Traditional Sliding Mode Control Research Articles

Robust adaptive sliding mode control of underactuated autonomous underwater vehicles with uncertain dynamics

This paper focuses on adaptive integral sliding mode control for a class of underactuated autonomous underwater vehicles (AUVs) with uncertain dynamics, where the vehicles moving in three-dimensional (3-D) space have only three available control inputs provided by the stern propellers, steering and diving rudders but five degrees of freedom to be controlled. Different from the traditional sliding mode control, the proposed dual closed-loop integral sliding mode control design can be described as comprising two distinct phases: 1) in outer-loop, the virtual velocity commands are determined for the following work; 2) in inner-loop, the actual control inputs are designed to achieve the trajectory tracking. Moreover, the practical situations that there exist systematic parametric uncertainties and external disturbances are also considered, and a novel direct adaptive neural network controller combined with a conditional integrator is presented, which provides the robustness and adaptation for the vehicle. In addition, the rigorous stability analysis based Lyapunov’s method demonstrates the uniform ultimate boundedness of all the tracking errors in the closed-loop system. Finally, simulation results are shown the effectiveness of the proposed controllers.

Stability Research of Distributed Drive Electric Vehicle by Adaptive Direct Yaw Moment Control

As one of the active safety technologies, stability control of vehicles has recently received great attention. In order to improve the handling stability of distributed drive electric vehicles under various extreme conditions, a direct yaw moment control (DYC) method based on a novel fuzzy sliding mode control (FSMC) is proposed. First, a linear 2DOF reference vehicle model as ideal value reference, a 7DOF vehicle model used for sideslip angle estimation, an electric-driving wheel model used to provide tire motion parameters based on CarSim platform are established. Then, FSMC is designed as the core decision-making layer of the control method to calculate the required additional yaw moment on the premise of estimating the sideslip angle. Four hub motors are allocated by the distribution method based on axle load proportion. Finally, under two typical working conditions, the four hub motors are allocated. Compared with traditional sliding mode control (SMC), the results show that FSMC can not only maintain vehicle stability more effectively under different working conditions, but also greatly reduce the occurrence of buffeting phenomenon, which has practical significance for engineering applications.

A Robust Second-Order Sliding Mode Control for Single-Phase Photovoltaic Grid-Connected Voltage Source Inverter

In this paper, a super-twisting algorithm (STA) second-order sliding mode control (SOSMC) is proposed for single-phase photovoltaic grid-connected voltage source inverters. The SOSMC approach is aimed to inject sinusoidal current to grid with low total harmonic distortion (THD), strong robustness to parameter variations, and fast dynamic response to solar irradiance changes. As the discontinuous sign function in the traditional sliding mode control (SMC) is replaced by the continuous super-twisting function, the chattering problem is eliminated. Furthermore, a robust sliding mode differentiator (SMD) is proposed to acquire the derivative of current reference which is difficult to obtain in practice. The stability of the system under the proposed method is proved through the Lyapunov theory. The experimental results validate that the proposed method has satisfactory performance in both dynamic and steady-state conditions, as well as disturbance rejection.

Robust Sliding Mode Control for Flexible Joint Robotic Manipulator via Disturbance Observer

In a flexible joint robotic manipulator, parametric variations and external disturbances result in mismatch uncertainties thus posing a great challenge in terms of manipulator’s control. This article investigates non-linear control algorithms for desired trajectory tracking of a flexible manipulator subjected to mismatch perturbations. The manipulator’s dynamics is derived based on Euler-Lagrange approach followed by the design of nonlinear control laws. The traditional Sliding Mode Control and Integral Sliding Mode Control failed to demonstrate adequate performance due to complex system dynamics. Disturbance Observer-based Sliding Mode Control has been thoroughly examined by defining a novel sliding manifold. The aforementioned control laws are designed and simulated in MATLAB/Simulink environment to characterize the control performance. Results demonstrated that the proposed Disturbance Observer-based Sliding Mode Control scheme over-performed on Sliding Mode Control variants and had three prominent features: robustness against mismatch uncertainty, improved chattering behaviour and ability to sustain nominal control performance of the system.

Improved Adaptive Backstepping Approach on STATCOM Controller of Nonlinear Power Systems

This paper proposes an improved backstepping control approach which uses error-compensation and the sliding mode variable structure control to achieve stability for a single machine infinite bus system (SMIBS) with a static synchronous compensator (STATCOM). An adaptive sliding mode control was also utilised to obtain strong response performance in order to avoid excitation and the unknown parameters generated by the recursive steps of traditional backstepping control. Increasing the error-compensation term was used to generate a new virtual control to guarantee that the system states are more rapid stable and eliminate system chattering effectively generated by traditional sliding mode control. The boundedness and convergence of the closed-loop system were then obtained based on Lyapunov stability theory. Finally, a simulation is demonstrated to illustrate the effectiveness and the practicality of the proposed control method.

Neural Network Sliding Mode Control of Intelligent Vehicle Longitudinal Dynamics

Longitudinal dynamics control is the basis for autonomous driving of intelligent vehicles, which have great significance to the development of intelligent transportation system (ITS). To solve the problems of traditional sliding mode control method when applied to intelligent vehicle longitudinal dynamics, such as large velocity tracking errors, strong chattering phenomenon and so on, a new sliding mode control strategy based on RBF (Radical Basis Function) neural network is presented in this paper. Firstly, a nonlinear mathematical model of the intelligent vehicle longitudinal motion is established by considering the dynamics of the engine, the torque converter, the automatic transmission and the brake system. On the basis of the system model, a variable structure control system with sliding mode is introduced to design a sliding mode variable controller with RBF neural network. This controller can adaptively adjust the switching gain and its stability is proved based on the Lyapunov theory. Finally, the effectiveness of the designed longitudinal velocity control strategy is verified by simulation under typical driving conditions. The simulation results show that the improved control algorithm can effectively suppress chattering, obtain the higher precision and stronger robustness than the traditional sliding mode control. Thus, the longitudinal motion control performance of intelligent vehicles is improved effectively.

A Hybrid Adaptive Control Strategy for Industrial Robotic Joints

This paper presents a hybrid adaptive approximation-based control (HAAC) strategy for a class of uncertain robotic joints' system. The proposed control structure consists of a robust sliding mode controller and an adaptive approximation-based controller. The robust sliding mode controller is designed by using the super-twisting algorithm, which is a particularly effective method to decrease the chattering caused by the traditional sliding mode control (SMC) and compensate the disturbances. Another improvement of the robust sliding mode controller is that the robust control parameters only subject to the upper bound of the derivative of the external disturbances, rather than choosing a relatively large value. Moreover, the designed adaptive approximation-based controller has the following two distinctive features: 1) the control parameters are designed to be adjusted in real time and 2) the prior knowledge of actual robotic model is not required to be known. These features contribute to compensating the uncertainties. The stability of the closed-loop system is proved by using the Lyapunov theory, and the simulation results demonstrate the effectiveness of the proposed control method. Finally, the proposed HAAC could apply in the experiments of industrial robotic joints' system.

Sliding mode control with PI-based saturation for nano-positioning

This paper proposes a modified sliding mode controller with proportion-integral (Pl)-based saturation (PISSMC) for nano-positioning of Piezoelectric Actuators (PEAs). Based on the sliding mode theory, the controller can consider hysteresis as the uncertainty of the system, which the non-linearities of hysteresis and model imperfection can be processed to achieve precise positioning and tracking control. The PI term of this controller can decrease the steady-state error of the system and alleviate the chattering of the discontinuous part of the Sliding Mode Controller (SMC). Further, as the only measurable information is the position state, a high-gain observer is adopted to estimate the other states. The designed controller employs a linear PEA system as parameters estimation of the model to estimate the control gain and compensate for the process non-linearity. The robust stability of the PISSMC is proved through a Lyapunov stability analysis. Experimental results demonstrate that compared with the traditional SMC, the proposed controller can accomplish better control performance, such as more accurate resolution, less steady-state error and slighter chattering.

Sliding-Mode Control With Multipower Approaching Law for DC-Link Voltage of Z-Source Photovoltaic Inverters

Z-source photovoltaic inverters feature a unique topology and a special modulation strategy that enables a traditional two-stage system function through a single-stage structure. Therefore, Z-source inverters are expected to gain an extensive application when inputs change significantly. Given the objective of achieving DC-link voltage control based on small-signal model analyses, this study proposes a sliding-mode control method with a multipower approaching law (MPAL) for the DC-link control of inverters. This novel approach can solve the slow convergence rate and serious buffeting of the traditional sliding-mode control. The proposed approach makes the system state reach the sliding surface rapidly. The inherent buffeting of the sliding-mode control is simultaneously weakened and even eliminated in a few cases. The simulation and experimental analyses prove that the proposed sliding-mode control with an MPAL features significant advantages unlike the traditional sliding-mode control and provides a certain practical value.

Adaptive Chattering‐Free Sliding Mode Control of Chaotic Systems with Unknown Input Nonlinearity via Smooth Hyperbolic Tangent Function

The design of adaptive chattering‐free sliding mode controller (SMC) for chaotic systems with unknown input nonlinearities is studied in this paper. A smooth hyperbolic tangent function is utilized to replace the discontinuous sign function; therefore, the proposed adaptive SMC ensures that not only the chaos phenomenon can be suppressed effectively but also the chattering often appearing in the traditional discontinuous SMC with sign function is eliminated, even when the unknown input nonlinearity is present. A sufficient condition for stability of closed‐loop system is acquired by Lyapunov theory. The numerical simulation results are illustrated to verify the proposed adaptive sliding mode control method.

Implicit Euler Implementation of Twisting Controller and Super-Twisting Observer without Numerical Chattering: Precise Quasi-Static MEMS Mirrors Control

The quasi-static operations of MEMS mirror are very sensitive to undesired oscillations due to its very low damping. It has been shown that closed-loop control can be superior to reduce those oscillations than open-loop control in the literature. For the closed-loop control, the conventional way of implementing sliding mode control (SMC) algorithm is forward Euler method, which results in numerical chattering in the control input and output. This paper proposes an implicit Euler implementation scheme of super twisting observer and twisting control for a commercial MEMS mirror actuated by an electrostatic staggered vertical comb (SVC) drive structure. The famous super-twisting algorithm is used as an observer and twisting SMC is used as a controller. Both are discretized by an implicit Euler integration method, and their implementation algorithms are provided. Simulations verify that, as compared to traditional sliding mode control implementation, the proposed scheme reduces the chattering both in trajectory tracking output and control input in presence of model uncertainties and external disturbances. The comparison demonstrates the potential applications of the proposed scheme in industrial applications in terms of feasibility and performance.

Complementary Sliding Mode Control via Elman Neural Network for Permanent Magnet Linear Servo System

The permanent magnet linear servo system is usually susceptible to uncertainties, such as parameter variations, external disturbances, and friction forces. To address this problem, a complementary sliding mode control (CSMC) via Elman neural network (ENN) was presented in this paper. First, the mathematical model of the permanent magnet linear synchronous motor (PMLSM) with a lumped uncertainty was established. Second, on the basis of the traditional sliding mode control (SMC), CSMC was designed by combining the integral sliding surface with the complementary sliding surface. CSMC is generally used to reduce the chattering phenomenon and, consequently, to improve the tracking performance. However, the values of the switching gain and the boundary layer thickness are difficult to select in CSMC. To deal with this problem, ENN was adopted in the proposed CSMC system to replace the switching control law. Due to its strong learning ability, ENN can estimate the value of the lumped uncertainty and adjust the parameters online, thus further improving the robustness of the system. In addition, to verify the control performance of the proposed method, a digital signal processor (DSP) was implemented as the experimental platform to control the mover of the PMLSM for the tracking of different reference trajectories. The experimental results show that the proposed control strategy not only improves tracking accuracy but also guarantees the robustness of the system.

Dynamic Sliding Mode Control of Active Power Filter With Integral Switching Gain

Owing to the fact that the active power filter with conventional sliding mode controller has a chattering problem, an improved dynamic sliding mode controller is proposed in this paper to increase the performance of the APF. A dynamic sliding mode controller with integral switching gain is developed. The first-order dynamic sliding surface has the characteristic of transferring the discontinuity in traditional sliding mode control to the first derivative of the controller. Therefore, a continuously dynamic sliding controller can be obtained, so that it can effectively weaken the chattering. In the meantime, the appropriate selection of switching gain can also reduce chattering. The simulation results show that the proposed control strategy possesses good performance to suppress the harmonics. Moreover, the hardware in the loop experiment proves the practicability of the proposed algorithm.

A Hybrid Control with PID⁻Improved Sliding Mode for Flat-Top of Missile Electromechanical Actuator Systems.

Electromechanical actuator (EMA) systems are widely employed in missiles. Due to the influence of the nonlinearities, there is a flat-top of about 64 ms when tracking the small-angle sinusoidal signals, which significantly reduces the performance of the EMA system and even causes the missile trajectory to oscillate. Aiming to solve these problems, this paper presents a hybrid control for flat-top situations. In contrast to the traditional PID or sliding mode controllers that missiles usually use, this paper utilizes improved sliding mode control based on a novel reaching law to eliminate the flat-top during the steering of the input signal, and utilizes the PID control to replace discontinuous control and improve the performance of EMA system. In addition, boundary layer and switching function are employed to solve the high-frequency chattering problem caused by traditional sliding mode control. Experiments indicate that the hybrid control can evidently reduce the flat-top time from 64 ms to 12 ms and eliminate the trajectory limit cycle oscillation. Compared with PID controllers, the proposed controller provides better performance—less chattering, less flat-top, higher precision, and no oscillation.

Optimal Sliding Mode Control for an Active Suspension System Based on a Genetic Algorithm

In order to improve the dynamic quality of traditional sliding mode control for an active suspension system, an optimal sliding mode control (OSMC) based on a genetic algorithm (GA) is proposed. First, the overall structure and control principle of the active suspension system are introduced. Second, the mathematical model of the quarter car active suspension system is established. Third, a sliding mode control (SMC) controller is designed to manipulate the active force to control the active suspension system. Fourth, GA is applied to optimize the weight coefficients of an SMC switching function and the parameters of the control law. Finally, the simulation model is built based on MATLAB/Simulink (version 2014a), and the simulations are performed and analyzed with the proposed control strategy to identify its performance. The simulation results show that the OSMC controller tuned using a GA has better control performance than the traditional SMC controller.

Discrete-Time Fast Terminal Sliding Mode Control for Permanent Magnet Linear Motor

The main objective of this paper is to solve the position tracking control problem for the permanent magnet linear motor by using the discrete-time fast terminal sliding mode control (SMC) method. Specifically, based on Euler's discretization technique, the approximate discrete-time model is first obtained and analyzed. Then, by introducing a new type of discrete-time fast terminal sliding surface, an improved discrete-time fast SMC method is developed and an equivalent-control-based fast terminal SMC law is subsequently designed. Rigorous analysis is provided to demonstrate that the fast terminal SMC law can offer a higher accuracy than the traditional linear SMC law. Numerical simulations and experimental results are finally performed to demonstrate the effectiveness of the proposed approach and show the advantages of the present discrete-time fast terminal SMC approach over some existing approaches, such as discrete-time linear sliding mode control approach and the PID control method.

Novel smooth sliding mode attitude control design for constrained re-entry vehicle based on disturbance observer

This paper investigates the attitude tracking control system design for reusable launch vehicle (RLV) in re-entry phase with input constraint, model uncertainty and external disturbance. The novel control scheme is designed via combining the advantages of the robust property of sliding mode control (SMC), the compensation ability of disturbance observer (DOB) and the systematic design procedure of backstepping technique. By applying DOB technique to estimate the lumped uncertainty, there is no need to choose the switch gain larger than the bound of uncertainty. Through designing the exponential form sliding surface and smooth sliding mode controller, the chattering and discontinuous problem inherent in the traditional SMC is alleviated. An additional system is constructed to handle input constraint. Based on Lyapunov theory, the asymptotic stability of the closed-loop system is proven. At last, compared simulations are presented to verify the effectiveness of the proposed control approach.

Control of a solid oxide fuel cell stack based on unmodeled dynamic compensations

To guarantee solid oxide fuel cell (SOFC) safe operation, plenty control strategies have been developed to control stack temperature and voltage within a reasonable range. However, these control approaches ignore unmodeled dynamics of the SOFC system, which may lead to unsatisfactory control results, sometimes even make the system unstable. To overcome this challenge, a unique control strategy which considers unmodeled dynamic compensations of the SOFC system is proposed in this paper. A model of the SOFC system is firstly built, which includes a known linear model and an unmodeled nonlinear dynamic estimation. A nonlinear controller based on the unmodeled dynamic compensation is then developed to force the SOFC to track desired stack temperature and voltage. To evaluate the control performance, the proposed control method is compared with a traditional sliding mode controller. The simulation results show if the unmodeled dynamics have a small effect on the SOFC, both the sliding mode controller and the proposed controller can achieve a precise tracking. If the unmodeled dynamics have a great impact on the SOFC, the temperature and voltage can be well controlled with the proposed control strategy. However, in the sliding mode controller, the temperature and voltage trajectories deviate largely from the reference values.

Research on Variable Cycle Engine Control Based on Model Reference Adaptive Sliding Mode Control Method

As to solve the problem of multivariable output tracking control of variable cycle engine under system uncertainties and external disturbances, an augmented model reference adaptive sliding mode control method based on LQR method was developed. Firstly, the model is augmented and the reference state is provided to the controller by designing the reference model using the optimal LQR method. Then, based on the state tracking sliding mode control method, the adaptive law is derived based on the strict stability condition of Lyapunov function to estimate the upper bound of the system perturbation matrix and the upper bound of the external disturbances. Finally, the controller achieves the asymptotic zero tracking error of the system under the conditions of uncertainty and external disturbance. The simulation results showed that the LQR-based augmented model reference adaptive sliding mode control method can solve the problem that the traditional sliding mode control method needs to specify the reference state in advance and improve the control performance of the variable cycle engine control with system uncertainties and external disturbance. The tracking of the control command is effectively achieved and the steady-state and dynamic performance are improved. The steady-state control errors under different conditions are less than 0.1%, the system overshoot is less than 0.5%, and the adjustment time is less than 1s, which conformed to the requirements of the aero engine control system technology.

Continuous Sliding Mode Control Strategy for a Class of Nonlinear Underactuated Systems

Sliding mode control (SMC), which is known to present strong robustness against various disturbances, has been extensively employed on underactuated systems, whose control problem has been a research focus in recent years. However, though received great attention, the study on SMC for underactuated systems still remains quite open since it is very challenging to construct a proper manifold which can simultaneously stabilize both actuated and unactuated system states. Motivated to promote the corresponding research, we propose an improved second-order SMC (IS-SMC) method for a class of nonlinear underactuated systems in this paper, which guarantees that the closed-loop system's equilibrium point is asymptotically stable even in the presence of unknown nondiminishing disturbances. Different from traditional SMC methods presenting with chattering problem, the control inputs of the proposed method are essentially continuous, which brings much convenience for practical applications. Moreover, for the disturbances which are second-order differentiable, an enhanced IS-SMC (EIS-SMC) method is derived to guarantee the smoothness for both the control inputs and their derivatives. Finally, the proposed approach is applied to a practical underactuated system: The overhead crane system, with sufficient simulation results provided to validate the efficiency of the proposed method.