Robust Adaptive Gain Higher Order Sliding Mode Observer Based Control-constrained Nonlinear Model Predictive Control for Spacecraft Formation Flying

This work deals with the development of a decentralized optimal control algorithm, along with a robust observer,for the relative motion control of spacecraft in leader-follower based formation. An adaptive gain higher order sliding mode observer has been proposed to estimate the velocity as well as unmeasured disturbances from the noisy position measurements.A differentiator structure containing the Lipschitz constant and Lebesgue measurable control input, is utilized for obtaining the estimates. Adaptive tuning algorithms are derived based on Lyapunov stability theory, for updating the observer gains,which will give enough flexibility in the choice of initial estimates.Moreover, it may help to cope with unexpected state jerks. The trajectory tracking problem is formulated as a finite horizon optimal control problem, which is solved online. The control constraints are incorporated by using a nonquadratic performance functional. An adaptive update law has been derived for tuning the step size in the optimization algorithm, which may help to improve the convergence speed. Moreover, it is an attractive alternative to the heuristic choice of step size for diverse operating conditions. The disturbance as well as state estimates from the higher order sliding mode observer are utilized by the plant output prediction model, which will improve the overall performance of the controller. The nonlinear dynamics defined in leader fixed Euler-Hill frame has been considered for the present work and the reference trajectories are generated using Hill-Clohessy-Wiltshire equations of unperturbed motion. The simulation results based on rigorous perturbation analysis are presented to confirm the robustness of the proposed approach.

Improved estimation of rotor position for sensorless control of a PMSM based on a sliding mode observer

This work proposes a new strategy to improve the rotor position estimation of a permanent magnet synchronous motor(PMSM) over wide speed range. Rotor position estimation of a PMSM is performed by using sliding mode observer(SMO). An adaptive observer gain was designed based on Lyapunov function and applied to solve the chattering problem caused by the discontinuous function of the SMO in the wide speed range. The cascade low-pass filter(LPF) with variable cut-off frequency was proposed to reduce the chattering problem and to attenuate the filtering capability of the SMO. In addition, the phase shift caused by the filter was counterbalanced by applying the variable phase delay compensation for the whole speed area. High accuracy estimation result of the rotor position was obtained in the experiment by applying the proposed estimation strategy.

Fractional order integral sliding mode control for PMSM based onfractional order sliding mode observer

In view of the variation of system parameters and external load disturbance affecting the high-performance control of permanent magnet synchronous motor(PMSM),a fractional order integral sliding mode control(FOISMC)strategy is developed for PMSM drive system by means of fractional order sliding mode observer(FOSMO).Based on FOISMC technology,a fractional order integral sliding mode regulator(FOISM-based regulator)is designed,and a global integral sliding mode surface design method is presented,which can guarantee the global robustness of the system.Combining fractional order theory and sliding mode control theory,the FOSMO is constructed to achieve better identification accuracy of the speed and rotor position.Meanwhile the sliding mode load observer is used to observe the load torque in real time,and the observed value is transmitted to speed regulator to improve the capability of accommodating the challenge of load disturbance.Simulation results validate the feasibility and effectiveness of the proposed scheme.

Decoupling Adaptive Sliding Mode Observer Design for Wind Turbines Subject to Simultaneous Faults in Sensors and Actuators

This paper proposes an adaptive sliding mode observer(ASMO)-based approach for wind turbines subject to simultaneous faults in sensors and actuators.The proposed approach enables the simultaneous detection of actuator and sensor faults without the need for any redundant hardware components.Additionally,wind speed variations are considered as unknown disturbances,thus eliminating the need for accurate measurement or estimation.The proposed ASMO enables the accurate estimation and reconstruction of the descriptor states and disturbances.The proposed design implements the principle of separation to enable the use of the nominal controller during faulty conditions.Fault tolerance is achieved by implementing a signal correction scheme to recover the nominal behavior.The performance of the proposed approach is validated using a 4.8 MW wind turbine benchmark model subject to various faults.Monte-Carlo analysis is also carried out to further evaluate the reliability and robustness of the proposed approach in the presence of measurement errors.Simplicity,ease of implementation and the decoupling property are among the positive features of the proposed approach.

Position Sensorless Control for Permanent Magnet Synchronous Motor Using Sliding Mode Observer

An approach of position sensorless control for permanent magnet synchronous motor （ PMSM ） is put forward based on a sliding mode observer. The mathematical model of PMSM in a stationary αβ reference frame is adopted, and the system is controlled by the digital signal processor （ DSP; TMS320LF2407 according to the control achieve closed loop operation of the motor, the stator theory of sliding mode observer. In order to magnetic field should be vertical with the rotor magnetic field and be synchronous with rotor rotating, so the position and speed of PMSM is estimated in real time and the estimated position is modified continuously. The simulation results indicate that the proposed observer has high precision is more robust to the parametric variation and load in estimation of PMSM position and speed, and torque disturbance.

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.

Sensorless Control of Permanent Magnet Synchronous Motor Based on New Sliding Mode Observer with Single Resistor Current Reconstruction

To solve the chattering problem caused by discontinuous switching function in traditional sliding mode observer,a piecewise square root switching function with continuously varying characteristics is designed,and its stability is analyzed by using Lyapunov stability criterion.Secondly,according to the relationship among bus current,switching state and phase current,a single bus resistance sampling current reconstruction scheme without current sensors is adopted,which effectively reduces the cost of motor system.Finally,the feasibility and effectiveness of the proposed scheme are verified by simulation.

An Extended Sliding Mode Observer for Speed, Position and Torque Sensorless Control for PMSM Drive Based Stator Resistance Estimator

This paper presents a robust sixth-order Discrete-time Extended Sliding Mode Observer (DESMO) for sensorless control of PMSM in order to estimate the currents, speed, rotor position, load torque and stator resistance. The satisfying simulation results on Simulink/Matlab environment for a 1.6 kW PMSM demonstrate the good performance and stability of the proposed ESMO algorithm against parameter variation, modeling uncertainty, measurement and system noises.

Sliding mode observer-based fault detection for helicopter system

Fault detection of non-linear systems is of great importance in control systems reliability.Undetected faults could lead to irreparable damage.This paper deals with fault diagnosis of helicopter system in the presence of uncertainties and disturbances.To deal with sensor,actuator and component faults,the observer-based diagnosis scheme which employs sliding mode observer is designed.Faults are modelled as an additive and multiplicative fault which is introduced as an abrupt and intermittent fault into the system.Observer inequality constraints and gain matrices are solved using a Lyapunov-based approach.The results display the effectiveness of the designed observer and the ability to handle faults.

Modified Sliding Mode Observer-based Direct Torque Control of Six-phase Asymmetric Induction Motor Drive

In this study,a six-phase induction asymmetric induction motor(SPAIM)was examined,whose performance surpasses that of its three-phase counterpart,with regard to the torque density,torque pulsation,fault tolerance,power rating per inverter lag,and noise characteristics.Speed-encoder-less direct torque control(DTC)for SPAIM with virtual voltage vectors(VVVs)and a modified sliding mode observer(MSMO)are described.The SPAIM model was developed using a stationaryα-βframe for DTC.The conventional DTC of the SPAIM drive is a simple extension of DTC for a 3-Φmotor drive that yields higher distortion in the stator currents.To mitigate the large amount of distortion in the stator current,VVVs were used to significantly reduce the harmonic content in the stator currents.Furthermore,to overcome the large amount of chattering observed in the case of a traditional sliding mode observer,particularly under low-speed operation,the MSMO was employed to reduce chattering even under low-speed operation.The performance of the proposed observer was verified under all the operating conditions suitable for the propulsion mode of an electric vehicle using Matlab/Simulink,and the results were experimentally validated.

Improved control strategy for PMSM based on fuzzy sliding mode control and sliding-mode observer

Aimed at the problems of large torque ripple,obvious chattering and poor estimation accuracy of back-EMFs in traditional permanent magnet synchronous motor(PMSM)control system with sliding mode observer(SMO),an improved control strategy for PMSM based on a fuzzy sliding mode control(FSMC)and a two-stage filter sliding mode observer(TFSMO)is proposed.Firstly,a novel reaching law(NRL)used in the speed loop based on hyperbolic sine function is studied,and fuzzy control ideal is shown to achieve the self-turning of the parameter for the reaching law,thus a fuzzy integral sliding mode controller based on the novel reaching law is designed in speed loop.Then the suppression effect upon chattering caused by the novel reaching law is analyzed strictly by discrete equation.Secondly,in order to restrain the high frequency components and measurement noise in back-EMFs,a two-stage filter structure based on a variable cut-off frequency low-pass filter(VCF-LPF)and a modified back-EMF observer(MBO)is conceived,and the rotor position is compensated reasonably.As a result,a TFSMO is designed.The stability of the proposed control strategy is proved by Lyapunov Criterion.The simulation and experiment results show that,compared with traditional SMO,the controller suggested above can obtain very nice system respond when the motor starts and is subjected to external disturbances,and effectively improve the problems about torque ripple,chattering and the estimation accuracy of back-EMF.

Robust SVM-direct torque control of induction motor based on sliding mode controller and sliding mode observer

This paper proposes a design of control and estimation strategy for induction motor based on the variable structure approach.It describes a coupling of sliding mode direct torque control(DTC)with sliding mode flux and speed observer.This algorithm uses direct torque control basics and the sliding mode approach.A robust electromagnetic torque and flux controllers are designed to overcome the conventional SVM-DTC draw・backs and to ensure fast response and full reference tracking with desired dynamic behavior and low ripple level.The sliding mode controller is used to generate reference voltages in stationary frame and give them to the controlled motor after modulation by a space vector modulation(SVM)inverter.The second aim of this paper is to design a sliding mode speed/flux observer which can improve the control performances by using a sensorless algorithm to get an accurate estimation,and consequently,increase the reliability of the system and decrease the cost of using sensors.The effectiveness of the whole composed control algorithm is investigated in different robustness tests with simulation using Matlab/Simulink and verified by real time experimental implementation based on dS pace 1104 board.

Sliding mode fault tolerant consensus control for multi-agent systems based on super-twisting observer

The fault-tolerant consensus problem for leader-following nonlinear multi-agent systems with actuator faults is mainly investigated.A new super-twisting sliding mode observer is constructed to estimate the velocity and undetectable fault information simultaneously.The time-varying gain is introduced to solve the initial error problem and peak value problem,which makes the observation more accurate and faster.Then,based on the estimated results,an improved sliding mode fault-tolerant consensus control algorithm is designed to compensate the actuator faults.The protocol can guarantee the finite-time consensus control of multi-agent systems and suppress chattering.Finally,the effectiveness and the superiority of the observer and control algorithm are proved by some simulation examples of the multi-aircraft system.

Fault Reconstruction for Lipschitz Nonlinear Systems Using Higher Terminal Sliding Mode Observer

This paper considers the design of an adaptive second order terminal observer for robust fault reconstruction of nonlinear Lipschitz systems with unknown upper bound of derivative fault.Firstly,a linear transforming matrix is introduced,which transforms the system into two subsystems,and thus to reduce the dimension of the system.One of the subsystem is affected by fault and disturbances,while the other is free,which simplifies the design of observer.Then,the design method of the observer gain matrix is transformed into a convex optimization problem under linear matrix inequalities(LMIs).A second order non-singular terminal sliding mode observer is designed for the transformed system to realize the accurate estimation of state and fault.Considering the unknown upper bound of derivative fault,an adaptive algorithm is designed in the equivalent output error injection signal to ensure the sliding mode motion reach the sliding surface within limited time.Finally,an example demonstrates the effectiveness of the proposed method in the paper.

Modified sliding mode observer for wide speed range operation of brushless DC motor

This paper describes an adaptive gain sliding mode observer for brushless DC motor for large variations in speed. Sensorless brushless DC motor based on sliding mode observer exhibits multiple zero crossing in back electromotive force （EMF） which leads to commutation problems at low speed. In this paper, a modified sliding mode observer incorporating a speed component in the estimation of back EMF is proposed. It is found that after incorporating the speed component in the back EMF observer gain, multiple zero crossings at low speeds and phase shift at higher speeds are eliminated. The trapezoidal back EMF observer is implemented experimentally on a digital signal processor （DSP） board. The effectiveness of the proposed method is demonstrated through simulations and experiments.

The Non-Singular Fast Terminal Sliding Mode Control of Interior Permanent Magnet Synchronous Motor Based on Deep Flux Weakening Switching Point Tracking

This paper presents a novel non-singular fast terminal sliding mode control(NFTSMC)based on the deep flux weakening switching point tracking method in order to improve the control performance of permanent interior magnet synchronous motor(IPMSM)drive systems.The mathematical model of flux weakening(FW)control is established,and the deep flux weakening switching point is calculated accurately by analyzing the relationship between the torque curve and voltage decline curve.Next,a second-order NFTSMC is designed for the speed loop controller to ensure that the system converges to the equilibrium state in finite time.Then,an extended sliding mode disturbance observer(ESMDO)is designed to estimate the uncertainty of the system.Finally,compared with both the PI control and sliding mode control(SMC)by simulations and experiments with different working conditions,the method proposed has the merits of accelerating convergence,improving steady-state accuracy,and minimizing the current and torque pulsation.

Model predictive current control for PMSM driven by three-level inverter based on fractional sliding mode speed observer

Based on the fractional order theory and sliding mode control theory,a model prediction current control(MPCC)strategy based on fractional observer is proposed for the permanent magnet synchronous motor(PMSM)driven by three-level inverter.Compared with the traditional sliding mode speed observer,the observer is very simple and eases to implement.Moreover,the observer reduces the ripple of the motor speed in high frequency range in an efficient way.To reduce the stator current ripple and improve the control performance of the torque and speed,the MPCC strategy is put forward,which can make PMSM MPCC system have better control performance,stronger robustness and good dynamic performance.The simulation results validate the feasibility and effectiveness of the proposed scheme.

Observer-based robust high-order fully actuated attitude autopilot design for spinning glide-guided projectiles

This paper investigates the design of an attitude autopilot for a dual-channel controlled spinning glideguided projectile(SGGP),addressing model uncertainties and external disturbances.Based on fixed-time stable theory,a disturbance observer with integral sliding mode and adaptive techniques is proposed to mitigate total disturbance effects,irrespective of initial conditions.By introducing an error integral signal,the dynamics of the SGGP are transformed into two separate second-order fully actuated systems.Subsequently,employing the high-order fully actuated approach and a parametric approach,the nonlinear dynamics of the SGGP are recast into a constant linear closed-loop system,ensuring that the projectile's attitude asymptotically tracks the given goal with the desired eigenstructure.Under the proposed composite control framework,the ultimately uniformly bounded stability of the closed-loop system is rigorously demonstrated via the Lyapunov method.Validation of the effectiveness of the proposed attitude autopilot design is provided through extensive numerical simulations.

Model-Free Sliding Mode Control for PMSM Drive System Based on Ultra-Local Model

This paper presents a novel model-free sliding mode control(MFSMC)method to improve the speed response of permanent magnet synchronous machine(PMSM)drive system.The ultra-local model(ULM)is first derived based on the input and the output of the PMSM.Then,the novel MFSMC method is presented,and the controller is designed based on ULM and MFSMC.A sliding mode observer(SMO)is constructed to estimate the unknown part of the ULM.The estimated unknown part is feedbacked to MFSMC controller to performcompensation for parameter perturbations and external disturbances.Compared with the sliding mode control(SMC)method,the results of simulation and experiment demonstrate that the presented MFSMC method improves the dynamic response and robustness of the PMSM drive system.

Output feedback adaptive super twisting sliding mode control for quadrotor UAVs

In this paper, a sliding mode control with adaptive gain combined with a high-order sliding mode observer to solve the tracking problem for a quadrotor UAV is addressed, in presence of bounded external disturbances and parametric uncertainties. The high order sliding mode observer is designed for estimating the linear and angular speed in order to implement the proposed scheme. Furthermore, a Lyapunov function is introduced to design the controller with the adaptation law, whereas an analysis of finite time convergence towards to zero is provided, where sufficient conditions are obtained. Regarding previous works from literature, one important advantage of proposed strategy is that the gains of control are parameterized in terms of only one adaptive parameter, which reduces the control effort by avoiding gain overestimation. Numerical simulations for tracking control of the quadrotor are given to show the performance of proposed adaptive control–observer scheme.