Second-order Sliding Mode Control Algorithm Research Articles

The Second-Order Sliding Mode Control Algorithm for Fixed-Time Stability of Nonlinear Systems

The Second-Order Sliding Mode Control Algorithm for Fixed-Time Stability of Nonlinear Systems

SOSM Controller Design for Output Constrained Systems Subject to Disturbances With Unknown Magnitudes

This brief aims to develop a new second-order sliding mode (SOSM) control method for nonlinear systems subject to output constraints and disturbances with unknown magnitudes. First of all, the problem of output constraint can be solved by proposing a novel barrier Lyapunov function. Then, in order to handle disturbances with unknown magnitudes, we establish an integral dynamics. Based on these, the SOSM control algorithm can be constructed by using the technique of adding a power integrator step by step. The proposed SOSM controller can not only guarantee that the output variable keeps staying within the preset boundary but also deal with disturbances with unknown magnitudes. Finally, the validity of the control scheme is verified through an academic example.

Research on the Trajectory Tracking of Adaptive Second-Order Sliding Mode Control Based on Super-Twisting

This article focuses on the trajectory tracking problem in the actuation control section of autonomous vehicles. Based on a two-degrees-of-freedom dynamics model, this paper combines adaptive preview control with a second-order sliding mode control method to develop a new control method. By designing an objective function based on lateral deviations, road boundaries, and the corresponding characteristics of the overall vehicle motion, the method adaptively adjusts the preview time to obtain the ideal yaw rate and then uses a second-order sliding mode control algorithm named Super-Twisting to calculate the steering wheel angle. Combining the low-pass filter with this controller can effectively suppress the chattering caused by the switching of the sliding mode plane while proposing a concept of smoothing based on gradient derivative, the smoothness after filtering is one-seventeenth of that before filtering, whereas the phase plane is used to prove its effectiveness and stability, it can be seen from the phase diagrams that all the state points are in the stable region. A joint simulation model of Matlab/Simulink and Carsim was built to verify the control effectiveness of the controller under the double-shift road, and the simulation results show that the designed controller has good control effect and high tracking accuracy. Meanwhile, the simulation model is also used for other simulations, firstly, simulation comparison tests were carried out with the Model Predictive Control algorithm at speeds of 36 and 54 km/h, compared to the MPC controller, the tacking accuracy of the ST controller has improved to 64.42% and 51.02% at 36 and 54 km/h; secondly, taking simulation of the designed controller against a conventional sliding mode controller based on isokinetic law of convergence, compared to the CSMC controller, the tracking accuracy of the ST controller has improved 41.78% at 54 km/h, and the smoothness of the ST controller is one-nineteenth of that of the CSMC controller; thirdly, carrying out simulations on parameter uncertainties, and replacing parameter uncertainty with Gaussian white noise, the maximum tracking error at 36 and 54 km/h did not exceed 0.3 m, and tracking remains good. Small fluctuations in the steering wheel angle do not affect the normal actuation of the actuator.

Attitude Decoupling Control of Semifloating Space Robots Using Time-Delay Estimation and Supertwisting Control

Dynamic coupling is an inherent behavior of the space robot system, which seriously affects the motion accuracy of the system. This article focuses on how to guarantee the base attitude stability of semifloating space robots, from a control perspective—namely, the base attitude decoupling control. The quaternion representation of the system dynamics is derived to avoid the representation singularity of the Euler angles. In consideration of the complicated system dynamics and the limited computing ability of the on-board computer, an efficient decoupling controller is designed based on the time-delay estimation (TDE) and the supertwisting control (STC). Herein, for the proposed TDE-based STC (TDE-STC) scheme, TDE is used to decouple and linearize the nonlinear dynamics, and STC is a second-order sliding mode control algorithm which can compensate for the TDE error and drive the state variables to converge to the equilibrium point robustly in finite time. The model-free decoupling principle of TDE is clearly illustrated by comparison with the classical computed torque control. The global asymptotical stability analysis of the closed-loop system is proven using the Lyapunov theory and the linear matrix inequality theorem. Finally, several comparative simulation studies on a 3-D space robot system with consideration of joint friction, disturbances, and model uncertainties are conducted to verify the effectiveness of the proposed TDE-STC scheme. The corresponding results show that the TDE-STC scheme can achieve a high-accuracy attitude decoupling performance with both the model-free merits and the chatter-free merits.

Super-twisting sliding mode control with defined boundary layer for chattering reduction of permanent magnet linear synchronous motor

The super-twisting algorithm (STA, a class of second-order sliding mode control (SOSMC)) is widely used in permanent magnet linear synchronous motor (PMLSM) systems for its least amount of information and simplest calculations among the SOSMC algorithms. Due to the discretization and sign function of the STA, the chattering problem may be induced. In this paper, we propose an STA method with a defined boundary layer (called δSTA) to further reduce chattering in high-precision positioning system. With the δSTA method, when the sliding variable crosses the zero point, the speed is adjusted via two different saturation functions, instead of discontinuous sign functions of the STA. The proposed control law was proven to be stable, ensuring the establishment of a second-order sliding mode. Both the simulation and experimental results showed that the proposed control scheme, with a defined boundary layer width, can improve the steady-state positioning accuracy and significantly reduce system chattering.

A hierarchical MPC and sliding mode based two-level control for freeway traffic systems with partial demand information

In this paper a hierarchical two-level control scheme is proposed in order to solve a ramp metering problem in freeway traffic systems. The proposal combines a Model Predictive Control (MPC) based supervisor with decentralized low-level Sliding Mode Controllers (SMCs). The considered freeway METANET model describes the traffic system, which is naturally affected by uncertainties since the mainstream inflow, the traffic demands on the on-ramps, and the flows exiting the off-ramps are not a priori known. In the proposed scheme, two control loops are present. A centralized MPC computes the optimal control inputs by minimizing the total time spent by the vehicles in the traffic system on the basis of a nominal model of the considered freeway stretch. The computed optimal inputs are used to generate the corresponding density references for the low-level on-ramp controllers, which rely on a saturated version of the Suboptimal Second-Order Sliding Mode (SSOSM) control algorithm. SSOSM controllers allow to regulate the density error to zero in a finite time, thus reducing the mismatch between the controlled traffic system dynamics and the model used by the MPC supervisor during the optimization. A simulation study encompassing several realistic scenarios is reported to assess the validity of the proposed approach also in comparison with other classical traffic control strategies. As confirmed by simulation, in spite of the uncertainties, the proposed control scheme produces satisfactory performance in terms of both total time spent minimization and capacity drop alleviation.

Comparison of two second-order sliding mode control algorithms for an articulated intervention AUV: Theory and experimental results

An articulated intervention autonomous underwater vehicle (AIAUV) is a slender, multi-articulated underwater robot. Accurate trajectory tracking is essential for AIAUV operations. Furthermore, due to hydrodynamic and hydrostatic parameter uncertainties, uncertain thruster characteristics, unknown disturbances, and unmodelled dynamic effects, robustness is crucial. In this paper, we present a super-twisting algorithm (STA) with adaptive gains and a generalized super-twisting algorithm (GSTA) for trajectory tracking of the position and orientation of AIAUVs. A higher-order sliding mode observer (HOSMO) for estimating the linear and angular velocities when velocity measurements are unavailable is also presented. The tracking errors for the resulting system are proven to converge asymptotically to zero. Finally, we demonstrate the applicability of the presented control laws with comprehensive simulation and experimental results and perform a comparison study, with two tests (C-shape and C-shape with a moving head), between the two algorithms and also a benchmark PID controller. The STA with adaptive gains exhibits the best overall tracking performance, with average position root mean square error (RMSE) 0.0121 m and average orientation RMSE 0.0335 rad. The GSTA also presented good results with average position RMSE 0.0267 m and average orientation RMSE 0.0292 rad. The PID controller gave average position RMSE 0.0371 m and average orientation RMSE 0.0491 rad.

Design and Analysis of Second-Order Sliding Mode Controller for Active Magnetic Bearing

An active magnetic bearing (AMB) is a kind of high-performance bearing that uses controllable electromagnetic force to levitate the rotor. Its control performance directly affects the operation characteristics of high-speed motors and other electromechanical products. The magnetic bearing control model is nonlinear and difficult to control. Sliding mode control algorithm can be used in the magnetic bearing control system, but the traditional sliding mode control has the problem of high-frequency chattering, which affects the operation stability of magnetic bearings. Based on the second-order sliding mode control algorithm, a new second-order sliding mode controller for active magnetic bearing control was designed, and the stability of the designed sliding mode control law was proven by Lyapunov criterion. On the basis of the established active magnetic bearing control model, the numerical analysis of the designed controller was carried out, and the control effect was compared with that obtained by the exponential reaching law for the sliding mode control algorithm. The experimental results show that the designed sliding mode controller has better dynamic performance and stability than the exponential reaching law for the sliding mode controller.

Second Order Sliding Mode Control of Oscillating Water Column Wave Energy Converters for Power Improvement

Ocean wave energy is a renewable energy which remains too costly for large-scale electricity generation. The oscillating water column (OWC) wave energy converter (WEC) is a promising device-type with a rectifying air turbine and generator which convert alternating airflow induced by the water motion into kinetic energy then into electric energy. Applying control at each stage of energy conversion could increase the electric energy output of the device. As researchers overcome the modeling challenges of OWC, such as the nonlinearities due to air compressibility and power take-off (PTO) dynamics, we can integrate specific control algorithms to test their ability to improve the efficiency of the OWC. Herein, we present a state-space model of an array of OWC WECs restricted to heave motion with nonlinear PTO dynamics. We apply second-order sliding mode control (SMC) which commands a smooth torque signal to a direct-drive generator to maintain a reference turbine angular velocity. Because the algorithm can yield high turbine torques, we investigate a simple feed-forward relation for the control of a valve to limit the turbine airflow and discard mechanical power. We find that implementing the SMC algorithm and valve control can improve electric energy conversion most effectively in less energetic sea states.

Second-order sliding mode controller design with output constraint

The output constraints widely exist in the physical systems and severely affect the performance of the closed-loop system. This paper considers the second-order sliding mode controller design subject to an output constraint. By constructing a new barrier Lyapunov function and applying the technique of adding a power integrator, a novel second-order sliding mode control algorithm, which can be used to deal with the output constraint problem, has been developed. The proposed sliding mode algorithm enables the output variable not to violate the boundary of the constraint region. Meanwhile, it has been shown that under the output constraint the sliding variable can still be stabilized to zero in a finite time. Finally, an academic example is given to verify the feasibility of the proposed second-order sliding mode algorithm.

Global smooth sliding mode controller for flexible air-breathing hypersonic vehicle with actuator faults

A global smooth sliding mode controller (GSSMC) is proposed for flexible air-breathing hypersonic vehicle (FAHV) under actuator faults and parametric uncertainties, consisting of global fast finite-time integral sliding surface (GFFIS), generalized smooth second-order sliding mode reaching law (GSRL) and smooth fixed-time observer. Firstly, nonlinear control-oriented model of FAHV is processed using input/output feedback linearization with flexible effects and actuator faults modeling as lumped matched disturbances. Secondly, a GFFIS is established to ensure finite-time convergence of states without singularity based on a newly proposed fast finite-time high-order regulator (FFR). The FFR is improved from standard finite-time high-order regulator via dilation rescaling, which can accelerate response speed avoiding complicated parameters selection. Meanwhile, GFFIS can eliminate initial reaching phase to enhance robustness of system due to characteristic of global convergence. Thirdly, a GSRL is presented to ensure finite-time convergence of sliding mode vector and its derivative without chattering based on a generalized smooth second-order sliding mode control algorithm, the stability and finite convergence time of which is analyzed via Lyapunov criteria in detail. Then, a smooth fixed-time observer is applied to estimate lumped disturbances in fixed time and avoid effects of parametric uncertainties. With the three components, GSSMC can drive FAHV subject to actuator faults and parametric uncertainties to follow desired values in finite time with smooth control signals. Ultimately, three sets of simulations are performed to verify the effectiveness of the methods proposed.

Application of multi-agent consistency analysis based on finite state machine in driverless vehicles formation control

The consensus problem in directed networks of multi-agents under fixed topology is studied. A second-order sliding mode control algorithm based on finite state machine is applied to mult-iagent system. Under the condition that the first derivative of sliding mode is unknown, the control output is generated by switching between multiple state machines according to the measured value of sliding mode, so that the sliding mode and its first derivative converge to zero in a finite time, and to achieve the goal that the multi-agent system can be consistent for a limited period of time.Finally, the multi-agent control idea based on finite state machine is applied to driverless vehicles formation control. The results show that this method can be successfully applied to driverless vehicles formation control.

Second order sliding mode control for nonlinear affine systems with quantized uncertainty

This paper deals with the design of a Second-Order Sliding Mode (SOSM) control algorithm able to enhance the closed-loop performance depending on the current working conditions. The novelty of the proposed approach is the design of a nonsmooth switching line, based on the quantization of the uncertainties affecting the system. The quantized uncertainty levels allow one to define nested box sets in the auxiliary state space, i.e., the space of the sliding variable and its first time derivative, and select suitable control amplitudes for each set, in order to guarantee the convergence of the sliding variable to the sliding manifold in a finite time. The proposed algorithm is theoretically analyzed, proving the existence of an upperbound of the reaching time to the origin through the considered quantization levels.

Second-Order Sliding Mode Control for Variable Speed Wind Turbine Experiment System

In this work, a second-order sliding mode control algorithm is proposed for variable speed laboratory size DC generator wind turbine experiment system in order to track a speed profile and operate the wind turbine at maximum power extraction. The turbine torque, which varies with the wind speed, is considered as an unknown disturbance and rejected by the sliding mode strategy. The sliding mode controller has been integrated into a multivariable control system to operate the experimental wind turbine. Experimental results show that the proposed control system can achieve favourable speed tracking performance and robust with regard to parameter variations and external turbine disturbance.

Adaptive-Gain Second-Order Sliding Mode Control of Attitude Tracking of Flexible Spacecraft

This paper investigates the robust finite-time control problem for flexible spacecraft attitude tracking maneuver in the presence of model uncertainties and external disturbances. Two robust attitude tracking controllers based on finite-time second-order sliding mode control algorithms are presented to solve this problem. For the first controller, a novel second-order sliding mode control scheme is developed to achieve high-precision tracking performance. For the second control law, an adaptive-gain second-order sliding mode control algorithm combing an adaptive law with second-order sliding mode control strategy is designed to relax the requirement of prior knowledge of the bound of the system uncertainties. The rigorous proofs show that the proposed controllers provide finite-time convergence of the attitude and angular velocity tracking errors. Numerical simulations on attitude tracking control are presented to demonstrate the performance of the developed controllers.

Stability Analysis of Second-Order Sliding Mode Control Systems With Input-Delay Using Poincaré Map

This note discusses the stability of dynamical systems with input-delay under the second-order sliding mode control algorithm. Poincaré Map is constructed to analyze the switching dynamics and to derive the stability conditions. Different parameter setting options are given for ensuring stability. Simulation examples are presented to verify the theoretical results.

Dynamic compensator‐based second‐order sliding mode controller design for mechanical systems

For mechanical systems using displacement measurements only, this study presents a dynamic compensator-based second-order sliding mode control algorithm without using any observer structure to estimate the velocity. Introducing the compensator into the sliding variable, a modified asymptotically stable second-order sliding mode control is developed. The proposed low-order dynamic controller inherently has low-pass filter property in which the effect of differentiators can be obtained. Using singular perturbation theory, the authors show that the system state is finally constrained in a small bound region when the gain is high enough. Finally, a numerical example is explained for demonstrating the applicability of the proposed scheme.

Boundary second-order sliding-mode control of an uncertain heat process with unbounded matched perturbation

The primary concern of the present paper is the regulation of an uncertain heat process with collocated boundary sensing and actuation. The underlying heat process is governed by an uncertain parabolic partial differential equation (PDE) with Neumann boundary conditions. It exhibits an unknown constant diffusivity parameter and it is affected by a smooth boundary disturbance, which is not available for measurements and which is possibly unbounded in magnitude. The proposed robust synthesis is formed by the linear feedback design and by the ”Twisting” second-order sliding-mode control algorithm, suitably combined and re-worked in the infinite-dimensional setting. A non-standard Lyapunov functional is invoked to establish the global asymptotic stability in a Sobolev space, involving spatial state derivatives of the same order as that of the plant equation. The stability proof is accompanied by a set of simple tuning rules for the controller parameters. The effectiveness of the developed control scheme is supported by simulation results.

Nonlinear fractional PI control of a class of fractional-order systems

This paper deals with the design of nonlinear PI control techniques for regulating a class of fractional-order dynamics governed by a commensurate-order model, possibly nonlinear, perturbed by an external disturbance. The suggested control algorithm is the combination between a fractional-order PI controller and a nonlinear robust version of it, namely a second-order sliding mode control algorithm called “super-twisting” controller in the literature. A key feature of the approach is the use of ad-hoc sliding manifolds whose construction involves fractional order derivatives. A constructive Lyapunov based synthesis is illustrated, which leads to simple tuning rules for the controller parameters guaranteeing the asymptotic rejection of the external disturbance under appropriate smoothness restrictions. Computer simulations illustrate the effectiveness of the proposed technique.

Loop tuning with specification on gain and phase margins via modified second-order sliding mode control algorithm

The modified second-order sliding mode algorithm is used for controller tuning. Namely, the modified suboptimal algorithm-based test (modified SOT) and non-parametric tuning rules for proportional-integral-derivative (PID) controllers are presented in this article. In the developed method of test and tuning, the idea of coordinated selection of the test parameters and the controller tuning parameters is introduced. The proposed approach allows for the formulation of simple non-parametric tuning rules for PID controllers that provide desired amplitude or phase margins exactly. In the modified SOT, the frequency of the self-excited oscillations can be generated equal to either the phase crossover frequency or the magnitude crossover frequency of the open-loop system frequency response (including a future PID controller) – depending on the tuning method choice. The first option will provide tuning with specification on gain margin, and the second option will ensure tuning with specification on phase margin. Tuning rules for a PID controller and simulation examples are provided.