Second-order Sliding Mode Observer Research Articles

Robust asymptotic super twisting sliding mode observer for non-linear uncertain biochemical systems

The problem of state estimation (reconstruction of the state vector) for a given class of biochemical systems under uncertain system dynamics has been addressed in this paper. In detail, the bioreactor at a water resource recovery facility represents the considered biochemical systems. The biochemical processes taking place in the bioreactor have been modelled using an activated sludge model. Based on this model, an appropriate utility model has been derived for estimation purposes. The internal dynamics of the model have been burdened with unstructured and parametric uncertainty due to the unknown reaction kinetics functions. Taking this uncertainty into account, an analysis of the observability and detectability of the utility model has been carried out. The utility model and the available set of inputs and measured outputs have been used to design a new robust non-linear observer that allows the estimation of state variables in the presence of uncertainty. In the synthesis of the observer, the asymptotic observer methodology has been combined with a second-order sliding mode observer, a so-called super twisting algorithm. The developed observer generates not only robust and stable estimates of the state variables but also enables the reconstruction of unknown kinetic functions. The stability of the designed observer has been proven using the Lyapunov stability theory. The observer has been implemented in the Matlab/Simulink environment. The comprehensive simulation studies carried out show the high efficiency of the estimation process using the developed state observer.

Multi-Parameter Fuzzy-Based Neural Network Sensorless PMSM Iterative Learning Control Algorithm for Vibration Suppression of Ship Rim-Driven Thruster

Aiming to reduce motor speed estimation and torque vibration present in the permanent magnet synchronous motors (PMSMs) of rim-driven thrusters (RDTs), a position-sensorless control algorithm using an adaptive second-order sliding mode observer (SMO) based on the super-twisting algorithm (STA) is proposed. In which the sliding mode coefficients can be adaptively tuned. Similarly, an iterative learning control (ILC) algorithm is presented to enhance the robustness of the velocity adjustment loop. By continuously learning and adjusting the difference between the actual speed and given speed of RDT motor through ILC algorithm, online compensation for the q-axis given current of RDT motor is achieved, thereby suppressing periodic speed fluctuations during motor running. Fuzzy neural network (FNN) training can be used to optimize the STA-SMO and ILC parameters of RDT control system, while improving speed tracking accuracy. Finally, simulation and experimental verifications have been conducted on the vector control system based on the conventional PI-STA and modified ILC-STA. The results show that the modified algorithm can effectively suppress the estimated speed and torque ripple of RDT motor, which greatly improves the speed tracking accuracy.

A Novel Composite Pitch Control Scheme for Floating Offshore Wind Turbines with Actuator Fault Consideration

It is of great importance to simultaneously stabilize output power and suppress platform motion and fatigue loads in floating offshore wind turbine control systems. In this paper, a novel composite blade pitch control scheme considering actuator fault is proposed based on an augmented linear quadratic regulator (LQR), a fuzzy proportional integral (PI) and an adaptive second-order sliding-mode observer. Collective pitch control was achieved via the fuzzy PI, while individual pitch control was based on the augmented LQR. In the case of actuator fault, an adaptive second-order sliding-mode observer was constructed to effectively eliminate the need for the upper bound of unknown fault derivatives and suppress the chattering effect. This paper conducted co-simulations based on FAST (Fatigue, Aerodynamics, Structures, and Turbulence) and MATLAB/Simulink to verify the effectiveness and superiority of the proposed scheme under different environmental conditions. It is shown that platform roll was reduced by approximately 54% compared to that under PI control. For the tower fore–aft moment, load reductions of 45% or more were achievable. The proposed scheme can greatly reduce the pitch and roll of the floating platform and loads in the windward direction of the wind turbine.

Variable-step close-loop angle compensation method of PMSM rotor position estimation based on super-twisting sliding-mode observer using tangent reaching law

Super-Twisting Sliding-Mode Observer (STSMO) is a kind of second-order sliding-mode observer which has been widely used in position sensorless control of permanent magnet synchronous motor (PMSM), for it can significantly reduce the chattering phenomenon of system near sliding-mode manifold. In theory, a low-pass filter (LPF) is not necessary to STSMO because of its low-chattering character near sliding-mode manifold, and as a result, phase delay should not exist in the observing result of STSMO, which means that there is no need to compensate the rotor position estimated by STSMO with phase-locked loop (PLL). However, in practical situations, a number of non-ideal factors such as sampling delay and data-updating delay can affect the accuracy of STSMO estimation, especially in dynamic process. Error contained in electric angle estimated by STSMO can be very high without compensation, which will make the stability as well as performance of system worse. In this article, the idea that STSMO needs a close-loop angle compensation method while estimating rotor position is proposed. First, on the basis of the mathematical model of angle compensation method established in this paper, traditional angle compensation method based on PI regulator is analyzed, which reveals that PI method is approximately equivalent to using a sliding-mode controller with exponential reaching law to control the angle estimation error. To improve the dynamic compensation performance together with ability against disturbances, a variable-step close-loop angle compensation method using tangent reaching law is proposed from the perspective of sliding-mode control and reaching law. Then, to measure the dynamic performance and ability against disturbances of a compensation method, the definition of normalized compensation sensitivity is proposed. Calculation results of normalized compensation sensitivities of both algorithms show that tangent reaching law method has better ability against disturbances as well as dynamic performance. Finally, this conclusion is verified through simulations. The simulation results suggest that compared with traditional method based on PI regulator, this new algorithm does achieve better dynamic compensation performance and ability against disturbances while keeping a good steady-state compensation accuracy. Meanwhile, it also simplifies the design of compensation algorithm.

Output feedback attitude control of flexible spacecraft under actuator misalignment and input nonlinearities

The attitude tracking control problem of flexible spacecraft subjected to parameter uncertainties, time-dependent external disturbances, actuator input nonlinearity, and input actuator misalignment is investigated in this paper. Explicitly, the proposed strategy addresses the input actuator misalignment and dead-zone issues that increase the controller design difficulties. Initially, a new second-order sliding mode observer (SoSMO) using an extended state approach is developed by adding a correction function to improve observer performance to estimate unwanted system perturbations. Then, a distinct SoSMO-based integral-type sliding mode control (ISMC) structure is designed in a unified manner to guarantee the asymptotic stability of the closed-loop system. Comparative numerical simulations under input actuator misalignment, the dead-zone nonlinearity, external disturbance, and inertia uncertainty are performed to illustrate the effectiveness of the proposed controller.

Observer-Based Second-Order Sliding Mode Current Controller for Thyristor-Controlled LC-Coupling Hybrid Active Power Filter

In this paper, a second-order sliding mode observer (SOSMO) based second-order sliding mode controller (SOSMC) for the TCLC-HAPF is proposed. The proposed SOSMO based SOSMC ensures the TCLC-HAPF low steady-state error, fast dynamic response, fixed switching frequency, and good system robustness under parameter variation and non-ideal grid conditions. First, the SOSMO for the TCLC-HAPF system model is proposed, and its parameter design is provided. Based on the SOSMO model, the SOSMC for the TCLC-HAPF is proposed and designed accordingly. Then, simulation studies and experiments on a three-phase TCLC-HAPF are carried out to verify the steady-state and dynamic performance of the proposed SOSMO based SOSMC compared with the other existing current controllers: proportional-integral controller, hysteresis current controller and multi-quasi-proportional-resonant controller. Finally, the system robustness, unbalance compensation capability, and DC-link voltage control performance of the proposed SOSMO based SOSMC under different non-ideal grid conditions are also verified by simulation and experimental results.

Study on a Second-Order Adaptive Sliding-Mode Observer Control Algorithm for the Sensorless Permanent Magnet Synchronous Motor

The control of a permanent magnet synchronous motor (PMSM) without a position sensor based on a sliding-mode observer (SMO) algorithm has a serious jitter problem in the process of motor phase tracking. A second-order adaptive sliding-mode observer algorithm was proposed, and the ideas and principles of the second-order sliding-mode observer algorithm based on the super-twisting algorithm were elaborated. In particular, adaptive estimation with the introduction of back-electromotive force (EMF) was investigated, and the Lyapunov stability criterion was used to determine the convergence properties of the algorithm. The results showed that the second-order adaptive sliding-mode observer algorithm had better jitter suppression and a better phase tracking performance than the traditional sliding-mode observer algorithm. The experimental results showed that when the motor velocity was 800 r/min, the velocity error of the second-order adaptive sliding-mode observer algorithm was 0.57 r/min and the position error was 0.018 rad, with accuracy improvements of 93.63% and 58.34%, respectively. When the motor velocity was 1000 r/min, the velocity error of the second-order adaptive sliding-mode observer algorithm was 0.94 r/min and the position error was 0.022 rad, with accuracy improvements of 90.55% and 55.10%, respectively. The jitter of the system was suppressed well, the curve of back-EMF was smoother, and the robustness of the system was high. Therefore, the second-order adaptive sliding-mode observer algorithm is more suitable for the position-sensorless control of a PMSM.

Precise Position Control Based on Resonant Controller and Second-Order Sliding Mode Observer for PMSM-Driven Feed Servo System

Precise position control and smooth feed speed are important research areas for permanent magnet synchronous motor (PMSM) driven computerized numerical control (CNC) servo feed systems, but it suffers from aperiodic disturbances caused by unmodeled dynamics, system parameter perturbations, variable cutting force and periodic disturbances caused by the current sampling error, aperiodic disturbances, and periodic disturbances that reduce the positional accuracy of the CNC feed servo. To address the problem, a control scheme is proposed for the position controller to suppress the disturbances. In the control scheme, the second-order sliding mode disturbance observer (SSMDO) is proposed to estimate and compensate for the aperiodic disturbances, and the resonant controller (RC) with phase adjustable is designed to suppress the periodic disturbances. The stability and antidisturbance capability of the studied scheme are analyzed systematically, and the flow of controller design and parameter tuning is presented considering the overall system. The proposed RC combined with SSMDO (RC-SSMDO) scheme can effectively alleviate the position tracking error and feed steady-state speed ripple, which is suitable for the actual working conditions of the CNC feed servo system. Experiment results confirm the validity of the proposed scheme.

PV Charging Station with VSS-IMSAF and SOSMCC Disturbance Observer Based Controls to Enhance the Distribution Grid Capability

This paper present a three-phase grid-tied (GT) charging station (CS) based on photovoltaic (PV) arrays. The purpose of the proposed CS is to support the distribution grid under heavy electric vehicles (EVs) loads with improved power quality. The variable step size improved multiband adaptive structured filter (VSS-IMSAF) technique is used to control voltage source converter (VSC). Due to the variable step size, the control regulates the grid currents and subjects to the proper step size selection to improve the performance of CS. Moreover, the charge/discharge operations of the electric vehicle battery (EVB) are also incorporated. For regulation of the DC bus voltage, second-order sliding mode cascaded control (SOSMCC) is used, which also controls the charge/discharge operations. The SOSMCC is equipped with the linear observer (LINO), second-order sliding mode observer (SOSMO), linear extended state observer (LESO), and nonlinear extended state observer (NESO), which reduce the overshoot, undershoot, and uncertainties in the voltage at DC link and EV battery current quickly and accurately. This charging station is also capable to operate under load unbalancing, unavailability and reduced insolation, and sudden change of the mode of operation (charging/discharging). The presented controls improve the performance of the CS and feed the reduced harmonic current to the grid under nonlinear load. The test results are presented using the OPAL-RT real-time simulator under various scenarios.

Model-based observer for direct methanol fuel cell concentration estimation by using second-order sliding-mode algorithm

Accurate estimation of the real-time methanol concentration of direct methanol fuel cell (DMFC) stack is a key technique for its feedback control and optimization. However, existing data-based methods as well as voltage fluctuation methods require a large amount of data to estimate methanol concentration, which increases the burden of embedded systems. What needs to be concerned is the methanol concentration inside the stack, because it directly affects its output power, while the existing research pay more attention to the methanol supplied concentration. To this end, a model-based observer based on second-order sliding-mode (SOSM) algorithm, is proposed to estimate the real-time methanol concentration inside DMFC stack utilizing the easily measured signals, such as DMFC stack voltage, current, and temperature. To validate the proposed method, the simulation comparisons between proposed SOSM observer and existing first-order sliding-mode (FOSM), extend Kalman filter (EKF) observer were carried out under certain operation conditions. Further, experimental verifications were implemented by using a real commercial DMFC system data to verify the performance of proposed approach. The comprehensive results demonstrates that proposed SOSM observer could estimate DMFC methanal concentration with robustness and accuracy.

Cascade-Free Modulated Predictive Direct Speed Control of PMSM Drives

Conventional predictive control for permanent magnet synchronous motors (PMSMs) contains dual speed and current loops, and has a complex structure and multiple parameters to be tuned. Conventional predictive direct speed control (PDSC) exhibits an unsatisfactory steady-state performance. To tackle these issues, this paper presents a cascade-free modulated PDSC (MPDSC) scheme for PMSM drives. First, a speed predictive model is built, where a second-order sliding mode observer is employed to quickly and robustly estimate the load torque. Then, a dual objective cost function with speed and stator current tracking is designed, which improves the system’s steady-state performance. Furthermore, the analytical solution of the constrained optimal voltage vector is derived and it is synthesized by space vector modulation, resulting in a fixed switching frequency. Experimental results show that the proposed MPDSC has stronger robustness, and lower torque ripples and stator current harmonics compared to conventional PDSC.

Novel non‐linear control of DFIG and UPFC for transient stability increment of power system

This paper offers novel non-linear control of a doubly fed induction generator (DFIG) and unified power flow controller (UPFC) for transient stability increment with transient energy function (TEF) and sliding mode observer in a power system. First, the TEF technique is considered for the damping control in a power system with a synchronous generator (SG), DFIG, and UPFC, and then the controller time-derivative signals are estimated by a second-order sliding mode observer. The importance of the issue is in the employ of a complete UPFC model. Also, a one-axis model is used for DFIG that is similar to the SG model. Another characteristic of the novel non-linear technique is robust versus system topology changes and variable time delay of the control signals. To evaluate the performance of the novel non-linear control method for increment transient stability, simulation studies are performed on a two-machine connected to an infinite bus (TMIB), the IEEE 9-bus, and the New England Standard 39-bus power system. The results determine that the novel non-linear control method decreases the first swing of fluctuations admissibly and enhancement stability margins considerably.

High-order sliding mode-based synchronisation of fractional-order chaotic systems subject to output delay and unknown disturbance

This work deals with chaos synchronisation. One of the commonly used methods is the master-slave configuration, where the response of the chaotic receiver (slave) system must converge to the chaotic trajectory of the transmitter (master). The major problem with this configuration is the delay that occurs during the transmission of the drive signal from the master to the slave, which can degrade the synchronisation. The objective of this paper is to propose a solution to the synchronisation problem of nonlinear fractional-order chaotic systems in the presence of a transmission delay at the output and unknown disturbance. The proposed approach consists of combining a fractional high-order sliding mode observer (FHOSMO) and a predictor arranged in a cascade to compensate for the delayed transmission signal from the transmitter to the receiver. The observer permits to estimate the delayed states and the delayed total disturbance (uncertainties and external disturbances) in finite time. These estimates are injected into the predictor to obtain the estimated states at the current time. The finite time convergence of the proposed method is established. The numerical simulations illustrate the theoretical results and the performance of the proposed method. The proposed synchronisation method is compared with other synchronisation methods using the chattering free sliding mode approach such as the fractional first-order sliding mode observer using the continuous function instead of the discontinuous sign function and the fractional second-order sliding mode observer. In addition, a conventional first-order sliding mode observer with the sign function is also considered.

Dependable Sensor Fault Reconstruction in Air-Path System of Heavy-Duty Diesel Engines.

This paper addresses the problem of robust sensor faults detection and isolation in the air-path system of heavy-duty diesel engines, which has not been completely considered in the literature. Calibration or the total failure of a sensor can cause sensor faults. In the worst-case scenario, the engines can be totally damaged by the sensor faults. For this purpose, a second-order sliding mode observer is proposed to reconstruct the sensor faults in the presence of unknown external disturbances. To this aim, the concept of the equivalent output error injection method and the linear matrix inequality (LMI) tool are utilized to minimize the effects of uncertainties and disturbances on the reconstructed fault signals. The simulation results verify the performance and robustness of the proposed method. By reconstructing the sensor faults, the whole system can be prevented from failing before the corrupted sensor measurements are used by the controller.

A Second-order Sliding Mode Observer Optimized by Neural Network for Speed and Position Estimation of PMSMs

A Second-order Sliding Mode Observer Optimized by Neural Network for Speed and Position Estimation of PMSMs

Robust fault tolerant control of robot manipulators with global fixed-time convergence

In this paper, a robust fault tolerant control, which provides a global fixed-time stability, is proposed for robot manipulators. This approach is constructed based on an integration between a fixed-time second-order sliding mode observer (FxTSOSMO) and a fixed-time sliding mode control (FxTSMC) design strategy. First, the FxTSOSMO is developed to estimate the lumped disturbance with a fixed-time convergence. Then, based on the obtained disturbance estimation, the FxTSMC is developed based on a fixed-time sliding surface and a fixed-time reaching strategy to form a global fixed-time convergence of the system. The proposed approach is then applied for fault tolerant control of a PUMA560 robot and compared with other state-of-the-art controllers. The simulation results verify the outstanding fault estimation and fault accommodation capability of the proposed fault diagnosis observer and fault tolerant strategy, respectively.

On the synthesis of a sliding-mode-observer-based adaptive fault-tolerant flight control scheme

This paper presents an active Fault-Tolerant Control (FTC) framework to accommodate the actuator faults by using a Fault Estimation (FE) module fitted with an adaptive control law. It focuses on the problem of fault estimation based fault tolerant control for linear uncertain system with mitigation of the reconfiguration transients. In this work, a second-order sliding mode observer is designed to reconstruct the Loss of Effectiveness (LoE) of the actuators. The use of a bumpless strategy to cleverly manage the transient behavior where fault estimation is different from the real one due to an abrupt fault occurrence. Signals provided by the FE module are next used by an augmented fault-tolerant control allocation scheme to accommodate the fault. More precisely, the flight state tracking problem has been addressed with a robust adaptive model-reference Integral Sliding Mode (ISM) control law in a state feedback setting. Next, the problem of stability and performance of the overall FTC scheme with taking into account both FE performance and control law is rigorously considered. At the end, simulation examples on an aircraft from a European program are used to illustrate the effectiveness of the proposed approach.

Observer-based event-triggered fixed-time control for nonlinear system with full-state constraints and input saturation

This paper investigates the continuous composite control scheme for the tracking of nonlinear system with mismatched disturbances, input saturation and full-state constraints. Based on the fixed-time stability theory, a novel fixed-time disturbance observer is proposed, which switches from a uniform second-order sliding mode observer with high-degree term to the classical continuous super-twisting observer. Then, a command filtered backstepping control scheme is designed to enforce the tracking error into a small neighbourhood of the origin in fixed time while the full-state constraint and input saturation constraint are satisfied. To further reduce the communication burden, an event-triggered communication strategy between the controller and the actuator input is also developed. Furthermore, all the signals in the closed-loop system are proven to be bounded. Finally, the effectiveness of the proposed control strategy is illustrated by numerical simulations.

Nested High Order Sliding Mode Controller with Back-EMF Sliding Mode Observer for a Brushless Direct Current Motor

This work presents a nested super-twisting second-order sliding mode speed controller for a brushless direct current motor with a high order sliding mode observer used for back electromotive force (back-EMF) estimation. Due to the trapezoidal nature of the back-EMF, a modified Park transformation is used in order to achieve proper field orientation. Such transformation requires information from the back-EMF that is not accessible. A second-order sliding mode observer is used to estimate the back electromotive forces needed in the modified transformation. Sliding mode control is known to be robust to matched uncertain disturbances and parametric variations but it is prone to unmatched perturbations that affect the performance of the system. A nested scheme is used to improve the response of the controller in presence of unmatched disturbances. Simulations performed under similar conditions to real-time experimentation show a good regulation of the rotor speed in terms of transient and steady-state responses along with a reduced torque ripple.

Sensorless flux adaption DTFC of an IPMSM based on an active flux‐based MTPA and an adaptive second‐order sliding mode observer

This study proposes a sensorless flux adaption direct torque and flux control (DTFC) for an interior permanent magnet synchronous motor (IPMSM), in which an maximum torque per ampere (MTPA) based on active flux and an adaptive second-order sliding mode observer (SOSMO) are adopted. Flux adaption DTFC is proposed based on the existing active flux concept. Thus, the stator current amplitude can be minimised in both steady state and transient state. Furthermore, to realise the sensorless control of the IPMSM, an adaptive SOSMO is proposed. Compared with constant gains SOSMO, the gains of the adaptive SOSMO can be adjusted adaptively with the motor speed changing. Then, the precision of position estimation is enhanced effectively in a wide speed range. Numerical simulations and experiments with a 60 kW IPMSM are implemented. In addition, the results validate the capability of the proposed sensorless flux adaption DTFC scheme.