First-order Sliding Mode Control Research Articles

Evaluation of control techniques for quadcopter UAV attitude tracking

ABSTRACT This paper evaluates the performance of six controllers used for the attitude tracking of the quadcopter. The evaluation is done by testing the tracking performance and robustness of each controller with respect to unknown dynamics, disturbances, gain variations, and noise. These controllers include the well-known Proportional-Integral-Derivative (PID) controller to establish a baseline, the Linear Active Disturbance Rejection Controller (LADRC), the first-order Sliding Mode Controller (SMC), the second-order Super-Twisting SMC (STSMC), the Backstepping Controller (BSC), and synergetic controller. To ensure a fair and systematic evaluation, the parameters of each control method were optimised using a Particle Swarm Optimizer (PSO), incorporating a penalty term to maintain realistic control signals while minimising error. The paper details the control techniques used and describes the optimisation process. The results suggest the superiority of LADRC over the other controllers. In the conclusion section, the paper presents several prospective strategies aimed at enhancing the discussed control techniques.

Improved islanded microgrid performance with sliding mode controller based electric spring

In this research manuscript, an innovative solution is proposed to address intermittency challenges in self-excited induction generator-based islanded microgrids. The approach makes the use of an electric spring to maintain a constant voltage across critical loads. For simplifying the design and reduce the need for additional storage devices, and lower costs, a novel voltage source-based electric spring concept is introduced, complete with a comprehensive modelling approach specifically tailored for microgrid applications. Furthermore, a first-order sliding mode controller is suggested to enhance voltage and frequency regulation, stability, and overall system efficiency. This control strategy is designed to linearize voltage errors and provide swift responses under varying steady-state and transient conditions. To validate the effectiveness of the proposed scheme, the model is compared against the widely used quadrature voltage injection scheme under different load and torque conditions. Moreover, the system exhibits a rapid settling time, typically requiring only one to two cycles to stabilize. This underscores the robustness and stability of the controller. The validation of this work is carried out in real-time using an OPAL-RT 4510 and MATLAB/Simulink platform.

Emulator of electrocardiographically biopotentials based on a sliding mode controlled buck power converter

The primary objective of this research is to present the design of an artificial signal generation system of electrocardiography continuous signals based on the application of a buck power converter. A first-order sliding mode control application for a buck direct current–direct current power converter induces the generation of continuous variations of a direct current voltage as the response of a power converter. The output voltage reproduces the required electrocardiography signals corresponding to the regular or pathological variants. The equivalent control method permits introducing a novel design of a kind of cascade-like sliding mode controller that can regulate both current and voltage operative loops simultaneously, which force the controlled tracking of the reference bioinspired voltages at the output of the buck power converter. For the developed control design, the current regulation is enforced as the primary outcome of the sliding mode controller. Consequently, the required voltage from the buck converter is produced, regulating the switching operation in the electrical power system. The suggested control operates robustly concerning the internal uncertainties and perturbations for both input and voltage signals. Furthermore, the variation of the needed gain for the designed sliding mode controller is developed by studying the online amplitude of the electrocardiography electrophysiological signals used as references and their time derivatives over time. Two reference signals were developed to validate the controllers with the same quality at the numerical simulation and using some experimental validations. The proposed signals used as references were successfully generated in both evaluated cases.

Trajectory Planning for Hopping Rover on Small Bodies Under Pre-Collision Attitude Adjustment Modulation

A novel pre-collision attitude adjustment (PCAA) modulation based on angular velocity and quaternions control is developed to more controllable and reliably adjust the non-spherical hopping rover's trajectory on small bodies. This corresponds to a hopping trajectory planning (HTP) framework that addresses inherent technical challenges, including attitude-trajectory coupled features, hard-to-depicting near-truth gravity and continues dynamical contact models, difficult-to-predetermine collision times with the small bodies’ surface, and complex judgments regarding whether the period of attitude adjustment is sufficient in current hops. Two main contributions are proposed, focusing on modeling and planning. To achieve a more realistic modeling of the rover's motion, its attitude-trajectory coupling dynamic model is researched, including a ground-truth irregular gravity model and continuous dynamical contact model. Additionally, a collision detection method based on the local surface smoothing technique is proposed for rapid and exact switching between the ballistic and contact motions for the subsequent planning purpose. On the other hand, redundancy planning and binary event-trigger techniques are combined for handling unpredictable available dimensions of optimization variables of PCAA-based HTP, which arise from the indeterminate scale of collision times and potential deficiency in ballistic flight time required for completing attitude maneuvers. Specifically, the solution space is preset to guarantee the unchanging dimensions of the design variables, which are activated or deactivated by coupling binary event variables for each dimension. These newly introduced events are triggered by comparing the realistic rebound time of the current hop with the necessary time for attitude maneuver, which is accurately computed by designing a first-order sliding mode controller. This approach enables an equivalent and easily implementable version of the problem to be obtained. Logically and numerically, the application of PCAA modulation is found to significantly enlarge or contract the area of the reachable region of the hopping rover and contribute to improving the convergence and reducing the relative final position error of the hopping trajectory planning problem.

Rotor Speed Analysis of SMC-based IFOC for Low-Speed Induction Motor Control

The control of electric motors, particularly three-phase induction motors, has developed rapidly due to their application in industry. Indirect Field Oriented Control (IFOC) is one of the most widely used control systems due to its ease of application. IFOC controls a three-phase induction motor in the same way as a DC motor. However, IFOC requires a Sliding Mode Control (SMC) controller with Lyapunov stability theory to ensure robustness and stability. In exceptional conditions, such as low-speed settings, the SMC-based IFOC requires unique sets to operate with a steady-state error (Ess) at a speed response of less than 2%. Other parameters to be considered are rise time and electromagnetic torque response at low speeds. The addition of the boundary layer of the hyperbolic tangent function to a first-order SMC can increase induction motor (IM) control up to 175 rpm with a value of Ess = 1.96% compared to the saturation and signum functions, which are only capable of a reference speed of 300 rpm in no-load conditions with a value of Ess = 2% for the saturation function and 1.94% for the signum function. SMC with the hyperbolic tangent function boundary layer performs best under load conditions. The rising time value does not significantly differ under no-load or torque-load conditions between the SMC with the saturation, hyperbolic tangent function boundary layers and without the boundary layer. Adding a boundary layer with the hyperbolic tangent function can reduce ripple significantly compared to the saturation function under no-load or load conditions.

ROBUST SUPER-TWISTING SLIDING MODE CONTROL FOR BALANCING REACTION WHEEL PENDULUM

Underactuated systems are one of the emerging research topics due to their challenging problems and applications in real-world engineering systems. In this paper, we consider the control problem of balancing the reaction wheel pendulum. Many control methods have been adopted to control the system and one of the common controls is based on sliding mode control (SMC). In SMC, the chattering phenomenon and its solution are widely discussed. Several approaches have been proposed, for example replacing the switching function, second-order SMC, and higher-order SMC. Here, the balancing of the reaction wheel pendulum with disturbances is considered. First, the system model derivation based on the Euler-Lagrange method is discussed. Second, a different approach to designing a controller is given where feedback linearization and robust super-twisting sliding mode control are used. The control performances are compared with those of standard and modified switching functions of first-order sliding mode control. For second-order sliding mode control, the super-twisting and PID super-twisting controllers are employed. In each controller, similar disturbances, namely, impulse signal and sinusoidal signal are used to verify the effectiveness of the controller. We conduct the comparison studies in Matlab/Simulink with fixed controller's gains and the controllers effectively stabilize the pendulum upright and reject the given external disturbances.

Super-Twisted Sliding Mode Control for Maximum Power Point Tracking of Wind Turbine Based on Neural Network

Given the difficulties in measuring the effective wind speed of wind turbine during the maximum power point tracking (MPPT) process and the unknown nature of the system, this paper proposes a neural network super-twisted sliding mode control (NNST-SMC) method with echo state network (ESN) wind speed estimation. The rotor speed and electromagnetic power are taken as ESN inputs, and the effective wind speed is estimated through the inverse model of wind turbine dynamics. The super-twisted algorithm (STA) can effectively improve the chattering problem of the traditional sliding mode control (SMC) system. The RBF neural network is introduced to compensate for disturbance and uncertainty characteristics of the wind turbine. Results show that compared with the neural network first-order sliding mode control (NNSMC) and super-twisted sliding mode control (ST-SMC), the proposed method can improve the efficiency of wind energy utilization.

Improvement DTC for Induction Motor Drives Using Modern Speed Controllers Tuning by PSO Algorithm

The work carried out in this paper proposes an improvement of the direct torque control (DTC) of induction machine by the design of modern, robust and more efficient controllers than the conventional PI controllers commonly used for speed control. A comparative study has been carried out using five controllers, i.e. PI anti-windup, first-order sliding mode control (SMC), second order sliding mode control (SOSMC), fuzzy logic controller (Fuzzy-PI) and hybrid Fuzzy second-order sliding mode controller (FSOSMC). An advanced optimization technique based on the particle swarm optimization (PSO) algorithm has been utilized to optimize all of these controllers, the use of PSO for the determination of the different gains used in all controllers gives on the one hand a high accuracy performance and ensures on the other hand a reliable comparison between the different controllers in their optimal states. The simulation and analysis of each method with respect to robustness to disturbances was performed externally under various operating conditions and variations of the machine parameters.

Finite-time sliding mode trajectory tracking control of an autonomous surface vehicle with prescribed performance

This paper investigates the finite-time sliding mode trajectory tracking control problem for the autonomous surface vehicle (ASV). A prescribed performance function is introduced to improve the transient and steady-state tracking performance simultaneously. Two PID-type sliding surfaces are constructed such that the closed-loop system can reach the sliding surface with good performance, on which the developed sliding mode controllers can make the system error go to zero. In order to demonstrate the effectiveness of the proposed algorithms, an application example of the surface vehicle CyberShip II is borrowed from Skjetne et al., (2005), for which detailed comparisons are made between finite-time second-order sliding mode control (2-SMC) and finite-time first-order sliding mode control (1-SMC). A large number of simulations show that the proposed 2-SMC algorithm can achieve better control accuracy in comparison with 1-SMC algorithm and existing results.

A New Efficient Cuckoo Search MPPT Algorithm Based on a Super-Twisting Sliding Mode Controller for Partially Shaded Standalone Photovoltaic System

The impact of Partial Shading Conditions (PSCs) significantly influences the output of Photovoltaic Systems (PVSs). Under PSCs, the Power-Voltage (P-V) characteristic of the PVS unveils numerous power peaks, inclusive of local maxima and a global maximum. The latter represents the optimum power point. Traditional Maximum Power Point Tracking (MPPT) algorithms struggle to track the Global Maximum Power Point (GMPP). To address this, our study emphasizes the creation of a novel algorithm capable of identifying the GMPP. This approach combines the Cuckoo Search (CS) MPPT algorithm with an Integral Super-Twisting Sliding Mode Controller (STSMC) using their benefits to enhance the PVS performance under PSCs in terms of high efficiency, low power losses, and high-speed convergence towards the GMPP. The STSMC is a second-order Sliding Mode Control strategy that employs a continuous control action that attenuates the “chattering” phenomenon, caused when the first-order SMC technique is employed. Indeed, the proposed CS-STSMC-MPPT algorithm consists of two parts. The first one is based on the CS algorithm used for scanning the power-voltage curve to identify the GMPP, and subsequently generating the associated optimal voltage reference. The second part aims to track the voltage reference by manipulating the duty cycle of the boost converter. The proposed CS-STSMC-MPPT algorithm is featured by its strength against uncertainties and modeling errors. The obtained simulation results underline a high convergence speed and an excellent precision of the proposed method in identifying and tracking the GMPP with high efficiency under varying shading scenarios. For comparative purposes, this method is set against the hybrid CS-Proportional Integral Derivative, the conventional CS, the Particle Swarm Optimization, and the Perturb and Observe algorithms under different PSCs, including zero, weak, and severe shading. Simulation conducted in the Matlab/Simulink environment confirms the superior performance of the proposed CS-STSMC-MPPT algorithm in terms of precision, convergence speed, efficiency, and resilience.

Reprint of: Adaptive supertwisting sliding mode control of multi-converter MVDC power systems

Medium Voltage DC (MVDC) integrated power systems are anticipated to feed the submarines and surface combatants. The MVDC based power systems use dc/dc converters tightly regulated via high bandwidth controllers act as constant power loads (CPL’s). The negative incremental impedance of the CPL’s may result in voltage instability in the system under disturbance. Thus for the efficient and robust control of the MVDC based power system, this paper proposes a high order sliding mode control (HOSMC) paradigm based on model-free adaptive super twisting sliding mode control (ASTA-SMC). This paper initially designs a first-order sliding mode control (FOSMC) and super twisting sliding mode control (STA-SMC) based on HOSMC DC link voltage controllers. The difficult task of gain tuning in timely varying conditions is resolved by incorporating adaptive control to STA-SMC. The proposed controller is validated and compared with pre-presented control schemes under two test cases using simulation and experimental workbench carried out in dSPACE based hardware in the loop (HIL) workbench. The adaptive STA-SMC (ASTA-SMC) is compared with FOSMC and feedback linearization-based control schemes. The stability of ASTA-SMC in finite time is validated using the Lyapunov stability theorem.

Anti-unwinding adaptive super-twisting attitude control for spacecraft

This article addresses the attitude maneuver control without unwinding based on variable gain(i.e. adaptive) super-twisting algorithm and the modified Rodrigues parameters(MRPs). First, a selection logic for the MRP set and its shadow set is designed in order to construct an attitude control system model for rigid spacecraft. Second, a nonlinear sliding function is presented, and on the sliding phase, finite-time convergence and anti-unwinding performance are guaranteed. As a result, a first order sliding mode controller is created to ensure finite-time convergence and anti-unwinding performance on the reaching phase. To alleviate the chattering and improve convergence speed, an adaptive super-twisting algorithm is presented, and the finite-time convergence and anti-unwinding performance are guaranteed on the reaching phase. Furthermore, the adaptive gains are designed based on dual-layer adaptive law, which allows the gains to be increased and decreased as appropriate. It is further demonstrated that when the controller gains are time-varying according to adaptive law, the convergence property and anti-unwinding performance are guaranteed. Numerical simulations are carried out to illustrate the closed-loop system's performance under the proposed control scheme.

Second-Order Sliding-Mode Control for Three-Level H-Bridge-Based Unified Power Quality Conditioner With Vanilla Feedforward Neural Network

This article proposes a modified three-wire three-level H-bridge-based unified power quality conditioner (UPQC) without any transformer in the shunt part and controlled by using second-order sliding-mode control (SOSMC). Thus, this topology has less component count than that in the flying-capacitor- and neutral-point-clamped-based UPQC. The isolated operation of the series part of the UPQC leads to distortion in the mitigated load voltage. An SOSMC based on the supertwisting algorithm is proposed to defeat this problem. The SOSMC eliminates the differentiation requirement, thereby suppressing noise amplification compared to the first-order sliding-mode control (FOSMC). In addition to these advantages, the chattering problems are also minimized compared to FOSMC. Thus, this technique provides robustness and dynamic response during systems' external and parameters' perturbation. Furthermore, in the SOSMC controller, the compensation voltage and current references are predicted by using an artificial neural network (ANN). The ANN model uses a vanilla feedforward neural network with only two hidden layers. The proposed ANN is developed by considering the instantaneous and delayed components. Consequently, it allows for a simpler model by reducing the number of hidden layers. The total harmonic distortion (THD) of the mitigated voltage is reduced to 0.65% and the mitigated current THD is 1.22%.

Disturbance-Observer-Based Second-Order Sliding Mode Controller for Speed Control of PMSM Drives

This paper explicitly proposes a novel second-order sliding mode (SOSM) controller based on disturbance observer (DOB) to optimize the disturbance rejection property of the permanent magnet synchronous motor (PMSM) system. Firstly, to tackle the inevitable chattering problem in conventional first-order sliding mode controllers, a new type of SOSM control technique is designed for the speed loop of PMSM system by retaining the discontinuous switching function in the derivative of the actual controller. The proposed controller can not only provide the strong anti-disturbance performance, but also significantly attenuate the potential chattering problem. Then, a DOB constructed based on the auxiliary system is further adopted to compensate the adverse effect generated by the disturbance to enhance dynamical performance. Finally, comprehensive experimental results are provided to verify the effectiveness of the proposed method.

Direct yaw-moment control of electric vehicles based on adaptive sliding mode.

The direct yaw-moment control (DYC) system consisting of an upper controller and a lower controller is developed on the basis of sliding mode theory and adaptive control technique. First, the two-degree of freedom (2-DOF) model is utilized to calculate the ideal yaw rate. Then, the seven-degree of freedom (7-DOF) electric vehicle model is given to design the upper controller by employing first-order sliding mode (FOSM) method, which is constructed to guarantee the actual yaw rate to approach the ideal value and gain the additional yaw moment. On this basis, an adaptive first-order sliding mode (AFOSM) controller is designed to enhance the system robustness against probable modelling error and parametric uncertainties. In order to mitigate the chattering issue present in the FOSM controller, a novel adaptive super-twisting sliding mode (ASTSM) controller is proposed for the design of DYC. Furthermore, the lower controller converting the additional yaw moment into driving or braking torque acting on each wheel is also developed. Finally, The simulation results indicate that the proposed DYC system can improve the electric vehicle driving stability effectively.

Sliding Mode Controllers Design based on Control Lyapunov functions for uncertain LTI systems

In this paper, a design method of sliding controllers based on control Lyapunov functions for uncertain LTI systems is proposed. Systems with matched non-vanishing disturbances, unmatched uncertainties and uncertain control coefficient matrix are considered. It is shown that whenever a robust nonlinear controller exists that renders the system quadratically stabilizable, in the absence of matched non vanishing disturbances, there is also an appropriate First-Order Sliding-Mode controller stabilizing the origin, that also renders the equilibrium point robustly stable in presence of perturbations. This shows that Sliding-Mode controllers are not more restrictive than other controllers, at least for the class of uncertain systems considered. Moreover, the design based on control Lyapunov functions provides a natural sliding surface, having an asymptotically stable sliding dynamics, so that with the corresponding sliding mode controller ensures global asymptotic stability of the uncertain system. The efficiency of the proposed SMC control is validated experimentally on a Furuta pendulum benchmark.

Design and Xilinx Virtex-field-programmable gate array for hardware in the loop of sensorless second-order sliding mode control and model reference adaptive system–sliding mode observer for direct torque control of induction motor drive

This article aims first to propose an improved space vector modulation–direct torque control in order to enhance the induction motor performance using: (1) a super-twisting controller and (2) a novel model reference adaptive system based on a sliding mode observer. Second, due to the complexity of the suggested control algorithm, this article deals also with a hardware implementation on a field-programmable gate array board. Indeed, the field-programmable gate array is mainly chosen to reduce the execution time, thanks to its parallel processing which significantly improves the quality of the control system by reducing the sampling period, and consequently the delays in the control loop. Besides, the super-twisting controller is proposed to enhance the speed regulation loop which is a second-order sliding mode control technique that uses a continuous control law to prevent the chattering phenomenon induced by the first-order sliding mode control technique. Moreover, the high performance control requires information about the rotor speed which can be obtained by a sensor. Generally, the use of the speed sensor increases the system cost and size, and reduces its system reliability. Therefore, a combination between a model reference adaptive system observer and a sliding mode observer is suggested for speed estimation and overcoming the sensitivity of the classical model reference adaptive system observer against uncertainties and stator resistance variations. The performance of the proposed space vector modulation--direct torque control--super-twisting controller with the model reference adaptive system--sliding mode observer algorithm of an induction motor is verified through simulation, hardware co-simulation and experimental validation utilizing a field-programmable gate array Virtex-5-ML507 board. The performance of the suggested sensorless control method is compared also with other recent published schemes.

Publisher’s Note

Medium Voltage DC (MVDC) integrated power systems are anticipated to feed the submarines and surface combatants. The MVDC based power systems use dc/dc converters tightly regulated via high bandwidth controllers act as constant power loads (CPL’s). The negative incremental impedance of the CPL’s may result in voltage instability in the system under disturbance. Thus for the efficient and robust control of the MVDC based power system, this paper proposes a high order sliding mode control (HOSMC) paradigm based on model-free adaptive super twisting sliding mode control (ASTA-SMC). This paper initially designs a first-order sliding mode control (FOSMC) and super twisting sliding mode control (STA-SMC) based on HOSMC DC link voltage controllers. The difficult task of gain tuning in timely varying conditions is resolved by incorporating adaptive control to STA-SMC. The proposed controller is validated and compared with pre-presented control schemes under two test cases using simulation and experimental workbench carried out in dSPACE based hardware in the loop (HIL) workbench. The adaptive STA-SMC (ASTA-SMC) is compared with FOSMC and feedback linearization-based control schemes. The stability of ASTA-SMC in finite time is validated using the Lyapunov stability theorem.

Practical Tracking of Permanent Magnet Linear Motor Via Logarithmic Sliding Mode Control

This article focuses on the fast position tracking problem for the permanent magnet linear motor (PMLM) system under a chattering-reduced sliding mode control signal. To this end, a class of globally nonsingular sliding mode control (SMC) laws, called logarithmic sliding mode (LnSM) control, is proposed in this article. Using the natural logarithm function, a high gain is established at the equilibrium of the sliding mode reduced-order system, which leads to a higher tracking precision and a faster local convergence rate than those of some classical SMCs. In addition, a super-twisting algorithm-based LnSM (ST-LnSM) control is constructed to reduce the chattering typical for first-order SMC, while stabilizing the position tracking system rapidly. Since only a few parameters need to be adjusted, and the employed natural logarithm function is conventionally integrated into most PMLM drivers, the proposed control law is easy to implement in PMLM systems or other industrial servo systems.

Chattering reduction effect on power efficiency of IFOC based induction motor

Nowadays, the strategies to control Induction Motor (IM) is growing fast. The vector control strategies give better performance than the scalar control to control IM. IFOC is one of the vector control strategies which more realistic to apply in industry, military, and transportation. However, IFOC requires Sliding Mode Control (SMC) with the Lyapunov function to ensure robustness and stability. The first-order SMC or ordinary SMC uses boundary layers technique such as the saturation function and the tangent-hyperbolic function to overcome the chattering phenomenon. The performance of boundary layer is analyzed in rotor speed response, stator current response in dq0 frame and power performance. In rotor speed response, the SMC with and without boundary layer has error steady-state less than 2%. In stator current response with dq0 frame, the boundary layer with tangent-hyperbolic function has the best performance. The power analysis shows that the boundary layer with saturation function has an active power loss of 39.16%, reactive power loss of 23.37% and apparent power loss of 30.30%. The boundary layer with tangent-hyperbolic functions has the best performance in reducing power consumption with active power loss of 41.24%, reactive power loss of 24.78% and apparent power loss of 31.96%.