Order Sliding Mode Algorithm Research Articles

One new composite control based smooth nonlinear fractional order sliding mode algorithm and disturbance compensation for PMSM with parameter uncertainties

To achieve high-quality control of PMSM with parameter uncertainties, a nonlinear smooth fractional order sliding mode composite control (NSFOSMCC) strategy is designed in this paper. This approach incorporates a novel nonlinear smooth fractional order sliding mode controller, a novel adaptive super-twisting (AST) algorithm, and a modified nonlinear extended state observer (ESO) to achieve enhanced motor performance. To effectively overcome the disadvantages of simplicity and toughness associated with the conventional fractional order sliding mode controller, a novel nonlinear smooth fractional order sliding mode controller is designed. A novel AST technique is introduced to effectively weaken chattering issues. The modified nonlinear ESO is used to estimate the uncertainty parameters of the PMSM. By combining the modified nonlinear ESO with the latest sliding mode controller, a new composite controller called NSFOSMCC strategy is developed for PMSM. The proposed NSFOSMCC strategy, utilizing a combination of “feedforward plus feedback,” is implemented for PMSM with parameter uncertainties. The reliability and stability of the controller are thoroughly established through the utilization of the Lyapunov stability theorem. Furthermore, comparative results show strong evidence supporting the effectiveness of the novel composite control strategy.

Design of Sensorless Speed Control System for Permanent Magnet Linear Synchronous Motor Based on Fuzzy Super-Twisted Sliding Mode Observer

To improve the tracking capability and sensorless estimation accuracy of a permanent magnet linear synchronous motor (PMLSM) control system, a sensorless control system based on a continuous terminal sliding mode controller (CT-SMC) and fuzzy super-twisted sliding mode observer (F-ST-SMO) was designed. Compared with a conventional slide mode control, CT-SMC can reach the equilibrium point in limited time to ensure the continuity of control and achieve fast tracking of reference speed. Based on the PMLSM design of F-ST-SMO, a super-twisted sliding mode algorithm is used to replace the traditional first order sliding mode algorithm. Meanwhile, fuzzy rules are introduced to adjust the sliding mode gain adaptively, which replaces the fixed gain of traditional SMO and reduces chattering of the system. Finally, the effectiveness and superiority of the designed control system are proven by simulation and experiment.

A modified generic second order algorithm with fixed-time stability

This paper introduces a modified second order sliding mode algorithm with fixed-time stability analysis based on the Lyapunov function approach. An existing second order sliding mode algorithm is generalized, which provides superior features on convergence rate, accuracy, and robustness against a class of perturbations. The performance of the proposed algorithm is compared with existing algorithms through designing observers first. Then, the proposed algorithm-based controller which displays the fixed-time convergence property is designed to validate its effectiveness and to confirm the theoretical analysis.

Terminal Sliding-Mode Control of Virtual Humanoid Robot with Joint Restrictions Walking on stepping objects

This manuscript deals with the problem of controlling a virtualized humanoid robot with 16 degrees of freedom (DOF). The aim of this study was to design an output feedback discontinuous controller which must resolve the sequence of articulation movements to walk over disjoint stepping objects placed in front of the humanoid robot. The suggested controller considers the state restrictions, via a nonstandard strong Lyapunov function, corresponding to the angular displacements and velocities at each articulation. This study implements an extended state terminal second order sliding mode controller with time dependent gains, to ensure the finite-time tracking trajectory of each articulation of the humanoid robot. The terminal sliding mode (TSM) is implemented in a virtual platform developed in a computer-aided design software. For comparison purposes, the controller was compared with a state feedback and a first order sliding mode algorithms.

Optimal adaptive super-twisting sliding mode control base on zero momentum point stability criterion of a lower limb exoskeleton

Disturbance and bounded uncertainty are the most important factors which can be degrade efficient performance of the lower limb exoskeleton. While sliding mode control is a robust control approach against such disturbances, however, by applying the boundary layer in spite of chattering phenomenon, robust performance becomes feeble. In order to overcome this drawback, high order sliding mode algorithms like supper twisting has been proposed in which, chattering phenomenon is mitigated by eliminating the boundary layer. In this paper, an adaptive supper twisting sliding mode control is proposed for a lower limb exoskeleton robot in which the sliding variable and its derivative tend to zero continuously in presence of the disturbance and bounded uncertainty. In addition, the desired trajectory of the upper limb is determined so that in each moment the stability of the robot is guaranteed based on zero momentum point criterion. To achieve maximum stability and minimum error in tracking of the desired trajectories, the controller parameters and the upper limb desired trajectory parameters are optimized using the Harmony Search algorithm. Robot is modeled in ADAMS and then control inputs are applied to the Adams model. Finally, Performance of two controllers is compared. Simulation results reveal the performance of the proposed controller is better than the optimal sliding mode controller.

Hybrid position–admittance realization of an adaptive output super-twisting controller for a robotic scalpel

This study proposes the design and implementation of a hybrid robust automatic controller based on the application of a high order sliding mode algorithm for a robotic scalpel prototype (RS). Two fully actuated arms with three degrees of freedom constitute the RS, one arm holds the sample and the second one has the scalpel to exert the cutting task. Each arm is attached to its corresponding cartesian robotic platform. The available measurements are the angular displacements, the linear displacement and the force vector describing the interaction between the scalpel and the biological sample. A hybrid position–admittance controller implements an output-based adaptive distributed super-twisting algorithm to mobilize the RS. A high order sliding mode observer estimates the unknown angular and linear velocities that were used in the hybrid controller. Once the end-effector of each arm reaches the desired cutting position, the designed controller switches to the admittance controller to avoid damaging the surrounding tissue. Numerical simulations show the advantages of the suggested controller in comparison with classical algorithms. The hybrid sliding mode admittance controller has been successfully evaluated on an self-constructed platform. The experimental results show a precise cut and efficient mobilization of the RS compared to other classical controllers such as proportional-differentiator, proportional-integral and first order sliding mode controllers.

Improved Control of the Web Winding System Based on a Super-Twisting Observer

The web winding system (WWS) presents a difficult problem at the level of control because of the strong nonlinearities of the models and the effects of internal or external disturbances. To improve the dynamic performance and robustness of the control of WWS, a robust control method based on the first and second order sliding mode algorithm is proposed in this work. The stability of the controllers is proved by the theory of Lyapunov stability using an appropriate switching function. In addition, an observer of super twisting tensions is suggested. The developed method allows a direct estimate "on line" of the tension. Finally, computer simulations are developed to show the performance of the sliding mode control and the proposed nonlinear observer.

Modified Super-Twisting Algorithm with an Anti-Windup Coefficient Adopted in PMSM Speed Loop Control

Permanent magnetic synchronous motors (PMSMs) have been widely used in many fields such as ship industry, aerospace industry, and electric locomotives, and it is also suitable for electric vehicles (EVs) as driving motors. Conventional proportional- integral (PI) control method is sensitive to perturbation when it is used to control the PMSM speed loop. The modified super-twisting (MST) algorithm is a continuous second order sliding mode algorithm, which can not only have strong robustness but also reduce chattering, and it can converge within finite time even in the condition of time-varying disturbance. The MST algorithm is introduced to enhance the disturbance rejection performance of the PMSM speed loop. Then, the control law for the speed loop is derived. An anti-windup coefficient is proposed to the MST algorithm to reduce the overshoot resulting from the MST algorithm. It is proved from the simulation results that the MST algorithm has a good performance of the disturbance rejection when adopted in the speed loop, and the proposed anti-windup coefficient can reduce the overshoot well for different speeds within rated rotational speed. The strategy can meet the requirement of complicated operating conditions of EVs well.

Growth rate maximization in fed-batch processes using high order sliding controllers and observers based on cell density measurement

A novel extremum seeking scheme is proposed for the optimization of the specific growth rate in fed-batch processes with substrate inhibited kinetics. The proposed controller is based on a high order sliding mode algorithm, which uses the gradient of the specific growth rate as switching coordinate. A gradient estimation is obtained through a high order sliding mode observer. Both the control and gradient estimation algorithms are finite-time stable. The stability of the controller is analysed using Lyapunov functions for both the unperturbed and perturbed cases and guidelines for the algorithm tuning are provided. The controller and observer algorithms are numerically assessed and simulation results are obtained for a set of different scenarios.

Global and exact HOSM differentiator with dynamic gains for output-feedback sliding mode control

In this paper we introduce a global differentiator based on higher-order sliding modes (HOSM) and dynamic gains to solve the problem of trajectory tracking via output-feedback for a class of uncertain nonlinear plants with arbitrary relative degree and disturbances. Norm observers for the unmeasured state are employed to dominate the disturbances as well as to adapt the gains of the proposed differentiator since the nonlinearities may be state-dependent and time-varying. Uniform global stability and robust exact tracking are guaranteed employing the proposed HOSM based exact differentiator. The obtained results are not restricted to first-order sliding mode control feedback, but applies for second order sliding mode algorithms (twisting, super-twisting and variable gain super-twisting) as well as quasi-continuous HOSM finite-time controllers. Simulations with an aircraft pitch-control application illustrate the claimed properties, even in the presence of measurement noise.

Application of second order sliding mode algorithms for output feedback control in hydraulic cylinder drives with profound valve dynamics

The application of second order sliding mode algorithms for output feedback control in hydraulic valve-cylinder drives appear attractive due to their simple realization and parametrization, and strong robustness toward bounded parameter variations and uncertainties. However, intrinsic nonlinear dynamic effects of hydraulic valves such as slew rate limitations and time delays arising in the electrical and mechanical amplification stages limits the applicability of such methods, and may lead to partial losses of robustness and limit cycles/oscillations in the outputs, internal states and the valve input signals. The application of some popular second order sliding mode controllers and their smooth counterparts are analyzed and experimentally verified. The controllers are considered for output feedback control and compared with a conventional PI control approach. The controllers under consideration are applied for position tracking control of a hydraulic valve-cylinder drive exhibiting strong variations in inertia- and gravitational loads, and furthermore suffer from profound valve dynamics. Results demonstrate that both the twisting- and super twisting algorithms may be successfully applied for this purpose, when continuous approximations of discontinuous are utilized, and furthermore that excellent performance may be achieved when applying their smooth counterparts directly.

Smooth extremum-seeking control for fed-batch processes

Many biotechnological processes have optimal substrate concentrations where a maximum growth rate is achieved. In this work an extremum seeking controller and a gradient estimator are proposed to maximize the growth rate in fed-batch bioprocesses even when the substrate to growth rate map is unknown. Both the controller and estimator are obtained with high order sliding mode algorithms. Stability proofs are given, and tools to tune the algorithms in terms of bounds of the hessian of the map are derived. Simulation results that illustrate the performance of the controller are shown.

Higher-order sliding mode based lateral guidance for unmanned aerial vehicles

A nonlinear sliding mode based scheme is developed for lateral guidance of unmanned aerial vehicles. The guidance and control system is considered as an inner and outer loop design problem, the outer guidance loop generates commands for the inner control loop to follow. Control loop dynamics is considered during derivation of the guidance logic, along with saturation constraints on the guidance commands. A nonlinear sliding manifold is selected for guidance logic design, the guidance loop generates bank angle commands for the inner roll control loop to follow. The real twisting algorithm, a higher order sliding mode algorithm is used for guidance logic design. Existence of the sliding mode along with boundedness of the guidance command is proved to ensure that controls are not saturated for large track errors. The proposed logic also contains an element of anticipatory or feed-forward control, which enables tight tracking for sharply curving paths. Efficacy of the proposed method is verified by flight testing on a scaled YAK-54 unmanned aerial vehicle. Flight results demonstrate robustness and effectiveness of the proposed guidance scheme in the presence of disturbances.

Active Control of Nonlinear Suspension System Using Modified Adaptive Supertwisting Controller

The suspension system is faced with nonlinearities from the spring, damper, and external excitations from the road surface. The objective of any control action provided to the suspension is to improve ride comfort while ensuring road holding for the vehicle. In this work, a robust higher order sliding mode algorithm combining the merits of the modified supertwisting algorithm and the adaptive supertwisting algorithm has been proposed for the nonlinear active suspension system. The proposed controller is robust to linearly growing perturbations and bounded uncertainties. Simulations have been performed for different classes of road excitations and the results are presented.

Super twisting controller for on-orbit servicing to non-cooperative target

A relative position and attitude coupled controller is proposed for rendezvous and docking between two docking ports located in different spacecraft. It is concerned with servicing to a tumbling non-cooperative target spacecraft in arbitrary orbit subjected to external disturbances. By considering both kinematic and dynamical coupled effects of relative rotation on relative translation, a coupled dynamic model is established to represent the relative motion of docking port on target spacecraft with respect to another on the service spacecraft. The spacecraft control is based on the second order sliding mode algorithm of super twisting (ST). It is schemed to manipulate the relative position and attitude synchronously. A formal proof of the finite time convergence property of the closed-loop system is derived theoretically by the second method of Lyapunov. Numerical simulations with the designed ST controller are presented to validate the analytic analysis by contrast with the twisting control algorithm. Simulation results demonstrate that the proposed relative position and attitude integrated controller is characterized by high precision, strong robustness and high reliability.

Transient Stability Improvement of Multi-machine Power System using Higher Order Sliding Mode Control

The main purpose of this paper is to design a non-linear second order sliding mode control for transient stability of two generator system (TGS). Second order sliding mode algorithms such as Twisting Algorithm (TA) and Super Twisting Algorithm (STA) have been applied and their simulation results are compared. The equilibrium point of TGS is maintained after the clearance of fault and the system is in post fault condition. Simulation results verify the proposed controller. The advantage with this type of control is that it does not require linearized model for its implementation and reduced chattering effect.

Time-Varying Gain Second Order Sliding Mode Differentiator

The problem of first order differentiation, when an estimation of an upper bound of the second derivative is available on-line, is studied in this paper. The proposed method include two approaches: Second Order Sliding Mode and High-Gain algorithms, and consider the differentiator gain as a continuous time varying function. This scheme provides chattering attenuation, increasing at the same time the overall performance. Experimental results, realized over an Industrial Hydraulic System, confirm the efficiency of the methodology.

Drive Line Control for Electrically Driven Vehicles Using Generalized Second Order Sliding Modes

The drive shaft torque of an electrically driven vehicle is controlled using a generalized second order sliding mode algorithm. Due to the absence of torque sensors the shaft torque is estimated by means of a higher order unknown input sliding mode observer. The observability of the linear drive line model is analyzed by means of observability measures for two different sensor configurations. Based on these results the observer is designed using a reduced sensor set. The control concept is evaluated with a multi body simulation model of an electrically driven rear axle of a hybrid prototype vehicle with unknown backlash in the drive line.

Avoidance High-Frequency Chattering Second-Order Sliding Mode Controller Design: Buck Converter in Wind Power System

This paper mainly discussed a method of high-frequency second-order sliding mode control for Buck converter in wind power systems. Because the wind energy of nature is always unpredictable and intermittent, the robust control such as sliding mode control is adopted in past literatures. In order to remove the high frequency chattering problem when the traditional sliding mode achieves convergence, the second order sliding mode algorithm is reviewed firstly. Meanwhile, the Buck converter taken as a step-down converter is usually adopted in wind power system, because of its simple structure and good linearity. Under those conditions, the second order sliding mode controller is designed based on Buck converter, especially in high-power wind generation system. The experimental results illustrate that the theory of second order sliding mode can be used in high-power Buck converter. It provides one novel avoidance high frequency chattering method for the technology development of new energy generation system.

A New Recursive Finite-Time Convergent Parameter Estimation Algorithm

AbstractA recursive algorithm for parameter estimation converging in finite time is introduced. It includes as special case the classical Linear Recursive Square algorithm, and is a generalization of the Super-Twisting Algorithm (STA), a second order sliding mode algorithm, to time-varying systems.