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To enhance the position and attitude-control of quadrotor for trajectory tracking, we propose a fast decay function utilizing exponential property to improve the performance of global sliding-mode control, allowing the initial value to quickly reach equilibrium. The main research is focused on deriving the finite settling time using the proposed decay function and presenting a detailed calculation process, instead of making a simple modification to a monotonic exponential-decay function. Moreover, we adopt an adaptive control law to ensure the robustness of the quadrotor, even without knowing the upper bound for disturbances. In addition, we perform time-varying mass simulations because the quadrotor’s load mass may change during maneuvering. Furthermore, using the Lyapunov function, the stability of the entire closed-loop system is ensured by the step-by-step stabilization of each subsystem. The simulation results show that the rapid global sliding-mode control (RGSMC) we designed is more effective than the conventional global sliding-mode control and adaptive sliding mode control with respect to stabilization and tracking against external disturbances. Hence, the fast decay property of the proposed global function is verified.

An improved non-singular fast terminal sliding mode control (INFTSMC) is proposed in this study, to improve the dynamic speed regulation and tracking accuracy of a surface-mounted permanent magnet synchronous motor (SPMSM) system. A sliding surface that completely removes singularities from the controller input is proposed. The key characteristics of the INFTSMC are fast convergence of errors, high tracking accuracy, and robustness against disturbances. The controller designed in this study is proven to be stable, with convergence in finite time and stability based on the Lyapunov theory. The proposed INFTSMC has a fast response and better performance than conventional sliding mode control and terminal sliding mode control, as demonstrated by simulation and hardware experiments in both virtual and real-time scenarios.

This study investigates the speed control of permanent magnet synchronous motors in the presence of external load disturbances via fast terminal sliding-mode control (FTSMC). First, to enhance the speed tracking performance, a logarithmic FTSMC method based on a novel sliding surface is proposed to improve the previously introduced FTSMC. Second, we have derived an enhanced settling time, demonstrating its superiority over that of recently introduced exponential FTSMC through the utilization of a logarithmic sliding surface. Third, the proposed logarithmic FTSMC and exponential FTSMC are compared to demonstrate that the convergence time of the logarithmic FTSMC is less than that of the exponential FTSMC. Forth, super-twisting reaching law is adopted in logarithmic FTSMC to counteract perturbations since it has an ability against various unknown disturbances, such as parameter mismatch, load torque variation, and friction force. Finally, the simulation results show that the proposed strategy can effectively improve the dynamic performance and robustness of permanent magnet synchronous motor systems.

The permanent magnet synchronous motor (PMSM) has been of interest to eco-friendly industries on account of its advantages such as high performance, efficiency, and precision control. However, perturbations due to PMSM parameter uncertainty, load torque, and external disturbance interfere with the construction of PMSM precision control systems. Therefore, a robust control system is needed to avoid unnecessary system movement caused by perturbations. In this paper, sliding mode control (SMC) is adopted to implement a robust control system for the PMSM. In order to reduce the reaching time from the initial system state to the sliding surface and the chattering phenomenon that can cause the system to malfunction, the adaptive quick sliding mode reaching law based on an exponential function and power equation is proposed. Although the SMC is robust to disturbance and parameter uncertainty, unexpected disturbances can destabilize the system. To estimate the unmatched disturbance in a short time, the second-order fast terminal sliding mode observer (SFTSMO) is proposed. The results show that the motor control system based on the proposed method has a fast convergence speed to an objective value, position tracking performance, and robustness.

As control algorithms evolve, their enhanced performance is often accompanied by increased complexity, reaching a point where practical experimentation becomes unfeasible. This situation has led to many theoretical studies relying solely on simulations without experimental verification. To address this gap, this study introduces a rapid experimentation protocol (REP) for applying field-oriented control (FOC) strategies to permanent magnet synchronous motors (PMSMs) based on model-based design (MBD) and automated code generation. REP is designed to be user-friendly and straightforward, offering a less complex and more accessible alternative to DSP toolboxes. Its excellent hardware compatibility is conducive to code porting and development. With this protocol, users can quickly conduct FOC strategy experiments with reduced dependency on the complex automated code generation tools often associated with toolboxes. Centered around the PMSM model, this method utilizes only the fundamental modules of MATLAB2023b/Simulink, greatly simplifying the user experience. To demonstrate the feasibility and efficiency of the protocol, models for both sensor-based and sensorless control are developed. The practicality of REP, including sensor-based and sensorless experiments, is successfully validated on an arm-cortex-M4-based GD32 microcontroller.

Abstract In this paper, a local magnitude estimation model using ridge regression is proposed for the accurate determination of the local magnitude of earthquakes. To increase its accuracy, an estimation model was derived from the hypocentral distance correction term and peak amplitude using ridge regression. The improved performance of the proposed estimation model was evaluated via the mean squared error. It was compared with the least squares model to confirm its superiority in predicting the real magnitude.

Although sliding mode control (SMC) provides powerful control performance, it exhibits chattering phenomena that can lead to operational issues in quadrotor systems when certain thresholds are reached. To address this limitation, this study introduces second-order sliding mode control (SOSMC), which significantly reduces chattering. Furthermore, a modified version of the SOSMC, called advanced second-order sliding mode control (ASOSMC), is proposed by incorporating an additional term to enhance its control capabilities. The ASOSMC exhibits a stability higher than that of traditional SOSMC during quadrotor flight. We established the stability of the ASOSMC system using a more powerful strict Lyapunov stability analysis instead of the conventional Lyapunov stability employed in SMC. This paper presents the design and performance evaluation of the ASOSMC via simulation and compares it with those of conventional SMC (CSMC) and SOSMC. The simulation results confirm that the ASOSMC offers superior control performance in quadrotor systems.

In this article, a novel strategy called enhanced super-twisting active disturbance rejection control (ESTADRC), as well as a nonlinear observer (NOB), is used to implement a speed control scheme for permanent-magnet synchronous motors with intricate internal dynamics, and it exhibits nonlinearity and variable parameters. A new reaching law is formulated within a super-twisting sliding mode control (STSMC) framework, and a comprehensive procedure for finite convergence time analysis is provided. The convergence region of the state variables of the system is obtained using a Lyapunov function. ESTADRC is developed by integrating STSMC and linear active disturbance rejection control (LADRC), whereas the NOB is employed to estimate the motor’s position or angle value. Simulations demonstrated that the proposed approach is valid and effective compared with super-twisting active disturbance rejection control and LADRC.

In this study, a sliding-mode controller is designed using an adaptive reaching law with a super-twisting algorithm. A dynamic model of a drone is designed with a quadrotor that has four motors and considers disturbances and model uncertainties. Given that the drone operates as an under-actuated system, its flight stability and maneuverability are influenced by the discontinuous signal produced by the reaching law of the sliding-mode control. Therefore, this study aims to improve the sliding-mode control and stability of drone flight using the proposed adaptive law, which is based on exponential properties. The discontinuous signal of a conventional strategy is overcome using the super-twisting algorithm, and the drone rapidly reaches equilibrium using the proposed adaptive law that utilizes the sliding surface value. The proposed control strategy covers a higher dimension than the conventional sliding-mode control strategy; the system stability is proven using the strict Lyapunov function. The reaching time estimation results are introduced and used to compare the respective reaching times of the control strategies. To verify the superior performance of the proposed control method, multiple experiments are conducted under various situations and realizations. The simulation results prove that the proposed control method achieved a superior rapid response, stable maneuvering, and robustness with shorter reaching time.

This paper proposes a sensorless speed control strategy for a permanent magnet synchronous motor system. Sliding mode control with a whale optimization algorithm was developed for robustness and chattering reduction. To estimate the position and speed of the rotor, an extended Kalman filter using Gaussian process regression was designed. In this controller, the whale optimization method adjusts the switching gain to minimize the tracking error. However, it provides chattering reduction and robustness, owing to the adaptive gain. The extended Kalman estimator calculates the rotor speed by using the current and voltage of the motor as an observer. The observer ensures the high reliability and low cost of the controller. The noise covariance and weight matrices that validated the performance of the estimation were optimized using a regression algorithm. The Gaussian process regression was trained to approximate the best covariance and matrices from the results of the motor controller execution. The performance of the proposed method was demonstrated through simulations under several conditions of tracking speed and load torque changes.

This paper focuses on the speed regulation of a permanent-magnet synchronous motor (PMSM) with an uncertain extended load disturbance. A novel super-twisting sliding-mode control (NSTSMC) was proposed via a nonlinear integral sliding surface and a modified reaching law, effectively suppressing the chattering phenomenon. In addition, the NSTSMC can improve the convergence performance with a 0.04 s settling time, satisfying the super-twisting algorithm stability condition. For the novel integral sliding surface, the integral power term of the system state variables was incorporated into the conventional sliding surface to effectively improve the convergence rate and anti-disturbance ability. Moreover, an extended sliding-mode disturbance observer (ESO) was used to estimate the lumped extended disturbance and add the corresponding feedback compensation value from the sliding-mode disturbance observer to the output of the speed controller for the improved robustness of the system. The ESO-NSTSMC was developed to improve the performance of PMSM speed regulation by combining the advantages of the novel integral sliding surface, achieving a settling time of 0.01 s without overshoot. We confirm the performance of the proposed NSTSMC through a PMSM speed simulation and demonstrate that the controller can enhance the dynamic performance and robustness of the system.

Sliding mode control and disturbance compensation techniques are applied to a nonlinear speed control algorithm for a permanent magnet synchronous motor (PMSM). Optimizing the speed control performance of PMSM systems with various disturbances and uncertainties is challenging. To achieve a satisfactory performance, a sliding mode control method based on the super-twisting algorithm reaching law (STRL) is presented. STRL can adapt dynamically to the variations of a controlled system. The STRL maintains a high tracking performance of the controller and allows the control input to eliminate chattering. To estimate the uncertainties and compensate for disturbances, a support vector regression-disturbance observer (SVR-DOB) is presented. The estimated uncertainties were used to minimize modeling errors and improve the disturbance rejection. A controller using SVR-DOB achieves a high precision, and the simulation results demonstrated the validity of the proposed control approach.

A modified sigmoid sliding mode control (MS-SMC) approach is proposed for stabilizing and tracking a quadrotor system with a nonlinear sliding surface, where the dynamics model is underactuated, highly coupled, and nonlinear. The constructed nonlinear sliding surface is based on the traditional sliding mode surface with a modified sigmoid function, allowing the initial value to quickly reach equilibrium. A new type of nonlinear SMC is applied for performance improvement of the quadrotor using the proposed modified sigmoid sliding surface. To control the quadrotor effectively, a double-loop control method is used to design the control rate, in which the position subsystem is the outer loop, and the attitude subsystem is the inner loop.With the Lyapunov function, the stability of the overall closed-loop system is ensured by stabilizing each subsystem step by step. Moreover, from a practical point of view, the system performance under the model uncertainties and external disturbances are also considered. The simulation results show that the proposed MS-SMC performs better than the conventional sliding mode control (CSMC) and the back-stepping sliding mode control (BS-SMC) in terms of stabilization and tracking against external disturbances.

The discrimination between earthquakes and artificial explosions is a significant issue in seismic analysis to efficiently prevent and respond to seismic events. However, the discrimination of seismic events is challenging due to the low incidence rate. Moreover, the similarity between earthquakes and artificial explosions with a local magnitude derives a nonlinear data distribution. To improve the discrimination accuracy, this paper proposes machine-learning-based seismic discrimination methods—support vector machine, naive Bayes, and logistic regression. Furthermore, to overcome the nonlinear separation problem, the kernel functions and regularized logistic regression are applied to design seismic classifiers. To efficiently design the classifier, P- and S-wave amplitude ratios on the time domain and spectral ratios on the frequency domain, which is converted by fast Fourier transform and short-time Fourier transform are selected as feature vectors. Furthermore, an adaptive synthetic sampling algorithm is adopted to enhance the classifier performance against the seismic data imbalance issue caused by the non-equivalent number of occurrences. The comparisons among classifiers are evaluated by the binary classification performance analysis methods.