Switching Surface Research Articles

Sliding Mode Control for Markov Jump Systems With Delays via Asynchronous Approach

In this paper, the problem of sliding mode control (SMC) is considered for a class of nonlinear continuous-time Markov jump systems (MJSs) with uncertainties and time delay. A novel integral-type switching sliding surface function is designed, where the controller gain may jump asynchronously with original MJSs. Then, an SMC law is constructed to force system trajectories onto the specified switching sliding surface in a finite time. The stochastic stability and dissipative performance of sliding mode dynamics are analyzed and the delay-dependent sufficient condition for the existence of the desired switching surface is developed. Moreover, we also extend SMC to investigate the finite-time stability problem during both reaching phase and sliding motion phase in the stochastic setting. Finally, simulation results are given to illustrate the effectiveness of the proposed design techniques.

Impact Time Guidance Law against Maneuvering targets using Sliding Mode Control

Control of impact time of missile to target has a great importance in applications such as Cooperative Attack of Multiple Missiles or Anti-Ship Missiles. This paper presents sliding mode control based guidance law against maneuvering targets with impact time constraints. Using nonlinear engagement dynamics, appropriate switching surface has been selected and sliding mode control has been designed using Lyapunov stability theorem. The sliding surface has been selected such that both the line of sight range and the error of the time remaining to target become zero to guarantee impacting the target at the desired time . By considering the non linear dynamic equations of maneuvering target , the proposed method can achieve the desired impact time against maneuvering target . In the proposed method , there is no need to consider small impact angle and non maneuvering target . Using the simulation model, the effectiveness of the proposed method in different scenarios (static and maneuvering) and taking into account different times for the impact time and its efficiency and its superiority as compared to other methods is shown.

Low‐order sliding mode repetitive control for discrete‐time systems under complex disturbance environment

AbstractA novel sliding mode repetitive control scheme is proposed for discrete‐time systems. It aims to address aperiodic disturbances, and simultaneously address a set of disturbances of known frequencies that can be unrelated. The sliding mode handles the former, and a repetitive control algorithm deals with the latter, creating a low‐order sliding model repetitive control law. The approach addresses each disturbance frequency individually. In contrast to the usual repetitive control approach, this allows one to address multiple unrelated frequencies without difficultly. Even when the addressed frequencies are harmonically related, but a relatively small number have significant error, this approach offers both substantial computation benefit, and benefit facilitating improved control of aperiodic disturbances. When both multiperiodic and aperiodic disturbances are present, the system trajectories can converge to a smaller switching band and keep moving within it. When there is only multiperiodic disturbance, the system trajectories will cross the switching surface within every specific steps when in the switching zone, and will converge to zero eventually. Simulation results demonstrate obvious advantages compared with the traditional method.

Memory-Based Integral Sliding-Mode Control for T-S Fuzzy Systems With PMSM via Disturbance Observer.

In this article, the disturbance observer (DOB)-based memory integral sliding-mode control (ISMC) is designed for the permanent magnet synchronous motor (PMSM) model subject to mismatched disturbance through the Takagi-Sugeno (T-S) fuzzy approach. Different from the previous studies, a memory-based ISMC scheme that has a constant delay is taken for the first time to design the ISMC for the T-S fuzzy systems. The DOB is given to estimate the disturbances, which are incorporated in the controller design to counteract the disturbance. To fully abide by the model characteristics of the PMSM-based T-S fuzzy systems and DOB, an integral-type fuzzy switching surface function (IFSSF), which involves state-dependent input matrix and memory parameter simultaneously, is defined. From the IFSSF, the fuzzy ISMC is designed to ensure the reachability condition in finite time. Besides that, the designed fuzzy ISMC can effectively attenuate the mismatched disturbances based on the H∞ control theory. Also, a set of sufficient conditions is derived to ensure the global asymptotic stability for the sliding-mode dynamics by the proposed controller. Finally, the applicability of designed DOB-based memory fuzzy ISMC methodology is demonstrated by a controller design for the PMSM model.

Passivity-Based Fuzzy ISMC for Wind Energy Conversion Systems With PMSG

This paper investigates the fuzzy integral sliding-mode control (ISMC) for permanent magnet synchronous generator (PMSG)-based wind energy conversion systems (WECSs). To do this, by using the double orthogonal complement and Frobenius theorem, the existence condition of the fuzzy sliding surface is presented. By constructing a suitable fuzzy Lyapunov function and introducing slack matrices, the sufficient conditions are gained via linear matrix inequalities (LMIs) for the concerned model to be asymptotically stable and passive. Further, the reachability of the switching surface is ensured by the considered fuzzy sliding-mode control laws. Besides that an adaptive fuzzy ISMC is constructed to derive the passivity criterion. For the demonstration, the presented control strategy is validated with nonlinear PMSG-based WECS. Finally, the effectiveness of the derived theoretical result is established by the numerical parameter values of PMSG-based wind-turbine model.

공압 계측을 통한 상용차량 ABS 용 압력 제어 밸브 모델링 및 On/Off 제어 전략

This paper reports on the modeling of a pneumatic brake system and valve control strategies for commercial vehicles with an ABS (Anti-lock Brake System). A PCV (Pressure Control Valve), consisting of two solenoid valves and two diaphragm valves, is a key part of a pneumatic ABS. To examine the pneumatic ABS, a PCV model that could accurately represent the dynamics of the air flowing through the PCV components was developed. The dynamic compressible airflow equations, which can describe the flow through an orifice, were adopted to describe the directional motion of the dynamic airflow, as commanded by the driver and modified by the PCV to facilitate the ABS activity. The discharge coefficient as a function of the pressure ratio was obtained experimentally. The PCV model was verified through pneumatic measurements of the relay valve and brake chamber. The verification results demonstrated that the simulation data were in agreement with those obtained experimentally. Furthermore, the PCV model was integrated with a whole vehicle model in Trucksim to conduct ABS simulation studies. The investigated system involved both the continuous wheel dynamics and inherent discontinuous characteristics of the PCV Two on/off valve control strategies based on the pressure and switching surface were introduced to regulate the slip ratio and analyzed via simulations. In addition, the switching-surface-based control strategy was evaluated through a hardware-in-loop experimental setup. The experimental results demonstrated that the implemented control strategy is effective even under uncertainties in the pneumatic ABS.

Load Frequency Control for Multi-Area Power Plants with Integrated Wind Resources

To provide a more practical method of controlling the frequency and tie-line power flow of a multi-area interconnected power system (MAIPS), a state observer based on sliding mode control (SOboSMC) acting under a second-order time derivative is proposed. The proposed design is used to study load frequency control against load disturbance, matched and mismatched uncertainty and parameter measurement difficulties of power systems that exist in the modern power plant, such as multi-area systems integrated with wind plants. Firstly, the state observer is designed to optimally estimate system state variables. The estimated states are applied to construct the model of the MAIPS. Secondly, a SOboSMC is designed with an integral switching surface acting on the second-order time derivative to forcefully drive the dynamic errors to zero and eliminate chattering, which can occur in the first-order approach to sliding mode control. In addition, the stability of the total power system is demonstrated with the Lyapunov stability theory based on a new linear matrix inequality (LMI) technique. To extend the validation of the proposed design control for practical purposes, it was tested in a New England system with 39 bus power against random load disturbances. The simulation results confirm the superiority of the proposed SOboSMC over other recent controllers with respect to overshoot and settling time.

Dissipativity-Based Fuzzy Integral Sliding Mode Control of Nonlinear Stochastic Systems

In this paper, both dissipation and stabilization of nonlinear T-S fuzzy systems with uncertain parameters are considered. By designing a new integral sliding mode control scheme, which sufficiently utilizes the special properties of T-S fuzzy membership functions, the difficulties induced by the uncertainties and external interference in T-S fuzzy systems are overcome by this new scheme. For the time delay and uncertainty, sufficient conditions are given to ensure the strict dissipation and asymptotic stability of the corresponding sliding mode dynamics. We propose a fuzzy integral sliding mode control law to drive the system trajectory to the fuzzy switching surface in the case of uncertainty and external interference. The realization of a fuzzy sliding mode controller for an inverted pendulum system proves the feasibility and superiority of our theoretical results.

Adaptive Global Sliding Mode Controller Design for Perturbed DC-DC Buck Converters

This paper proposes a novel adaptive intelligent global sliding mode control for the tracking control of a DC-DC buck converter with time-varying uncertainties/disturbances. The proposed control law is formulated using a switching surface that eliminates the reaching phase and ensures the existence of the sliding action from the start. The control law is derived based on the Lyapunov stability theory. The effectiveness of the proposed approach is illustrated via high-fidelity simulations by means of Simscape simulation environment in MATLAB. Satisfactory tracking accuracy, efficient suppression of the chattering phenomenon in the control input, and high robustness against uncertainties/disturbances are among the attributes of the proposed control approach.

Sliding mode control for singularly perturbed Markov jump descriptor systems with nonlinear perturbation

This paper develops a stochastic integral sliding mode control strategy for singularly perturbed Markov jump descriptor systems subject to nonlinear perturbation. The transition probabilities (TPs) for the system modes are considered to switch randomly within a finite set. We first present a novel mode and switch-dependent integral switching surface, based upon which the resulting sliding mode dynamics (SMD) only suffers from the unmatched perturbation that is not amplified in the Euclidean norm sense. To overcome the difficulty of synthesizing the nominal controller, we rewrite the SMD into the equivalent descriptor form. By virtue of the fixed-point principle and stochastic system theory, we give a rigorous proof for the existence and uniqueness of the solution and the mean-square exponential admissibility for the transformed SMD. A generalized framework that covers arbitrary switching and Markov switching of the TPs as special cases is further achieved. Then, by analyzing the stochastic reachability of the sliding motion, we synthesize a mode and switch-dependent SMC law. The adaptive technique is further integrated to estimate the unavailable boundaries of the matched perturbation. Finally, simulation results on an electronic circuit system confirm the validity and benefits of the developed control strategy.

Effect of varying the TD-lc-DFTB range-separation parameter on charge and energy transfer in a model pentacene/buckminsterfullerene heterojunction.

Atomistic modeling of energy and charge transfer at the heterojunction of organic solar cells is an active field with many remaining outstanding questions owing, in part, to the difficulties in performing reliable photodynamics calculations on very large systems. One approach to being able to overcome these difficulties is to design and apply an appropriate simplified method. Density-functional tight binding (DFTB) has become a popular form of approximate density-functional theory based on a minimal valence basis set and neglect of all but two center integrals. We report the results of our tests of a recent long-range correction (lc) [A. Humeniuk and R. Mitrić, J. Chem. Phys. 143, 134120 (2015)] for time-dependent (TD) lc-DFTB by carrying out TD-lc-DFTB fewest switches surface hopping calculations of energy and charge transfer times using the relatively new DFTBABY [A. Humeniuk and R. Mitrić, Comput. Phys. Commun. 221, 174 (2017)] program. An advantage of this method is the ability to run enough trajectories to get meaningful ensemble averages. Our interest in the present work is less in determining exact energy and charge transfer rates than in understanding how the results of these calculations vary with the value of the range-separation parameter (Rlc = 1/μ) for a model organic solar cell heterojunction consisting of a gas-phase van der Waals complex P/F made up of a single pentacene (P) molecule together with a single buckminsterfullerene (F) molecule. The default value of Rlc = 3.03 a0 is found to be much too small as neither energy nor charge transfer is observed until Rlc ≈ 10 a0. Tests at a single geometry show that the best agreement with high-quality ab initio spectra is obtained in the limit of no lc (i.e., very large Rlc). A plot of energy and charge transfer rates as a function of Rlc is provided, which suggests that a value of Rlc ≈ 15 a0 yields the typical literature (condensed-phase) charge transfer time of about 100 fs. However, energy and charge transfer times become as high as ∼300 fs for Rlc ≈ 25 a0. A closer examination of the charge transfer process P*/F → P+/F- shows that the initial electron transfer is accompanied by a partial delocalization of the P hole onto F, which then relocalizes back onto P, consistent with a polaron-like picture in which the nuclei relax to stabilize the resultant redistribution of charges.

Integral Sliding Mode Control Design for a Quarter-Car Active Suspension System

This paper utilizes the design of a robust integral sliding mode control (ISMC) for a quarter-car active suspension system. The main goal is to increase the ride comfort, whilst the road holding and rattle space remain within the safety bound. According to ISMC, the system state starts at the switch surface where the system nonlinearity, parameter changes, and road disturbances are rejected by a discontinuous control term present strongly in the suspension dynamics. This feature allows the design of a continuous controller, i.e. ideal controller during sliding motion from the first instant. Consequently, the car body is isolated from the wheel unit to perform the desired suspension requirements characteristics. The ISMC shows a high robustness control design of the suspension system, and can suppress chattering in the high-frequency band. The effectiveness of the proposed controller is performed by simulating the 2- DOF quarter car system with controlled and uncontrolled cases. The Matlab 2019a software is used to simulate the suspension models with bump road profiles as excitation disturbance.

Nonsingular terminal sliding mode control for micro-electro-mechanical gyroscope based on disturbance observer: Linear matrix inequality approach

The aim of this article is to design a nonsingular terminal sliding mode control method based on disturbance observer for the stabilization of the micro-electro-mechanical systems under lumped perturbation. By using the nonsingular terminal sliding mode control scheme, the state trajectories of the system achieve the switching surface and approach to the origin in the finite time. Also, by utilizing the disturbance observer, the finite-time convergence of disturbance error is assured. In the process of design, the optimized coefficients of the sliding surface are calculated in the form of linear matrix inequality. Simulation results for a micro-electro-mechanical gyroscope are illustrated to exhibit the validity of the planned approach in comparison with the other methods.

Nonadiabatic Dynamics at Metal Surfaces: Fewest Switches Surface Hopping with Electronic Relaxation.

A new scheme is proposed for modeling molecular nonadiabatic dynamics near metal surfaces. The charge-transfer character of such dynamics is exploited to construct an efficient reduced representation for the electronic structure. In this representation, the fewest switches surface hopping (FSSH) approach can be naturally modified to include electronic relaxation (ER). The resulting FSSH-ER method is valid across a wide range of coupling strengths as supported by tests applied to the Anderson-Holstein model for electron transfer. Future work will combine this scheme with ab initio electronic structure calculations.

Model-free high-order terminal sliding mode controller for Lipschitz nonlinear systems. Implemented on Exoped® exoskeleton robot

In this paper, a model-free high-order terminal sliding mode controller (TSMC) is developed for single input–single output Lipschitz nonlinear systems in presence of external disturbances. The proposed method is data-driven, i.e. it is based on online input and output information. In another word, the method is not model-based and can be applied to systems with unknown dynamics. The proposed method employs a high-order switching surface to mitigate the chattering problem. The disturbance estimation technique is also applied to overcome external disturbances. Rigorous theoretical analysis is carried out to verify convergence of states to the switching surface. To demonstrate the effectiveness and applicability of the proposed approach in different situations, several simulations are provided in addition to experimental studies. Experimental tests are implemented on an exoskeleton robot which follows the human gait trajectory in normal and uncertain conditions. In all studies, the results of the proposed method are compared with model free Linear Sliding Mode Control. It is shown that the proposed method has a better performance.

Applying sliding mode technique for the nonlinear DTC-SPWM control strategy of sensorless squirrel cage asynchronous motor

The classical Direct Torque Control has been elaborated to achieve advanced performance of asynchronous motor, especially in speed behaviours. Due to its high level of ripples and variable frequency, several modifications have been proposed to improve it. In this paper, two modified strategies of the direct torque control dedicated to asynchronous motors are presented, the first method is based on the sinusoidal pulse width modulation and PI regulators for regulating torque, speed and stator flux. The second is based on sliding mode control where the principal purpose is to force the system’s trajectory to slide along the switching surface by a well-defined control law. Furthermore, this paper aims to design two observers; the first will be evaluated by the direct calculation method and the second will be formed by sliding mode. These observers can improve control performance while eliminating mechanical sensors and thereby increasing the overall system’s reliability.

Estimation of Synchronization Errors between Master and Slave Chaotic Systems with Matched/Mismatched Disturbances and Input Uncertainty

This study is concerned with robust synchronization for master–slave chaotic systems with matched/mismatched disturbances and uncertainty in the control input. A robust sliding mode control (SMC) is presented to achieve chaos synchronization even under the influence of matched/mismatched disturbances and uncertainty of inputs. A proportional-integral (PI) switching surface is introduced to make the controlled error dynamics in the sliding manifold easy to analyze. Furthermore, by using the proposed SMC scheme even subjected to input uncertainty, we can force the trajectories of the error dynamics to enter the sliding manifold and fully synchronize the master–slave systems in spite of matched uncertainties and input nonlinearity. As for the mismatched disturbances, the bounds of synchronization errors can be well estimated by introducing the limit of the Riemann sum, which is not well addressed in previous works. Simulation experiments including matched and mismatched cases are presented to illustrate the robustness and synchronization performance with the proposed SMC synchronization controller.

Direct Nonadiabatic Simulations of the Photoinduced Charge Transfer Dynamics.

We apply direct nonadiabatic dynamics simulations to investigate photoinduced charge transfer reactions. Our approach is based on the mixed quantum-classical fewest switches surface hopping (FSSH) method that treats the transferring electron through time-dependent density functional theory and the nuclei classically. The photoinduced excited state is modeled as a transferring single-electron that initially occupies the LUMO of the donor molecule/moiety. This single-particle electronic wave function is then propagated quantum mechanically by solving the time-dependent Schrödinger equation in the basis of the instantaneous molecular orbitals (MOs) of the entire system. The nonadiabatic transitions among electronic states are modeled using the FSSH approach within the classical-path approximation. We apply this approach to simulate the photoinduced charge transfer dynamics in a few well-characterized molecular systems. Our results are in excellent agreement with both the experimental measurements and high-level (yet expensive) theoretical results.

Finite-Time Tracking Controller Design of Perturbed Robotic Manipulator Based on Adaptive Second-Order Sliding Mode Control Method

This article presents an adaptive finite time second-order sliding mode tracking control scheme for robotic manipulators. A new control law is suggested to force the trajectories of the robot manipulator to move from all initial conditions to proportional-integral-derivative switching surface in the finite time and stay on it. Moreover, the adaptation law rejects the requirement of knowledge about upper bound of the external perturbations. It is difficult to exactly determine the upper bound of the perturbations in the practical systems, such as robot manipulators. Unlike the existing methods, the new adaptive finite time second-order sliding mode tracker for $n$ -link robot manipulators enables accurate tracking control, robust performance and parameter tuning. The suggested approach presents the design of a robust controller such that the tracking errors of robot manipulator can reach the equilibrium in the finite time. Through the combination of the finite time tracker and disturbance observer, the position tracking purpose of manipulator joints is accurately performed not only in the nominal environment, but also in the existence of different types of perturbations. The robustness performance and effectiveness of the offered technique are studied in simulation and experimental results.

Design of a Non-Singular Adaptive Integral-Type Finite Time Tracking Control for Nonlinear Systems With External Disturbances

This paper proposes an adaptive non-singular fast terminal sliding mode control (FTSMC) with integral surface for the finite time tracking control of nonlinear systems with external disturbances. An appropriate parameter-tuning adaptation law is derived to tackle the disturbances. A new fast terminal sliding scheme with self-tuning algorithm is proposed to synthesize the adaptive non-singular fast integral terminal sliding approach. The proposed approach has the following features: 1) It does not require the derivative of the fractional power terms with respect to time, thereby eschewing the singularity problem typically associated with TSMC; 2) It guarantees the existence of the switching phase under exogenous disturbances with unknown bounds; 3) Because of the integral terms in the sliding surface, the power functions are hidden behind the integrator; 4) It ensures chattering-free dynamics. The effectiveness of the proposed approach is assessed using both a simulation and an experimental study. The obtained results showed that the FTSM control technique guarantees that when the switching surface is reached, tracking errors converge to zero at a fast convergence rate. Additionally, the integral term offers one extra degree-of-freedom and since the time-derivative of fractional power terms is not needed in the controller, the proposed switching surface provides a comprehensive framework for singularity avoidance.