Research on consensus problems with second-order sliding mode algorithm in multi-agent systems

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.

A generalized proportional Caputo fractional model of multi-agent linear dynamic systems via impulsive control protocol

DC/DC converters are widely used in new generation applications such as microgrid electric vehicles and storage systems. Controllers which ensure the converters output voltage on the reference value are designed with many different methods. Sliding mode control is a prominent controller design for power converters that has recently attracted the attention of researchers. Although the conventional sliding mode control has many advantages chattering and relative degree restriction are its outstanding weaknesses. The second-order sliding mode control which eliminates the disadvantages of the conventional sliding mode control uses different algorithms according to the relative degree of the system controlled. Algorithm with prescribed convergence law twisting algorithm and super twisting algorithm are commonly implemented second-order sliding mode control algorithms. In this paper controllers using second-order sliding mode control algorithms have been designed for a DC/DC buck converter feeding a resistive load. Tests realized in the Matlab/Simulink environment have revealed the robustness and performance of the controllers designed different sliding mode controller algorithms under various operating scenarios such as input voltage variation and load variation. As a result of the simulations the dynamic responses of these control algorithms have been analyzed and compared with each other and.

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

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

This paper shows the effectiveness of disturbance observer (DO) based sliding mode control (SMC) scheme as compared to traditional SMC. Both the methods are simulated for variable speed wind turbine (VSWT) to ensure asymptotic tracking of rotor speed even in the presence of disturbances. Two mass model of VSWT is derived which includes the damping effect of the rotor's blade and generator. The stiffness and damping effect of low-speed shaft are also taken into account while modelling the system. The dynamic model of VSWT contains both matched and mismatched uncertainties. Traditional SMC can only attenuate the effect of match uncertainties. The DO-based SMC overcomes the drawback of traditional SMC by attenuating mismatch uncertainties. In the proposed approach, a sliding manifold is chosen based on the estimation of an uncertain parameter (aerodynamic torque), which drives the system's states to equilibrium point in a finite time.

In this paper, a sliding mode control (SMC) design approach using embedding process, measure theory and optimal control techniques is proposed. In this method, a state trajectory starting from a given initial point reaches a definite point on a surface, the so-called sliding surface, in a finite time, and then tends to the origin along the sliding surface (SS). A measure theory approach with embedding process is used to solve such a problem in two phases. In the first phase, using an appropriate measure, an embedding is constructed to solve an appropriate optimal control problem such that the system trajectory reaches the SS in a finite time, and in the second phase, using measure theory, a control is usually designed such that the system trajectory tends to the origin along the SS. It is well-known that the main disadvantage of the use of the traditional SMCs is the chattering phenomenon. The proposed SMC is piecewise continuous and chattering free. Also, the sliding mode reaching point is selected prior to the design of the SMC and it is not necessary to verify the sliding mode reaching condition as it is guaranteed during the design process. In addition, a numerical example is presented to illustrate the effectiveness of the proposed method.

High-precise and high-dynamic control is the most important requirement of permanent magnet linear synchronous motor (PMLSM) system. The main problem is to suppress the disturbances existing in PMLSM system. Sliding mode control (SMC) is one of the most robust control algorithms now, it can achieve high response speed and high robustness at the same time. But chattering problem is the main weakness of SMC. To solve that, higher order SMC algorithms have been developed. Super-twisting sliding mode control (STSMC) is a kind of second-order sliding mode control algorithm and has attract wide attention now. This paper presents a position controller for PMLSM based on STSMC, and demonstrates the advantages of this controller by comparing it with normal SMC controllers. Then a disturbance observer based on STSMC is presented, and with the observation result, the disturbance can be compensated, and the robustness of system can be further improved.

In this paper, the consensus problem is studied for a class of multi-agent systems with sampled data and packet losses, where random and deterministic packet losses are considered, respectively. For random packet losses, a Bernoulli-distributed white sequence is used to describe packet dropouts among agents in a stochastic way. For deterministic packet losses, a switched system with stable and unstable subsystems is employed to model packet dropouts in a deterministic way. The purpose of this paper is to derive consensus criteria, such that linear multi-agent systems with sampled-data and packet losses can reach consensus. By means of the Lyapunov function approach and the decomposition method, the design problem of a distributed controller is solved in terms of convex optimization. The interplay among the allowable bound of the sampling interval, the probability of random packet losses, and the rate of deterministic packet losses are explicitly derived to characterize consensus conditions. The obtained criteria are closely related to the maximum eigenvalue of the Laplacian matrix versus the second minimum eigenvalue of the Laplacian matrix, which reveals the intrinsic effect of communication topologies on consensus performance. Finally, simulations are given to show the effectiveness of the proposed results.In this paper, the consensus problem is studied for a class of multi-agent systems with sampled data and packet losses, where random and deterministic packet losses are considered, respectively. For random packet losses, a Bernoulli-distributed white sequence is used to describe packet dropouts among agents in a stochastic way. For deterministic packet losses, a switched system with stable and unstable subsystems is employed to model packet dropouts in a deterministic way. The purpose of this paper is to derive consensus criteria, such that linear multi-agent systems with sampled-data and packet losses can reach consensus. By means of the Lyapunov function approach and the decomposition method, the design problem of a distributed controller is solved in terms of convex optimization. The interplay among the allowable bound of the sampling interval, the probability of random packet losses, and the rate of deterministic packet losses are explicitly derived to characterize consensus conditions. The obtained criteria are closely related to the maximum eigenvalue of the Laplacian matrix versus the second minimum eigenvalue of the Laplacian matrix, which reveals the intrinsic effect of communication topologies on consensus performance. Finally, simulations are given to show the effectiveness of the proposed results.

The cooperative output regulation of a linear multi-agent system can be viewed as a generalization of the leader-following consensus problem and was studied recently for the case where the system uncertain parameters vary in a sufficiently small neighborhood of their nominal value. This case was handled by the internal model design which converts the problem into a simultaneous eigenvalue placement problem of an augmented multi-agent system. In this paper, we further consider the cooperative robust output regulation problem for a class of minimum phase linear multi-agent systems in the sense that the controller allows the system uncertain parameters to vary in an arbitrarily prescribed compact subset. For this purpose, we introduce a new type of internal model that allows the cooperative robust output regulation problem of the given plant to be converted into a robust stabilization problem of an augmented multi-agent system. We then solve our problem by combining a simultaneous high-gain state feedback control technique and a distributed high-gain observer technique. A special case of our result leads to the solution of the leader-following robust consensus problem for a class of uncertain multi-agent systems. Copyright © 2013 John Wiley & Sons, Ltd.

Permanent Magnet Synchronous Motors (PMSMs) exhibit inherent symmetry in their electromagnetic structure yet behave as nonlinear and strongly coupled systems that are susceptible to internal parameter perturbations and external disturbances, posing challenges to effective control under dynamic operating conditions. To address these issues, this paper proposes a sliding mode control strategy for PMSMs that integrates a Novel Adaptive Reaching Law (NARL) and an Improved Terminal Fuzzy Sliding Mode Disturbance Observer (IFTSMDO), denoted as SMC-NARL-IFTSMDO. The NARL is designed with a state-dependent dynamic gain adjustment mechanism and terminal attractive factor characteristics: it increases the gain to ensure fast convergence when the system state is far from the sliding mode surface, and adaptively attenuates the gain to suppress chattering when approaching the sliding mode surface, thereby balancing the contradiction between convergence speed and chattering in traditional sliding mode control. The IFTSMDO constructs a composite sliding mode surface incorporating error derivatives, terminal power terms, and saturation functions, which enhances the sensitivity of disturbance estimation in the small-error stage, avoids high-frequency chattering caused by sign functions, and provides accurate feedforward compensation for the speed loop controller to improve the system’s anti-disturbance capability. Additionally, the asymptotic stability of the proposed control strategy is strictly proven using the Lyapunov stability theory, laying a solid theoretical foundation for its application. Experiments are conducted on a TMS320F28379D DSP-based platform, and quantitative results show that compared with the traditional sliding mode control (SMC-TRL), the proposed strategy reduces the no-load startup response time by 60%, the steady-state speed fluctuation by 60%, and the speed fluctuation under load disturbance by 81.5%, fully demonstrating its superiority in dynamic response and anti-disturbance performance.

As an essential component of human–computer interaction in steer-by-wire (SBW) vehicles, the steering feel feedback system provides drivers with accurate steering feel by precisely controlling the output torque of the steering feel motor. Meanwhile, the existence of uncertainties makes the accurate control of steering feel feedback torque become an acknowledged challenging issue. This article proposes an adaptive super-torque sliding mode control strategy based on barrier functions for the steering feel feedback system of SBW vehicles with highly complex dynamics in the presence of uncertainties. First, to achieve intelligent modeling under the influence of uncertainty factors, a dynamic system with unknown uncertainty based on adaptive fuzzy logic system (FLS) is proposed. In the framework of this model, the uncertainty factors introduced by unknown external disturbance, parameter uncertainty, and model couplings are considered as a lumped uncertainty function. Furthermore, the membership functions of the FLS are dynamically adjusted based on nearest neighbor clustering, aiming to enhance the modeling accuracy beyond traditional fuzzy modeling. To further offset the system uncertainty and FLS approximation error, an adaptive super-twisting sliding mode control (STSMC) method based on barrier function is proposed. This algorithm retains the advantages of traditional sliding mode control (SMC) methods in dealing with systems with uncertainty and eliminates the need for a priori knowledge of the upper bound of uncertainties by introducing the adaptive law based on barrier function, avoiding the use of complex identification algorithms. Moreover, it eliminates the gain of overestimation and significantly reduces chattering phenomenon in traditional sliding mode control. Finally, based on Lyapunov stability theory, this article proves the proposed system can achieve convergence within a finite time. Compared with STSMC, traditional SMC and proportional–integral–derivative (PID) control, the results verify the effectiveness of the proposed control method. The proposed strategy provides a new solution to reduce the steering feel feedback torque error under the influence of uncertain factors.

This study proposes a finite-time tracking control system for an unmanned aerial vehicle (UAV) in the presence of dynamic payloads and external disturbances. Changes in payload result in time-varying parametric uncertainties, making traditional control strategies ineffective. A sliding mode control (SMC) scheme is designed to handle uncertainties in both translational and rotational dynamics. A finite-time SMC (FTSMC) approach is developed to handle unknown time-varying mass and external disturbances in the translational dynamics. Furthermore, differences in the payload influence the inertia characteristics of the UAV, introducing further uncertainties in the feedback control design. A finite-time sliding mode controller is also implemented for rotational dynamics to guarantee the attitude stabilization under unknown inertia parameter variations. The proposed method has the objective to attenuate the chattering effect associated with traditional SMC within a finite time frame. Theoretical stability analysis with rigorous mathematical proofs is presented to confirm the effectiveness of the control scheme. Numerical simulations are provided to validate its performance under dynamic operating conditions.

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.

In this brief, a novel distributed leader-following consensus controller for linear multi-agent systems (MASs) with one leader and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> followers is designed for optimal leader-following consensus control. A user-friendly global objective function is well designed in a quadratic form. The proper choice of the weighting matrices and necessary and sufficient conditions for optimizing the objective function are given. The proposed controller can guarantee the optimization of the objective function and the achievement of the leader-following consensus of the MASs. To deal with the coupling in the controllers, we propose a dynamic average consensus-based algorithm to estimate the controller distributedly, and the estimate errors converge to zero in finite time. A simulation example is provided to demonstrate the results.