Conventional Sliding Mode Control Method Research Articles

Adaptive control of nonlinear time-varying systems with unknown parameters and model uncertainties

This paper investigates the adaptive control problem for nonlinear time-varying systems with unknown parameters and model uncertainties. A novel class of switching functions is designed, and its construction method is detailed, along with a proof of the continuity of its n−1 order derivatives. Two simple examples are provided to illustrate how the proposed congelation of variables method handles unknown high-frequency time-varying parameters in both the feedback and input paths. A new neural network control scheme is then developed, integrating an adaptive neural network controller with a robust controller. The smooth transition between these two controllers is ensured by the novel switching function, which guarantees global system stability. Furthermore, by combining the congelation of variables method with adaptive backstepping, a new adaptive tracking control scheme is proposed. This scheme effectively handles unknown high-frequency time-varying parameters while achieving asymptotic tracking of arbitrary reference signals. Simulation results show that the proposed novel adaptive control method delivers superior control accuracy while reducing energy consumption: it achieves an order of magnitude improvement over the traditional adaptive robust control method and two orders of magnitude improvement over the conventional sliding mode control method.

Torque Ripple Reduction of Nonsinusoidal Brushless DC Motor Based on Super-Twisting Sliding Mode Direct Power Control

In this paper, a second-order sliding mode control, based on super-twisting algorithm, is proposed for direct power control of the brushless DC (BLDC) motor. The proposed controller uses a super-twisting scheme that requires only sliding surface information and can handle system uncertainties and external disturbances, well. This scheme can improve the BLDC motor torque ripple by solving the disadvantages of the conventional sliding mode control method, such as the chattering effect and high frequency switching control. This method is simple and robust for the BLDC motor’s biggest challenge, torque ripple, which does not require any voltage and current control loops or complex reference frame transformations. The simulation results of the proposed method are compared with the direct power control (DPC) and model predictive control (MPC) methods, which indicate the superiority of the proposed method in both the steady- and transient-states. Moreover, the motor parameters variation in the tracking of active and reactive power are discussed. In addition, the practical results of the proposed method in both cases of speed and load variation show the effectiveness of this method in reducing power (torque) ripple and current total harmonic distortion (THD) and increasing the system’s efficiency compared to other methods.

Adaptive Fractional-Order Fast-Terminal-Type Sliding Mode Control for Underwater Vehicle-Manipulator Systems

Abstract This article proposes an adaptive fractional-order fast-terminal-type sliding mode control method to solve the trajectory tracking problem of the underwater vehicle-manipulator system in the presence of large dynamic uncertainties and strong external disturbances. For improving the control continuity and accuracy of the conventional sliding mode control method, a modified fractional-order sliding mode control scheme with a novel fractional-order sliding manifold and a fast-terminal-type reaching law is proposed. In addition, an auto-tuning law of switching gains is presented and combined with the fractional-order sliding mode control scheme to overcome the problem that the fixed switching gain may lead to obvious tracking performance degradation under complicated lumped disturbances. Finally, the superiorities of the proposed adaptive fractional-order fast-terminal-type sliding mode control method are verified through a series of comparative simulations of a 6-degrees-of-freedom (DOF) UVMS carrying a 6DOF manipulator.

Sliding-Mode Control for PMLSM Position Control—A Review

Owing to the competitive advantages of fast response speed, large pushing force, high reliability, and high precision, the permanent magnet linear synchronous motor (PMLSM) has played an increasingly vital role in various high-speed and high-precision control systems. However, PMLSM exhibits nonlinear behavior in actual operation, and position tracking precision is negatively affected by friction, load changes, and other external disturbances. To meet the growing demand and solve the position tracking control problem for the PMLSM, the control system is critical. Sliding-mode control (SMC) has been used extensively in nonlinear control systems due to its superior performance characterized by simplicity, good dynamic response and insensitivity to parameter perturbation and external disturbances, and has been implemented in PMLSMs to track practical position. The objective of this article is to classify, scrutinize and review the major sliding-mode control approaches for position control of PMLSM. The three different conventional SMC methods, namely the boundary layer approach, the reaching law approach and the disturbance observer-based SMC, are discussed in detail. The four advanced forms of SMC, namely terminal SMC, super-twisting SMC, adaptive SMC and intelligent SMC, are also presented. A comparison of these approaches is given, in which the advantages and disadvantages of each approach are presented; additionally, they are presented in table form in order to facilitate reading. It is anticipated that this work will serve as a reference and provide important insight into position control of PMLSM systems.

Adaptive neural network-based sliding mode control for a hydraulic rotary drive joint

Hydraulic system has specific nonlinear and unknown modeling characteristics, realizing precise tracking control is a very challenging task. In this study, a sliding mode controller based on an adaptive higher-order neural network is proposed for realizing precise position-tracking control of a hydraulic rotary drive joint. First, the structural design and working principle of the target joint are introduced, and the mathematical model of the corresponding valve-controlled hydraulic position servo system is developed. Then, the adaptive neural network algorithm and sliding mode control are effectively combined. Based on the measurement information obtained from the control process, the feedback error is used to adaptively approximate the control parameters and realize online adjustment of the controller output. Finally, the parameter identification and position tracking of the system are validated, and the results indicate that the proposed strategy exhibits a 20% improvement in position-tracking control compared to the conventional sliding mode control methods.

Design of adaptive sliding mode controller applied to ultrasonic motor

PurposeThe purpose of this paper is to achieve high-precision sliding mode control without chattering; the control parameters are easy to adjust, and the entire controller is easy to use in engineering practice.Design/methodology/approachUsing double sliding mode surfaces, the gain of the control signal can be adjusted adaptively according to the error signal. A kind of sliding mode controller without chattering is designed and applied to the control of ultrasonic motors.FindingsThe results show that for a position signal with a tracking amplitude of 35 mm, the traditional sliding mode control method has a maximum tracking error of 0.3326 mm under the premise of small chattering; the boundary layer sliding mode control method has a maximum tracking error of 0.3927 mm without chattering, and the maximum tracking error of continuous switching adaptive sliding mode control is 0.1589 mm, and there is no chattering. Under the same control parameters, after adding a load of 0.5 kg, the maximum tracking errors of the traditional sliding mode control method, the boundary layer sliding mode control method and the continuous switching adaptive sliding mode control are 0.4292 mm, 0.5111 mm and 0.1848 mm, respectively.Originality/valueThe proposed method not only switches continuously, but also the amplitude of the switching signal is adaptive, while maintaining the robustness of the conventional sliding mode control method, which has strong engineering application value.

Nonlinear Incremental Control for Flexible Aircraft Trajectory Tracking and Load Alleviation

This paper proposes a nonlinear control architecture for flexible aircraft simultaneous trajectory tracking and load alleviation. By exploiting the control redundancy, the gust and maneuver loads are alleviated without degrading the rigid-body command tracking performance. The proposed control architecture contains four cascaded loops: position control, flight path control, attitude control, and optimal multi-objective wing control. Because the position kinematics are not influenced by model uncertainties, the nonlinear dynamic inversion control is applied. On the contrary, the flight path dynamics are perturbed by both model uncertainties and atmospheric disturbances; thus the incremental sliding mode control is adopted. Lyapunov-based analyses show that this method can simultaneously reduce the model dependency and the minimum possible gains of conventional sliding mode control methods. Moreover, the attitude dynamics are in the strict-feedback form; thus the incremental backstepping sliding mode control is implemented. Furthermore, a novel load reference generator is designed to distinguish the necessary loads for performing maneuvers from the excessive loads. The load references are realized by the inner-loop optimal wing controller, whereas the excessive loads are naturalized by flaps without influencing the outer-loop tracking performance. The merits of the proposed control architecture are verified by trajectory tracking tasks in spatial von Kármán turbulence fields.

Design of Adaptive Sliding Mode Controller for Uncertain Pendulum System

This work aims to study and apply the adaptive sliding mode controller (ASMC) for the pendulum system with the existence of the parameters uncertainty, external disturbances, and coulomb friction. The adaptive sliding mode controller has several features over the conventional sliding mode control method. Firstly, the magnitude of the control signal is reduced to the minimally acceptable level defined by special conditions concerned with ASMC algorithm. Secondly, the upper bounds of uncertainties are not necessary to be defined before starting the work. For this reason, the ASMC can be used successfully to control the pendulum system with minimum control effort. These properties of the ASMC are confirming graphically by the simulation results using MATLAB 2019. The ASMC achieves an asymptotically stable system better than the Classical Sliding Mode Controller (CSMC). The unwanted phenomenon is called “chattering", which is appearing in the control action signal. These drawback properties are suppressed by employing a saturation function. Finally, the comparison between the results of the ASMC and CSMC showed that ASMC is the better one.

Fault-tolerant control for turbocharged diesel engine air path via disturbance observer

ABSTRACT This paper investigates fault-tolerant control algorithm for diesel engine air path system with consideration of system parametric uncertainties, external disturbances and actuator faults. Initially, a finite-time disturbance observer is developed for estimating the synchronised uncertainties including parametric uncertainties and external disturbances. Based on the reconstructed information from the observer, a fault-tolerant control law is designed by using sliding mode control incorporated adaptive method. Furthermore, to attenuate the chattering problem caused by conventional sliding mode control method, the hyperbolic tangent function is utilised. A novel sliding variable is employed for improving the performance of the modified chattering-free control approach. The proposed fault-tolerant control algorithm is feasible for implementing and unnecessary caculations can be avoided, because the synchronised uncertainties and the actuator faults are tackled separately. Besides, the observer does not require the priori knowledge of the upper bounds of the synchronised uncertainties. Finally, simulation results and comparison are carried out and analysed for illustrating the effectiveness and validness of the proposed control schemes.

USDE-Based Sliding Mode Control for Servo Mechanisms With Unknown System Dynamics

This article proposes an unknown system dynamics estimator (USDE) based sliding mode control for servo mechanisms with unknown dynamics and modeling uncertainties. An invariant manifold is first constructed by introducing an auxiliary variable based on a first-order low-pass filter. This is used to design a USDE with only one tuning parameter (i.e., time constant for the filter) and a simpler structure than other estimators. The USDE is used to compensate for the effect of the lumped unknown system dynamics since it can be easily incorporated into control synthesis. Moreover, to avoid the chattering phenomenon in the conventional sliding mode control methods, a novel reaching law is designed based on hyperbolic functions to guarantee that the sliding mode variable infinitely approaches to the equilibrium point instead of crossing it. Consequently, the fast convergence and chattering-free property can be achieved simultaneously. Simulations and experiments are provided to validate the effectiveness and superior performance of the proposed method.

Indirect Sliding Mode Control for DC–DC SEPIC Converters

This article presents an indirect sliding mode control (SMC) for single-ended primary-inductor converters (SEPIC). Unlike the conventional SMC methods, the proposed SMC method employs a sliding surface function based on the input current error only. The use of such sliding surface function not only simplifies the implementation but also reduces the cost of implementation. It is shown that the output voltage control can be achieved indirectly. The input current reference is generated by a proportional–integral (PI) regulator. The existence condition and the region of the closed-loop system are determined for all possibilities of the PI gains. The performance of the proposed SMC method is investigated on a laboratory prototype converter, operated in buck and boost modes, in terms of the voltage regulation ability under abrupt changes in the input voltage and load resistance. Simulation and experimental results are presented and discussed.

Sliding Mode Control for Permanent Magnet Synchronous Motor Drive Based on an Improved Exponential Reaching Law

Permanent magnet synchronous motor (PMSM) is a typical nonlinear and multi-variable coupled system, which is sensitive to the uncertainty or variations in the motor parameters and the external disturbance which lead to the deterioration of the steady-state performance. Therefore, it is necessary to introduce effective control methods to improve the drive quality. In this paper, the DQ-axes inductances considering the magnetic saturation of the PMSM which has a significant influence on the operating characteristics are obtained, and the variable parameters are substituted into the control system. Then, a novel sliding mode control strategy is analyzed and adopted. An improved exponential reaching law is proposed in order to solve the chattering problem and improve the performance, which is verified by the theory and simulation. It demonstrates the smooth and quick responses using the new approach can be achieved to enhance the robustness of the drive system compared with conventional sliding mode control method.

Two Novel Approaches of NTSMC and ANTSMC Synchronization for Smart Grid Chaotic Systems

The presence of uncertainties and external disturbances is one of the unavoidable problems with various practical systems which might be unavailable in real-time. Sliding Mode Control (SMC) is one of the effective robust control methods to deal with these uncertainties and external disturbances. In this paper, two novel controllers are designed by using Nonsingular Terminal SMC (NTSMC) and Adaptive Nonsingular Terminal SMC (ANTSMC) methods for synchronization of dual smart grid chaotic systems with various uncertainties and external disturbances. Indeed, both adaptive and non-adaptive controllers based on NTSMC are proposed to provide two alternatives which can adjust by changing operating conditions and dynamics. The concept of SMC method guarantees controller robustness against various uncertainties and external disturbances. Elimination of the undesirable chattering phenomenon is addressed in this study which is one of the common deficiencies with conventional SMC method. Additionally, finite time concept is used to speed up the convergence rate. Finite time stability proof is performed by using Lyapunov stability theory. The numerical simulation is carried out in Simulink/MATLAB to reveal the validity of the proposed controllers for the smart grid chaotic system. A comprehensive comparison is made by performing simulation for the Fractional Order Adaptive Sliding Mode Control (FOASMC) controller and defining three performance criteria, among the proposed controllers in this study and FOASMC controller.

Application of moving sliding mode control for a DC motor driven four-bar mechanism

The angular velocity of the input link of a mechanism fluctuates due to the inertia of links and the external forces, although it is generally assumed constant in design. The control of the crank angular velocity of a four-bar mechanism driven by a DC motor by moving sliding mode control is considered in this study. A time-varying slope is proposed based on the error state. The mathematical model of the motor-mechanism system is derived using Eksergian’s equation of motion. First, the state space equations are solved numerically for constant motor voltage to show the velocity fluctuations of the crank. Then both the conventional sliding mode control method and the proposed moving sliding mode control method are applied to obviate this unwanted velocity fluctuation. The method is verified by numerical simulations as well as experimental studies. The results of both the sliding mode control and the moving sliding mode control methods are compared. It is shown that a moving sliding surface in the sliding mode control increases the robustness of conventional sliding mode control by decreasing the reaching time. Also, the performance of the moving sliding mode control against parametric variations and external disturbances is experimentally investigated by adding a mass and applying an unexpected force on one of the links of the mechanism.

Sliding Mode Tracking Control With Perturbation Estimation for Hysteresis Nonlinearity of Piezo-Actuated Stages

Piezo-actuated stages are widely applied in the field of high-precision positioning. However, piezo-actuated stages produce hysteresis between the input voltage and the output displacement that negatively influences the positioning accuracy. In this paper, the Bouc-Wen model is established and identified using the bat-inspired optimization algorithm. Subsequently, based on the established hysteresis model, we propose a sliding mode control method with a new reaching law to suppress the hysteresis nonlinearity and achieve high-precision tracking control for the piezo-actuated stages. In addition, the proposed control method contains the perturbation estimation part, which can estimate online the modeling uncertainty and the unknown external disturbances. The stability of the proposed control method is demonstrated through the Lyapunov theory. Finally, to validate the effectiveness of the proposed control method, experiments are conducted on the piezo-actuated stages. Experimental results demonstrate that the proposed control method is superior to the feed-forward control and the conventional sliding mode control method.

High-performance torque controller design for AC driving 4WD electric vehicle in two time scales

In this paper, a novel torque control method of AC induction motor in two time scales is proposed for 4WD electric vehicles. A two-time-scale sliding-mode control (SMC) observer and a SMC controller are synthesised to ensure high-performance torque control. Two time scales are considered based on the natural time scale separation existed in the AC induction motor driving system, i.e., rotor flux and speed corresponding to the slow dynamics and the stator current corresponding to the fast dynamics. The convergence property of the controller is considered when performing the observer design rather than the conventional control method where the controller and observer are designed separately. Moreover, the more advanced space vector modulation (SVM) technology instead of the sinusoidal pulse width modulation (SPWM) method used in the conventional SMC is also introduced in the proposed method to achieve minimum torque ripple. The effectiveness of the proposed torque control method is illustrated through simulations on a 4WD electric vehicle. Simulation results illustrate the improved performance compared with the conventional SMC method.

Sliding Mode Control with Nonlinear Disturbance Observer based on Genetic Algorithm for Inverted Pendulum with Mismatched Disturbances

Objective: This study proposes the application of optimized Sliding Mode Control (SMC) with Nonlinear Disturbance Observer (NDO) for the Inverted pendulum, which is subjected to mismatched disturbances. Methods/Statistical Analysis: Sliding Mode Control (SMC) with Nonlinear Disturbance Observer (NDO) solves the main problem of chattering present in traditional sliding mode controllers while retaining the nominal performance even with mismatched disturbances. Chattering defines the presence of finite frequency and finite amplitude oscillations in the control input. Genetic Algorithm is used for searching the optimal controller parameters, which includes switching function coefficient, switching gain and observer gain. Findings: Simulation results shows the advantages of NDO based SMC and proves that NDOSMC can observe the mismatched disturbances very effectively. The conventional SMC method is also used in the control design the Inverted pendulum for comparison studies. The two main issues to be tackled in conventional Sliding Mode Control (SMC) are convergence time and chattering. Chattering and convergence time can be reduced in SMC by getting the optimal values of controller parameters using intelligent optimization techniques such as Genetic Algorithm (GA). In the present study convergence time and chattering of the controlled system are considered as the performance index of objective function. Application/Improvements: This study can further be extended for Multi-Input Multi-Output (MIMO) systems subjected to mismatched disturbances and parametric uncertainties.

Continuous terminal sliding mode control with extended state observer for PMSM speed regulation system

In this paper, we discuss the speed regulation problem of permanent magnet synchronous motor (PMSM) servo systems. Firstly, a continuous terminal sliding mode control (CTSMC) method is introduced for speed loops to eliminate the chattering phenomenon while still ensuring a strong disturbance rejection ability for the closed-loop system. However, in the presence of strong disturbances, the CTSMC law still needs to select high gain which may result in large steady-state speed fluctuations for the PMSM control system. To this end, an extended state observer (ESO)-based continuous terminal sliding mode control method is proposed. The ESO is employed to estimate system disturbances and the estimation is employed by the speed controller as a feed-forward compensation for disturbances. Compared to the conventional sliding mode control method, the proposed composite sliding control method obtains a faster convergence and better tracking performance. Also, by feed-forward compensating system disturbances and tuning down the gain of the CTSMC law, the fluctuation of steady-state speed of the closed-loop system is reduced while the disturbance rejection capability of the PMSM system is still maintained. Simulation and experimental results are provided to demonstrate the superior properties of the proposed control method.

Modified group preserving methods and applications in chaotic systems

The tracking control of chaotic system has been one of the research focus areas of nonlinear control in recent years, in which the vital problem is to enable chaotic system to stabilize to an equilibrium point or to track a deterministic trajectory quickly. The conventional chaos control methods make the control power unnecessarily large and generate the phenomenon of chattering easily, resulting in the instabilities of the systems.The problems above can be transformed into the solutions of differential algebraic equations effectively. Considering that the group preserving scheme not only approximates the original system, but also preserve as much as possible the geometric structure and invariants of the original system, this paper takes advantage of the group preserving method to study the control method in chaotic system from two different perspectives.A new group preserving scheme based on the fast descending control method is presented, which enables chaotic system to stabilize to an equilibrium point quickly. Firstly, we introduce a novel approach to replace the optimal control problem of nonlinear system by directly specifying a time-decaying Lagrangian function, which helps us to transform the optimal control problem into a system of differential algebraic equations. Then we derive a modified group preserving scheme for the system.Similarly, we propose a new group preserving scheme based on the sliding mode control method for chaotic system to track a deterministic trajectory quickly. Owing to numerical discretization errors, signal noises and structural uncertainties in dynamical systems, the conventional sliding mode control method cannot guarantee to maintain the trajectories on the sliding surface, unless the numerical integration method is designed to do so. On the other hand, the conventional sliding mode control method easily induces high frequency chattering of the control force. Therefore, we modify the conventional sliding mode control method and use the modified group preserving scheme to find the control force.The above two methods are the combination of traditional control method and the Lie-group method. An invariant manifold is properly designed, and the original system is transformed into the differential algebraic system, in which the modified group preserving scheme can be used to find the control force. The resulting controlled system is stable.Finally, the proposed methods are applied to the classic Lorenz system and Duffing system correspondingly. Numerical experimental results show that the new approaches are very accurate and stable. Since the two controlled methods are fast in convergence and chattering-free, each of them has a good application prospect in the tracking control of chaotic systems.

Intelligent voltage control strategy for three-phase UPS inverters with output LC filter

This paper presents a supervisory fuzzy neural network control (SFNNC) method for a three-phase inverter of uninterruptible power supplies (UPSs). The proposed voltage controller is comprised of a fuzzy neural network control (FNNC) term and a supervisory control term. The FNNC term is deliberately employed to estimate the uncertain terms, and the supervisory control term is designed based on the sliding mode technique to stabilise the system dynamic errors. To improve the learning capability, the FNNC term incorporates an online parameter training methodology, using the gradient descent method and Lyapunov stability theory. Besides, a linear load current observer that estimates the load currents is used to exclude the load current sensors. The proposed SFNN controller and the observer are robust to the filter inductance variations, and their stability analyses are described in detail. The experimental results obtained on a prototype UPS test bed with a TMS320F28335 DSP are presented to validate the feasibility of the proposed scheme. Verification results demonstrate that the proposed control strategy can achieve smaller steady-state error and lower total harmonic distortion when subjected to nonlinear or unbalanced loads compared to the conventional sliding mode control method.