemented for estimating these derivatives without a-priori knowledge of the upper bounds of their higher order time derivatives. The performance of the proposed method is validated through experiments on a Hardware-In-Loop (HIL) test bench. These results illustrate the feasibility and effectiveness of the proposed approach.

Takagi-Sugeno Observers: Experimental Application for Vehicle Lateral Dynamics Estimation

This brief presents a contribution to nonlinear observer design for both the estimation of vehicle lateral dynamics and road curvature. The latter is recovered by a simple algebraic technique and high-order sliding mode differentiator, which allows to estimate exactly the time derivatives of measured signals. For the lateral dynamics of the vehicle, a new approach is developed by the use of a Takagi-Sugeno (TS) model representing exactly, with no loss of information, the nonlinear vehicle behavior in a compact set of the state space. The TS model involves unmeasured premise variables. The proposed new observer starts with the estimation of these premise variables. Second, the design of an observer with weighting functions depending on these estimated premise variables is considered. Theoretically, the proposed observer ensures exponential convergence of the state estimation error toward zero. This convergence is studied by the Lyapunov theory and the obtained stability conditions are expressed in terms of linear matrix inequalities. Finally, experimental results are given for vehicle lateral dynamics and road curvature estimation with real data.

High-Order Mismatched Disturbance Compensation for Motion Control Systems Via a Continuous Dynamic Sliding-Mode Approach

A new continuous dynamic sliding-mode control (CDSMC) method is proposed for high-order mismatched disturbance attenuation in motion control systems using a high-order sliding-mode differentiator. First, a new dynamic sliding surface is developed by incorporating the information of the estimates of disturbances and their high-order derivatives. A CDSMC law is then designed for a general motion control system with both high-order matched and mismatched disturbances, which can attenuate the effects of disturbances from the system output. The proposed control method is finally applied for the airgap control of a MAGnetic LEViation (MAGLEV) suspension vehicle. Simulation results show that the proposed method exhibits promising control performance in the presence of high-order matched and mismatched disturbances.