Fractional-Order Super-Twisting Sliding-Mode Procedure Design for a Class of Fractional-Order Nonlinear Dynamic Underwater Robots

The purpose of this study is to design a fractional-order super-twisting sliding-mode controller for a class of nonlinear fractionalorder systems.The proposed method has the following advantages:(1)Lyapunov stability of the overall closed-loop system,(2)output tracking error’s convergence to zero,(3)robustness against external uncertainties and disturbances,and(4)reduction of the chattering phenomenon.To investigate the performance of the method,the proposed controller is applied to an autonomous underwater robot and Lorenz chaotic system.Finally,a simulation is performed to verify the potential of the proposed method.

Sliding-mode observers for systems with unknown inputs and measurement disturbances

The method to design sliding-mode observers for systems with unknown inputs and measurement disturbances is presented in the paper. An augmented system is constructed by viewing the measurement disturbances as unknow inputs. For such an augmented system, the so-called observer matching condition is not satisfied. Based on the construction of auxiliary outputs, the observer matching condition may be satisfied. High-order sliding-mode differentiators are developed to obtain the estimates of those unmeasurable variables contained in the auxiliary output vector. Employing the estimate of auxiliary output vector, a sliding-mode observer is designed. The simulation results to a real model show that the proposed method is effective.

Sliding-mode control of path following for underactuated ships based on high gain observer

A nonlinear robust control strategy is proposed to force an underactuated surface ship to follow a predefined path with uncertain environmental disturbance and parameters.In the controller design,a high-gain observer is used to estimate velocities,thus only position and yaw angle measurements are required.The control problem of underactuated system is transformed into a control of fully actuated system through adopting an improved line-of-sight(LOS) guidance law.A sliding-mode controller is designed to eliminate the yaw angle error,and provide the control system robustness.The control law is proved semi-globally exponentially stable(SGES) by applying Lyapunov stability theory,and numerical simulation using real data of a monohull ship illustrates the effectiveness and robustness of the proposed methodology.

Robust Fractional-Order Proportional-Integral Observer for Synchronization of Chaotic Fractional-Order Systems

In this paper, we propose a robust fractional-order proportional-integral(FOPI) observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities(LMIs) approach by using an indirect Lyapunov method. The proposed FOPI observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional(FOP) observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.

Sliding Mode Control Approach with Integrated Disturbance Observer for PMSM Speed System

The research on high-performance vector control of permanent magnet synchronous motor(PMSM)drive system plays an extremely important role in electrical drive system.To further improve the speed control performance of the system,a fast non-singular end sliding mode(FNTSM)surface function based on traditional NTSM control is developed.The theoretical analysis proves that the FNTSM surface function has a faster dynamic response and more finite-time convergence.In addition,for the self-vibration problem caused by high sliding mode switching gain,an FNTSM control method with anti-disturbance capability was designed based on the linear disturbance observer(DO),i.e.the FNTSMDO method was employed to devise the PMSM speed regulator.The comparative simulation and experiment results with traditional PI control and NTSM control methods indicate that the FNTSMDO method could improve the dynamic performance and anti-interference of the system.

Observer-Based Control for a Cable-Driven Aerial Manipulator under Lumped Disturbances

With the increasing demand for interactive aerial operations,the application of aerial manipulators is becoming more promising.However,there are a few critical problems on how to improve the energetic efficiency and pose control of the aerialmanipulator forpractical application.In this paper,a novel cable-drivenaerialmanipulatorused for remote water sampling is proposed and then its rigid-flexible coupling dynamics model is constructed which takes joint flexibility into account.To achieve high precision joint position tracking under lumped disturbances,a newly controller,which consists of three parts:linear extended state observer,adaptive super-twisting strategy,and fractional-order nonsingular terminal sliding mode control,is proposed.The linear extended state observer is adopted to approximate unmeasured states and unknown lumped disturbances and achieve model-free control structure.The adaptive super-twisting strategy and fractional-order nonsingular terminal sliding mode control are combined together to achieve good control performance and counteract chattering problem.The Lyapunovmethod is utilized to prove the overall stability and convergence of the system.Lastly,various visualization simulations and ground experiments are conducted,verifying the effectiveness of our strategy,and all outcomes demonstrate its superiorities over the existing control strategies.

Sliding-mode Observer-based Grid Voltage-observation Method with Frequency-fixed Dual SOGI and Cross-compensated Phase-locked Loop

Conventional sliding-mode observer(SMO)-based grid-voltage observation methods often require a low-pass filter(LPF)to remove high-frequency sliding-mode noise.However,a complicated phase-and amplitude-compensation method,which is highly sensitive to the DC-offset,is required.A frequency-adaptive dual second-order generalized integrator(SOGI)can be used to replace the LPF,eliminating the compensation link and the effects of the DC-offset;however,strong coupling is introduced between the front-end SOGI block and back-end phase-locked loop(PLL)block,thereby reducing the dynamic performance.To solve this problem,this study proposes an SMO-based grid-voltage observation method with a frequency-fixed dual SOGI and cross-compensated PLL that can eliminate the frequency coupling between the front-end SOGI block and back-end PLL blocks,thereby increasing its dynamic performance.In this study,the phase and amplitude are compensated simultaneously using the proposed cross-compensation method,achieving an accurate observation of the grid voltage under off-nominal frequencies.An analysis of the small-signal model theoretically verified that the proposed method has good dynamic performance.Finally,the superiority of the proposed method is verified through comparative experiments.

Controllability, Observability and Stability for a Class of Fractional-Order Linear Time-Invariant Control Systems

The definitions of controllability, observability and stability were presented for fractional-order linear systems. Using the Cayley-Hamilton theorem and Mittag-Leffler function in two parameters, the sufficient and necessary conditions of controllability and observability for such systems were derived. In terms of Lyapunov’s stability theory, using the theorems of Mittage-Leffler function in two parameters this paper directly derived the sufficient and necessary condition of stability for such systems. The results obtained are useful for the analysis and synthesis of fractional-order linear control systems.

IMPULSIVE EXPONENTIAL SYNCHRONIZATION OF FRACTIONAL-ORDER COMPLEX DYNAMICAL NETWORKS WITH DERIVATIVE COUPLINGS VIA FEEDBACK CONTROL BASED ON DISCRETE TIME STATE OBSERVATIONS

This article aims to address the global exponential synchronization problem for fractional-order complex dynamical networks(FCDNs)with derivative couplings and impulse effects via designing an appropriate feedback control based on discrete time state observations.In contrast to the existing works on integer-order derivative couplings,fractional derivative couplings are introduced into FCDNs.First,a useful lemma with respect to the relationship between the discrete time observations term and a continuous term is developed.Second,by utilizing an inequality technique and auxiliary functions,the rigorous global exponential synchronization analysis is given and synchronization criterions are achieved in terms of linear matrix inequalities(LMIs).Finally,two examples are provided to illustrate the correctness of the obtained results.

PMSM speed control using adaptive sliding mode control based on an extended state observer

In this study,a composite strategy based on sliding-mode control( SMC) is employed in a permanent-magnet synchronous motor vector control system to improve the system robustness performance against parameter variations and load disturbances. To handle the intrinsic chattering of SMC,an adaptive law and an extended state observer( ESO) are utilized in the speed SMC controller design. The adaptive law is used to estimate the internal parameter variations and compensate for the disturbances caused by model uncertainty. In addition,the ESO is introduced to estimate the load disturbance in real time. The estimated value is used as a feed-forward compensator for the speed adaptive sliding-mode controller to further increase the system's ability to resist disturbances. The proposed composite method,which combines adaptive SMC( ASMC) and ESO,is compared with PI control and ASMC. Both the simulation and experimental results demonstrate that the proposed method alleviates the chattering of SMC systems and improves the dynamic response and robustness of the speed control system against disturbances.

Sliding Mode Control of Fractional-Order Memristive System

A sliding mode controller for a fractional-order memristor-based chaotic system is designed to address its problem in stabilization control.Firstly,aphysically realizable fractional-order memristive chaotic system was introduced,which can generate a complex dynamic behavior.Secondly,a sliding mode controller based on sliding mode theory along with Lyapunov stability theory was designed to guarantee the occurrence of the sliding motion.Furthermore,in order to demonstrate the feasibility of the controller,a condition was derived with the designed controller＇s parameters,and the stability analysis of the controlled system was tested.A theoretical analysis shows that,under suitable condition,the fractional-order memristive system with a sliding mode controller comes to a steady state.Finally,numerical simulations are shown to verify the theoretical analysis.It is shown that the proposed sliding mode method exhibits a considerable improvement in its applications in a fractional-order memristive system.

Adaptive Fractional-Order PID Control for VSC-HVDC Systems via Cooperative Beetle Antennae Search with Offshore Wind Integration

Since the voltage source converter based high voltage direct current(VSC-HVDC)systems owns the features of nonlinearity,strong coupling and multivariable,the classical proportional integral(PI)control is hard to obtain content control effect.Hence,a new perturbation observer based fractional-order PID(PoFoPID)control strategy is designed in this paper for(VSC-HVDC)systems with offshore wind integration,which can efficiently boost the robustness and control performance of entire system.Particularly,it employs a fractional-order PID(FoPID)fra-mework for the sake of compensating the perturbation estimate,which dramatically boost the dynamical responds of the closed-loop system,and the cooperative beetle antennae search(CBAS)algorithm is adopted to quickly and effi-ciently search its best control parameters.Besides,CBAS algorithm is able to efficiently escape a local optimum because of a suitable trade-off between global exploration and local exploitation can be realized.At last,comprehensive case studies are carried out,namely,active and reactive power tracking,5-cycle line-line-line-ground(LLLG)fault,and offshore wind farm integration.Simulation results validate superiorities and effectiveness of PoFoPID control in com-parison of that of PID control and feedback linearization sliding-mode control(FLSMC),respectively.

Adaptive Sliding-Mode Disturbance Observer-Based Nonlinear Control for Unmanned Dual-Arm Aerial Manipulator Subject to State Constraints

The unmanned dual-arm aerial manipulator system is composed of a multirotor unmanned aerial vehicle(UAV)and two manipulators.Compared to a single manipulator,dual-arm always provides greater°exibility and versatility in both goods delivery and complex task execution.However,the practical application of the system is limited due to nonlinearities and complex dynamic coupling behavior between the multirotor and the manipulator,as well as the one between the inner and outer loop of the multirotor.In this paper,a holistic model of the dual-arm aerial manipulator system is¯rst derived with complete model information.Subsequently,an adaptive sliding-mode disturbance observer(ASMDO)is proposed to handle external disturbances and unmeasurable disturbances caught by unmeasurable angular velocity and acceleration of the manipulators.Moreover,for safety concerns and transient performance requirements,the state constraints should be guaranteed.To this end,an auxiliary term composed of constrained variable signals is introduced.Then,the performance of the designed method is proven by rigorous analysis.Finally,the proposed method is validated through two sets of simulation tests.

Research on Anti-Fluctuation Control of Winding Tension System Based on Feedforward Compensation

In the fiber winding process,strong disturbance,uncertainty,strong coupling,and fiber friction complicate the winding constant tension control.In order to effectively reduce the influence of these problems on the tension output,this paper proposed a tension fluctuation rejection strategy based on feedforward compensation.In addition to the bias harmonic curve of the unknown state,the tension fluctuation also contains the influence of bounded noise.A tension fluctuation observer(TFO)is designed to cancel the uncertain periodic signal,in which the frequency generator is used to estimate the critical parameter information.Then,the fluctuation signal is reconstructed by a third-order auxiliary filter.The estimated signal feedforward compensates for the actual tension fluctuation.Furthermore,a time-varying parameters fractional-order PID controller(TPFOPID)is realized to attenuate the bounded noise in the fluctuation.Finally,TPFOPID is enhanced by TFO and applied to control a tension control system considering multi-source disturbances.The stability of the method is analyzed by using the Lyapunov theorem.Finally,numerical simulations verify that the proposed scheme improves the tracking ability and robustness of the system in response to tension fluctuations.

Intelligent fractional-order integral sliding mode control for PMSM based on an improved cascade observer

In this paper,an intelligent fractional-order integral sliding mode control(FOISMC)strategy based on an improved cascade observer is proposed.First,an FOISMC strategy is designed to control a permanent magnet synchronous motor.It has good tracking performance,is strongly robust,and can effectively reduce chattering.The proposed FOISMC strategy associates strong points of the integral action(which can eliminate steady-state tracking errors)and the fractional calculus(which is flexible).Second,an improved cascade observer is proposed to detect the rotor information with a smaller observation error.The proposed observer combines an adaptive sliding mode observer and an extended high-gain observer.In addition,an improved variable-speed grey wolf optimization algorithm is designed to enhance controller parameters.The effectiveness of the strategy is tested using simulations and an experiment involving model uncertainty and external disturbance.

Non-fragile Observer Design for Fractional-order One-sided Lipschitz Nonlinear Systems

This paper is concerned with the problem of the full-order observer design for a class of fractional-order Lipschitz nonlinear systems. By introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach, the sufficient condition for asymptotic stability of the full-order observer error dynamic system is presented. The stability condition is obtained in terms of LMI, which is less conservative than the existing one. A numerical example demonstrates the validity of this approach.

Polynomial robust observer implementation based passive synchronization of nonlinear fractional-order systems with structural disturbances

A robust polynomial observer is designed based on passive synchronization of a given class of fractional-order Colpitts(FOC)systems with mismatched uncertainties and disturbances.The primary objective of the proposed observer is to minimize the effects of unknown bounded disturbances on the estimation of errors.A more practicable output-feedback passive controller is proposed using an adaptive polynomial state observer.The distributed approach of a continuous frequency of the FOC is considered to analyze the stability of the observer.Then we derive some stringent conditions for the robust passive synchronization using Finsler’s lemma based on the fractional Lyapunov stability theory.It is shown that the proposed method not only guarantees the asymptotic stability of the controller but also allows the derived adaptation law to remove the uncertainties within the nonlinear plant’s dynamics.The entire system using passivity is implemented with details in PSpice to demonstrate the feasibility of the proposed control scheme.The results of this research are illustrated using computer simulations for the control problem of the fractional-order chaotic Colpitts system.The proposed approach depicts an efficient and systematic control procedure for a large class of nonlinear systems with the fractional derivative.

A Synthesized Design of Adaptive and Sliding-Mode Observer-Based Incipient Fault Detection for a Quadrotor

This study in westigatn the fault detection and fault atimation problem of a quadrotar with disturbanea.A synthesiand design of adaptive and sliding mode obeerver is propoeed to addres the efkctive detection and atimation of inepient faulta.First,the decom pased subaystems are obtalned through the coardinate transdormation,and the in Stial and ineipkent faults are sea rated from the disturbanon.Second,an adaptive obeerver is applied to the decamposd un petubad subaystem to atimate ineipient faults,while the sliding mode obearver remalns robust to disturbanos for the perturbed subaytem.Lyapumov stahility theory mmas the mavergenae o dynamic erors and the stability of the quadrotor ayatem.Pinally,the dfc tiveess of the proposed synthated algod thm of ineipient fault detection is weified by the quadrotor simulation.

Cascaded Sliding-mode Observer and Its Applications in Output Feedback Control Part II:Adaptive Output Feedback Control

Part II proposes a cascaded sliding-mode observer based output feedback controller for control of multi-input multi-output(MIMO)system.The controller,designed based on feedback linearization control strategy,requires the information of the states and perturbations of the system for realization of disturbance rejection.The observer studied in part I[1]is then utilized to provide the accurate estimates of states and perturbations.As is proved,the proposed observer-based controller can ensure Lyapunov stability of the closed-loop system.Also,it can be used for output tracking control.Simulation studies are carried out on a single-wind-energy-conversion-system-infinite-bus(SWNCSIB)system to test the performances of the proposed observer-based output feedback controller.

Cascaded Sliding-mode Observer and Its Applications in Output Feedback Control Part I:Observer Design and Stability Analysis

This paper proposes a cascaded sliding-mode observer for systems with high relative degree and studies its applications in output feedback controller design.In part I,the working principle and parameter design of the proposed observer are discussed in detail.It is proved that,within a sufficiently short period of time,the states of the proposed observer will reach the intersection of all the sliding surfaces.On sliding surfaces,the observation error of the proposed observer will converge to sufficiently small values.Compared with traditional high-gain observers,the proposed observer has smaller gain coefficients.In addition,the peaking-phenomenon occurred in the proposed observer is less severe.Furthermore,the proposed observer has a convergence rate of observation error as fast as that of traditional high-gain observers.Simulation studies are carried out on a fifth-order system to verify the properties of the proposed observer.