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This study aims to propose an adaptive fractional-order sliding mode controller to solve the problem of train speed tracking control and position interval control under disturbance environment in moving block system, so as to improve the tracking efficiency and collision avoidance performance.

The mathematical model of information interaction between trains is established based on algebraic graph theory, so that the train can obtain the state information of adjacent trains, and then realize the distributed cooperative control of each train. In the controller design, the sliding mode control and fractional calculus are combined to avoid the discontinuous switching phenomenon, so as to suppress the chattering of sliding mode control, and a parameter adaptive law is constructed to approximate the time-varying operating resistance coefficient.

The simulation results show that compared with proportional integral derivative (PID) control and ordinary sliding mode control, the control accuracy of the proposed algorithm in terms of speed is, respectively, improved by 25% and 75%. The error frequency and fluctuation range of the proposed algorithm are reduced in the position error control, the error value tends to 0, and the operation trend tends to be consistent. Therefore, the control method can improve the control accuracy of the system and prove that it has strong immunity.

The algorithm can reduce the influence of external interference in the actual operating environment, realize efficient and stable tracking of trains, and ensure the safety of train control.

This paper aimed a fractional-order sliding mode-based lateral lane-change control method that was proposed to improve the path-tracking accuracy of vehicle lateral motion.

In this paper the vehicle presighting and kinematic models were established, and a new sliding mode control isokinetic convergence law was devised based on the fractional order calculus to make the front wheel turning angle approach the desired value quickly. On this basis, a fractional gradient descent algorithm was proposed to adjust the radial basis function (RBF) neuron parameter update rules to improve the compensation speed of the neural network.

The simulation results revealed that, compared to the traditional sliding mode control strategy, the designed controller eliminated the jitter of the sliding mode control, sped up the response of the controller, reduced the overshoot of the system parameters and facilitated accurate and fast tracking of the desired path when the vehicle changed lanes at low speeds.

This paper combines the idea of fractional order calculus with gradient descent algorithm, proposed a fractional-order gradient descent method applied to RBF neural network and fast adjustment the position and width of neurons.

To meet the need of reducing the cost of industrial systems, sensorless control applications on electrical machines are increasing day by day. This paper aims to improve the performance of the sensorless induction motor control system. To do this, the speed observer is designed based on the combination of the sliding mode and the fractional order integral.

Super-twisting sliding mode (STSM) and Grünwald–Letnikov approach are used on the proposed observer. The stability of the proposed observer is verified by using Lyapunov method. Then, the observer coefficients are optimized for minimizing the steady-state error and chattering amplitude. The optimum coefficients (c₁, c₂, k_i and λ) are obtained by using response surface method. To verify the effectiveness of proposed observer, a large number of experiments are performed for different operation conditions, such as different speeds (500, 1,000 and 1,500 rpm) and loads (100 and 50 per cent loads). Parameter uncertainties (rotor inertia J and friction factor F) are tested to prove the robustness of the proposed method. All these operation conditions are applied for both proportional integral (PI) and fractional order STSM (FOSTSM) observers and their performances are compared.

The observer model is tested with optimum coefficients to validate the proposed observer effectiveness. At the beginning, the motor is started without load. When it reaches reference speed, the motor is loaded. Estimated speed and actual speed trends are compared. The results are presented in tables and figures. As a result, the FOSTSM observer has less steady-state error than the PI observer for all operation conditions. However, chattering amplitudes are lower in some operation conditions. In addition, the proposed observer shows more robustness against the parameter changes than the PI observer.

The proposed FOSTSM observer can be applied easily for industrial variable speed drive systems which are using induction motor to improve the performance and stability.

The robustness of the STSM and the memory-intensive structure of the fractional order integral are combined to form a robust and flexible observer. This paper grants the lower steady-state error and chattering amplitude for sensorless speed control of the induction motor in different speed and load operation conditions. In addition, the proposed observer shows high robustness against the parameter uncertainties.

This paper aims to design the fractional order sliding mode controller for highly maneuverable remote piloted unmanned aircraft with time-varying delays.

With the assumption that the time-varying delays are bounded and identical for different outputs, an observer-based control technique is implied which reformulates the state variables based on the system model and delayed outputs. The estimated state variables are fed as feedback into the controller. Based on the delayed output observer, a fractional order sliding mode controller is designed. Further, the stability of the closed-loop system is analyzed and asymptotical convergence is realized using Lyapunov–Razumikhin theorem.

The simulation is done in Matlab and Simulink. The parametric variations and trajectory tracking results are illustrated which looks propitious.

In practical operation, measurement signal is often delayed, which significantly degrade the control performance or even disturb the stability. It is emphasized to choose attitude as the evaluation indicator for unmanned aerial vehicle time delay.

A novel fractional order sliding mode control technique is designed to enhance the trajectory tracking, thus autonomous flight performance, of the aircraft system. Also, the main idea behind this novel procedure is formulated for minimizing the parametric variations in presence of time delays.

With the development of integrated circuit and communication technology, digital secure communication has become a research hotspot. This paper aims to design a five-dimensional fractional-order chaotic secure communication circuit with sliding mode synchronous based on microcontroller (MCU).

First, a five-dimensional fractional-order chaotic system for encryption is constructed. The approximate numerical solution of fractional-order chaotic system is calculated by Adomian decomposition method, and the phase diagram is obtained. Then, combined with the complexity and 0–1 test algorithm, the parameters of fractional-order chaotic system for encryption are selected. In addition, a sliding mode controller based on the new reaching law is constructed, and its stability is proved. The chaotic system can be synchronized in a short time by using sliding mode control synchronization.

The electronic circuit is implemented to verify the feasibility and effectiveness of the designed scheme.

It is feasible to realize fractional-order chaotic secure communication using MCU, and further reducing the synchronization error is the focus of future work.

The purpose of this paper is to address a fractional order fuzzy PID (FOFPID) control approach for solving the problem of enhancing high precision tracking performance and robustness against to different reference trajectories of a 6-DOF Stewart Platform (SP) in joint space.

For the optimal design of the proposed control approach, tuning of the controller parameters including membership functions and input-output scaling factors along with the fractional order rate of error and fractional order integral of control signal is tuned with off-line by using particle swarm optimization (PSO) algorithm. For achieving this off-line optimization in the simulation environment, very accurate dynamic model of SP which has more complicated dynamical characteristics is required. Therefore, the coupling dynamic model of multi-rigid-body system is developed by Lagrange-Euler approach. For completeness, the mathematical model of the actuators is established and integrated with the dynamic model of SP mechanical system to state electromechanical coupling dynamic model. To study the validness of the proposed FOFPID controller, using this accurate dynamic model of the SP, other published control approaches such as the PID control, FOPID control and fuzzy PID control are also optimized with PSO in simulation environment. To compare trajectory tracking performance and effectiveness of the tuned controllers, the real time validation trajectory tracking experiments are conducted using the experimental setup of the SP by applying the optimum parameters of the controllers. The credibility of the results obtained with the controllers tuned in simulation environment is examined using statistical analysis.

The experimental results clearly demonstrate that the proposed optimal FOFPID controller can improve the control performance and reduce reference trajectory tracking errors of the SP. Also, the proposed PSO optimized FOFPID control strategy outperforms other control schemes in terms of the different difficulty levels of the given trajectories.

To the best of the authors’ knowledge, such a motion controller incorporating the fractional order approach to the fuzzy is first time applied in trajectory tracking control of SP.

The purpose of this paper is to present a two-loop approach for velocity control of a permanent magnet synchronous motor (PMSM) under mechanical uncertainties.

The inner loop calculates the two-axis stator reference voltages through a feedback linearization method. The outer loop employs an RST control structure to compute the q-axis stator reference current. To increase the robustness of the proposed method, the RST controller parameters are adapted through a fractional order model reference adaptive system (FO-MRAS). The fractional order gradient and Lyapunov methods are utilized as adaptation mechanisms.

The effect of the fractional order derivative in the load disturbance rejection, transient response speed and the robustness is verified through computer simulations. The simulation results show the effectiveness of the proposed method against the external torque and mechanical parameters uncertainties.

The proposed FO-MRAS based on Lyapunov adaptation mechanism is proposed for the first time. Moreover, application of the FO-MRAS for velocity control of PMSM is presented for the first time.

This paper aims to develop sliding mode control (SMC) methods for second-order multi-agent systems (MAS) in the presence of mismatched uncertainties.

Based on the disturbance observer (DOB), discontinuous and continuous sliding mode protocols are designed to achieve finite-time consensus in spite of the disturbances.

Compared with integral SMC, numerical simulation results show that the proposed control methods exhibit better performance with respect to reduction of chattering.

The main contributions are the following: MAS described with mismatched uncertainties are considered; both discontinuous and continuous sliding mode controllers are considered; with the proposed sliding mode controller, the desired sliding surface can be reached in finite time and the DOB is introduced in the controller to alleviate the chattering phenomenon.

This study aims to design and implement a novel tilt integral sliding mode controller and observer for sensorless speed control of a permanent magnet synchronous motor (PMSM).

A control strategy combining the tilt integral derivative (TID) with sliding mode control (SMC) is proposed to determine the tilt integral sliding mode manifold. Using this manifold, tilt integral sliding mode controller (TISMC) and observer (TISMO) are designed. The stabilities are verified by using Lyapunov method. To prove the effectiveness and robustness of proposed methods, sensorless speed control of PMSM is performed for various operating conditions such as constant and variable speed references, load disturbance injection, parameter perturbation, whereas sensor noises are not taken into account. The performance of proposed method is compared with TID controller, proportional integral derivative controller and conventional SMO.

Simulation results demonstrate that TISMC and TISMO have better performance in all operating conditions. They are robust against parameter uncertainties and disturbances. TISM based sensorless control of PMSM is well guaranteed with superior performance.

The proposed method has not been tackled in the literature. By combining TID and SMC, novel tilt integral sliding manifold is presented and used in designing of the controller and observer. It is proven by Lyapunov method that errors converge to zero.

The proposed Sliding Mode Control-Global Regressive Neural Network (SMC-GRNN) algorithm is an integration of Global Regressive Neural Network (GRNN) and Sliding Mode Control (SMC). Through this integration, a novel structure of GRNN is designed to enable online and. This structure is then combined with SMC to develop a stable adaptive controller for a class of nonlinear multivariable uncertain dynamic systems.

In this study, a new hybrid (SMC-GRNN) control method is innovatively developed.

A novel structure of GRNN is designed that can be learned online and then be integrated with the SMC to develop a stable adaptive controller for a class of nonlinear uncertain systems. Furthermore, Lyapunov stability theory is utilized to ensure the hidden-output weighting values of SMC-GRNN adaptively updated in order to guarantee the stability of the closed-loop dynamic system. Eventually, two different numerical benchmark tests are employed to demonstrate the performance of the proposed controller.

A novel structure of GRNN is originally designed that can be learned online and then be integrated with the sliding mode SMC control to develop a stable adaptive controller for a class of nonlinear uncertain systems. Moreover, Lyapunov stability theory is innovatively utilized to ensure the hidden-output weighting values of SMC-GRNN adaptively updated in order to guarantee the stability of the closed-loop dynamic system.